A FLOOR SPACE VALUATION METHOD FOR AUTOMOTIVE
ELECTRONICS MANUFACTURING
Except where reference is made to the work of others, the work described in
this dissertation is my own or was done in collaboration with my advisory committee.
This dissertation does not include proprietary or classified information.
______________________________
Gokhan Sarpkaya
Certificate of Approval:
_____________________________ _____________________________
Chan S. Park John L. Evans, Chair
Professor Associate Professor
Industrial and Systems Engineering Industrial and Systems Engineering
_____________________________ _____________________________
Kevin R. Gue George T. Flowers
Associate Professor Dean
Industrial and Systems Engineering Graduate School
A FLOOR SPACE VALUATION METHOD FOR AUTOMOTIVE
ELECTRONICS MANUFACTURING
Gokhan Sarpkaya
A Dissertation
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Doctor of Philosophy
Auburn, Alabama
May 9, 2009
iii
A FLOOR SPACE VALUATION METHOD FOR AUTOMOTIVE
ELECTRONICS MANUFACTURING
Gokhan Sarpkaya
Permission is granted to Auburn University to make copies of this dissertation at its
discretion, upon request of individuals or institutions and at their expense.
The author reserves all publication rights.
______________________________
Signature of Author
______________________________
Date of Graduation
iv
VITA
Gokhan Sarpkaya, son of Oktay Sarpkaya and Gulser Pehlivaner, was born on
December 25, 1969 in Istanbul, Turkey. He graduated with Bachelor of Science degree
(E&E Engineering (Computer)) from Turkish Naval Academy in August 31, 1993. After
working as a Navy Officer in Turkish Navy, he entered University of Pittsburgh in
January, 1999, and graduated with a Master of Science degree (Industrial Engineering),
in December, 1999. Sarpkaya taught undergraduate operations research classes at Turkish
Naval Academy from 2000 to 2002 before he came to the United States to continue his
further studies in Industrial and Systems Engineering at Auburn University College of
Engineering, Auburn, Alabama, United States.
v
DISSERTATION ABSTRACT
A FLOOR SPACE VALUATION METHOD FOR AUTOMOTIVE
ELECTRONICS MANUFACTURING
Gokhan Sarpkaya
Doctor of Philosophy, May 9, 2009
(MISE, University of Pittsburgh, 1999)
(BCPE, Turkish Naval Academy, 1993)
210 Typed Pages
Directed by John L. Evans
Manufacturing complex products in order to survive the competition in the
automotive electronics industry requires high volume manufacturing combined with high
levels of quality and automation at a very low cost. All of the above require carefully
engineered logistics, effective material handling, material identification and tracking at
individual component levels, irreversible equipment and tooling investment, and
dedicated floor space. Since electronics manufacturing facilities also require specific
facility systems, floor space becomes an extremely valuable asset. Effective utilization of
this valuable asset results in competitive advantages where the embedded flexibility to
vi
manage the capacity to generate more revenue or more cost savings significantly
contributes to the profitability of enterprises.
Considering the business volume generated by the automotive industry, the
primary goal of this research is to formally investigate the contribution of effective floor
space valuation to strategic decision making in automotive electronics manufacturing
industry. Thus it is intended to describe a conceptual framework by developing a method
to evaluate the value of the additional floor space generated by manufacturing logistics
investments.
The scope of this research is limited to plant level capital investment decisions of
a global publicly held highvolume highmix automotive electronics manufacturer, where
the facility in question is located in the United States of America. The specific focus of
this research is the valuation of the additional floor space generated by automated capital
equipment replacement for the logistics department of Continental Automotive Systems,
Inc. Huntsville facility. The aforementioned equipment is fully depreciated, outdated, and
causing extreme downtime, thus interrupting the manufacturing operations. Several
decision alternatives are analyzed and a floor space valuation method utilizing traditional
discounted cash flow techniques, decision tree analysis, and real options analysis is
developed. The results of the conceptual framework are discussed in order to provide
better understanding for the implications of the model, and an outline for future research
opportunities is discussed.
vii
ACKNOWLEDGEMENTS
First and foremost, the author would like to express his heartfelt gratitude to Dr.
John L. Evans for his patient guidance and unwavering support throughout this study; his
guidance and support were vital to the success of this research. The author also feels
indebted to Dr. Alice E. Smith for her encouragement and generous financial support
throughout his graduate studies.
The author is particularly grateful to Dr. Chan S. Park, Dr. Kevin R. Gue, Dr.
Joseph B. Hanna, and Dr. Brian J. Gibson for their outstanding insight, their very
valuable time, and for sharing their knowledge.
Special thanks are due to Mr. Harald Augustin, Mr. Charles N. Lang, Jr., and Dr.
Duoxing Zhang for their unending assistance, support, and provision of very valuable
information to make this research a success.
Finally, all my family members deserve very special thanks for their patience,
encouragement, and support. Without them the author would never have been able to
finish this research.
viii
Style manual used: This dissertation follows The Chicago Manual of Style.
Computer software used: @Risk 5.0 for Excel Student Version, BestFit 4.5 Student
Version, Precision Tree 1.0 for Excel, Microsoft Word,
Excel, and Visio 2003 were used to type and edit the
dissertation.
ix
TABLE OF CONTENTS
LIST OF FIGURES xi
LIST OF TABLES xv
1 INTRODUCTION 1
2 VALUE AND FINANCIAL DECISION MAKING 13
2.1 Value 13
2.2 Financial Decision Making 14
2.3 Research Plan 20
3 LITERATURE REVIEW 24
3.1 Introduction 24
3.2 The DNA of Decision Making: Valuation 27
3.3 Options Pricing Theory 35
3.4 Real Options Analysis 39
3.5 Modeling Approaches 45
3.6 ROA Application Areas 49
4 PRACTICAL BUSINESS APPLICATION 58
4.1 Introduction 58
4.2 Facility Overview 59
4.3 Practical Business Application 62
4.4 MiniLoad AS/RS and MHCS 67
4.5 AGV System Analysis 80
5 FLOOR SPACE VALUATION METHOD 89
5.1 Introduction 89
5.1.1 MiniLoad AS/RS Related Alternatives 89
5.1.1.1 MiniLoad AS/RS and WMS Replacement 89
5.1.1.2 JustinTime Delivery 90
5.1.2 AGV System Related Alternatives 91
5.1.2.1 AGV Control Software Replacement and
Mechanical Component Retrofitting
92
5.1.2.2 Water Spider Deployment 93
5.2 Discounted Cash Flow Approach 96
x
5.2.1 Alternative1 96
5.2.2 Alternative2 97
5.2.3 Alternative3 98
5.2.4 Alternative4 99
5.2.5 Combinations of the Options Based on Implementation
Start Time 100
5.2.6 Sensitivity and Scenario Analysis 102
5.3 Monte Carlo Simulation Approach 109
5.3.1 First Phase 111
5.3.2 Second Phase 114
5.3.3 Third Phase 122
5.4 DecisionTree Analysis 126
5.5 Real Options Analysis 130
5.6 Summary of Results 144
6 CONCLUDING REMARKS AND FUTURE RESEARCH 147
6.1 Concluding Remarks 147
6.2 Future Research Areas 150
BIBLIOGRAPHY 154
APPENDIXA 161
APPENDIXB 165
APPENDIXC 171
APPENDIXD 193
xi
LIST OF FIGURES
NUMBER DESCRIPTION PAGE NUMBER
Figure 1.1 U.S. Logistics Costs Over Time 3
Figure 1.2 Sample PCB 8
Figure 3.1 Valuation Process 32
Figure 3.2 Profit of a Call Option Contract as the Function of the Stock
Price 37
Figure 3.3 Profit of a Put Option Contract as the Function of the Stock
Price 37
Figure 3.4 OneStep Binomial Tree 47
Figure 3.5 Numerous ROA Modeling Approaches for Option Calculation 49
Figure 4.1 Overall Facility Area Distribution 61
Figure 4.2 Manufacturing Building Area Distribution 62
Figure 4.3 MiniLoad AS/RS Aisle 68
Figure 4.4 MiniLoad AS/RS Layout 69
Figure 4.5 Inventory Activity Profiling 73
Figure 4.6 Chair Lift System for Partial Picks 74
Figure 4.7 Travel Trajectory for MiniLoad AS/RS Cranes 77
Figure 4.8 AGV 80
xii
Figure 4.9 MiniLoad AS/RS Accumulation Stands 82
Figure 4.10 Pick and Drop Stand 82
Figure 4.11 Deadheading Analysis of the AGV System 85
Figure 5.1 Alternative1 NPV vs. Percentage Change of Inputs 103
Figure 5.2 Alternative2 NPV vs. Percentage Change of Inputs 104
Figure 5.3 Alternative3 NPV vs. Percentage Change of Inputs 105
Figure 5.4 Alternative4 NPV vs. Percentage Change of Inputs 106
Figure 5.5 Option1 NPV Probability Density Function 113
Figure 5.6 Option1 NPV Cumulative Distribution Function 114
Figure 5.7 Plant I Monthly Demand Distribution 116
Figure 5.8 Monthly Plant I Revenue Distribution 117
Figure 5.9 Option4 NPV Probability Density Function 121
Figure 5.10 Option4 NPV Cumulative Distribution Function 122
Figure 5.11 Option2 NPV Probability Density Function 125
Figure 5.12 Option2 NPV Cumulative Distribution Function 126
Figure 5.13 Action Node Structure for DecisionTree Analysis 128
Figure 5.14 DecisionTree Diagram of the Suggested Policy 129
Figure 5.15 ROA Model Framework 133
Figure 5.16 Binomial Lattice Logic 136
Figure 5.17 Binomial Lattice for Group2 with Low Marketing
Performance 138
xiii
Figure 5.18 Binomial Lattice for Group1 with Low Marketing
Performance 138
Figure 5.19 Suggested Policy for Low Marketing Performance 139
Figure 5.20 Binomial Lattice for Group2 with Medium Marketing
Performance 140
Figure 5.21 Binomial Lattice for Group1 with Medium Marketing
Performance 140
Figure 5.22 Suggested Policy for Medium Marketing Performance 141
Figure 5.23 Binomial Lattice for Group2 with High Marketing
Performance 142
Figure 5.24 Binomial Lattice for Group1 with High Marketing
Performance 142
Figure 5.25 Suggested Policy for High Marketing Performance 143
Figure 5.26 Pascal's Triangle 143
Figure C.1 The Relation Between Option Value and Stock Price 173
Figure C.2 Generalized Wiener Process 178
Figure C.3 The Profit Pattern of a Long Position in a Stock Combined with
Short Position in a Call 180
Figure C.4 The Profit Pattern of a Short Position in a Stock Combined with
Long Position in a Call 180
Figure C.5 The Profit Pattern of a Long Position in a Put Combined with
Long Position in a Stock 181
xiv
Figure C.6 The Profit Pattern of a Short Position in a Put Combined with
Short Position in a Stock 181
Figure C.7 The Profit Pattern of a Bull Spread Using Call Options 183
Figure C.8 The Profit Pattern of a Bull Spread Using Put Options 183
Figure C.9 The Profit Pattern of a Bear Spread Using Put Options 184
Figure C.10 The Profit Pattern of a Bear Spread Using Call Options 185
Figure C.11 The Profit Pattern of a Butterfly Spread Using Call Options 186
Figure C.12 The Profit Pattern of a Butterfly Spread Using Put Options 187
Figure C.13 The Profit Pattern of a Calendar Spread Using Call Options 188
Figure C.14 The Profit Pattern of a Calendar Spread Using Put Options 178
Figure C.15 The Profit Pattern of a Bottom Straddle 189
Figure C.16 The Profit Pattern of a Strip 190
Figure C.17 The Profit Pattern of a Strap 191
Figure C.18 The Profit Pattern of a Bottom Vertical Combination 191
Figure D.1 North Dock Layout 193
xv
LIST OF TABLES
NUMBER DESCRIPTION PAGE NUMBER
Table 1.1 U.S. Inventory Carrying Cost Breakdown 4
Table 2.1 Conditional Benefit Table of the Sample Problem 16
Table 4.1 Slot Heights by Tier 68
Table 4.2 Tote Size Specifications 69
Table 4.3 Identification Number Block Allocations 70
Table 4.4 Horizontal Velocity of MiniLoad AS/RS Cranes 78
Table 4.5 MiniLoad AS/RS Crane Utilization 79
Table 4.6 Dedicated Manpower of the MiniLoad AS/RS 79
Table 4.7 Average Number of Distribution Center AGV Trips 84
Table 4.8 Daily Average Number of Trips per Distribution Center AGV 85
Table 4.9 Average Number of Finished Goods Warehouse AGV Trips 87
Table 4.10 Daily Average Number of Trips Per Finished Goods AGV 88
Table 5.1 Decision Alternative Combinations 94
Table 5.2 DCF Analysis of Alternative1 97
Table 5.3 DCF Analysis of Alternative2 98
Table 5.4 DCF Analysis of Alternative3 99
Table 5.5 DCF Analysis of Alternative4 100
xvi
Table 5.6 DCF Analysis of All Possible Option Combinations 101
Table 5.7 Input Variations 102
Table 5.8 Scenario Analysis for NPV of Each Alternative 107
Table 5.9 Best Case DCF Analysis for All Possible Option Combinations 107
Table 5.10 Worst Case DCF Analysis for All Possible Option
Combinations 108
Table 5.11 Input Variable Distribution Summary 111
Table 5.12 Phase1 Monte Carlo Simulation Analysis 112
Table 5.13 Fitted Distributions for Plant I Monthly Demand 116
Table 5.14 Fitted Distributions for Plant I Monthly Revenues 117
Table 5.15 Annual Demand Estimation with Direct Proportionality 118
Table 5.16 Annual Revenue Estimation with Direct Proportionality 118
Table 5.17 Distributions of the Required Capital Investment 119
Table 5.18 Phase2 Monte Carlo Simulation Analysis 120
Table 5.19 Revenue Distributions for Additional Market Share 123
Table 5.20 Phase3 Monte Carlo Simulation Analysis 124
Table 5.21 Revenue Distributions for Low Marketing Performance 127
Table 5.22 Revenue Distributions for Medium Marketing Performance 127
Table 5.23 Revenue Distributions for High Marketing Performance 127
Table 5.24 Weighted Average Floor Space Value 144
Table 5.25 Decision Recommendations Summary 146
Table B.1 Sample Cash Transaction 166
xvii
Table B.2 Sample Amortized Loan Transaction 167
Table B.3 Sample Cash Flow Transaction for Discounted Payback Period
Calculation 168
Table C.1 Payoff from a Bull Spread Using Call Options 183
Table C.2 Payoff from a Bull Spread Using Put Options 183
Table C.3 Payoff from a Bear Spread Using Put Options 184
Table C.4 Payoff from a Bear Spread Using Call Options 185
Table C.5 Payoff from a Butterfly Spread Using Call Options 186
Table C.6 Payoff from a Butterfly Spread Using Call Options 187
Table C.7 Payoff from a Calendar Spread Using Call Options 188
Table C.8 Payoff from a Calendar Spread Using Put Options 189
Table C.9 Payoff from a Straddle 190
Table C.10 Payoff from a Bear Spread Using Call Options 192
1
CHAPTER 1
INTRODUCTION
According to the 17
th
The 16
Annual State of Logistics Report published by the Council
of Supply Chain Management Professionals (hereafter CSCMP), logistics costs during
2005 were $1.2 billion and were equal to 9.5 percent of the Gross Domestic Product. The
largest share of the increase can be accounted for by rising transportation costs, which
represent approximately 63 percent of total logistics costs. Inventory carrying costs rose
to 15 percent in 2005, surpassing the 2001 level. The average investment in all business
inventories in agriculture, mining, construction, services, manufacturing, wholesale, and
retail trade was $1.76 trillion, a new record high.
th
Annual State of Logistics Report states that in North America, nearly
$115 billion was spent on outsourced valueadded logistics services worldwide.
Armstrong & Associates, Inc. reports that gross revenues for contract logistics services
grew by 16.3 percent in 2004 to $89.4 billion. For the tenth consecutive year, U.S.
growth in thirdparty, contract logistics services exceeded the U.S. economic growth.
Warehouse based integrated services grew by 7.1 percent in 2004. United States based
thirdparty logistic providers (hereafter 3PL) with international operations grew by 34
percent. Armstrong attributes some of the growth to acquisitions, where large 3PL's grow
through the acquisition of smaller logistics providers to broaden their offerings.
2
According to the CSCMP, logistics management activities typically include
? Inbound and outbound transportation management
? Fleet management
? Warehousing
? Materials handling
? Order fulfillment
? Logistics network design
? Inventory management
? Supply/demand planning
? Management of third party logistics services providers
The 16
th
Annual State of Logistics Report explains the distinct elements of
warehousing industry as the public and general warehousing that is generally operated as
a profit center and contracted out and the private warehousing that is operated by
corporations as a part of conducting their primary line of business. In addition, the values
measured include valueadded services similar to those offered by 3PL's. While there is
no regularly released data series that captures the entire warehousing industry, the public
warehouse segment is measured at regular intervals by the U.S. Department of
Commerce. Periodically, special studies are undertaken to measure the size and scope of
the private sector.
3
Figure 1.1 below summarizes the U.S. logistics costs over time. The impact of
rising fuel costs over transportation costs is easily observed. Fluctuating, slightly
increasing trends in inventory carrying costs, which account for approximately 39 percent
of the total logistics costs, according to the 17th Annual State of Logistics Report, are due
to higher interest rates and increasing investments in main industries, resulting in
increased inventories.
U.S. Logistics Costs Over Time
0
100
200
300
400
500
600
700
1981 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Year
$ B
illions
Inventory Carrying Costs Transportation Costs Administrative Cos ts
Figure 1.1 U.S. Logistics Costs Over Time
The 17
th
Annual State of Logistics Report breaks the inventory carrying costs
down into three subcategories for the most recent five years, as indicated in Table 1.1
below.
4
Table 1.1 U.S. Inventory Carrying Cost Breakdown (In Billions of US Dollars)
Year 2001 2002 2003 2004 2005
Interest 53 25 17 23 58
Taxes, Obsolescence,
Depreciation, Insurance
191 198 206 227 245
Warehousing 76 78 78 82 90
The report also indicates that the cost of warehousing increased substantially in
2005 based on expenditures for public warehousing reported by the Commerce
Department?s Census Bureau and corroborated by several other studies. According to
ProLogis, a leading global provider of distribution facilities and services, the warehouse
leasing market continued to be tight in 2005. They reported that vacancy rates dropped to
7.3 percent at yearend 2005 from a high of 9.7 percent the year before. In addition,
burgeoning demand has led to higher rents, which increased an average of 5 percent in
2005. New warehouse construction has increased, also a sign that investors have
confidence that the market will continue to grow.
The 17
th
Annual State of Logistics Report indicates that warehousing costs
account for approximately 25 percent of inventory costs and 10 percent of logistics costs.
While the quantity of a certain material an enterprise decides to store in a warehouse
depends heavily on supply chain resiliency and transportation system performance,
inventory carrying costs change for reasons completely unrelated to transportation.
Factors such as economic slowdown and significant changes in business cycle variables
result in unexpected increases in inventory carrying costs.
5
Warehousing is an activity where buildings, equipment, design and continuous
planning efforts, and physical and intellectual human resources are pooled together to
provide and regulate simultaneous, consistent and continuous flow of the goods, services,
and information between the upstream links of the supply chain and the downstream
processes of the link that they concern. Welldesigned and implemented warehousing,
together with an adequate information system (hereafter IT) infrastructure, translates into
a substantial competitive advantage.
Since controlling fuel prices, interest rates, investments in other industries and/or
competitors, tax system, and insurance costs is impossible, warehousing and
obsolescence costs become the most accessible targets for industries in terms of logistic
costs. The 17
th
Annual State of Logistics Report indicates that obsolescence accounts for
nearly 40 percent of total inventory carrying costs, thus demonstrating the challenges
facing inventory managers in the world of fast cycles and justintime procurement. In
addition to obsolescence costs, each link pertaining to the supply chain can control
warehousing costs as well as immediate internal extensions such as inbound delivery
scheduling, inventory planning and analysis, process streamlining, and waste elimination.
The aforementioned warehousing cost control challenges encompass public warehouses,
plant warehouses, leased warehouses, and private warehouses operated by manufacturing
and third or fourth party logistics providers.
Controlling warehousing costs starts with accurate warehouse sizing, adequate
floor space allocation, thus accurate inventory allocation, and streamlining the relevant
processes which can be translated as waste removal out of the warehousing activities.
6
Srinivasan (2004) emphasizes that lean thinking must be applied to all the processes in
the enterprise to remove waste thoroughly. Otherwise while some waste is removed,
creating islands of excellence, some will be queued up elsewhere.
To varying degrees, the logistics function also includes sourcing and procurement
of noncorecompetency materials and services, production planning and scheduling,
packaging and assembly, and customer service. It is involved in all levels of planning and
execution ? strategic, operational, and tactical.
Measuring corresponding costs is not straightforward because logistics
management activities involve a substantial amount of inhouse operations. Inhouse
operations refer to the business operations that an enterprise conducts to provide services
for its own use. In contrast to the services from forhire operations that are bought and
sold in marketplaces, inhouse operations are provided and consumed internally without
market mediation. Some auxiliary functions which may not be considered within the
scope of logistics, such as maintenance and repair of the material handling systems,
should also be taken into account because they are the natural and immediate extensions
of logistics activities.
Overall inhouse logistics operations can be considered as a natural resource
acquisition and exploitation activity, depending on the contingent circumstances:
? A portion of the existing floor space in a facility can be dedicated for material
handling, storage, staging, replenishment, and/or other relevant noncore
competency activities.
? A new facility offering sufficient floor space can be bought or leased in case
existing floor space does not meet the requirements.
7
? A contract can be negotiated with a 3PL such that logistics operations are
managed externally without any inhouse floor space requirements.
Similarly, any operation that does not require corecompetency of the
corresponding enterprise can either be handled inhouse or contracted out to effectively
utilize the existing floor space depending on the generated value. The fundamental
tradeoff is whether or not to allocate all floor space to revenuegenerating activities.
However sufficient floor space needs to be allocated to the non valueadded activities that
cannot be outsourced in order to avoid dependencies on third parties. The bottom line is
to effectively utilize the existing floor space in order to obtain the greatest return for an
investment in order to compete in today's environment.
The fiercest competition today is in the automotive and high technology industries
due to globalization, rapid technological improvements, and the need for new energy
resources. Original equipment manufacturers (hereafter OEM) in the aforementioned
industries exert their power mostly over their firsttier suppliers. Moreover, high market
demand volatility, short product life cycles, long design and production lead times, high
capital investment requirements, and irreversibility of the investments require extremely
intelligent decision making.
Evans, Zhang, Vogt, and Thompson (2004) propose that the most challenging
environment described above is that of automotive electronics manufacturing, which has
similar manufacturing issues common in all electronics production but has the added
difficulty of meeting very stringent quality and reliability requirements in a globally
competitive market.
8
They discuss the fact that electronics manufacturing is a cornerstone of the current global
economy and, as such, presents many unique issues and opportunities to manufacturing
and investment planners.
Automotive electronics manufacturing involves placing hundreds of tiny
components accurately on a minute printed circuit board (hereafter PCB) with high
precision, soldering to ensure robust and reliable mechanical and electrical contact,
applying a protective coating, and placing the mechanical assembly into a housing
designed to operate in harsh conditions such as very cold or hot temperatures, mechanical
and thermal shock, vibration, etc.
Figure 1.2 Sample PCB
The need to manufacture complex products in order to survive the competition in
the automotive electronics industry requires high volume manufacturing combined with a
high level of quality and automation and, more importantly a very low cost. All of the
above require carefully engineered logistics, effective material handling, material
identification and tracking at individual component levels, if possible, and dedicated and
irreversible equipment and tooling investment ranging from $45 million to $60 million
per dedicated assembly line depending on the flexibility of the line and floor space,
which is ranging from 10,000 sq. ft. to 30,000 sq. ft. for a typical automotive electronics
product (Evans, Zhang, Vogt, and Thompson 2004).
9
Because electronics manufacturing facilities also require specific facility systems
like 480Volt power, nitrogen supply, adequate ventilation, hazardous material storage
area, and humidity control, floor space becomes an extremely valuable asset. Effective
utilization of this valuable asset results in competitive advantages where intelligent
decisions can be made by outsourcing activities that are not included in the core
competency list of the enterprise or by keeping them inhouse with accurately justified
automation investments.
Effective floor space utilization brings in the flexibility to manage the capacity to
generate more revenue or more cost savings, hence more contribution to competitive
advantage in favor of the subject matter enterprise. Wu, Erkoc and Karabuk (2005) argue
that a firm?s ability to manage its capacity is the most critical factor for its long term
success. Hence, considering floor space as a primary resource for capacity planning
should not be controversial.
Assume a scenario for a firsttier automotive electronics supplier where the
quarterly sales forecast of its main customer, an automotive OEM, declines significantly
due to globally changing market dynamics, resulting in early contract termination with its
suppliers. Collaborative planning, replenishment, and forecasting efforts result in
assigning the forecasting task to OEM's in today's automotive industry, thus allowing
OEM suppliers not to have to deal with forecasting in order to avoid compounding effect
of the amplified forecast errors upstream. However, early contract termination can
potentially hurt firsttier suppliers the most due the amount of inventory onhand beyond
the committed order quantity placed by the OEM.
10
This could potentially generate a ripple effect upstream through the corresponding supply
chain if the contracts are negotiated myopically by relying on ample floor space on hand
and on na?vely optimistic sales forecasts provided by OEM's. The loss of the firsttier
suppliers is the highest because the value of production material at this level is higher
before they are converted to finished goods.
Assume another scenario where a decision must be made about whether or not to
invest in manufacturing logistics systems in order to save floor space for a new, and state
oftheart revenue generating manufacturing technology. In this scenario, almost 80
percent of a dedicated assembly line footprint is required in order to erect a hermetically
sealed cleanroom for a new flexible manufacturing cell. The tradeoff is between losing an
existing business to another facility and making irreversible manufacturing logistics
investments to generate the required floorspace for the new business, resulting in
significant learning curve challenges and significant changes regarding the way the
logistics operations are performed. Generating additional floor space out of an existing
layout by means of manufacturing logistics investments could generate additional
revenues of $120 million per year, and provide knowledge transfer with stateoftheart
manufacturing technology.
The unpleasant consequences of the aforementioned scenarios range from losing
potential business to plant closeout or even bankruptcy due to ineffective floor space
utilization. In order to avoid these consequences, better contract management with
suppliers and customers, more intelligent warehousing, inventory allocation, and
investment decisions are required for firsttier suppliers.
11
In this way floor space is not underutilized as an idle component of the business for
stagnant or obsolete stock keeping units or nonrevenue generating activities. In both
scenarios floor space value acts as a proxy for valuation to make intelligent decisions.
The largest challenge faced by manufacturing businesses today is the full
utilization of an asset by proper valuation and/or finding the real value. Boer (2002)
quotes that the greatest challenge facing any organization today is in understanding the
huge differential between its balance sheet and market valuation. He argues that as long
as most transactions involve physical goods and tangible assets, the accounting approach
to valuation works well. However financial statements measure transactions only in a
tangible oriented setting where physical assets exist and even the existence of slight
uncertainty makes the accuracy of these statements questionable. Moreover, the
traditional methods that those financial statements are based on have several drawbacks.
They naively assume perfect project cash flows. However future cash flows are barely
certain. The discount rate that the traditional methods are utilizing is kept constant all
along the project life, where it needs to be adjusted from high to low as the uncertainty
resolves representing the risk premium changing based on the arrival of new information.
Finally, the traditional methods dictate the decision maker to make "goornogo" or
"nowornever" decisions ignoring the flexibility of switching between alternatives or
delaying the decision.
The purpose of this research is to formally investigate the contribution of effective
floor space valuation to strategic decision making in the automotive electronics
manufacturing industry. This research specifically addresses the value of manufacturing
floorspace related to different usage options for the facility.
12
Currently, finance specialists divide the budget by the total available floor space in order
to calculate the floor space value without taking into account the embedded revenue
generating potential. However, with ongoing lean initiatives, floorspace is included in
waste elimination efforts for manufacturing facilities and considered as an asset. The
effective utilization of any asset in manufacturing positively contributes to the financial
statements. Generating additional floor space will add additional capacity to the
corresponding facility, where future cash flows can be generated. Traditional methods
cannot incorporate uncertain future cash flows into associated calculations that financial
statements are based on. This research will have specific focus on developing a new
financial method, which utilizes a series of both traditional and relatively new techniques
addressing the uncertainty aspect of the project cash flows. Considering there are only six
first tier automotive electronics facilities in U.S.A., it is crucial to have a better floor
space valuation method, especially when the economic circumstances are not favorable,
and the aforementioned method will help corporate executives and corporate planners to
make better business decisions regarding future product allocations to manufacturing
plants based on the floor space value.
13
CHAPTER 2
VALUE AND FINANCIAL DECISION MAKING
2.1 Value
Valuation is the financial translation of revenue?generating or lossincurring
potential. It is not only important in driving financial transactions, but also in decision
making. Boer (2002) defines valuation as assigning a quantitative value, in dollars, for
example, to an asset whether that asset is a share of stock, an oil painting, or an invention.
He also argues that the economic value is defined as the present value of the future cash
flows, and strategic value is defined as the value of unrealized opportunities.
Copeland, Koller, and Murrin (1995) define value as the best metric for
performance, and they argue that enterprises that do not perform will find that capital
flows toward their competitors. Hence one can conclude that value is an effective key
performance indicator where valuation plays a significant role in decision making.
Copeland, Koller, and Murrin (1995) also propose that there is strong correlation
between the market value of a company and its discounted cash flows. Valuation is
currently being accomplished by using discounted cash flow (hereafter DCF) techniques,
where it is assumed that perfect and complete information exists for both future cash
flows and risk adjustment of the discount rate. Information is complete when the state of
the nature moves first and these moves are known to every player.
14
Information said to be in perfect order describes a state of complete knowledge about the
actions of other players that is instantaneously updated as new information arises when
the corresponding information sets are singleton (Rasmusen 1994). However these
assumptions about the information seem unrealistic for managing an organization's cash
flows, and decision making using perfect and complete information is rarely possible. In
most decision problems, the decision maker might chose a "wait and see" approach in
order to gather more information by postponing the action rather than immediately
adopting it. It is the decision maker's responsibility to evaluate the tradeoff between the
cost of postponing the action, thus gathering more information and the value generated
thereby. Hence other decisionmaking techniques sustaining the DCF techniques must be
deployed to avoid the aforementioned assumptions and accomplish proper valuation.
This research study is about evaluating options that generate revenue through
effective utilization of the floor space dedicated to nonvalue added activities, with
accurately adjusted risk and more realistically projected cash flows using a new method
sustaining traditional DCF techniques.
2.2 Financial Decision Making
Where there is no perfect and complete information, there is uncertainty and risk.
Consistent decisions under uncertainty can be made by using several different techniques.
A decision maker who has a set of alternatives faces uncertain events where there is a
payoff or penalty for each alternative and event combination.
15
The likelihood of occurrence is represented by a probability and, since almost all of the
decisions in a manufacturing environment are sequential, a decision tree can be used to
structure the decision problem. There are various analytic approaches for decision
making including intelligent and formal decision making under uncertainty where
tradeoffs between using one or another stem from their limitations.
Expected Monetary Value (hereafter EMV) approach is adequate if the amounts
of money involved are small or if the decision is a repetitive one, such as an inventory
stocking policy (Bierman, Bonini, and Hausman 1997). However, maximizing the EMV
does not seem to generate satisfactory results when risk is involved.
Dominance approach is applied in three different forms. Outcome dominance is
the form where the worst benefit of one act is at least as good as the best of another act.
Event dominance is the case where the benefit of an act is equal or better than that of
another one for each event. Probabilistic or stochastic dominance is the third and final
form of dominance criterion where the cumulative probabilities for each outcome of an
act outweigh the cumulative probabilities of each outcome of the other act for each value
of the outcomes. Based on the sample problem provided by Bierman, Bonini, and
Hausman (1997), the conditional benefit table of which is indicated below, act d
1
dominates d
2
by outcome dominance and event dominance, and act d
4
stochastically
dominates act d
1
. They conclude that, of all the three forms, outcome dominance is the
strongest, event dominance is the next strongest, and the stochastic dominance is the
weakest.
16
Table 2.1 Conditional Benefit Table of the Sample Problem
Event Probability
Acts
d d
1
d
2
d
3
4
q 0.3
1
2 1 1 1
q 0.2
2
1 0 0 0
q 0.5
3
0 1 1 2
Von Neumann and Morgenstern (1967) argue that decisions are made so as to
maximize expected utility rather than EMV. They developed a procedure for quantifying
a person?s utility function for commodities or money depending on one?s attitude towards
risk. The utility theoretical approach uses lotteries to explain judgments behind decisions.
Since the attitude towards risk changes based on the subject matter wealth, the utility
function is not always linear. Hence, EMV criterion is only valid when the decision
maker is risk neutral. His utility function is then linear over the range of all possible
outcomes. This criterion uses a measure called marginal utility: for large benefits the
slope of the utility function increases gradually and becomes smaller as smaller additions
are contributed. This is also known as the diminishing marginal utility. Bierman, Bonini,
and Hausman (1997) explain the utility scale by using a Celcius and Fahrenheit scales
analogy: both measure the temperature but have different readings. They discuss that a
utility function represents the subjective attitude of a decision maker to risk. Basically, it
is a descriptive theory. They also interpret the notion of certainty equivalency used in
utility theory as either the maximum insurance that the decision maker is willing to pay to
be freed of an undesirable risk or the minimum certain amount that the decision maker is
willing to accept for selling a desirable but uncertain set of outcomes.
17
The above approaches establish the basis for financial decision making. EMV
approach is effectively used where there is not any risk involved. Dominance approach
fails to select an act in the existence of multiple alternatives that dominate all of the
others; however, it sustains EMV criterion in case of risk involvement. Bierman, Bonini,
and Hausman (1997) explain that utility analysis does not work effectively since
? It is extremely difficult to estimate the correlation of returns of a decision
alternative with others (portfolio effect).
? Decision makers sometimes violate basic assumptions on which the utility
analysis is based (Allais paradox).
Decision analytic approaches are not limited to the above. Analytic Hierarchy
Process (hereafter AHP) developed by Saaty is a multiattribute decision analysis
approach through ratio scales. AHP requires pairwise comparison judgments which are
used to develop overall priorities for ranking the alternatives. It also allows the decision
maker(s) to evaluate and improve consistency in ranking the criteria and alternatives
within the framework of pairwise comparisons (Saaty and Vargas 2001).
Goal programming, based on linear programming, uses simplex algorithm for
multiattribute decision making which is able to handle conflicting objectives by taking
priorities into account (Canada and Sullivan 1989). The most significant limitation of
goal programming reported by Canada and Sullivan (1989) is the formulation complexity
of a model for realworld problems.
Artificial intelligence techniques like expert systems are powerful tools to solve
complex decision problems.
18
However, these techniques have limitations such as the availability of inference
mechanisms, the lack of common sense, and the domain size. The suitability of any
artificial intelligence technique should be carefully investigated before deploying
(Canada and Sullivan 1989).
Simulation is another descriptive approach to design a model of a real system and
to conduct experiments with this model. However, the most significant limitation of this
approach is that it is descriptive rather than prescriptive. It provides information for
decision making by letting the decision maker know how a system behaves rather than
indicating how the system should react to uncertain events.
In addition to these decision analysis methodologies, there are two other
methodologies described by Herath and Park (2000): Capitalasset pricing and real
options analysis.
Capital asset pricing captures the investor's perspective by measuring the value of
an investment decision in terms of its value to the market or its contribution to the
investor's wealth. The risk attitude is involved by adding a "market risk premium" to the
riskfree discount rate when calculating the riskadjusted discount rate used to discount
the expected future cash flows (Herath and Park 2000).
Real options analysis (hereafter ROA) is based on the opportunity to make a firm
decision after observing the events. ROA is a passive methodology using optionpricing
theory to evaluate the decisions.
19
Under ROA framework, decision makers have the right, but not the obligation, to
exercise a firm decision such as investment, divestment, expansion, contraction,
postponement, or abandonment at a predetermined cost and during the predetermined life
of the option. Net present value (hereafter NPV), as a DCF technique, can be interpreted
as a special ROA case where the discount rate is constant, the risk is perfectly adjusted,
and the expiration date and the future cash flows are known with certainty, which can be
considered as an extremely hypothetical situation.
Park and Herath (2000) define ROA as the version of decision analysis that has
adopted the market perspective, i.e. the market risk allowing determination of expected
values using riskneutral probabilities and discounting at the riskfree rate. The
advantages of ROA are discussed in detail in Appendix A.
Decisions in electronics manufacturing environments require sequential decision
making since
? The majority of the decisions involve significant irreversible capital
investments.
? Exercising an action takes a significant amount of time.
? Business dynamics such as customer demand, product life cycle, production
lead time, technological developments, and acquisitions change fairly
frequently and result in significant changes about the contingent
circumstances.
The complexity in decision making goes hand in hand with the complexity in the
associated manufacturing processes.
20
Printed circuit boards designed to host up to several hundreds of minuscule electronic
components require extreme precision in terms of solder paste dispensing and component
placement before they are thermally cured during subassembly process. Final assembly
process mainly composed of both manual and automated steps consists of mounting the
printed circuit boards into the casings where the finished good product is adapted to its
pointofuse environment. For both subassembly and final assembly processes, onthego
structural, electrical, and functional testing is a strict business requirement, hence a
significant capital burden, as well. Therefore heavily automated and expensive equipment
is required. Moreover, managers face the challenge of establishing a diverse customer
portfolio in order to reduce the business risks associated with global competition
stemming from low labor cost pressure and the need for new energy sources. Under the
aforementioned circumstances, adapting the electronics manufacturing enterprises to the
fastchanging business dynamics is only possible through managerial flexibility in
allocating resources. Managerial flexibility to switch between alternatives, to speed up or
to slow down a project, and ability to gather additional information contribute more value
than is assumed by making use of ROA methodology.
2.3 Research Plan
The research question that will be tackled is indicated as follows: How can the
value of the options or unrealized opportunities embedded in the additional floor space be
calculated?
21
Considering the business volume and the associated floor space required by the
automotive electronics industry, the primary goal of this research is to formally develop a
method to evaluate the value of the additional floor space generated by capital
investments. The supporting objectives are to develop the method utilizing traditional
DCF analysis, Monte Carlo Simulation (hereafter MCS) analysis, decision tree analysis
(hereafter DTA), and ROA, to apply the method to a practical business application using
real data, and to compare the resulting decision recommendations.
The research hypothesis is that if a floor space valuation method consists of the
aforementioned different financial decision making techniques, then decision makers can
value the opportunities embedded in additional floor space by incorporating the
probabilistic nature of the input variables and the managerial flexibility.
The scope of this research is limited to plant level capital investment decisions of
a global, publicly held highvolume highmix automotive electronics manufacturer,
where the facility in question is located in the United States of America.
It is assumed that macroeconomic parameters are not subject to unexpected
changes stemming from regional or global economic and/or geopolitical crises. However
the corporation can be exposed to various market and business dynamics such as demand
fluctuations, capital cost readjustments, acquisitions, etc.
Chapter 3 presents the review of the relevant literature, where the past research
analysis of floor space valuation, option pricing theory, and real options are highlighted.
In addition, current application areas and relevant modeling approaches are discussed.
22
This chapter mainly provides theoretical and practical aspects of ROA based on the past
research work in order to establish a basis for using the floor space valuation as a proxy
of the overall project valuation.
Chapter 4 presents the methodology and a realworld practical business
application concerning a series of capital investment decisions for an automotive
electronics manufacturing facility. The projects that are subject to the aforementioned
decisions are
? Replacing the existing outdated AS/RS and corresponding WMS with a new
AS/RS and WMS to generate floor space and cost savings supported by a
throughput analysis through a simulation study.
? Eliminating the existing outdated miniload AS/RS by switching to a justin
time delivery system together with threeshift 3PL support and transportation
operation.
? Replacing the existing outdated AGV control software and retrofitting the
vehicles of the existing AGV system in order to generate floor space by
eliminating pick and drop stands and by reducing the aisle space supported by
a throughput analysis through a simulation study and to extend the useful life
of the mechanical AGV components.
? Replacing the existing outdated AGV system with water spiders utilizing
tuggers with associated trailers.
In Chapter 5 traditional valuation models will be discussed with respect to the
realworld practical business application presented in Chapter 4.
23
Then DTA and ROA framework based on floor space valuation will be utilized. In
general, an effort will be put forth to strip a layer or two from the surface of the floor
space valuation.
In Chapter 6 the conclusions of the conceptual framework that will be provided in
Chapter 5 will be explained in order to provide better understanding for the implications
of the method. Finally, an outline for future research areas with emphasis upon the
results and the contributions associated with this research is discussed.
24
CHAPTER 3
LITERATURE REVIEW
3.1 Introduction
Floor space value has not been studied in detail in the existing body of research,
and there are not many publications mentioning floor space utilization. There are two
relevant perspectives. The first perspective is that AS/RS requires minimal floor space by
utilizing the vertical storage space. These systems are parttoman systems increasing
productivity. Automated storage and retrieval system (hereafter AS/RS) is a dense
storage alternative that can be used as a buffer or fast pick area to store and retrieve,
replacing the manual picking with automation. The design of such systems can be
customized to allow for no interruption in plant production and to minimize installation
through timely system implementation. These systems fit within the limited floor space
and, therefore, reduce the need for additional nonmanufacturing floor space which can
be very valuable in case customer demand increases and new manufacturing floor space
is needed. Two AS/RS installed within Air Canada's main maintenance base in Montreal
are reducing floor space for storing spare parts from 100,000 sq. ft. to 70,000 sq. ft. or
less (Rees 1994).
25
Rees (1994) also emphasizes that the AS/RS equipment and related conveyors, operator
workstations, and warehousing software, plus pneumatic tube delivery of small parts to
shops and hangars, are boosting productivity and reports that the overall system provided
a rapid, 3.5year investment payback for Air Canada. Other benefits include a major
provision in the AS/RS software to provide cycle counting, resulting in a more accurate
inventory. Also faster and more certain picking of priority items is possible. To improve
the use of available nonmanufacturing floor space and to take advantage of material
handling technical advances, Air Canada evaluated two storage automation technologies:
AS/RS and horizontal carousel equipment, where AS/RS proved to be the most effective
system. Ten factors were considered including
? Floor space utilization;
? Picking rate;
? Workstation design;
? Warehousing software;
? Reliability and access during a breakdown, hence robust exception handling;
? Expansion flexibility;
? Maintenance;
? Security;
? Airline industry acceptance for 24hour, 7day operations; and
? Price
The second perspective is that of employment densities. Thompson (1997)
conducted an empirical study to examine the results of a longrunning study of floor
spacetoemployment ratios for industrial properties in the United Kingdom.
26
His objectives were to identify the densities generated by a range of industrial building
types and to gain a picture of how these densities move over time, in particular relation to
economic cycles. According to his research, there are five subtypes of the industrial
sector that may behave discretely. These are factories, factory warehouses, warehouses,
longterm storage facilities, and workshops. Employees are the main economic influence
on each of the subsectors with the exception of longterm storage. Thompson (1997)
represents employment density by:
EmployeesEquivalentTimeFullofNumber
AreaExternalGross
?
(3.1)
By the comparisons existing in the aforementioned study the factory warehouse
combination dropped dramatically over the course of the study from 525 sq. ft. per
employee to 419 in 1994, and then, in 1996, it rose back to 439. The pattern is difficult to
explain. The mean size of building for this property type is much smaller than for the
overall sample at just under 3,000 sq. ft. The warehouse returns show densities falling
consistently over the fiveyear period. This is consistent with anecdotal evidence from the
market as to the great deal of demand for highspecification distribution centers at the end
of 1980's. Since then the recession and slow recovery seems to have been mitigated
against rapid growth in this sector. The impact of technology has been particularly fierce
in the distribution sector, where high employment densities are often the norm,
particularly in the larger, purposebuilt facilities.
27
Although there is no particular bias towards these large, national distribution centers in
the sample studied by Thompson (1997), the overall trend serves to raise densities
substantially throughout the distribution industry. According to Thompson (1997) the
behavior of mixeduse factory/warehouses remains a puzzle.
Another study related to office floor space indicates that as employees become
more mobile, companies are realizing that dedicating floor space to the service of a
person who is not always there to occupy it is considered a waste of resources. Itinerant
members of staff need only as many workstations as there are itinerants actually in the
office at any one time. Companies like Ernst & Young, Accenture, and IBM are saving
floor space through office hotelling by taking advantage of information technology at the
expense of psychological, general privacy, and personal storage arrangementrelated
concerns (Anonymous, 1995). However office hotelling requires extensive planning and
finetuned booking procedures so that disastrous effects on efficiency can be averted. The
main goal is to adopt more openplan offices, to reduce individual office sizes, and to
move excessive material except workinprogress out of the prime office space. The
space requirement consequently drops even further, while flexibility is increased.
3.2 The DNA of Decision Making: Valuation
Luehrman (1997) defines valuation as the financial analysis skill that general
managers want to learn and master more than any other. The value of a business is equal
to the present value of its expected cash flows discounted at a predetermined discount
rate.
28
Accurate encoding of the inherited value leads businesses towards the correct direction
contributing additional value. Copeland, Koller, and Murrin (1995) propose two
frameworks for valuation: Entity DCF model and Economic Profit Model.
The Entity DCF Model values the equity of a company's operations less the value
of debt and other investor claims that are superior to common equity. The values of
operations and debt are equal to their respective future free cash flows discounted at rates
that reflect the riskiness of these cash flows. Free cash flow is equal to the aftertax
operating earnings of the company, plus noncash charges, less investments in operating
working capital, property, plant and equipment, and other assets. It does not incorporate
any financingrelated cash flows such as interest expense or dividends. This framework
gives the exact same equity value as if the discounted cash flow to the share holders is
directly discounted. According to Copeland, Koller, and Murrin (1995) the discount rate
applied to the free cash flow should reflect the opportunity costs to all the capital
providers weighted by their relative contribution to the company's total capital, which is
also called weighted average cost of capital (hereafter WACC). However the limitation is
the selection of the appropriate discount rate to estimate the future free cash flows and to
estimate the life of the business. In order to mitigate these limitations and to make the
problem mathematically more tractable, they discuss separating the value of the business
into two time periods: during and after an explicit forecast period. The present value of
the cash flow during an explicit forecast period, and the value of the cash flow after an
explicit forecast period, which is referred to as continuing value, can be calculated easily.
They argue that the formula below is simple enough to estimate the continuing value
without the need to forecast the company's cash flow in detail for an indefinite period.
29
WACC
NOPAT
CV = (3.2),
where NOPAT represents the net operating profit after taxes.
Another framework proposed by Copeland, Koller, and Murrin (1995) is the
Economic Profit Model, where the value of a company equals the amount of capital
invested plus a premium equal to the present value of the value created each year going
forward. The advantage of the Economic Profit Model over DCF model is that the
economic profit is a useful measure for understanding a company's performance in any
single year, while free cash flow is not. The Economic Profit Model measures the value
created in a company in a single period of time and is defined as follows:
Economic Profit Model = Invested Capital x (ROIC ? WACC) (3.3),
where ROIC represents the return on invested capital calculated by dividing NOPAT by
the amount of invested capital.
Both the Entity DCF Model and the Economic Profit Model are incapable of
incorporating the value of future opportunities such as growth, expansion, disinvestment
or investment, abandonment, and future borrowings together with associated riskiness.
There are other DCF frameworks discussed by Copeland, Koller, and Murrin,
(1995) each of which has specific drawbacks and limits to its the practical usefulness.
Direct discounting of equity cash flow is the most straightforward technique that
involves discounting the cash flow to equity holders. However this framework is only
useful for financial institutions. This technique provides less information about the
sources of value creation and is not useful for identifying value creation opportunities.
30
The increase in dividend of the stock price is projected by assuming that operating
performance is constant.
Using real instead of nominal cash flow and discount rates involves projecting
cash flow in constant dollars and discounting this cash flow using a real discount rate,
which is calculated by subtracting the expected inflation from the nominal rate. Most
managers use nominal rates since they are easier to communicate. However for large
corporations operating in a geography consisting of countries with both high and low
inflation rates, valuation using nominal rates is not mathematically tractable and thus
becomes more complicated.
According to Copeland, Koller, and Murrin (1995) discounting pretax cash flow
instead of aftertax cash flow involves simple formulation, which is expressed as follows:
ratediscount tax After
FlowCash tax After
Value = (3.4)
Rate)Tax (1 FlowCash tax PreFlowCash tax After ??= (3.5)
Rate)Tax (1 RateDiscount tax PreRateDiscount tax After ??= (3.6)
Rate)Tax (1 RateDiscount tax Pre
Rate)Tax (1 FlowCash tax Pre
ratediscount tax After
FlowCash tax After
Value
??
??
== (3.7)
RateDiscount tax Pre
FlowCash tax Pre
Value
?
?
= (3.8)
Since taxes are based on accrual accounting, not cash flow, aftertax free cash
flow is not simply equal to pretax cash flow multiplied by a tax rate, although the above
formulation is logically valid. Hence this approach is not realistic.
31
Formulabased DCF approach instead of explicit DCF involves a formulation
with simplifying assumptions in order to capture the value of the business in a concise
formula referred to as the MillerModigliani (hereafter MM) formula. It basically values
a company as the sum of the value of the cash flow of its assets currently in place and the
value of its growth opportunities. The MM formula is defined as follows:
( )
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+
?
???+=
WACCWACC
WACCROIC
NOPATNK
WACC
NOPAT
Value
1
(3.9),
where K is the percentage of NOPAT invested for growth in new projects, and N is the
expected number of years that the company will continue to invest in new projects and
earn the projected ROIC, also called the interval of competitive advantage. Again, this
formulation is based on a single investment period and is not accurate for precise
valuation.
Options pricing theory offers particular models based on the variations on
standard DCF models. The rationale for these models is the managerial flexibility to
modify decisions through multiple periods as more information becomes available in
terms of discount rate and future free cash flows. Valuing managerial flexibility such as
exploring new opportunities and reevaluating investments that are classified as inthe
money, atthemoney, or outofthemoney by traditional DCF techniques under changing
circumstances is very promising since it avoids undervaluing or overvaluing underlying
assets. A detailed review of the traditional DCF techniques is presented in Appendix B at
the end of the dissertation.
32
Copeland, Koller and Murrin (1995) define the valuation process as follows:
Figure 3.1 Valuation Process
Valuation is the unique communication tool expressing all of the business
dynamics to the management by incorporating the financial aspects of the decision
alternatives in order to provide a fair comparison of the potential opportunities.
Uncertainty requires that decision makers make more intelligent decisions to assess risks.
However computational tractability becomes an issue due the existing complexity of
decision making under uncertainty in today's business environment, since practical
decision making and computational complexity seldom go hand in hand.
ANALYZE
HISTORICAL
PERFORMANCE
FORECAST
PERFORMANCE
ESTIMATE
COST OF
CAPITAL
ESTIMATE
CONTINUING
VALUE
CALCULATE
AND
INTERPRET
RESULTS
33
Addressing the decision making process is more important than computational
refinements for realworld decisionmaking problems.
The traditional DCF approaches have several drawbacks in terms of uncertainty
resolution and, thus, incorporating the valuation of the opportunities embedded in the
subject matter capital investment projects.
The first drawback is the selection of a riskadjusted discount rate. The risk
adjusted discount rate is supposed to reflect the riskiness of the project. In other words, if
the riskiness of the project increases, the discount rate increases and vice versa. It is also
interpreted as the hurdle rate. If the return on investment or the internal rate of return of
the project is below the hurdle rate, then the project is not undertaken. Another
interpretation is the cost of capital used in the capital budgeting process, which is the rate
of return that could be earned in the capital market on securities of equivalent risk to
satisfy shareholders' or investors' expectations. One approach recommended for
calculating the riskadjusted discount rate is the capital asset pricing model (hereafter
CAPM). Hull (2006) defines the steps of CAPM as follows:
? Take a sample of companies, whose main line of business is the same as that
of the project being contemplated.
? Calculate the betas of the companies and average them to obtain a proxy beta
for the project.
? Set the required rate of return equal to the riskfree rate plus the beta times the
excess return of the market portfolio over the risk freerate.
34
The formulation of CAPM can be represented as follows:
( )
ff
rMRrr ?+= ? (3.10),
where r represents the risk adjusted rate, r
f
? The NPV, EVA, AEW, or FW of the project is either positive or negative,
respectively;
represents the risk free rate, and MR
represents market return. Beta measures how closely a security's performance correlates
with broader stock market movements (Park, 2002). A Beta value of 1 indicates that the
performance of the associated security matches its index.
However, due to the embedded opportunities, companies have options to expand
or abandon a project depending on the success of the project. These options exhibit
different risk characteristics. In this case using a riskadjusted discount rate does not
allow capturing the value of the corporate management's flexibility to choose either one
of the options (Hull, 2006).
The second drawback is that DCF approaches overlook the resolution of
uncertainty along the progress of, especially, multistage capital investment projects. In
that sense the arrival of new information at any stage of the project is not incorporated in
the valuation of the project, resulting in either undervaluing or overvaluing of the
projects.
The third drawback is that the DCF approaches require either accepting or
rejecting the projects if
? The IRR of the project is either above or below the riskadjusted discount rate,
respectively;
35
? The payback period is above or below the predetermined payback period,
respectively;
In that sense the capital investment decisions translate themselves into "now or never" or
"goornogo" decisions.
The final drawback is that DCF approaches suggest a "onesizefitsall" approach
in terms of decision timing. Time lag between the decision and the implementation
phases of the projects, the delay duration of the project stages, and the time to switch
between potential options, are ignored by traditional DCF approaches.
3.3 Options Pricing Theory
Fischer Black, Myron Scholes, and Robert Merton developed a model to price the
stock options in the early 1970's, the importance of which was recognized when Myron
Scholes and Robert Merton were awarded the Nobel Prize for Economics in 1997 (Hull,
2006). The model is known as BlackScholes or BlackScholesMerton. Stock options are
derivatives or, in other words, they are financial instruments, the values of which are
derived from the associated stock, i.e., from another asset.
BlackScholes model is a theoretical valuation formula which is derived for stock
options. Black and Scholes (1973) define an option as a security giving the right to buy or
sell an asset, subject to certain conditions, within a specified period of time. According to
their seminal work an "American option" is one that can be exercised at any time up to
the date the option expires, and a "European option" is one that can be exercised only on
a specified future date.
36
The price that is paid for the asset when the option is exercised is called the "exercise
price" or "striking price." The last day on which the option may be exercised is called the
"expiration date" or "maturity date."
The option that gives the holder the right to buy a single unit of the underlying
asset for the exercise price by or at a certain date is referred to as a call option, whereas
the option that gives the holder the right to sell a single unit of the underlying asset for
the exercise price by or at a certain date is referred to as a put option. These are the
simplest kinds of options.
Suppose the stock price of ABC Company is $10 today at the close of trading, and
an investor buys one European call option contract having a maturity date three months
from today on ABC Company stock with an exercise price of $14 at $1. If the
performance of ABC Company is good and the stock price is $17 at the maturity date,
then the investor exercises the option, buys one stock at $14, and immediately sells it for
$17. As a result, (s)he makes $2 net profit since (s)he already paid $1 for the option
contract. On the other hand, if ABC Company does not do well and the stock price is less
than $15, then the investor does not exercise the option and loses $1. The contract price
paid by the investor is received by another trader who agreed to sell that stock for $14 at
the maturity date.
37
$2.00
$1.00
$0.00
$1.00
$2.00
$3.00
$4.00
$5.00
$1 $3 $5 $7 $9 $11 $13 $15 $17 $19 $21
Stock Price
P
r
of
i
t
`
Figure 3.2 Profit of a Call Option Contract as the Function of the Stock Price
If the same investor in the above example buys one European put option contract
having a maturity date three months from today on ABC Company stock with an exercise
price of $14 at $1, and, if the stock price is $11 at the maturity date, then the investor
exercises the option and makes $2 net profit since (s)he already paid $1 for the option
contract. On the other hand, if ABC Company performs well and the stock price is
greater than $14, then the investor loses $1. The contract price paid by the investor is
received by another trader who agreed to buy that stock for $14 at the maturity date.
$3.00
$1.00
$1.00
$3.00
$5.00
$7.00
$9.00
$11.00
$13.00
$1 $3 $5 $7 $9 $11 $13 $15 $17 $19 $21
Stock Price
P
r
of
i
t
`
Figure 3.3 Profit of a Put Option Contract as the Function of the Stock Price
There are four types of participants and three categories of traders in options
market (Hull, 2006).
38
Participants are classified as follows:
? Buyers of calls
? Sellers of calls
? Buyers of puts
? Sellers of puts
Hull (2006) identifies the broad categories of traders as hedgers, speculators, and
arbitrageurs. Hedgers use derivatives to reduce the risk that they face from potential
future movements in a market variable. Speculators use them to bet on the future
direction of a market variable. Arbitrageurs take offsetting positions in two or more
instruments to lock in a profit.
A hedger can be an investor who owns 1 share of ABC Company with $10 price
per share and who expects a decline in the near future. Since that investor wants
protection, (s)he buys a put option contract on ABC stock at $1 with an exercise price of
$9. If the ABC stock price drops to $4, then (s)he exercises the option and makes $8.
A speculator can be an investor who expects an increase in the stock price of
ABC Company. Suppose the current stock price of ABC Company is $10, and a call
option contract for the same stock is $1 with an exercise price of $12. If the investor has
$100 to invest, then there are two different ways to do so. (S)He can buy 10 shares and, if
circumstances become favorable and the stock price increases by $5, (s)he makes $50 net
profit. Or (s)he can buy 100 call option contracts by paying $100 and, if circumstances
become favorable and the stock price increases by $5, (s)he makes $200 net profit instead
of $50.
39
In case the speculator's expectations are not realized, then (s)he loses $100 that (s)he paid
for the options contract. Hull (2006) points out that options can give rise to dramatic
gains and losses if they are used for speculative purposes.
An arbitrageur can be an investor who wants to obtain risk free profit by trading
the same derivative simultaneously in different markets. If the price of the stock that
(s)he wants to trade is $4 in New York Stock Exchange, while it is $7 in Istanbul Stock
Exchange with a transaction cost of $1, (s)he can make a $2 risk free and instantaneous
profit. A detailed review and discussion of the option pricing theory and the associated
trading strategies is presented in Appendix C.
3.4 Real Options Analysis
The dilemma of the contemporary corporate planners is the idiosyncrasy of
deploying myopic techniques for the valuation of strategic investments with the
expectation of long term payoffs under uncertainty. The existing techniques are far from
evaluating irreversible strategic investment decisions which may or may not create
profitable opportunities in the future.
Kester (1984) argues that a company should not spend time and effort trading off
growth with return on investment or market share with profitability in lieu of focusing on
the kind of value the investment will create, its durability, and the auxiliary decisions
required to protect or enhance it over time.
The real options framework is first coined by Myers (1977) after Black, Scholes,
and Merton provided a method to value the options in their seminal work on options
pricing in 1973.
40
Today's research efforts are built upon their seminal work starting with pricing all
derivative products. Their work obtained significant acceptance by the creation of
Chicago Board of Options Exchange. The aforementioned acceptance exhibits a similar
pattern as the traditional DCF techniques did earlier. Miller and Park (2002) argue that
academia usually identifies evaluation techniques that are inline with theory, and it takes
many years for practitioners to adopt such ideas. DCF tools first identified in the 1950's
did not replace payback period until the 1980's. ROA, which was first identified 20 years
ago, has begun its acceptance for corporate decisionmaking process in a similar fashion.
Luehrman (1997) discusses that understanding valuation has become a
prerequisite for meaningful participation in a company's resource allocation decisions.
The key to valuing a corporate investment opportunity as an option is the ability to
discern a simple correspondence between project characteristics and option
characteristics. The potential investment to be made corresponds to an option's exercise
price. The operating assets the company would own, assuming it made the investment,
are like the stock one would own after exercising a call option. The length of time the
company can wait before it has to decide is like the call option's time to expiration.
Uncertainty about the future value of the operating assets is captured by the variance of
returns on them; this is analogous to the variance of stock returns for call options. The
analytical tactic here is to perform this mapping between the real project and a simple
option. Luehrman (1997) proposes that a pragmatic way to use option pricing is as a
supplement, not a replacement, for the valuation methodology already in use.
Trigeorgis (1993) provides a comprehensive overview of the existing real options
literature and applications.
41
He presents practical principles for quantifying the value of various real options and takes
a first step towards extending the real options literature to recognize interactions with
financial flexibility. He suggests that management's flexibility to adapt its future actions
in response to altered future market conditions expands an investment opportunity's value
by improving its upside potential while limiting downside losses relative to
management's initial expectations under passive management. Trigeorgis (1993) proposes
that the resulting asymmetry caused by managerial adaptability calls for an "expanded
NPV" rule, reflecting both value components: the traditional (static or passive) NPV of
direct cash flows and the option value of operating and strategic adaptability. This does
not mean that the traditional NPV should be scrapped, but rather should be seen as a
crucial and necessary input to an optionsbased, expanded NPV analysis.
Dixit and Pindyck (1994) support Luehrman (1997) and agree that irreversibility,
uncertainty, and the choice of timing alter the investment decision in critical ways. They
discuss that conventional approaches to decision making have shortcomings where two
basic issues need to be addressed. First, how to determine the expected stream of profits
that the proposed project will generate and the expected stream of costs required to
implement the project; and, second, how to choose the discount rate for the purpose of
calculating net present value. Their research is based on an important analogy with
financial options. A company with an opportunity to invest is holding something much
like a financial call option; it has the right, but not the obligation to buy an asset at a
future time of its choosing.
By deciding to go ahead with expenditure, the company gives up the possibility of
waiting for new information that might affect the desirability or timing of the investment.
42
It cannot disinvest should market conditions change adversely. The lost option value is an
opportunity cost that must be included as part of the cost of investment. Thus the simple
NPV rule needs to be modified. Instead of just being positive, the present value of the
expected stream of cash from a project must exceed the cost of the project by an amount
equal to the value of keeping the investment option alive. Investment expenditures are
irreversible when they are specific to a company or to an industry. They are sunk costs.
Even investments that are not company or industry specific are partially irreversible (the
average value of used equipment, vehicles, etc.).
When a company makes irreversible investment expenditures, it "exercises", in
effect, its call option. Uncertainty plays a crucial role in the timing of capital investment
decisions and in recognizing an investment opportunity like a financial call option. It is
considered that the more volatile the price of the stock on which the option is written, the
more valuable the option and the greater the incentive to wait and keep the option alive
rather than exercise it. Economies of scale can be an important source of cost savings for
companies. Dixit and Pindyck (1995) support their argument with the example of
building one large plant instead of two or three smaller ones, so that companies might be
able to reduce their average unit cost while increasing profitability. When the growth of
demand is uncertain, there is a tradeoff between the scale of economies and the
flexibility gained by investing more frequently in small additions to capacity as they are
needed. Hence they suggest that irreversibility, uncertainty, and the choice of timing alter
the investment decision in critical ways.
43
Miller and Park (2002) identify and systematize the current body of research and
discuss a concise summary of modeling concerns, applications, and a roadmap for future
modeling efforts. Their argument is that the DCF techniques ignore the flexibility to
modify decisions along the value chain as new information arrives. NPV is a passive
method that works well in deterministic situations, but under conditions of uncertainty it
has limited capability. ROA is a promising tool for strategic investment decisions
whereby projects are viewed as real options that can be valued using financial option
pricing techniques. Technically, ROA enables managers to bundle a number of possible
mutually exclusive outcomes into a single investment. Under ROA, any corporate
decision to invest or divest in real assets is simply an option.
Copeland and Antikarov (2003) explain ROA by using the turnpike theorem
analogy. It is preferable to deviate from your present direction to take advantage of
higher speed paths until something unexpected such as a traffic jam or an unplanned
detour occurs. However investing in a more detailed map, a global positioning system
and satellite radio that broadcasts frequent traffic updates allows you to detect the
unexpected events so that you can dynamically plan your itinerary by taking advantage of
shortcuts. In this way, you are investing in flexibility in order to increase the resolution of
potential uncertainties. ROA behaves more realistically than the traditional DCF
techniques to capture the value of the flexibility, and it is an insurance against under or
over valuation risk of the investment decisions.
44
Hence real options can be defined as the right, but not the obligation to make
further investments in order to increase the throughput of a project, to defer a project, to
extend the useful life of a project, to reduce the scale of a project, to switch between
strategies, to invest contingently, or to terminate a project using intelligent timing
decisions.
Assume Company ABC is a software provider, and the senior management is
considering investing $5 million in a new stateofthe art ERP system development. The
estimated net cash inflow per year is $1 million during the project life of five years. Since
the demand to ERP systems is volatile due to the global knowledge transfer, the cash
volatility is estimated as 40 percent. The riskfree interest rate is 6 percent, and the ABC
Company's MARR is 8 percent. Even though there is volatility in cash inflows, the senior
management has an option to delay this project for two years with an estimated initial
investment increase of 15 percent per year. The chief financial officer of Company ABC
recommends not investing since the NPV of the project is
( ) ( ) 01.1$5%,8,/1$5$%8 ?=+?= APMMNPV
However if the investment is made two years from today the estimated project value is
V
2
=$3.99 million with today's value of V
0
=$3.42 million. Valuing this investment using
the BlackScholesMerton model, Company ABC realizes that the delay option is worth
$455,000. Thus Company ABC decides to invest in this project two years from now
instead of making a "now or never" decision today made through underestimation of the
flexibility stemming from traditional DCF techniques.
45
3.5 Modeling Approaches
Miller and Park (2002) identify and systematize the current body of ROA research
and classify the current modeling approaches as discrete time and continuous time
models.
Continuous time modeling consists of closedform equations, stochastic
differential equations, and MCS. Black and Scholes (1973) developed the first closed
form equation for option and warrant valuation. Their research is the backbone of today's
option pricing technique. Margrabe (1978) developed a closedform equation for the
valuation of an option where one asset is exchanged for another. Margrabe (1978)
assumes that the exercise price is a stochastic variable, where the Black and Scholes
model treats the exercise price as a deterministic variable. Fischer (1978) also developed
a closedform equation with exercise price as a stochastic variable, while Geske (1979)
used deterministic exercise prices for compound option valuation in his closedform
equation. Later Carr (1988) treated the exercise prices as stochastic variables for the
sequential investment decisions discussed in Geske (1979). Kumar (1996) presents a
theoretical analysis of the variation of option values with project risk and a comparison of
BlackSholes and Margrabe models, where he examines the relationship between project
risk and option values of investments in new information technologies and illustrates how
this relationship is significantly different from wellknown results in the case of financial
option pricing. Taudes (1998) proposes using option pricing formulas, which consist of
closedform equations to obtain the estimate value of flexibility of an information system
platform.
46
He also discusses the various assumptions of the option pricing models and the
limitations of the real options approach in the context of information system investments
by introducing option pricing formulas for the valuation of various types of software
growth options.
The derivation of the closedform equations is performed through the solution of
stochastic differential equations. The solutions to the stochastic differential equations do
not always exist and partial differential equations must be solved either using finite
difference methods or MCS (Miller and Park, 2002). Kulatilaka (1993) develops a
flexibility model using continuous time dynamics of a state variable that is
computationally simple and is more amenable to empirical implementation than those
that rely on analytical solutions. The model is applied to the case of an industrial steam
boiler that can switch between using residual fuel oil and natural gas. Cortazar and
Schwartz (1993) develop a continuous time model for valuing a copper mine that has a
production bottleneck and for determining its optimal output rate and capacity using
stochastic differential equations under boundary conditions. Their objective is to extend
the real option approach by modeling the firm as a twostage process with bounded
output rates, in which the output of the first stage may be held as workinprocess
inventory, where the underlying asset is a compound option, which, if exercised, has an
option to finish the workinprocess inventory and sell the output as its payoff.
47
Mauer and Ott (1995) analyze the determinants of sequential replacement
investment decisions in a contingent claims model with maintenance and operation cost
uncertainty and realistic tax effects by deriving a closedform solution through solving
partial differential equations. Hull (2006) provides an overview of MCS together with
finite difference methods.
Assume that a portfolio consists of a long position in ? shares and a short position
in one call option. The number of shares that generates a riskless portfolio is calculated as
follows using the formulation given in Hull (2006):
dSuS
ff
du
00
?
?
=? (3.11),
where S
0
is the stock price, f
u
is the option price if the stock price moves up to S
0
u, f
d
is
the option price if the stock price moves down to S
0
d, u is the up movement coefficient,
where u>1 and u1 is the percentage increase in the stock price S
0
, and d is the down
movement coefficient, where d<1 and 1d is the percentage decrease in the stock price
S
0
Figure 3.4 OneStep Binomial Tree (Hull 2006)
.
In the above onestep binomial tree the portfolio is valued using the riskfree rate. Since
the option is not exercised if the stock price goes down, the present value of the portfolio
is calculated as follows using the formulas given in Hull (2006):
48
( )
rT
u
efuSfS
?
??=??
00
(3.12)
or
( )
rT
u
rT
efueSf
??
+??= 1
0
(3.13)
Substituting Equation (3.11) in Equation (3.13):
( )[ ]
du
rT
fppfef ?+=
?
1 (3.14),
where
du
de
p
rT
?
?
= (3.15)
The lattice approach assumes the underlying asset follows a discrete, multinomial,
multiplicative stochastic process through time to form some form of tree, where the
option value is solved recursively from the end nodes of the tree (Miller and Park, 2002).
Cox, Ross and Rubinstein (1979) developed the standard binomial approach. Rendleman
and Barter (1979) present an elemental twostate option pricing model, which is
mathematically simple, yet can be used to solve many complex option pricing problems.
In contrast to widely accepted option pricing models which require solutions to stochastic
differential equations, their model is derived algebraically by using a binomial lattice
approach since solving continuous time option pricing problems using closed form
solutions is unattainable. Boyle (1988) developed an extension of the Cox, Ross,
Rubinstein binomial lattice algorithm to handle the situation in which the payoff from the
option depends on more than one state variable. His modification to the Cox, Ross,
Rubinstein algorithm consists of replacing the twojump process with a fivejump
process. Madan, Milne, and Shefrin (1989) derived a multinomial option pricing formula
where they generalized the Cox, Ross, Rubinstein binomial model to multinomial case.
49
Tian (1993) developed a modified approach to the selection of lattice parameters
including probabilities and jumps by conducting numerical simulations to investigate the
comparative accuracy of the approach with that of the Cox, Ross, Rubinstein and Boyle
trinomial procedures. Tian (1993) found that all trinomial approaches are more accurate
than binomial procedures. Detemple and Sunderesan (1999) provide a simple framework
to value derivative assets subject to trading decisions using a computationally tractable
and easy to implement binomial model. Herath and Park (2002) present a lattice approach
to value a compound real option. Miller and Park (2002) summarize the modeling
approaches for option calculation as follows:
Figure 3.5 Numerous ROA Modeling Approaches for Option Calculation
3.6 ROA Application Areas
The adoption of ROA into practice, like the adoption of the net present value and
cost of capital techniques, is slow.
50
Miller (2004) reports that the use of net present value and cost of capital techniques,
which was first identified in the 1950's, did not replace payback period until the 1980's.
Considering the aforementioned 30year adoption period, expecting an increasing trend
of ROA adoption for decision making in the offing must not be considered as ambitious.
However, it should be noted that DCF tools are still required for utilizing ROA.
The ROA application areas where the majority of publications have been made
within the last decade are stock valuation, natural resource valuation, research and
development project valuation, manufacturing and inventory decisions, strategic decision
making, technology selection and deployment, and biotechnology (Miller, 2004).
Based on his research into the investment and capital budgeting decisions of
companies, Kester (1984) thinks of future investment opportunities as analogous to
ordinary call options on securities.
The design of an optimal mesh of contingent claims with purchasing
commitments that will best meet the riskreward preferences of the decision maker can be
viewed in Ritchken and Tapiero (1986). Under risk preferences, their study examines
conditions under which option contracts serve as superior or complementary strategies to
inventory building.
Chung (1990) utilizes the option pricing model for the evaluation of the firm's
output decision under uncertainty. He presents a contingent claim analysis of output
decisions for the firm facing uncertain demand and uncertain technology.
McLaughlin and Taggart (1992) evaluate capital budgeting problems that arise
when a new project proposal calls for the use of existing, but currently idle, equipment or
facilities. Basically they discuss a new framework for capacity planning.
51
The essence of their option framework is as follows: capacity in place gives the firm an
option to produce. Thus, if a firm diverts capacity from Product A to Product B, it
forgoes the option to produce Product A immediately, but it acquires an option to replace
the diverted capacity.
Pickles and Smith (1993) attempt to explain in a simple, tutorial way the
application of developments in the theory of finance to the valuation of certain types of
petroleum property and investment. Specifically, they are concerned with the valuation of
discovered but undeveloped oil and gas reserves, which then leads to the valuation of an
exploration lease where some amount is to be spent for a chance at finding reserves
which could subsequently be developed.
Kemna (1993) suggests that the main contribution of options pricing theory in
capital budgeting is twofold. First, it helps management to structure the investment
opportunity by defining the different investment alternatives with their underlying
uncertainties and their embedded options. Second, options pricing theory can handle
flexibilities within the project more easily than the traditional DCF analysis.
Cortazar and Schwartz (1993) extend the real option approach by modeling the
firm as a twostage process with bounded output rates, in which the output of the first
stage may be held as workinprocess. They consider the asset as a compound option,
which, if exercised, has an option to finish the workinprocess and sell the output as its
payoff. They discuss that the existence of intermediate inventories may arise, not only
because of inefficiencies in the production system, but also as an optimal investment
strategy for exploiting possible future price increases.
52
They provide analytical expressions for valuing a firm that has a production bottleneck
and for determining its optimal output rate and capacity.
A general model of flexible manufacturing that is computationally simple and is
more amenable to empirical implementation than those that rely on analytical solutions
can be found in Kulatilaka (1993). The model is applied to the case of an industrial steam
boiler that can switch between using residual fuel oil and natural gas.
Kogut and Kulatilaka (1994) analyze the platform investments, and are engaged
in developing heuristics to aid the understanding of how capabilities must be built in
anticipation of the future. They argue that the world is witnessing a new era of
competition with the development of new principles of organizing work, radical
technologies, and globalization. They propose that there have been two streams of
thought aimed at correcting this bias. The first theory is to formulate the strategic
investments as real options, and the second idea consists of recent work on organizational
capabilities and core competencies (e.g., quality programs, kanban systems, valuebased
activity analysis, etc.).
Smith and Nau (1995) analyze a simple twoperiod capital budgeting problem.
They first employ the na?ve DTA fundamental idea of discounted cash flow approach,
where the problem is that the appropriate discount rate is unknown. Then, they employ
options pricing technique seeking a portfolio of securities that exactly replicates the
project's payoffs. Next, they approach the problem with full DTA by using subjective
probabilities instead of riskadjusted or riskneutral probabilities to capture time and risk
preferences using its utility function. The result obtained by the latter is exactly the same
as the one obtained by options pricing analysis.
53
Finally they utilize an integrated approach using both DTA and options pricing technique
by decomposing project cash flows into its market and private components. They
conclude that option pricing and decision analysis methods are fully compatible and can
be profitably integrated by separating market and private risks.
Mauer and Ott (1995) analyze the determinants of sequential replacement
investment decisions in a contingent claims model with maintenance and operation cost
uncertainty and realistic tax effects. The optimal replacement policy is characterized by a
critical level of maintenance and operation cost, which is the replacement barrier at which
the firm should replace an existing asset with another stochastically equivalent asset.
Stowe and Su (1997) present a contingentclaims approach to inventorystocking
decision. Their approach incorporates the economic principles of assetpricing models,
such as the BlackScholes option pricing model, to replace the expected profit
maximization logic of the conventional approach.
Brown and Davis (1998) examine a situation, in which an organization is faced
with making a mutually exclusive choice between two projects with unequal lives. Their
objective is to illustrate the impacts of the ignored existence of options that can occur as a
result, using a simple example of choice between mutually exclusive projects. They
demonstrate that the standard techniques can lead to errors in a stochastic environment
assuming interest rate uncertainty.
As noted in Chen, Kensinger, and Conover (1998), option pricing methods can be
applied to evaluate capital budgeting of equipment, such as computercontrolled machine
tools, that convert a generic input into any of a variety of different machined parts.
54
Option pricing models offer the possibility of improving the decision makers' ability to
analyze investments in computer integrated manufacturing (hereafter CIM) systems.
Kelly (1998) applies a binomial approach to the investment timing option. His
approach relies on data that is readily available from published sources such as futures
and spot markets. Although the method eliminates the need to estimate both future cash
flows over the life of the project and riskadjusted discount rates, it requires the existence
of a futures market in the underlying asset.
Ottoo (1998) models an internal growth option for a biotechnology firm, which
gains access to productive technology by successfully completing a research and
development project before its competitors and introducing a new product to the market.
In a competitive market marked by rapid change and uncertainty, very little is known
about valuing opportunities, especially for startup and emerging firms.
The analysis of multistage or compound real options that involve a staged capital
commitment and offer the right to make future followon investments under favorable
developments can be found in Panayi and Trigeorgis (1998). Such growth option
investments may have negative net present values when considered in isolation, but can
add strategic value to a firm by serving as the first stage necessary to generate profitable
followon investment opportunities in the future. They analyze the actual case of an
informationtechnology infrastructure investment decision faced by a state
telecommunications authority. They then examine the option facing a bank to expand its
operations into another country as part of multinationalizing its operations. In both cases,
by making a costly firststage investment, the firm involved essentially acquires a
foothold on future investment opportunities.
55
Such multistage options are of strategic import to the firms that invest to acquire,
nurture, develop further, and optimally exercise or abandon them over time, based on
future market developments. They develop an expanded or strategic NPV criterion
reflecting both the traditional NPV and the value of managerial flexibility, or, in other
words, value of option flexibility given by the following Equation (3.16):
Expanded (Strategic) NPV = Traditional NPV + Value of option flexibility (3.16)
Bollen (1999) develops a real option valuation framework that explicitly
incorporates a stochastic product life cycle. The product life cycle is represented using a
regimeswitching process. The cycle begins in a growth regime, characterized by
increasing demand, and switches stochastically to a decay regime, in which demand
generally falls. The option to change a project's capacity is valued, and it is shown that
option values consistent with a product life cycle are significantly different than those
from a standard model that makes simplifying assumptions about the demand process.
Park and Herath (2000) develop a singleperiod binomial lattice approach to price
a call option and riskfree arbitrage principle of valuation. Their basic idea is to develop a
hedge portfolio to replicate the future returns on the call. They conceptualize how the
financial options approach can be used to value flexibility associated with a real
investment opportunity. They formulize the value of this flexibility or the real options
premium by the following Equation (3.17):
ROP = SNPV ? Conventional NPV (3.17),
where ROP represents the value of the real options premium or the value of the flexibility
and SNPV represents the strategic NPV.
56
As noted in Childs and Triantis (1999), the multinomial lattice approach can also be used
to develop a trinomial lattice approach to value research and development case studies.
Lint and Pennings (2001) consider the product development process as a series of
real options for reducing uncertainty over time. They develop criteria to decide whether
to speed up or delay the development process for Philips Electronics. Any particular
project can be assigned within a twobytwo matrix of uncertainty versus research and
development option value. The matrices support portfolio management throughout the
different phases of development and enable management to decide on an appropriate
point at which to abandon individual projects.
Nembhard, Shi, and Aktan (2005) develop a supply chain model, in which a
manufacturing firm can have the flexibility to select different suppliers, plant locations,
and market regions considering that there can be an implementation time lag for the
supply chain operations. The main purposes of their study were to place the difference
between immediate implementation and the time lag into this framework and then to
analyze the effect on the outcome and hence the managerial course of action. They use a
real options approach to estimate the value of flexibility and to determine the optimum
strategy to manage the flexibility under uncertainty in the currency exchange rate.
Burnetas and Ritchken (2005) investigate real option contracts in a supply chain
contract when the demand curve is downward sloping. They consider call (put) options
that provide the retailer with the right to reorder (return) goods at a fixed price, where
goods have long lead times, short selling seasons, and high demand uncertainties. They
argue that these options are not zerosum games.
57
Cucchiella and Gastaldi (2006) study a supply chain strategy for limiting the
damages that can be stemming from the sources of uncertainty recoverable inside a
supply chain. Firstly, a set of sources of uncertainty have been selected; subsequently the
risks connected with each sources have been defined. They study and simulate the ability
of the outsource option to cover, at the same time, the risks of production capacity and
price fluctuations of a high technology company that produces medical devices.
It should be noted that the real option approach has also some disadvantages with
respect to traditional discounted cash flow methodologies, since it requires more data on
the variability of considered parameters as well as models that well match the project
under examination, it could be seen as a black box not so easily understood and utilized.
Finally, the analysis is more complex and needs ad hoc computer programs to solve the
real option algorithm.
58
CHAPTER 4
PRACTICAL BUSINESS APPLICATION
4.1 Introduction
This chapter presents a realworld business application concerning a series of
capital investment decisions for an automotive electronics manufacturing facility. Data
availability has not been a challenge; financial and operational data have been available
on a daily basis through the associated databases of the subject matter facility since
October 2006. The valuation of the aforementioned series of capital investments is
performed through discounted cash flow techniques, MCS, DTA, and real options
analysis in Chapter 5. The results obtained in Chapter 5 are interpreted in Chapter 6.
Hence a combination of both quantitative and experimental research methodologies is
utilized.
The practical business application is about a series of capital investment decisions
that will allow the facility management to generate additional floor space to
accommodate additional assembly lines, cleanrooms, and manufacturing cells for
potential future business opportunities.
59
4.2 Facility Overview
Huntsville Electronics operations began business in 1952 when Chrysler arrived
in Huntsville to provide support and engineering services to Dr. Werner Von Braun's
Mercury rocket team. Chrysler engineers supported breadboard operations such as
cathode ray and vacuum tubes, preelectrical devices and electrical configurations.
The company grew in the 1960's to over 4,000 people as a prime contractor on
Redstone, Mercury, and Saturn 1 rocket programs. The original 65,000 sq. ft.
Wynn
Drive Plant (hereafter Plant II), built in 1965 to support the Saturn/Apollo space projects,
was expanded to 100,000 sq. ft. in 1972 for car radio manufacturing, with approximately
70 people making the first inroads to automotive electronics with the electronically tuned
radio.
In 1974, another 120,000 sq. ft.
expansion allowed the manufacture of electronic
ignition control units for all Chrysler Motors passenger cars. In July 1977, the Huntsville
Division completed an additional 200,000 sq. ft. manufacturing plant across the road
from Plant II in response to the expanding electronics market and electronic content in
vehicles, such as the "learn burn" engine controllers, radios, pressure units, and other
products. From the 1970's through the 1980's, Chrysler Huntsville was one of the fastest
growing hightech automotive electronics engineering and manufacturing operations in
the southeast.
In 1988, Acustar Inc., Chrysler's wholly owned parts subsidiary, formally opened
its $170 million Huntsville Electronics Complex with a ribboncutting ceremony at the
Huntsville plant (hereafter Plant I).
60
Acustar's Huntsville Electronics Division developed and produced automotive electronic
systems and components, including radios; sound systems; electronic and
electromechanical gauges and instrument panel clusters; driver information and trip
computers; fuel injection control systems; spark control computers and speedometers;
odometers; engine oil pressure sensors; and pressure switches. By 1988, the Huntsville
Electronics Division of Acustar produced thousands of electronic components and
systems daily. Plant I became a DaimlerChrysler operation on November 11, 1998, when
two OEM's merged. Later it became an integrated part of Siemens VDO Automotive
Corporation from April 2, 2004 until December 3, 2007, when Continental AG acquired
Siemens VDO Automotive Corporation.
The facility has been serving the community and the industry as a leading first
tier automotive electronics supplier. With the compounding effects of globalization and
improvements in technology, the competition is not between individual business entities
anymore. Collaborative planning, replenishment, and forecasting synergy generated by
supply chains carried the competition up to the supply chain level. Continental AG has
strengthened its market position in the NAFTA region by acquiring the second of the six
firsttier automotive electronics manufacturing facilities located in the U.S.A. In addition
to Chrysler, GM, Ford, VW, and BMW, more OEM's need to be added to the customer
portfolio of Plant I in order to hedge against the variability in automotive sales due to
fairly frequent changes market dynamics of the automotive industry.
61
Plant I is a $1 billion annual sales automotive electronics manufacturing facility.
After Plant II was shut down at the end of fiscal year 2007, instrument panel cluster
manufacturing operations were transferred to the Guadalajara facility in Mexico, leaving
additional floor space for revenue generating purposes. Plant I is one of the six firsttier
automotive electronics manufacturing facilities located in the U.S.A., with a total facility
area of 816,299 sq. ft. The breakdown of the total area is as follows: The engineering and
administration building area is 239,915 sq. ft., the manufacturing building area is 564,286
sq. ft., the waste and chemical storage building area is 10,984 sq. ft., and the area for
pump houses is 1,114 sq. ft. The following Figure 4.1 indicates the overall area
distribution of Plant I.
Figure 4.1 Overall Facility Area Distribution
Overall Facility Area Distribution
239,915
29%
564,286
70%
1,114
0%
10,984
1%
Engineering and Administration Building
Manufacturing Building
Waste and Chemical Storage Building
Pump Houses for Fire Protection
62
The manufacturing building has an aspect ratio of 1.2:1 and houses 15 assembly
lines measuring 600 feet long by 25 feet wide, which are laid out in a northsouth
orientation and have a total area of 308,400 sq. ft., the distribution center located in the
North Dock with a total area of 50,385 sq. ft., while the finished goods warehouse is
located in the South Dock with a total area of 26,952 sq. ft. Finally the administrative,
social, quality control, and facilities systems related area consists of 178,550 total sq. ft.
Manufacturing B uilding Area D istribution
308,400
54%
178,550
32%
26,952
5%
50,385
9%
Assembly Lines
Distribution Center
Finished Goods Warehouse
Adm./Eng./Soc./QC/Facility Systems
Figure 4.2 Manufacturing Building Area Distribution
4.3 Practical Business Application
Fierce competition in the automotive electronics industry is forcing corporations
that are operating in the U.S.A. to develop innovative technologies that will provide them
with a competitive advantage and/or to generate significant cost savings by moving their
operations to other countries, where the labor cost is relatively low.
63
Since moving operations to other countries results in loss of domestic expertise, increased
transportation costs, and decreased supply chain resiliency, corporations investigate
opportunities that will allow them to generate additional revenues to compensate for the
high labor costs. Capacity plays an important role in additional revenue generation since
floor space is a significant component.
Plant I management started to evaluate a replacement/retrofitting project for the
existing, but outdated miniload AS/RS and the AGV system in January 2005 which
offered opportunities for increasing the overall throughput capacity with additional floor
space generation totaling up to approximately 70,000 sq. ft. The management's primary
objective was to diversify the customer portfolio for hedging against the variability in
domestic automotive sales while also keeping the existing customer portfolio. Thus, they
need additional floor space to achieve their objective.
Considering the aforementioned circumstances, facility officials were diligently
investigating the floor space availability that involves minimum capital investment.
Although the average floor space requirement for an assembly line is approximately
15,000 sq. ft., utilizing a floor space of 5,000 sq. ft. is becoming a common practice for
manufacturing high valuelow volume products. This practice is made possible by
utilizing such technologies as chipandwire, tapeautomated bonding, flipchip, and
multichip module through ClassOne cleanroom applications or by deploying
manufacturing cells rather than conventional Ishape assembly lines.
64
However, according to Plant I management, there are two major sources of
uncertainty:
? The volatility of the OEM demand.
? The corporate marketing performance that realizes as additional business
volume, i.e., additional market share.
As of January 2005, there is not any available floor space for additional potential
business opportunities. Therefore the facility management is analyzing the utilization of
the current floor space dedicated to such nonvalue added activities as logistics and
maintenance.
The decision portfolio is composed of the following options that are embedded in
the practical business application:
? Replacing the existing outdated AS/RS and corresponding WMS with a new
AS/RS and WMS to generate floor space and cost savings, which is supported
by a throughput analysis through a simulation study.
? Eliminating the existing outdated miniload AS/RS by switching to a justin
time delivery system together with threeshift 3PL support and transportation
operation.
? Replacing the existing outdated AGV control software and retrofitting the
vehicles of the existing AGV system in order to generate floor space by
eliminating pick and drop stands and by reducing the aisle space supported by
a throughput analysis through a simulation study and extends, which is the
useful life of the mechanical AGV components.
65
? Replacing the existing outdated AGV system with water spiders utilizing
tuggers with associated trailers.
The Plant I distribution center operates three shifts per day and houses five
different types of storage: Miniload AS/RS storage, static rack storage, nonproduction
material crib, launch crib, and refrigerated storage.
The miniload AS/RS storage consists of a sixaisle miniload AS/RS that was
commissioned in 1987 and manufactured by Litton Industrial Automation Systems, Inc.
It features a 6,691.2 sq. ft. footprint laid out in an eastwest orientation. The 80foot long
and 14.5foot high aisles of the miniload AS/RS were designed to hold relatively small
electronic components for subassembly processes randomly assigned to 9,000 storage
locations.
Inbound bulk production material, the demand for which is a full pallet load, are
stored in single deep selective and threehigh static racks with a net total footprint of
3,667.3 sq. ft. and 564 storage locations. The static racks that are located on the east and
north side of the miniload AS/RS are referred to as "East Rack," and the static racks that
are located on the west side of the miniload AS/RS are referred to as "West Rack."
Racks are laid out in a northsouth orientation, where the associated layout is provided in
Appendix D.
The nonproduction material crib is used for onetime purchase order material
storage, receiving expedited and/or rush package deliveries, and storage of non
production material like cleaners, gloves, and tapes. The total storage area is 7,073 sq. ft.
66
The launch crib is a caged set of rack locations where pilot or launch parts are
stored. These parts are used in assembly prototyping for a product that will be launched
in the future. The total storage area is 552 sq. ft.
Chemical production materials such as solder paste, adhesives, and flux are stored
in the refrigerated storage area for longer shelf life. The total storage area is 260 sq. ft.
Inbound production material delivery to assembly lines, finished goods delivery
to the finished goods warehouse, empty dunnage delivery to the dunnage return station
located in the distribution center, and linetoline movements are performed by AGV's.
There are 24 AGV's in the distribution center and eight AGV's in the finished goods
warehouse, which were manufactured by Egemin Automation, Inc. and deployed in 1987.
There are 370 pick and drop stands, together with ergonomic lifts, located on the
manufacturing floor which occupy approximately 8000 sq. ft.
Plant I performs scheduled receiving functions by using a prereceiving tool:
Electronic data interchange (hereafter EDI). The receiving function is performed in the
North Dock of the facility (see Appendix D for the layout of the North Dock). Plant I has
been using SAP R/3 as the enterprise resource planning (hereafter ERP) host system
since April 2, 2004. Miniload AS/RS is managed and controlled by a legacy proprietary
material handling control software (hereafter MHCS), whereas static rack storage is
deprived of the handling unit management (hereafter HUM) module of SAP R/3 between
the ERP host system and physical receiving at the operational level. There are three on
campus 3PL's: J.I.T. Services Inc., Mtronics.com, and Span Ltd. 3PL's provide vendor
managed inventory (hereafter VMI) service to the majority of international/domestic
suppliers.
67
In addition to 3PL's, there are six directshipping local domestic suppliers, and the "Span
Triana" facility that provides a reusable container management service in close proximity
of Plant I.
Inbound production material is delivered by a dedicated regional lessthan
truckload trucking company called AAA Cooper Transportation. There are nine
scheduled inbound deliveries per day during the first and second shift operations.
However, depending on spontaneous daily changes in the production schedule, expedited
deliveries might occur, either through the transportation company or by using company
owned vehicles.
4.4 MiniLoad AS/RS and MHCS
The miniLoad AS/RS consists of a sixaisle, miniload AS/RS that was
commissioned in 1987 and manufactured by Litton Industrial Automation Systems, Inc.
It features a 6,691.2 sq. ft. footprint laid out in an eastwest orientation. It was designed
for a service life of 15 years and is fully depreciated. The 80foot long and 14.5foot high
aisles of the miniload were designed to hold relatively small electronic components for
subassembly processes that are randomly assigned to storage locations. The parts are
ordered by assembly lines in quantities less than a whole palletload and are stored in
plastic returnable totes or recyclable cardboard boxes placed in metal pans that are
accessible by miniload AS/RS cranes. Each storage location has a 26inch by 51inch
pan that is able to hold loads up to 500 lbs. Pans are stored in slots located on the left and
right sides of the aisles. Each side has 25 bays of 10 tiers of slots.
68
The first three tiers from the top in each aisle, i.e., tiers 8, 9, and 10, are sized for large
totes. The slot heights by tier are given in Table 4.1 below:
Table 4.1 Slot Heights by Tier
Tier Number Slot Height (inches)
1 11
2 11
3 11
4 13
5 11
6 13
7 11
8 21
9 19
10 21
Figure 4.3 MiniLoad AS/RS Aisle
The total storage capacity is designed to be 9,000 tote storage locations; however
the total number of the net available tote storage locations was reported to be 8,814 by
the plant engineering department.
69
Some slots and/or tote storage locations in slots are reported to be unavailable for storage
due to monuments like columns, pipes, and conduits, while some are unavailable due to
software problems. With ongoing efforts toward resolving software problems, the number
of available storage locations is shifted back up to 8,868.
Figure 4.4 MiniLoad AS/RS Layout
Miniload parts are received in totes and cardboard boxes with three different
sizes shipped on 40inch by 48inch plastic pallets. Size specifications of the returnable
totes are given in Table 4.2 below:
Table 4.2 Tote Size Specifications
Tote Size Dimensions (Length x Width x Height) (inches)
HalfSize 12 x 16 x 9
Small 24 x 16 x 8
Large 24 x 16 x 15
MHCS was originally designed to store six halfsize and three small and/or large
size totes in a miniload AS/RS pan. However, currently only three halfsize totes can be
stored in each miniload pan, just as if they were the small size. Totes are tracked by one
dimensional barcoded unique identification tags.
N
70
Each unique identification tag consists of six numerical digits indicating the size and
whether it is a plastic returnable tote or a recyclable cardboard box. Table 4.3 below
indicates the identification number block allocations:
Table 4.3 Identification Number Block Allocations
Identification Number Container Type Container Size
100000199999 Plastic Reusable Tote HalfSize
200000299999 Cardboard Box HalfSize
300000399999 Plastic Reusable Tote Large
400000499999 Cardboard Box Large
500000899999 Plastic Reusable Tote Small
900000999999 Cardboard Box Small
Each storage location in the miniload is assigned a unique name of the form
"MLAANNN," where ML represents miniload AS/RS storage, AA represents an aisle
number ranging from 01 to 06, and NNN represents a slot number ranging from 001 to
500 starting from the lefthand side bottom slot. The original design allows zoning, where
fast moving items can be stored in slots which the crane takes the least amount of time to
access from the endofaisle starting position. However random storage policy is being
used in consideration of the following reliability concern: Zoning is believed to cause
overutilization of the equipment, i.e., brakes and rails, functioning within the fastpick
zone, which results in increased machine downtime due to increased nonuniform wear
and tear.
There are frequent mechanical and electrical failures together with
communication breakdowns between the MultiCrane Interface (hereafter MCI) and
cranes.
71
MCI refers to the miniload AS/RS controller system with a backup option to
communicate directly with the cranes. Cranes can be operated manually; however it is not
efficient to do so in terms of throughput and human resource considerations. The cranes
and MHCS communicate through MCI sustained by hard wire, where excessive
communication failures are being experienced. Equipment downtime significantly
increased due to normal wear and tear. Moreover, since the equipment manufacturer does
not exist anymore, spare part availability is becoming a serious maintenance challenge.
MHCS interfaces with SAP, which is an enterprise wide multimodule
information system operating on a centralized database server located in Wetzlar,
Germany. SAP is used to conduct the direct information interchange and establish
integration between suppliers, customers, and corresponding internal entities locally
and/or globally by means of a network infrastructure. MHCS refers to the VAX 6410
computer and all controls for peripheral systems such as AGV's, workstations, RF
terminals, miniload AS/RS cranes, communication media, and programmable logic
controllers (hereafter PLC).
The VAX 6410 was designed to operate for 10 years when it was introduced in
1987 and is fairly fragile after almost 20 years of service. One of the significant
limitations of the current system is that MHCS must be shut down between 02:30 a.m.
and 03:15 a.m. every day for "housekeeping" purposes like data cleaning and database
refreshment. During the shut down period, miniload AS/RS and AGV system are not
operational. The manufacturing company Digital was subsequently purchased by
Compaq, and Compaq was subsequently purchased by HewlettPackard, making spare
parts challenging to procure.
72
Cooling and reheating old electronic components is estimated as the most common cause
of failures. Furthermore, the existing source code to run MHCS was written in
FORTRAN IV, a procedural programming language that is outdated for MHCS purposes.
It is not a highlevel object oriented programming language and limits the extent of
modifications to the existing configuration by inhouse personnel. Severe database
corruption problems necessitate contracting with the original developer, who currently
resides in San Diego, California. The source code for the SiGEN database is not available
since it is proprietary in nature. Thus managing and maintaining the database, especially
in case of database corruptions, is very troublesome.
Since overall system reliability and throughput is severely jeopardized,
necessitating immediate retrofitting and/or replacement of the existing systems in order to
sustain manufacturing operations, Plant I management has decided to first launch an
analysis effort in January 2005 in collaboration with the Auburn University Industrial and
Systems Engineering Department. The effort involves activity profiling and throughput
analysis.
Plant I management set the onhand inventory target as two days for
approximately 3,500 miniload AS/RS part numbers. Scheduled requirements are
adjusted daily based on the customers' weekly production schedule utilizing MRP II
methodology. There is not enough computational capability to make Pareto analysis of
the onhand inventory on a daily basis. Therefore detailed inventory activity profiling at
part number level based on onhand inventory is extremely challenging. Hence inventory
activity profiling is performed based on the storage period of the parts packaged in totes.
73
It has been discovered that miniload AS/RS storage is not being utilized as a fast pick
area. Almost 20 percent of the totes stored at miniload AS/RS consists of service parts
consumed by one of the 15 assembly lines, the demand for which is extremely low for
miniload AS/RS storage. Similarly, obsolete parts occupy approximately 10 percent of
the storage locations. Further investigation also indicated that, when the acquisition took
place in April 2004, transition from one ERP system to the other was not planned
effectively enough, resulting in a lack of operational data visibility, invalid obsolete
inventory elimination process, and misinterpretation of float, i.e., the amount of stock
placed between two manufacturing operations, safety stock, and safety time calculations.
Figure 4.5 below summarizes the inventory activity profiling.
Number of Storage Locations Based on Storage Period
0
200
400
600
800
1000
1200
1400
1600
1800
1 t
o 7
D
a
ys
2 t
o 4
W
e
e
ks
2 t
o 3
M
ont
hs
4 t
o 6
M
ont
hs
7 M
ont
hs
t
o 1 Y
e
a
r
2 t
o 5
Y
e
a
r
s
5 t
o 9
Y
e
a
r
s
Figure 4.5 Inventory Activity Profiling
74
Order activity profiling revealed that on average 1,600 pick and 750 store
transactions are performed per day. The inbound transportation is built around a twoshift
production/operation schedule of the 3PL's and direct shipping domestic suppliers.
Together with the assembly line operators' traditional behavior of ordering more parts
during shift change, the aforementioned inbound transportation schedule triggers an
hourly average peak of 125 pick and 75 store transactions around 3:00 p.m. In addition,
inbound production material pack sizes, order quantities, and tote sizes have not been
revisited since the acquisition. Therefore almost 800 part numbers are partially picked
from the inbound totes by the crane operators resulting in excessive material handling
and deployment of an additional mechanical system called the "chair lift system," which
is designed to feed internally circulated 500 pickto totes to crane operators.
Figure 4.6 Chair Lift System for Partial Picks
System throughput is defined as the number of storage or retrieval transactions
per unit time; the rate at which the storage system receives and stores loads and retrieves
and delivers loads to the output station is the main performance measure (Heragu, 1997).
75
In addition to the system throughput, utilization is defined as the proportion of time that
the system is actually up and running for its original design purposes to its total available
time and availability, i.e., the ratio of time that the system is ready for operation to total
scheduled time, are other relevant performance measures. Groover (2001) utilizes the
method recommended by the Material Handling Institute of America. According to that
method, it is assumed that randomized storage of loads is used, storage compartments are
of equal size, the pick and drop station is located at the base and end of the aisle,
horizontal and vertical speeds of storage and retrieval equipment are constant, and
horizontal and vertical travels are simultaneous. The equations associated with the
method are provided by Groover (2001) and are indicated below. The single command
cycle time is expressed as
pd
zy
cs
T
v
H
v
L
MaxT 2
5.0
,
5.0
2 +
?
?
?
?
?
?
?
?
?
?
= (4.1),
where L is the length of the AS/RS rack structure, v
y
is the velocity of the crane along the
length of the aisle, H is the height of the rack structure, v
z
is the vertical velocity of the
crane, and T
pd
pd
zy
cd
T
v
H
v
L
MaxT 4
75.0
,
75.0
2 +
?
?
?
?
?
?
?
?
?
?
=
is the pickup and deposit time. The dual command cycle time is expressed
as
(4.2)
76
The relative number of single and dual command cycles performed by the system
defines the system throughput, and the amount of time spent in performing single and
dual command cycles each hour is formulated as
R
cs
T
cs
+R
cd
T
cd
= 60U (4.3),
where U is the system utilization, R
cs
is the number of single command cycles performed
per hour, and R
cd
is the number of dual command cycles per hour. It should be noted that
the relative proportions of R
cs
and R
cd
must be determined, or assumptions must be
made.
The total hourly cycle rate is given by
R
c
= R
cs
+ R
cd
(4.4)
The total number of transactions performed per hour is given as:
R
t
= R
cs
+ 2R
cd
(4.5)
The length, L, and the height, H, of the miniload AS/RS rack structure used in
Plant I is 702 inches and 121 inches, respectively. Although there is not any specific
zoning for high turnover items since the first top three tiers of the bays are reserved for
large totes, it is assumed that there is spontaneous zoning depicted as in Figure 4.7 below.
77
Figure 4.7 Travel Trajectory for MiniLoad AS/RS Cranes
Together with the aforementioned zoning and the slight vertical location shift of
the pick and drop station, the single and dual cycle time for both the A and B zone is
formulated as follows:
( )
pd
zy
csA
T
vv
MaxT 2
11815.0
,
7025.0
2 +
?
?
?
?
?
?
?
?
?
?
???
= (4.6)
( )
pd
zy
cdA
T
vv
MaxT 4
118175.0
,
70275.0
2 +
?
?
?
?
?
?
?
?
?
?
???
= (4.7)
( )
pd
zy
csB
T
vv
MaxT 2
405.070
,
7025.0
2 +
?
?
?
?
?
?
?
?
?
?
?+?
= (4.8)
( )
pd
zy
cdB
T
vv
MaxT 4
4075.070
,
70275.0
2 +
?
?
?
?
?
?
?
?
?
?
?+?
= (4.9)
The equation for how each aisle spends its time during one hour is given as
UTRTRTRTR
cdBcdBcsBcsBcdAcdAcsAcsA
60=+++ (4.10)
B
A
40 in.
81 in.
11 in.
702 in.
78
Based on the information gathered from the transaction logs generated by SiGEN
database, it is observed that the number of single command cycles is approximately five
times as many as the number of dual command cycles (R
cs
= 5 R
cd
Crane Number
) and that the
transactions in A zone account for 75 percent of the total transactions, while the
transactions in B zone account for the remaining 25 percent.
The pick and deposit time for the storage and retrieval equipment is 7 seconds.
The vertical velocity of the cranes is 60 ft/min or 12 in/sec. The horizontal velocity of
each crane is indicated in Table 4.4 below.
Table 4.4 Horizontal Velocity of MiniLoad AS/RS Cranes
Horizontal Velocity (feet per minute/inches per second)
1 180/36
2 180/36
3 180/36
4 180/36
5 250/50
6 200/40
The crane utilization, based on the collected data and calculations using the
formulation mentioned above, is summarized in Table 4.5 below.
79
Table 4.5 MiniLoad AS/RS Crane Utilization
Crane1 Crane2 Crane3 Crane4 Crane5 Crane6
Total
Transactions/Day
394 409 394 239 414 372
Single Command
Cycles/Day
280 290 280 175 294 256
Dual Command
Cycles/Day
57 59 57 32 60 58
A Zone
Transactions/Day
100 110 100 46 119 102
B Zone
Transactions/Day
294 299 294 193 295 270
T
csA
33.5 (seconds) 33.5 33.5 33.5 28.04 31.55
T
csB
33.5 (seconds) 33.5 33.5 33.5 29 31.55
T
cdA
57.25 (seconds) 57.25 57.25 57.25 49.06 54.325
T
cdB
57.25 (seconds) 57.25 57.25 57.25 49.06 54.325
R
csA
9
(transactions/hour)
9 9 6 10 8
R
csB
3
(transactions/hour)
3 3 2 3 3
R
cdA
2
(transactions/hour)
2 2 1 2 2
R
cdB
1
(transactions/hour)
1 1 0 1 1
Total transactions
per hour
17 17 17 10 18 16
Utilization 15.45% 15.83% 15.29% 9.29% 13.58% 13.58%
The findings indicated in Table 4.5 are confirmed by the Plant I maintenance team since
they spend more time in repair on Crane4, Crane5, and Crane6.
The dedicated manpower of the existing miniload AS/RS is indicated in Table
4.6.
Table 4.6 Dedicated Manpower of The MiniLoad AS/RS
Shift
Workstation 1 2 3
Buyin 2 2 0
Cranes 4 4 2
AGV Accumulation Stands 3 2 1
Maintenance and Repair 2 2 1
Total 11 10 4
80
4.5 AGV System
AGV's are driverless industrial trucks utilized for material handling purposes
within the facility. They are remotely controllable, wheeled vehicles driven by electric
motors using storage batteries, and they follow a magnetic path along aisles. Plant I
deployed 32 inertialguided shuttle arm AGV's manufactured by Egemin Automation,
Inc. in 1987. There are 24 AGV's in the distribution center and eight AGV's in the
finished goods warehouse. AGV availability is 60 minutes per hour with the use of a
second set of batteries. The nominal velocity of each AGV is 110 ft/min, but it decreases
to 60 ft/min in curves and turns. The maximum weight capacity is 1,000 lbs, and the
maximum dunnage height is 54 inches.
Figure 4.8 AGV
Distribution center AGV's pick parts from 12 accumulation stands in order to
deliver production material from miniload AS/RS storage and static rack storage to
assembly lines. They also return empty dunnage from assembly lines to the dunnage
return station located in the distribution center.
81
The average round trip for distribution center AGV's takes approximately 30 minutes. It
should be noted that inbound bulk production material is delivered to the drop stands
located along the southern half of the assembly lines that are, in average, 500 feet away
from the distribution center.
Finished goods warehouse AGV's deliver finished goods packaging material,
referred to as replenishment dunnage, from the finished goods warehouse to assembly
lines. They also deliver finished goods from assembly lines to the finished goods
warehouse whenever a pickup order is placed for finished goods. Thus the efficiency of
the finished goods warehouse AGV's is increased by eliminating deadheading. In
addition, finished goods warehouse AGV's are also deployed for:
? Line to line subassembly transfer from Line 14, which is manufacturing car
radio keyboards to the southern half of Line 5, which is dedicated to final
assembly of the car radios.
? Empty container transfer from the southern half of Line 5 to Line 14.
? Finished goods transfer from a third party quality control unit that is called
3PVA to the banding equipment for the final functionality test of car radios
within the finished goods warehouse.
The average round trip for finished goods warehouse AGV's takes approximately 20
minutes.
82
Figure 4.9 MiniLoad AS/RS Accumulation Stands
The inbound production material deliveries and empty dunnage returns are made
to and from approximately 370 pick and drop stands throughout the facility that are
located alongside the assembly lines. The number and location of pick and drop stands is
dynamically changing due to frequent changes in assembly line layouts.
Figure 4.10 Pick and Drop Stand
83
The existing AGV system is operating under two independent control systems:
External Control System?1 (hereafter ECS1) controls the eight S700 type AGV's
assigned to the finished goods warehouse, and External Control System?2 (hereafter
ECS2) controls 24 S700 type AGV's assigned to the distribution center. Changing AGV
assignment between the finished goods warehouse and the distribution center is
extremely labor intensive and cumbersome due to the existing control structure. The
AGV system uses using a wireless communication system operating on 2.4GHz
frequency that is also referred to as 802.11b. Both the software and the hardware of the
aforementioned control systems are outdated and fully depreciated. Hence the
deployment of a new WMS also requires the deployment of a new control system called
E'tricc, which is provided by Egemin Automation, Inc. E'tricc consolidates existing ECS
1 and ECS2 and is expected to provide a more efficient AGV utilization by pooling all
of the vehicles under a single control system. It also allows for the elimination of the pick
and drop stands and monodirectional aisle traffic. However, since the AGV's have not
had preventive maintenance in the last three years, 80 percent of the AGV's experience
severe mechanical failures and spare part availability is extremely challenging.
The inbound production material delivery transfer is handled by 24 AGV?s
assigned to the distribution center. AGV?s make three different types of trips:
? Drop: AGV?s leave the distribution center loaded with inbound production
material destined for assembly lines and then return empty.
? Single Dunnage Trip: AGV?s leave the distribution center empty and bring
back empty dunnage, or they leave the distribution center full and come back
empty.
84
? Dual Dunnage Trip: AGV?s leave the distribution center loaded with inbound
production material destined for assembly lines and bring back dunnage
return, i.e., reusable containers, from assembly lines.
Since overall system reliability and throughput is severely jeopardized,
necessitating immediate replacement of the existing system in order to sustain
manufacturing operations, Plant I management decided to first launch an analysis effort
in January 2005 in collaboration with the Auburn University Industrial and Systems
Engineering Department.
The average number of trips per day performed by distribution center AGV's
based on the data provided by MHCS over 82 consecutive days is indicated in Table 4.7.
Table 4.7 Average Number of Distribution Center AGV Trips
Trip Type Average Number of Trips per Day
Drop from MiniLoad AS/RS 452
Drop from Static Racks 259
Total Drops 711
Single Dunnage Trips 137
Dual Dunnage Trips 372
Total Dunnage Trips 508
Uncompleted Drops 64
Total Trips 912
Table 4.8 below indicates the daily average number of trips per AGV, assuming
that trips are uniformly distributed to AGV's.
85
Table 4.8 Daily Average Number of Trips Per Distribution Center AGV
Trip Type Daily Average Number of Trips per AGV
Drop from MiniLoad AS/RS 19
Drop from Static Racks 11
Total Drops 30
Single Dunnage Trips 6
Dual Dunnage Trips 16
Total Dunnage Trips 22
Uncompleted Drops 3
Total Trips 39
Approximately 65 percent of the total completed drops are made from miniload
AS/RS, while 35 percent are made from static racks. The reason for the higher number of
AGV trips is considered to stem from the relatively large number of partial picks from
miniload AS/RS storage. Single dunnage, which is referred to as deadheading, has
negative impact on AGV system utilization; therefore minimizing or eliminating single
dunnage trips will increase the efficiency.
Deadheading Percentage by Assembly Line
0%
20%
40%
60%
80%
100%
1
2
3
4
5
6
7
89
10
11
12
13
14
15
Deadheading Percentage
Figure 4.11 Deadheading Analysis of the AGV System
86
Another source of waste in the AGV system are uncompleted drops.
Approximately 10 percent of the attempted drops are wasted. They are considered to be
caused by the following reasons:
? The line of sight between the AGV sensor and the diagonal reflector on the
drop stand is blocked because the material handler assigned to the destined
assembly line does not pick up the inbound production material from the drop
stands or the diagonal reflector is disoriented.
? The line of sight between the AGV sensor and the diagonal reflector on the
drop stand is blocked because the AGV sensor is malfunctioning.
? The centrally located and vertically oriented reflector on the drop stand is not
aligned with the AGV sensor.
In case the diagonal reflector is blocked, the AGV generates a sound signal until
the material handler of the destined assembly line shifts the AGV to "Manual" mode,
then back to "Auto" mode. Then, depending on whether the inbound production material
is manually loaded to the drop stand or not by the corresponding material handler, the
AGV returns to the distribution center either empty or full, respectively. Upon returning
to the distribution center, the AGV enters the buffer, where it waits for the next
assignment. If it is still loaded, it will not be able to pick up the next load and will block
the accumulation stand until it is taken care of.
In case the centrally located and vertically oriented reflector is not aligned with
the AGV sensor, the AGV makes two more drop attempts and then returns to the AGV
buffer located in the distribution center.
87
Upon returning to the distribution center, the AGV control system generates a "purge
request" for the corresponding AGV. The AGV enters the buffer in the south portion of
the east miniload AS/RS and blocks the buffer lane until the purge request is taken care
of, while any the other AGV's waiting behind are blocked. Then the ECS operator directs
the AGV to the dunnage return station, where the subject matter load is repositioned on
an AGV pick stand and reassigned for delivery. However currently there is not a
designated ECS operator, and this task is being performed randomly by either a miniload
AS/RS crane operator or an AGV accumulation stand operator. Moreover it has also been
reported that there have been occurrences where the ECS operator directs the AGV to an
irrelevant AGV drop stand on the manufacturing floor and the associated parts become
obsolete as they are staged somewhere on the manufacturing floor.
The average number of trips per day performed by AGV's that are assigned to the
finished goods warehouse based on the data provided by MHCS over 82 days is indicated
in Table 4.9.
Table 4.9 Average Number of Finished Goods Warehouse AGV Trips
Trip Type Average Number of Trips per Day
From Warehouse to Assembly Lines 100
From Assembly Lines to Warehouse 120
Line to Line 6
From 3PVA to Banding Equipment 6
Total Trips 232
Table 4.10 below indicates the daily average number of trips per AGV, assuming
that trips are uniformly distributed to AGV's.
88
Table 4.10 Daily Average Number of Trips Per Finished Goods AGV
Trip Type Average Number of Trips per Day
From Warehouse to Assembly Lines 13
From Assembly Lines to Warehouse 15
Line to Line 1
From 3PVA to Banding Equipment 1
Total Trips 30
The mechanical retrofitting of the AGV's requires upgrading of the following
components:
? The main board of the AGV's onboard micro computer called "NT Box"
? The gear box assembly called "Hurth Drive" and wheels
? The shuttle arm assembly
The maintenance and inhouse repair operations are performed by one electrician
per shift for three shifts a day in the AGV shop located on the east side of the
manufacturing building, the floor space of which is 3800 sq. ft. There are two battery
charge areas located in the distribution center and the finished goods warehouse; the floor
space of each is 660 sq. ft. and 2000 sq. ft., respectively.
89
CHAPTER 5
FLOOR SPACE VALUATION METHOD
5.1 Introduction
This chapter presents the valuation of the capital investment decision alternatives
together with the floor space associated with each alternative. Plant I management started
to evaluate a decision portfolio in order to replace and/or to retrofit the existing, but
outdated miniload AS/RS and the AGV system in January 2005. The portfolio consists
of four decision alternatives, which are evaluated in two groups: the alternatives related
to the miniload AS/RS and the ones related to the AGV system. Although the decisions
are made utilizing NPV criterion, the floor space value perspective is also included in the
decision making process in order to emphasize and communicate its significance.
5.1.1 MiniLoad AS/RS Related Alternatives (Group1)
The alternatives included in this group are considered as mutually exclusive, and
they need to be implemented within the next two years.
5.1.1.1 MiniLoad AS/RS and WMS Replacement (Alternative1)
This alternative consists of replacing the existing outdated miniload AS/RS and
the associated WMS with a new miniload AS/RS and a proprietary WMS.
90
Based on the activity profiling and the throughput analysis of the simulation study
performed by the Auburn University Industrial and Systems Engineering Department, it
is recommended to initially phase out Crane4, Crane5, and Crane6, to reduce the mini
load AS/RS inventory by 50 percent, and to deploy a new fouraisle miniload AS/RS,
together with a new WMS. In order to justify the investment through labor cost savings,
it is also recommended to deploy two palletizing robots for the order picking process and
an RFID system for the receiving process. The implementation of this alternative is
estimated to take 12 months, while the warehouse operations are maintained by Crane1,
Crane2, and Crane3 and supported by the existing WMS during the implementation
period. As soon as the implementation is accomplished Crane1, Crane2, and Crane3
will be phased out. The required investment for this alternative is $2.7 million with a
fiveyear useful project life. The annual preventive maintenance cost is estimated as
$30,000. The estimated labor cost savings and inventory holding cost savings are $1
million and $200,000 per year, respectively. Finally, the estimated floor space savings are
5,000 sq. ft. through additional facility layout modifications, which involve moving the
AGV repair shop and AGV battery charge areas to the distribution center.
5.1.1.2 JustinTime Delivery (Alternative2)
This alternative consists of eliminating the miniload AS/RS and the associated
WMS and requires thirdshift 3PL support and transportation operations, together with
J.I.T. delivery efforts. It is recommended to first phase out Crane4, Crane5, and Crane
6, and then to employ a flowthrough conveyor system equipped with diverters that has a
capacity of a full truck load of totes as well as a handling unit management system.
91
In order to sustain J.I.T. delivery, it is imperative to use an electronic Kanban system
between Plant I and the 3PL's. Direct shipping suppliers are required to ship the raw
material to the 3PL's for storage and staging purposes. In order to justify the investment
through labor cost savings, it is also recommended to deploy two palletizing robots for
the order picking process and an RFID system for the receiving process. The
implementation of this alternative is estimated to take nine months, while the warehouse
operations are maintained by Crane1, Crane2, and Crane3 and supported by the
existing WMS during the implementation period. As soon as the implementation is
accomplished Crane1, Crane2, and Crane3 will be phased out. The required investment
is $1 million with a fiveyear useful project life. The annual preventive maintenance cost
is estimated as $20,000. The annual 3PL and transportation costs in order to support
thirdshift operations are estimated as $600,000. The estimated labor cost savings and
inventory holding cost savings are $700,000 and $400,000 per year, respectively. The
estimated floor space savings are 10,000 sq. ft. through additional facility layout
modifications, which include moving the AGV repair shop, AGV battery charge areas,
and machine shop to the distribution center. This alternative is mutually exclusive to
Alternative1.
5.1.2. AGV System Related Alternatives (Group2)
The alternatives included in this group are considered to be mutually exclusive
and they need to be implemented within the next four years.
92
5.1.2.1 AGV Control Software Replacement and Mechanical Component
Retrofitting (Alternative3)
This alternative requires the replacement of the existing outdated AGV control
software with the new version, where ECS1 and ECS2 are consolidated and the
mechanical AGV components are retrofitted.
The new version of the control software allows all of the vehicles to be pooled
under a single control system and also permits dynamic task allocation by eliminating
fixed task allocation windows and brings in the flexibility of
? Eliminating pick and drop stands
? Switching to monodirectional AGV traffic through bidirectional shuttle arm
motion
The current reliability of the mechanical AGV components is defined as being as
low as 70 percent. Based on the throughput analysis through the simulation study
performed by the Auburn University Industrial and Systems Engineering Department, it
is recommended to reduce the number of AGV's by 37.5 percent (i.e. 12 vehicles) after
mechanical retrofitting, which requires upgrading the following components:
? The main board of the AGV's onboard micro computer called "NT Box"
? The gear box assembly called "Hurth Drive" and wheels
? The shuttle arm assembly
The implementation of this alternative is estimated to take eight months assuming
that the purchase order is issued. The required investment for this alternative is $1.15
million with a fiveyear useful project life.
93
The estimated maintenance and repair cost savings are estimated as $350,000 per year,
while the estimated floor space savings through pick and drop stand elimination and a
switch to monodirectional aisle traffic is estimated as 45,000 sq. ft. through additional
facility layout modifications. However, either Alternative1 or Alternative2 must
precede or be simultaneously implemented with this alternative.
5.1.2.2 Water Spider Deployment (Alternative4)
This alternative requires replacing the AGV system with water spiders equipped
with tugger vehicles and associated trailers. The water spider is a lean manufacturing
term representing a material handler who is more involved in the process or cell (s)he
supports than just a pickup and dropoff material handler. In this type of material
handling system, the material handler performs a standard route through a facility at
precisely determined time intervals such as every 20 minutes. The amount of material
moved each time may vary, but the time interval is exact. During this interval, the
material handler follows a predetermined, standard route, picking up kanban cards,
signaling what materials to deliver next, and delivering the materials to production
locations. This system often is coupled with a heijunka box in which the withdrawal
intervals in the columns of the box correspond to the time required for the standard
material handling route. This type of system often is employed in assembly operations
where a large number of components need to be delivered to many points along a line. It
is also called mizusumashi or waterspider conveyance.
The implementation of this alternative is estimated to take two months. The
required investment for this alternative is $1 million with a fiveyear useful project life.
94
It is estimated that there will be an additional labor cost of $200,000 since Plant I
management is considering employing additional material handlers and training them as
water spiders. The estimated maintenance and repair cost savings due to the elimination
of the AGV system are estimated as $350,000 per year. The estimated floor space savings
are estimated as 60,000 sq. ft. since Plant I management is considering switching to a
more flexible cellular manufacturing layout by avoiding the aisle requirement due to the
elimination of the AGV system. This alternative is mutually exclusive to Alternative3
while either Alternative1 or Alternative2 must precede or be simultaneously
implemented with this alternative.
Each decision alternative from Group1 is combined with decision alternatives
from Group2 to form all possible options indicated in the following Table 5.1.BBBBBB
Table 5.1 Decision Alternative Combinations
Decision Alternative Combination Option
Alternative1 and Alternative3 Option1
Alternative1 and Alternative4 Option2
Alternative2 and Alternative3 Option3
Alternative2 and Alternative4 Option4
The second section presents the valuation of the decision portfolio through
discounted cash flow techniques and the associated sensitivity and scenario analysis
based on the decision criterion adopted by the corporate management of the subject
matter business application. The third section presents the MCS model of the decision
portfolio, taking into account the variability of the input parameters with and without the
financial impact of the free cash flows that can potentially be generated by the additional
floor space.
95
The fourth section presents DTA of the decision portfolio utilizing the average WACC
and the riskfree interest rate. The fifth section presents the real options analysis of the
decision portfolio through the combination of DTA and a binomial lattice, where the
volatility factor is estimated using the logarithmic cash flow returns method and MCS.
In order to reduce the complexity of the calculations and to be able to narrow
down the scope of the analysis in the aforementioned sections, the following assumptions
are made:
? Lost sales are not taken into account since the demand that cannot be met by
Plant I can be satisfied by another plant of the corporation as it actually is.
? Opportunity cost stemming from the implementation delay of the alternatives
is not taken into account since different interpretations of the opportunity cost
can significantly impact the results of the analysis in each section.
? Implementation start time lag for the alternatives is not taken into account
because the required resolution negatively impacts the mathematical
tractability.
? A new contract requires deployment of the dedicated floor space as long as
the useful project life once it is negotiated with the customer.
The quality of the valuation process depends on the validity of different valuation
techniques together with the effectiveness of the associated free cash flow streams,
discount rate, and contingent alternatives. In a very broad sense, the value of any
alternative is the difference between the revenues and the costs through the overall life
cycle.
96
The objective of the valuation is to evaluate an alternative from both project NPV and
floor space value perspective, to compare it against others competing for the same
investment pool, and also to decide the changes on the course of the alternative, together
with the associated timing scheme.
5.2 Discounted Cash Flow Approach
This section presents the valuation of each option utilizing DCF techniques
including sensitivity and scenario analysis. The decision criterion adopted by the
corporate management is the NPV. Any alternative is considered acceptable if it has a
positive NPV. It should be noted that the corporate finance department is utilizing the
straightline depreciation method.
5.2.1 Alternative1
The implementation of this alternative is estimated to take 12 months. The
required investment is $2.7 million with a fiveyear useful project life. The annual
preventive maintenance cost is estimated as $30,000. The estimated labor cost savings
and inventory holding cost savings are $1 million and $200,000 per year, respectively,
while the estimated floor space savings are 5,000 sq. ft. through additional facility layout
modifications, which include moving the AGV repair shop and the AGV battery charge
areas to the distribution center. The WACC and the tax rate are defined as seven percent
and 30 percent, respectively. The DCF analysis of Alternative1 is given in Table 5.2
below.
97
Table 5.2 DCF Analysis of Alternative1 (In Thousands of US Dollars)
Year 0 1 2 3 4 5
Income Statement
Revenues
Labor Cost Savings $1,000 $1,000 $1,000 $1,000 $1,000
Inventory Holding Cost
Savings
$200 $200 $200 $200 $200
Expenses
O & M $30 $30 $30 $30 $30
Depreciation $540 $540 $540 $540 $540
Taxable Income $630 $630 $630 $630 $630
Income Taxes (30%) $189 $189 $189 $189 $189
Net Income $441 $441 $441 $441 $441
Cash Flow Statement
Cash from Operation
Net Income $441 $441 $441 $441 $441
Depreciation $540 $540 $540 $540 $540
Investment ($2,700)
Net Cash Flow ($2,700) $981 $981 $981 $981 $981
NPV (7%) $1,322.3
5.2.2 Alternative2
The implementation of this alternative is estimated to take nine months. The
required investment is $1 million with a fiveyear useful project life. The annual
preventive maintenance cost is estimated as $20,000. The annual 3PL and transportation
costs in order to support thirdshift operations are estimated as $600,000. The estimated
labor cost savings and inventory holding cost savings are $700,000 and $400,000 per
year, respectively, while the estimated floor space savings are 10,000 sq. ft. through
additional facility layout modifications, which include moving the AGV repair shop,
AGV battery charge areas, and machine shop to the distribution center. The WACC and
the tax rate are defined as seven percent and 30 percent respectively. The DCF analysis of
Alternative2 is given in Table 5.3 below.
98
Table 5.3 DCF Analysis of Alternative2 (In Thousands of US Dollars)
Year 0 1 2 3 4 5
Income Statement
Revenues
Labor Cost Savings $700 $700 $700 $700 $700
Inventory Holding Cost Savings $400 $400 $400 $400 $400
Expenses
O & M $20 $20 $20 $20 $20
Depreciation $200 $200 $200 $200 $200
3PL & Transportation $600 $600 $600 $600 $600
Taxable Income $280 $280 $280 $280 $280
Income Taxes (30%) $84 $84 $84 $84 $84
Net Income $196 $196 $196 $196 $196
Cash Flow Statement
Cash from Operation
Net Income $196 $196 $196 $196 $196
Depreciation $200 $200 $200 $200 $200
Investment ($1,000)
Net Cash Flow ($1,000) $396 $396 $396 $396 $396
NPV (7%) $623.68
5.2.3 Alternative3
The implementation of this alternative is estimated to take eight months, assuming
that the purchase order is issued. The required investment is $1.15 million with a five
year useful project life. The estimated maintenance and repair cost savings are estimated
as $350,000 per year, while the estimated floor space savings through pick and drop stand
elimination and a switch to monodirectional aisle traffic are estimated as 45,000 sq. ft.
through additional facility layout modifications. However, either Alternative1 or
Alternative2 must precede or be simultaneously implemented with this alternative. The
WACC and the tax rate are defined as seven percent and 30 percent, respectively. The
DCF analysis of Alternative3 is given in Table 5.4 below.
99
Table 5.4 DCF Analysis of Alternative3 (In Thousands of US Dollars)
Year 0 1 2 3 4 5
Income Statement
Revenues
O & M Cost Savings $350 $350 $350 $350 $350
Expenses
Depreciation $230 $230 $230 $230 $230
Taxable Income $120 $120 $120 $120 $120
Income Taxes (30%) $36 $36 $36 $36 $36
Net Income $84 $84 $84 $84 $84
Cash Flow Statement
Cash from Operation
Net Income $84 $84 $84 $84 $84
Depreciation $230 $230 $230 $230 $230
Investment ($1,150)
Net Cash Flow ($1,150) $314 $314 $314 $314 $314
NPV (7%) $137.46
5.2.4 Alternative4
The implementation of this alternative is estimated to take two months. The
required investment is $1 million with a fiveyear useful project life. It is estimated that
there will be an additional labor cost of $200,000 since Plant I management is
considering employing water spiders. The estimated maintenance and repair cost savings
due to the elimination of the AGV system are estimated as $350,000 per year. The
estimated floor space savings is estimated as 60,000 sq. ft. since Plant I management is
considering switching to a more flexible cellular manufacturing layout by avoiding the
aisle requirement due to the elimination of the AGV system. However, either Alternative
1 or Alternative2 must precede or be simultaneously implemented with this alternative.
The WACC and the tax rate are defined as seven percent and 30 percent, respectively.
The DCF analysis of Alternative4 is given in Table 5.5 below.
100
Table 5.5 DCF Analysis of Alternative4 (In Thousands of US Dollars)
Year 0 1 2 3 4 5
Income Statement
Revenues
O & M Cost Savings $350 $350 $350 $350 $350
Expenses
Labor $200 $200 $200 $200 $200
Depreciation $200 $200 $200 $200 $200
Taxable Income ($50) ($50) ($50) ($50) ($50)
Income Taxes (30%) ($15) ($15) ($15) ($15) ($15)
Net Income ($35) ($35) ($35) ($35) ($35)
Cash Flow Statement
Cash from Operation
Net Income ($35) ($35) ($35) ($35) ($35)
Depreciation $200 $200 $200 $200 $200
Investment ($1,000)
Net Cash Flow ($1,000) $165 $165 $165 $165 $165
NPV (7%) ($323.47)
5.2.5 Combinations of the Options Based on Implementation Start Time
Since both Group1 and Group2 alternatives need to be implemented within the
next two and four years, respectively, eight combinations are formed for each option in
accordance with the implementation start time of each alternative. The implementation
start time combination of each option is numbered such that the first digit represents the
Group1 decision alternative, the second digit represents the implementation start time of
the aforementioned Group1 decision alternative as Year 0 or Year 1, the third digit
represents the Group2 decision alternative, and the fourth digit represents the
implementation start time of the aforementioned Group2 decision alternative as Year 0,
Year 1, Year 2, or Year 3. The DCF analysis of all possible implementation start time
combinations for each option is given in Table 5.6 below.
101
Table 5.6 DCF Analysis of All Possible Option Combinations
Option
Generated
Floor Space
(in sq. ft. )
Implementation
Start Time
Combination
NPV
NPV
per sq. ft.
Option1 50,000
1030 $1,459,756 $29.20
1031 $1,450,763 $29.02
1032 $1,442,358 $28.85
1033 $1,434,504 $28.69
1130 $1,373,250 $27.47
1131 $1,364,258 $27.29
1132 $1,355,853 $27.12
1133 $1,347,998 $26.96
Option2 65,000
1040 $998,826 $15.37
1041 $1,019,988 $15.69
1042 $1,039,765 $16.00
1043 $1,058,248 $16.28
1140 $912,321 $14.04
1141 $933,482 $14.36
1142 $953,260 $14.67
1143 $971,743 $14.95
Option3 55,000
2030 $761,140 $13.84
2031 $752,147 $13.68
2032 $743,743 $13.52
2033 $735,888 $13.38
2130 $720,339 $13.10
2131 $711,346 $12.93
2132 $702,941 $12.78
2133 $695,087 $12.64
Option4 70,000
2040 $300,211 $4.29
2041 $321,372 $4.59
2042 $341,149 $4.87
2043 $359,632 $5.14
2140 $259,409 $3.71
2141 $280,571 $4.01
2142 $300,348 $4.29
2143 $318,831 $4.55
Based on the most likely static inputs, DCF analysis of all possible combinations
indicates that the best course of action is Option1 by investing in both Alternative1 and
Alternative3 at Year 0 with respect to the NPV and NPV per square foot.
102
5.2.6 Sensitivity and Scenario Analysis
The DCF techniques presented in the previous sections utilize the most likely
values for such inputs as WACC, labor cost savings, inventory holding cost savings,
O&M cost savings, labor costs, O&M costs, and 3PL and transportation costs. However,
it is not realistic to assume one set of deterministic values for the inputs. Thus sensitivity
analysis is used to analyze the impact of the variations of the input variables on the
decision criterion. The input variations identified by the management are presented in the
following Table 5.7.
Table 5.7 Input Variations
Input Variation from the BaseCase
WACC 6% to 12%
Labor Cost Savings ? 10%
Inventory Holding Cost Savings ? 30%
O & M Cost Savings ? 10%
Labor Costs ? 10%
3PL & Transportation Costs ? 25%
O & M Costs ? 10%
WACC is the input that has the most impact on the NPV of Alternative1. The
variation in WACC stems from the different target capital structures of the corporations
involved in the acquisition of Plant I. Detailed graphical data are provided in Figure 5.1.
103
Figure 5.1 Alternative1 NPV vs. Percentage Change of Inputs
3PL and transportation costs is the input that has the most impact on the NPV of
Alternative2, where the variation stems from the variability of the fuel price and the
price changes that may potentially be imposed by 3PL's. Detailed graphical data are
provided in Figure 5.2.
104
Figure 5.2 Alternative2 NPV vs. Percentage Change of Inputs
Operations and maintenance cost savings has the most impact on the NPV of
Alternative3. The variation in operations and maintenance cost savings stems from the
total price of the spare parts, depending upon the magnitude of the failure and the
variability of the labor category utilized for repair. Detailed graphical data are provided in
Figure 5.3.
105
Figure 5.3 Alternative3 NPV vs. Percentage Change of Inputs
Operations and maintenance cost savings has the most impact on the NPV of
Alternative4. The variation in operations and maintenance cost savings stems from the
total price of the spare parts depending upon the magnitude of the failure and the
variability of the labor category utilized for repair. Detailed graphical data are provided in
Figure 5.4.
106
Figure 5.4 Alternative4 NPV vs. Percentage Change of Inputs
Sensitivity analysis is not able to specify the interdependencies among the input
variables, since it only allows holding one input variable constant at a time. However,
input variables do not behave in that manner. Thus, analyzing the sensitivity of the
decision criterion to the movement of one variable is not realistic. Scenario analysis is a
technique that allows for the consideration of extreme values of the input variables
simultaneously. Although scenario analysis provides the range of the possible values that
the decision criterion can take considering the extreme values of the input variables, the
likelihoods and the risks are not known to the decision maker. The scenario analysis for
the NPV, considering input variations indicated in Table 5.7, is summarized in the
following Table 5.8, Table 5.9, and Table 5.10.
107
Table 5.8 Scenario Analysis for NPV of Each Alternative
Criterion: NPV Best Case Base Case Worst Case
Alternative1 $1,912,959.58 $1,322,293.68 $424,980.49
Alternative2 $1,676,535.95 $623,678.18 ($435,492.05)
Alternative3 $275,885.14 $137,461.99 ($106,417.29)
Alternative4 ($142,783.97) ($323,467.42) ($543,995.81)
Table 5.9 Best Case DCF Analysis for All Possible Option Combinations
Option
Generated Floor
Space
(in sq. ft. )
Implementation
Start Time
Combination
Best Case
NPV
Best Case NPV
per sq. ft.
Option1 50,000
1030 $2,188,845 $43.78
1031 $2,173,229 $43.46
1032 $2,158,496 $43.17
1033 $2,144,598 $42.89
1130 $2,080,564 $41.61
1131 $2,064,948 $41.30
1132 $2,050,216 $41.00
1133 $2,036,317 $40.73
Option2 65,000
1040 $1,770,176 $27.23
1041 $1,778,258 $27.36
1042 $1,785,882 $27.48
1043 $1,793,075 $27.59
1140 $1,661,895 $25.57
1141 $1,669,977 $25.69
1142 $1,677,602 $25.81
1143 $1,684,795 $25.92
Option3 55,000
2030 $1,952,421 $35.50
2031 $1,936,805 $35.21
2032 $1,922,073 $34.95
2033 $1,908,174 $34.69
2130 $1,857,523 $33.77
2131 $1,841,907 $33.49
2132 $1,827,174 $33.22
2133 $1,813,276 $32.97
Option4 70,000
2040 $1,533,752 $21.91
2041 $1,541,834 $22.03
2042 $1,549,459 $22.14
2043 $1,556,652 $22.24
2141 $1,438,854 $20.56
2142 $1,446,936 $20.67
2143 $1,454,560 $20.78
2144 $1,461,754 $20.88
108
Table 5.10 Worst Case DCF Analysis for All Possible Option Combinations
Option
Generated Floor
Space
(in sq. ft. )
Implementation
Start Time
Combination
Worst Case
NPV
Worst Case NPV
per sq. ft.
Option1 50,000
1030 $318,563 $6.37
1031 $329,965 $6.60
1032 $340,145 $6.80
1033 $349,235 $6.98
1130 $273,030 $5.46
1131 $284,431 $5.69
1132 $294,612 $5.89
1133 $303,701 $6.07
Option2 65,000
1040 ($119,015) ($1.83)
1041 ($60,730) ($0.93)
1042 ($8,690) ($0.13)
1043 $37,775 $0.58
1140 ($164,549) ($2.53)
1141 ($106,264) ($1.63)
1142 ($54,223) ($0.83)
1143 ($7,759) ($0.12)
Option3 55,000
2030 ($541,909) ($9.85)
2031 ($530,507) ($9.65)
2032 ($520,327) ($9.46)
2033 ($511,238) ($9.30)
2130 ($495,249) ($9.00)
2131 ($483,848) ($8.80)
2132 ($473,667) ($8.61)
2133 ($464,578) ($8.45)
Option4 70,000
2040 ($979,488) ($13.99)
2041 ($921,203) ($13.16)
2042 ($869,162) ($12.42)
2043 ($822,698) ($11.75)
2141 ($932,828) ($13.33)
2142 ($874,543) ($12.49)
2143 ($822,502) ($11.75)
2144 ($776,038) ($11.09)
109
Scenario analysis supported by sensitivity analysis indicates that the best course
of action is Option1 by investing in Alternative1 and Alternative3 at Year 0 for the
best case, and in Alternative1 at year 0 and Alternative3 at Year 3 for the worst case,
respectively.
5.3 Monte Carlo Simulation Approach
DCF techniques involve the use of only one set of input variables; therefore it is a
deterministic approach. However, the input variables exhibit probabilistic behavior. The
impact of the aforementioned probabilistic behavior is explored by conducting sensitivity
and scenario analysis on a limited basis. One limitation is that sensitivity analysis does
not investigate the interactions among the input variables and the probability of the
deviations from the basecase. It is assumed that the outcome has a fixed path while
contingent decisions generating different outcomes than the expected are ignored. The
other limitation is that only the downside risk is accounted for by DCF techniques since
the higher the risk is, the higher is the added risk premium, with no consideration for the
upside potential. In other words, as the discount rate is increased with an increase in risk,
the reward potential is ignored.
MCS is an extension to DCF techniques, which calculates the outputs for as many
times as the number of simulation runs by varying the input variables in accordance with
their associated probability distributions. MCS generates the outputs in the form of
probability distribution. As an extension to DCF techniques MCS has the same
drawback; the management's flexibility to change the course and the timing of the
decision alternative are not taken into account.
110
MCS analysis is performed for the NPV utilizing the student version of @Risk
Software with 10,000 iterations in each run, for which Monte Carlo sampling is used
instead of Latin Hypercube. Although Latin Hypercube is a specialized method that helps
insure that the entire range of random variate is adequately covered and reduces the
number of replications required to obtain a representative sample, Monte Carlo sampling
is easier than using Latin Hypercube. Also fixed initial random number seed is utilized in
order to reduce the variance between the simulation runs of each option and to have more
control on the simulation runs.
MCS is applied to the practical business application in three phases. The first
phase involves scenarios generated by using random values for each one of the input
variables indicated in Table 5.7. Since there is no historical data for the input variables
utilized in Section 5.2.6, parameters such as mean, standard deviation, and optimistic and
pessimistic estimates are provided based on management's judgment. The second phase
assumes that the additional floor space generated by each option is fully utilized and the
associated demand generates free cash flows that are directly proportional to the
historical cash flows generated by the existing manufacturing floor space. The third phase
involves the additional free cash flows that can potentially be generated by the new
business associated with the additional floor space, which is contributed by each
respective option under the impact of the two major sources of uncertainty mentioned in
Section 3.3:
? The volatility of the OEM demand.
? The corporate marketing performance that realizes as additional business
volume, i.e., additional market share.
111
5.3.1 First Phase
The probability distribution and the associated parameters for each input variable
are provided based on management's judgment. Table 5.11 summarizes the probability
distribution and the associated parameters for each input variable utilized in the DCF
analysis of each option.
Table 5.11 Input Variable Distribution Summary
Input
Probability
Distribution
Variation
from
the BaseCase
WACC
Triangular
(Most likely value is 7%)
6% to 12%
Labor Cost Savings Uniform ? 10%
Inventory Holding Cost Savings Uniform ? 30%
O & M Cost Savings Uniform ? 10%
Labor Costs Uniform ? 10%
3PL & Transportation Costs
Normal
N(600,60)
? 25%
O & M Costs Uniform ? 10%
The MCS analysis results for the NPV are indicated in Table 5.12 below, which
presents all of the implementation start time combinations of each option. The results are
in parallel with the results of the DCF techniques used in the former sections. Option1 is
still the best course of action by investing in Alternative1 and Alternative3 at Year 0.
The reason that the mean NPV for each option and its associated combinations is
relatively less than the NPV calculated using DCF techniques is the combined stochastic
behavior of the input variables.
112
Table 5.12 Phase1 MCS Analysis
Option
Generated
Floor Space
(in sq. ft. )
Implementation
Start Time
Combination
Mean NPV
Standard
Deviation
Mean
NPV
per sq.
ft.
Option1 50,000
1030 $1,278,744.47 $196,947.52 $25.57
1031 $1,274,207.83 $189,823.38 $25.48
1032 $1,268,898.65 $190,985.59 $25.38
1033 $1,263,615.89 $188,105.70 $25.27
1130 $1,190,539.33 $195,239.25 $23.81
1131 $1,186,069.67 $190,453.77 $23.72
1132 $1,181,138.87 $188,025.11 $23.62
1133 $1,170,323.13 $187,095.88 $23.41
Option2 65,000
1040 $840,004.69 $178,615.40 $12.92
1041 $866,848.96 $173,562.87 $13.34
1042 $891,501.95 $167,731.41 $13.72
1043 $914,277.30 $165,040.37 $14.07
1140 $750,364.99 $178,062.60 $11.54
1141 $777,210.17 $172,248.46 $11.96
1142 $801,924.56 $167,524.02 $12.34
1143 $824,634.00 $162,947.12 $12.69
Option3 55,000
2030 $662,711.55 $160,243.76 $12.05
2031 $656,016.92 $157,494.88 $11.93
2032 $649,729.91 $156,063.64 $11.81
2033 $643,926.75 $153,928.84 $11.71
2130 $619,664.47 $153,050.62 $11.27
2131 $612,953.13 $154,268.41 $11.14
2132 $606,662.01 $149,630.15 $11.03
2133 $600,844.26 $147,682.88 $10.92
Option4 70,000
2040 $222,484.26 $149,964.95 $3.18
2041 $249,285.38 $146,558.56 $3.56
2042 $273,998.84 $142,496.50 $3.91
2043 $296,773.80 $140,336.69 $4.24
2141 $179,328.81 $142,336.29 $2.56
2142 $206,208.63 $138,805.50 $2.95
2143 $230,887.43 $135,012.43 $3.30
2144 $253,730.18 $134,038.69 $3.62
113
The detailed graphical results for Option1 are represented in Figure 5.5 and
Figure 5.6 in the form of a probability density function and cumulative distribution
function respectively. The probability of Option1 the NPV being negative is .0.
Therefore it is considered as a riskfree option for Plant I management.
Option1 NPV Probability Density Function
1.573
0.936
5.0%90.0%5.0%
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0
.6
0
.8
1
1
.2
1
.4
1
.6
1
.8
2
Values in Millions of US Dollars
@RISK Student Version
For Academic Use Only
Figure 5.5 Option1 NPV Probability Density Function
114
Option1 NPV Cumulative Distribution Function
0.937 1.580
5.0% 90.0% 5.0%
0
0.2
0.4
0.6
0.8
1
0
.6
0
.8
1
1
.2
1
.4
1
.6
1
.8
Values in Millions of US Dollars
@RISK Student Version
For Academic Use Only
Figure 5.6 Option1 NPV Cumulative Distribution Function
5.3.2 Second Phase
It is assumed that the additional floor space contributed by each option is fully
utilized and the associated demand generates free cash flows that are directly proportional
to the historical cash flows generated by the existing manufacturing floor space. In other
words, the second phase can be considered as the best case MCS analysis, where
additional floor space is fully utilized. The aforementioned strong assumption requires
the following data:
? The historical data including the automotive electronics demand of the
OEM's, Plant I revenues, and associated cash outflows.
115
? The capital investment amount required in order to productively utilize each
additional floor space option.
The distribution into which the historical data are fit is investigated using two
different statistical software packages: BestFit 4.5 and Minitab 15. The AndersonDarling
statistic is utilized to measure how well the data follow a particular distribution and to
compare the fit of several distributions to see which one is the best or to test whether a
sample of data comes from a population with a specified distribution. The better the
distribution fits the data, the smaller this statistic will be. The primary purpose of using
the AndersonDarling statistic is to verify whether the data meets the assumption of
normality for hypothesis testing.
The hypotheses for the AndersonDarling test are
H
0
: The data follow a specified distribution
H
1
: The data do not follow a specified distribution
If the pvalue for the AndersonDarling test is available and lower than the chosen
significance level, then it can be concluded that the data do not follow the specified
distribution. Minitab 15 does not always display a pvalue for the AndersonDarling test
because it does not mathematically exist for certain cases. It should be noted that, in order
to determine which distribution the data follow when using multiple AndersonDarling
statistics, it is generally correct to compare them. The distribution with the smallest
AndersonDarling statistic has the closest fit to the data. If distributions have similar
AndersonDarling statistics, then the one based on practical knowledge must be chosen.
The results of the test conducted for the Plant I monthly demand are indicated in the
following Table 5.13.
116
Table 5.13 Fitted Distributions for Plant I Monthly Demand
Distribution AndersonDarling Statistic PValue
Logistic 0.7507 0.027
Normal 0.7083 0.065
Triangular 0.4598 N/A
Uniform 0.7895 N/A
Weibull 0.6053 0.090
Although the Plant I monthly demand data fit best with Triangular
(930292,1800232,2059000) distribution, the normality assumption is utilized in order to
be able to perform parametric statistical tests and for statistical tractability considerations.
Hence, the Plant I monthly demand is concluded to fit with Normal (1577178,264406)
distribution through the aforementioned AndersonDarling test. The graphical results of
the aforementioned distribution are represented in the following Figure 5.7.
Normal(1577178, 264406)
X <= 1120414
5.0%
X <= 1966053
95.0%
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Values in Millions of Units
V
a
l
ue
s
x 10^

6
BestFit Student Version
For Academic Use Only
Figure 5.7 Plant I Monthly Demand Distribution
117
Although the Plant I monthly revenues fit best with Logistic (87523893,9173440)
distribution, the normality assumption is utilized in order to be able to perform parametric
statistical tests and for statistical tractability considerations. Hence, the Plant I monthly
revenues are concluded to fit with Normal (87618597,16523385) distribution through the
aforementioned AndersonDarling test. The tabular and graphical results of the conducted
test are indicated in the following Table 5.14 and Figure 5.8, respectively.
Table 5.14 Fitted Distributions for Plant I Monthly Revenues
Distribution AndersonDarling Statistic PValue
Beta General 0.1999 N/A
Logistic 0.1640 >0.250
Normal 0.1900 0.890
Triangular 0.3192 N/A
Weibull 0.2980 >0.250
Normal(87618597, 16523385)
X <= 114797148
95.0%
X <= 58000000
3.7%
0
0.5
1
1.5
2
2.5
3
3.5
40 50 60 70 80 90 100 110 120 130
Values in Millions of US Dollars
V
a
l
ue
s
x 10^

8
BestFit Student Version
For Academic Use Only
Figure 5.8 Monthly Plant I Revenue Distribution
118
Monthly demand and revenue distributions are converted to annual distributions
to be able to replicate the simulation effort presented in the previous section. Hence
annual demand and revenue distributions are estimated as Normal (18926136,915929.25)
and Normal (1051423164,57238684.7), respectively. The demand and revenue
estimations for each option are presented in the following Table 5.15 and Table 5.16.
Table 5.15 Annual Demand Estimation with Direct Proportionality
Floor Space (In Thousands of sq. ft.) Demand (In Units)
225 Normal (18926136,915929.25)
5 (Alternative1) Normal (420580.8,20353.98)
10 (Alternative2) Normal (841161.6,40707.96)
45 (Alternative3) Normal (3785227.2,183185.82)
60 (Alternative4) Normal (5046969.6,244247.76)
50 (Option1) Normal (4205808,203539.83)
65 (Option2) Normal (5467550.4,264601.783)
55 (Option3) Normal (4626388.8,223893.817)
70 (Option4) Normal (5888131.2,284955.76)
Table 5.16 Annual Revenue Estimation with Direct Proportionality
Floor Space (In Thousands of sq. ft.) Revenue (In US Dollars)
225 Normal (1051423164,57238684.7)
5 (Alternative1) Normal (23364959.2,1271970.771)
10 (Alternative2) Normal (46729918.4,2543941.542)
45 (Alternative3) Normal (210284632.8,11447736.94)
60 (Alternative4) Normal (280379510.4,15263649.25)
50 (Option1) Normal (233649592,12719707.71)
65 (Option2) Normal (303744469.6,16535620.02)
55 (Option3) Normal (257014551.2,13991678.48)
70 (Option4) Normal (327109428.8,17807590.8)
The distribution of the capital investment amount required to productively utilize
each floor space option is estimated by Plant I management. The aforementioned
distribution is specified as PERT distribution, which is a special form of a scaled Beta
distribution. It is a pragmatic and readily understandable distribution.
119
It can generally be considered as superior to the Triangular distribution when the
parameters result in a skewed distribution, as the smooth shape of the curve places less
emphasis in the direction of the skew. Hence capturing tail or extreme events increases
the emphasis in the direction of the skew. PERT distribution is considered to be more
suited to model the capital investment. Table 5.17 below indicates the capital investment
distribution for each floor space alternative and option.
Table 5.17 Distributions of the Required Capital Investment
Floor Space (In Thousands of sq. ft.) Capital Investment (US Dollars)
5 (Alternative1) PERT (5000000,7000000,10000000)
10 (Alternative2) PERT (10000000,14000000,20000000)
45 (Alternative3) PERT (75000000,120000000,150000000)
60 (Alternative4) PERT (100000000,160000000,200000000)
50 (Option1) PERT (80000000,127000000,160000000)
65 (Option2) PERT (105000000,167000000,210000000)
55 (Option3) PERT (85000000,134000000,170000000)
70 (Option4) PERT (110000000,174000000,220000000)
Although the salvage value of the storage and material handling equipment
utilized for each decision alternative is assumed negligible, capital equipment used for
valueadding purposes is assumed to have a salvage that is equivalent to 10 percent of its
associated initial investment amount.
The MCS analysis results for the NPV are indicated in Table 5.18 below for all of
the implementation start time combinations of each option. The results reveal that the full
utilization of the additional floor space leads Plant I management to pick Option4 as the
best course of action by investing in Alternative2 and Alternative4 at Year 0, while
delaying Alternative4 by one year can be considered as the second best course of action.
120
It is very intuitive that the value of the generated floor space significantly increases by
when utilized it for valueadding purposes.
Table 5.18 Phase2 MCS Analysis
Option
Generated
Floor Space
(in sq. ft. )
Implementation
Start Time
Combination
Mean NPV
Standard
Deviation
Mean
NPV
per sq. ft.
Option1 50,000
1030 $56,046,933 $20,549,318 $1,121
1031 $52,385,389 $18,971,941 $1,048
1032 $48,998,115 $17,425,771 $980
1033 $45,880,170 $16,196,346 $918
1130 $55,469,776 $20,032,884 $1,109
1131 $51,800,227 $19,192,760 $1,036
1132 $48,437,621 $17,748,640 $969
1133 $45,312,213 $16,527,359 $906
Option2 65,000
1040 $71,741,674 $26,840,510 $1,104
1041 $66,924,890 $24,661,410 $1,030
1042 $62,424,039 $23,024,597 $960
1043 $58,291,138 $21,077,303 $897
1140 $71,161,885 $26,425,955 $1,095
1141 $66,335,786 $24,961,521 $1,020
1142 $61,839,682 $23,018,182 $951
1143 $57,754,165 $21,502,648 $888
Option3 55,000
2030 $61,757,833 $22,556,165 $1,123
2031 $58,065,949 $20,800,446 $1,056
2032 $54,714,175 $18,838,594 $995
2033 $51,591,286 $17,125,022 $938
2130 $60,738,487 $21,658,883 $1,104
2131 $57,079,874 $21,048,928 $1,038
2132 $53,710,745 $19,281,875 $977
2133 $50,557,879 $17,624,876 $919
Option4 70,000
2040 $77,460,233 $28,605,133 $1,107
2041 $72,636,938 $26,637,473 $1,038
2042 $68,140,403 $24,067,039 $973
2043 $63,990,098 $22,270,709 $914
2140 $76,028,124 $27,723,528 $1,086
2141 $71,613,985 $27,052,597 $1,023
2142 $67,148,002 $24,481,239 $959
2143 $62,992,094 $22,484,083 $900
121
The detailed graphical results for Option4 are represented in Figure 5.9 and
Figure 5.10 in the form of a probability density function and cumulative distribution
function, respectively. The probability of the Option4 NPV being negative is .003.
Therefore it is considered as an attractive option for Plant I management due to the risk
associated with it.
Option4 NPV Probability Density Function
125.10.0
5.0%94.7%0.3%
0
0.2
0.4
0.6
0.8
1
1.2
1.4
5
0 0
50
100 150 200
Values in Millions of US Dollars
V
a
l
ue
s
x 10^

8
@RISK Student Version
For Academic Use Only
Figure 5.9 Option4 NPV Probability Density Function
122
Option4 NPV Cumulative Distribution Function
125.20.0
5.0%94.7%0.3%
0
0.2
0.4
0.6
0.8
1
5
0 0
50
100 150 200 250
Values in Millions of US Dollars
@RISK Student Version
For Academic Use Only
Figure 5.10 Option4 NPV Cumulative Distribution Function
5.3.3. Third Phase
Since the demand for automotive OEM's is volatile and the corporate marketing
performance is variable, Plant I management is expecting a fluctuating automotive
electronics demand pattern for the fiveyear planning horizon. Since Plant I is serving
NAFTA automotive OEM's, they use historical demand data to estimate the NAFTA
automotive electronics sales. The annual demand distribution for automotive electronics
products in NAFTA region that are not manufactured by Plant I is estimated as Normal
(171769069,6952221) in number of units. Plant I management is estimating the corporate
marketing performance in terms of the additional market share distribution for Plant I as
PERT (1%,2%,5%).
123
Hence the average additional business volume in number of units and average additional
revenue in US dollars for Plant I are estimated to be distributed as Normal
(4007944.94,162218.49) and Normal (222686883.05,10137434.74), respectively.
However, not every alternative and not every option is capable of meeting the
aforementioned demand. Thus the additional revenue that can be generated by each
alternative and each option is calculated using their associated demand meeting
probabilities and then represented in Table 5.19 below.
Table 5.19 Revenue Distributions for Additional Market Share
Floor Space (In Thousands of sq. ft.) Mean Standard Deviation
5 (Alternative1) $23,364,959.20 $1,271,970.77
10 (Alternative2) $46,729,918.40 $2,543,941.54
45 (Alternative3) $152,969,148.62 $6,962,390.18
60 (Alternative4) $206,000,532.26 $9,376,113.39
50 (Option1) $174,363,829.42 $7,937,611.40
65 (Option2) $215,048,722.96 $9,789,720.73
55 (Option3) $193,334,230.32 $8,803,348.33
70 (Option4) $219,373,740.32 $9,990,441.94
The MCS analysis results for the NPV are indicated in Table 5.20 below for all of
the implementation start time combinations of each option using the revenue distributions
indicated in Table 5.19. The results reveal that the full utilization of the additional floor
space encourages Plant I management to pick Option4 as the best course of action by
investing in Alternative2 at Year 1 and Alternative4 at Year 0, while Option2 is
considered as the second best course of action by investing in Alternative1 at Year 1 and
Alternative4 at Year 0.
124
Table 5.20 Phase3 MCS Analysis
Option
Generated
Floor Space
in sq. ft.
Implementation
Start Time
Combination
Mean NPV
Standard
Deviation
Mean
NPV
per sq. ft.
Option1 50,000
1030 $35,039,738 $22,763,463 $701
1031 $33,030,016 $20,849,567 $661
1032 $31,168,912 $18,990,327 $623
1033 $29,467,615 $17,155,507 $589
1130 $34,539,794 $22,171,267 $691
1131 $32,414,520 $21,227,519 $648
1132 $30,594,430 $19,344,003 $612
1133 $28,832,263 $17,520,711 $576
Option2 65,000
1040 $42,915,520 $29,440,298 $660
1041 $40,969,968 $26,766,391 $630
1042 $39,204,587 $24,982,108 $603
1043 $37,590,731 $22,785,665 $578
1140 $43,369,219 $28,872,918 $667
1141 $39,708,758 $27,110,446 $611
1142 $37,914,521 $25,009,103 $583
1143 $36,291,364 $23,146,027 $558
Option3 55,000
2030 $40,549,984 $25,350,016 $737
2031 $38,755,125 $23,065,785 $704
2032 $36,990,148 $20,811,394 $672
2033 $35,397,437 $18,657,814 $644
2130 $39,862,193 $24,522,684 $725
2131 $37,655,337 $24,016,822 $685
2132 $35,851,063 $21,572,734 $652
2133 $34,267,364 $19,287,375 $623
Option4 70,000
2040 $42,423,074 $29,786,091 $606
2041 $41,968,813 $27,156,999 $600
2042 $41,537,244 $25,103,356 $593
2043 $41,141,104 $23,309,210 $588
2140 $44,061,720 $29,492,982 $629
2141 $39,244,253 $27,385,026 $561
2142 $38,878,737 $25,562,328 $555
2143 $38,442,482 $23,415,930 $549
The detailed graphical results for Option4 are represented in Figure 5.11 and
Figure 5.12 in the form of a probability density function and cumulative distribution
function, respectively. The probability of the Option4 NPV being negative is .031.
125
Therefore it is considered as a slightly risky option for Plant I management due to the risk
associated with it.
Option4 NPV Probability Density Function
99.43.4
5.0%90.0%5.0%
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
5
0 0
50
100 150 200
Values in Millions of US Dollars
V
a
l
ue
s
x 10^

8
@RISK Student Version
For Academic Use Only
Figure 5.11 Option4 NPV Probability Density Function
126
Option4 Cumulative Distribution Function
99.73.5
5.0%90.0%5.0%
0
0.2
0.4
0.6
0.8
1
5
0 0
50
100 150 200
Values in Millions of US Dollars
@RISK Student Version
For Academic Use Only
Figure 5.12 Option2 NPV Cumulative Distribution Function
5.4 DecisionTree Analysis
Plant I management estimates the probabilities of low, high, and medium
marketing performance levels as 55 percent, 5 percent, and 40 percent, respectively, due
to increasing oil prices and therefore expected future decrease in automotive OEM sales.
The corresponding revenues that are generated by each alternative and option are
indicated in the following Table 5.21, Table 5.22, and Table 5.23.
127
Table 5.21 Revenue Distributions for Low Marketing Performance
Floor Space (In Thousands of sq. ft). Mean Standard Deviation
5 (Alternative1) $23,364,959.20 $1,271,970.77
10 (Alternative2) $46,729,918.40 $2,543,941.54
45 (Alternative3) $95,424,734.23 $4,344,614.89
60 (Alternative4) $95,424,734.23 $4,344,614.89
50 (Option1) $95,424,734.23 $4,344,614.89
65 (Option2) $95,424,734.23 $4,344,614.89
55 (Option3) $95,424,734.23 $4,344,614.89
70 (Option4) $95,424,734.23 $4,344,614.89
Table 5.22 Revenue Distributions for Medium Marketing Performance
Floor Space (In Thousands of sq. ft.) Mean Standard Deviation
5 (Alternative1) $23,364,959.20 $1,271,970.77
10 (Alternative2) $46,729,918.40 $2,543,941.54
45 (Alternative3) $190,849,214.87 $8,689,229.78
60 (Alternative4) $190,849,214.87 $8,689,229.78
50 (Option1) $190,849,214.87 $8,689,229.78
65 (Option2) $190,849,214.87 $8,689,229.78
55 (Option3) $190,849,214.87 $8,689,229.78
70 (Option4) $190,849,214.87 $8,689,229.78
Table 5.23 Revenue Distributions for High Marketing Performance
Floor Space (In Thousands of sq. ft.) Mean Standard Deviation
5 (Alternative1) $23,364,959.20 $1,271,970.77
10 (Alternative2) $46,729,918.40 $2,543,941.54
45 (Alternative3) $210,284,632.80 $11,447,736.94
60 (Alternative4) $280,379,510.40 $15,263,649.25
50 (Option1) $233,649,592.00 $12,719,707.71
65 (Option2) $303,744,469.60 $16,535,620.02
55 (Option3) $257,014,551.20 $13,991,678.48
70 (Option4) $327,109,428.80 $17,807,590.80
The decision tree consists of four tiers, and the tier structure for the action nodes
is represented in Figure 5.13 below.
128
All three branches of the chance nodes, which represent low, high, and medium
marketing performance levels with 55 percent, 5 percent, and 40 percent probability,
respectively, are located at the origin of each branch stemming from the action nodes
called "Group1 Alternatives" and "Options".
Figure 5.13 Action Node Structure for DTA
Precision Tree 1.0 for MS Excel is used to make the DTA as described above,
which, together with the simulated cash flow inputs and the suggested policy, is indicated
in Figure 5.14 below.
129
The recommended solution for Plant I management is to pick Alternative3 at Year 0 for
all marketing performance levels, Alternative2 at Year 1 in case the marketing
performance turns out to be high, and Alternative1 at Year 1 in case the marketing
performance turns out to be low and medium. The mean and the standard deviation of the
NPV that is calculated through DTA are $28,225,882 and $12,854,312, respectively,
utilizing the average WACC of 8.33 percent. The floor space value per square foot for
each branch of the chance node is calculated as $1,103.97, $868.06, and $257.08 for
high, medium, and low marketing performance levels, respectively, where the weighted
average floor space value per square foot is calculated as $543.81.
Figure 5.14 DecisionTree Diagram of the Suggested Policy
130
Since there is no consensus in the financial community on what is the most
appropriate discount rate utilized inside the decision tree and since it is not clear whether
it is the private risk that dominates the cash flows inside the decision tree, DTA is
replicated using a riskfree rate of 5 percent. The mean and the standard deviation of the
NPV that is calculated through DTA are $28,277,438 and $12,889,077, respectively,
where the suggested policy scheme is the same as depicted in Figure 5.14 above. The
floor space value per square foot for each branch of the chance node is calculated as
$1,111.02, $868.75, and $257.78 for high, medium, and low marketing performance
levels, respectively, where the weighted average floor space value per square foot is
calculated as $544.83.
5.5 Real Options Analysis
Since the Black and Scholes equation promotes a black box approach, where the
mathematical complexity might risk the management buyin and since it does not allow
more than one strike price, which does not conform to this practical business application,
a binomial lattice approach is utilized. The main advantage of the binomial lattice model
over the Black and Scholes equation is the transparency and simplicity of the underlying
framework, although the calculated option value is a close approximation to the one
calculated through the Black and Scholes equation.
A sixstep process described in Kodukula and Papudesu (2006) is used to perform
the analysis, where the steps are
? Frame the application
? Identify the input parameters
131
? Calculate the option parameters
? Build the binomial tree and calculate the asset values at each node of the tree
? Calculate the option values at each node of the tree by backward induction
? Analyze the results
The challenge in the real options analysis is the identification of such parameters
as the underlying asset value and the volatility of the underlying asset value. As
mentioned in the previous chapter, there are two sources of volatility pertaining to this
practical business application:
? The volatility of the OEM demand interpreted as the market risk
? The corporate marketing performance interpreted as the private risk
This practical business application consists of multiple options combined in a
parallel compound option structure since the Group2 alternatives can be implemented
simultaneously or after the Group1 alternatives, where the option life for Group2 is
longer than Group1. The options consist of all possible implementation start time
combinations of the Group1 alternatives (Alternative1 and Alternative2) with the
Group2 alternatives (Alternative3 and Alternative4):
? Alternative1 with manufacturing equipment: Introduce a new miniload
AS/RS, expand floor space by 5,000 sq. ft., and use capital equipment for
manufacturing.
? Alternative1 without manufacturing equipment: Introduce a new miniload
AS/RS and expand floor space by 5,000 sq. ft. without using any capital
equipment for manufacturing.
132
? Alternative2 with manufacturing equipment: Deploy J.I.T. deliveries, expand
floor space by 10,000 sq. ft., and use capital equipment for manufacturing.
? Alternative2 without manufacturing equipment: Deploy J.I.T. deliveries and
expand floor space by 10,000 sq. ft. without using any capital equipment for
manufacturing.
? Alternative3 with manufacturing equipment: Replace AGV control software,
retrofit mechanical AGV components, expand floor space by 45,000 sq. ft.,
and use capital equipment for manufacturing.
? Alternative3 without manufacturing equipment: Replace AGV control
software, retrofit mechanical AGV components, expand floor space by
45,000 sq. ft. without using capital equipment for manufacturing.
? Alternative4 with manufacturing equipment: Utilize water spiders, expand
floor space by 60,000 sq. ft., and use capital equipment for manufacturing.
? Alternative4 without manufacturing equipment: Utilize water spiders and
expand floor space by 60,000 sq. ft. without using capital equipment for
manufacturing.
In order to be able to reduce the complexity of the model, the private risk is
incorporated in the form of a decisiontree model as represented in Figure 5.15 below.
133
ROA
ROA
ROA
Low Marketing Performance
(p=.55)
High Marketing Performance
(p=.05)
Medium Marketing Performance
(p=.45)
Figure 5.15 ROA Model Framework
The underlying asset value for this practical business application is estimated as
the NPV of all the revenue streams for every level of the marketing performance,
regardless of the capability of each option to meet the demand. The logic behind the
aforementioned setting is a simple analogy: The additional revenue for each marketing
performance level can be compared to an oil reserve under the ground waiting to be
extracted. The amount and the value of the extracted oil depend on the magnitude of the
extraction investment and hence the quality of the corresponding extraction equipment in
addition to all other market variables.
Thus, the underlying asset value for low, medium, and high marketing
performance levels at Year 0 is defined as $375,049,491.55, $750,098,955.39, and
$1,875,247,588.60, respectively.
134
The option life is given as two and four years for Group1 and Group2 options,
respectively, where the exercise price for each level of the marketing performance is
estimated by the following equation:
ij
Option theof FlowsCash Free NPVRevenues NPV ?=
i
X (5.1),
where i = Alternative1 and Alternative2 with and without manufacturing equipment for
Group1 and Alternative3 and Alternative4 with and without manufacturing equipment
for Group2 and j = low, medium, and high marketing performance levels.
The volatility is estimated through the logarithmic cash flow returns method by
utilizing numerous simulated cash flow profiles (Kodukula and Papudesu, 2006). The
method consists of calculating the relative returns of each interval starting with the
second period by dividing the current cash flow (CF
t
) by the preceding one (CF
t1
1?
=
t
t
t
CF
CF
R
),
which is described in the following equation.
(5.2)
Then the standard deviation of the natural logarithms of the relative returns (R
t
1
ln
ln
2
1
1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
?
=
=
n
n
R
R
n
t
n
t
t
t
?
) becomes
the volatility factor of the underlying revenue streams that is estimated by the following
equation 5.3 (Kodukula and Papudesu, 2006). The resulting volatility is estimated as 6.45
percent.
(5.3)
135
The riskneutral probability approach is used instead of the replicating portfolio
approach due to its mathematical convenience in terms of adjusting the cash flows so that
they may be discounted at a riskfree rate. It is also difficult to find a twin security with
perfectly correlated cash flows. Thus the discount rate becomes consistent and stays
constant along the lattice. The up and down movement factors are calculated as 1.066 and
0.937 using the following equations 5.4 and 5.5, respectively, where 1 t =? .
( ) texp ??=u (5.4)
ud 1= (5.5)
The riskneutral probability, p, is calculated as 88.1 percent through the following
equation 5.6, where r is the riskfree interest rate defined as 5 percent:
( )
du
dr
p
?
?
=
texp ?
(5.6)
The asset values for the longest option group, which, in this case, becomes Group
2, are calculated at each node of the lattice over the life of the option starting with the
underlying asset value (S
0
). The underlying asset value at time 0 is multiplied by the up
and down movement factors u and d, respectively, for the next year. Then the binomial
underlying asset valuation lattice is completed by moving right and continuing in the
same fashion for every node until the last time step. The option values are then calculated
by backward induction for the longest option starting from the rightmost nodes. The
discounting between time intervals is performed by utilizing the risk neutral probabilities
and the continuous riskfree interest rate. The binomial option valuation lattice of the
longest option becomes the underlying asset valuation tree of the shortest option group,
which, in this case, becomes Group1.
136
The process described above is replicated for the Group1 options, as well. The
aforementioned binomial lattice logic is represented in the following Figure 5.16 and the
corresponding equations 5.7 through 5.16.
Figure 5.16 Binomial Lattice Logic
C
u
3
=Max[S
0
u
3
X
i
, I
k
] (5.7)
C
u
2
d
= Max[S
0
u
2
dX
i
, I
k
] (5.8)
C
ud
2
= Max[S
0
ud
2
X
i
, I
k
] (5.9)
C
d
3
= Max[S
0
d
3
X
i
, I
k
] (5.10)
C
u
2
= Max[S
0
u
2
X
i
, ((p* C
u
3
)+(1p)* C
u
2
d
)*e
r?t
, I
k
C
] (5.11)
ud
= Max[S
0
udX
i
, ((p* C
u
2
d
)+(1p)* C
ud
2
)*e
r?t
, I
k
] (5.12)
137
C
d
2
= Max[S
0
d
2
X
i
, ((p* C
ud
2
)+(1p)* C
d
3
)*e
r?t
, I
k
] (5.13)
C
u
= Max[S
0
uX
i
, ((p* C
u
2
)+(1p)* C
ud
)*e
r?t
, I
k
] (5.14)
C
d
= Max[S
0
dX
i
, ((p* C
ud
)+(1p)* C
d
2
)*e
r?t
, I
k
] (5.15)
C= Max[S
0
X
i
, ((p* C
u
)+(1p)* C
d
)*e
r?t
, I
k
] (5.16),
where I
k
is the initial net present value for Alternative1 (k=1), Alternative2 (k=2),
Alternative3 (k=3), and Alternative4 (k=4), respectively, without deploying any capital
equipment for manufacturing purposes. Utilizing the net present value for alternatives
with material handling equipment only and without exercising the option of deploying
any capital equipment for manufacturing purposes can be considered analogous to not
exercising an option and thus resulting in an option value of $0. The aforementioned
difference in the binomial lattice logic is the interpretation of "donothing" approach for
this practical business application in terms of manufacturing equipment deployment.
The resulting binomial lattices for the options of Group1 and Group2 and the
suggested policy, where the marketing performance is low, are represented in the
following Figure 5.17, Figure 5.18, and Figure 5.19, respectively. The italicized numbers
at the bottom of each node represent the option values.
138
Figure 5.17 Binomial Lattice for Group2 with Low Marketing Performance
Figure 5.18 Binomial Lattice for Group1 with Low Marketing Performance
139
Figure 5.19 Suggested Policy for Low Marketing Performance
The resulting binomial lattices for the options of Group1 and Group2 and the
suggested policy, where the marketing performance is medium, are represented in the
following Figure 5.20, Figure 5.21, and Figure 5.22, respectively. The italicized numbers
at the bottom of each node represent the option values.
140
Figure 5.20 Binomial Lattice for Group2 with Medium Marketing Performance
Figure 5.21 Binomial Lattice for Group1 with Medium Marketing Performance
141
Figure 5.22 Suggested Policy for Medium Marketing Performance
The resulting binomial lattices for the options of Group1 and Group2 and the
suggested policy, where the marketing performance is high, are represented in the
following Figure 5.23, Figure 5.24, and Figure 5.25, respectively. The italicized numbers
at the bottom of each node represent the option values.
142
Figure 5.23 Binomial Lattice for Group2 with High Marketing Performance
Figure 5.24 Binomial Lattice for Group1 with High Marketing Performance
143
Figure 5.25 Suggested Policy for High Marketing Performance
Pascal's Triangle in the following Figure 5.26 is utilized in order to define the
weighted average floor space value per square foot by calculating the probability
distribution of each option.
Figure 5.26 Pascal's Triangle
144
The weighted average floor space for Group1 with low, medium, and high
marketing performance is 7,500 sq. ft. The weighted average floor space for Group2
with low and medium marketing performance is 45,000 sq. ft., while it is 52,500 sq. ft.
with high marketing performance. The corresponding weighted average floor space value
utilizing the real option value and the associated weighted average floor space for each
marketing performance level is represented in the following Table 5.24.
Table 5.24 Weighted Average Floor Space Value
Marketing Performance
Low Medium High
Option Value $18,466,868 $26,740,827 $47,773,040
Weighted Average Floor Space 52,500 sq. ft.
60,000 sq. ft.
Probability of Marketing Performance .55 .40 .05
Weighted Average Real Option Value $23,241,760.2
Floor Space Value per Square Foot $351.75 $509.35 $796.22
Weighted Average Floor Space Value $437.01
5.6 Summary of Results
The decision recommendations are summarized in the following Table 5.25. With
no additional business volume, the decision recommendation is always to replace the
existing miniload AS/RS, to replace AGV control software, to retrofit mechanical AGV
components, and to expand the existing floor space by 50,000 sq. ft. without utilizing any
manufacturing equipment. As the additional business volume increases, the decision
recommendations proposed by the techniques that include stochastic behavior of the
input variables shift toward generating more floor space in order to meet additional
demand.
145
While MCS analysis takes the stochastic behavior of all the input variables into
account simultaneously, DTA includes the private risk into the valuation through the
management's subjective assessment. ROA supported by DTA, on the other hand, adds
the market risk into the valuation more realistically through risk neutral probability
approach by estimating the volatility utilizing historical data instead of the probability
distribution that is subjectively assessed by the management. It should be noted that the
riskneutral probability approach does not depend on the state of the nature at each node;
it is a function of the up and down movements, and the riskfree rate. Moreover, since it
remains constant from node to node, it is considered more convenient to include the
market risk through ROA than utilizing a subjectively assessed probability distribution
through DTA, which may be rarely perfectly correlated with the state of the nature at
each node. Similarly to the results of the former techniques, ROA indicates that, as the
additional business volume increases, the decision recommendation shifts from using less
expensive alternatives without manufacturing equipment, which offer less floor space,
toward using expensive alternatives with manufacturing equipment, which offer more
floor space. Hence, DCF approach is recommended to be supported by a combination of
MCS analysis, DTA, and ROA in order to include the stochastic behavior of the input
variables, the private risk, and the market risk, respectively.
The sequence of the utilized techniques is evolutionary in nature. As the
techniques evolve from the very basic DCF approach toward more sophisticated
techniques, stochastic behavior of the inputs are more included into the valuation. The
recommendations generated by this method are inline with intuition, which is to use
more floor space when there is an opportunity to generate more revenue.
146
Table 5.25 Decision Recommendations Summary
Decision
Technique
Implementation
Time
Combinations
of the
Alternatives
Additional
Business
Volume
Total
Floor
Space in
sq. ft.
Floor
Space
Value
Mfg.
Equipment
Gr.1/Gr.2
DCF 1030 None 50,000 $29.20 No/No
DCF Best Case 1030 None 50,000 $43.78 No/No
DCF Worst Case 1033 None 50,000 $6.98 No/No
MCS Phase1 1030 None 50,000 $25.57 No/No
MCS Phase2 2040 Maximum 70,000 $1,106.57 Yes/Yes
MCS Phase3 2140 Medium 70,000 $629.45 Yes/Yes
DTA (WACC) 1130 Low 50,000 $257.08 Yes/Yes
DTA (WACC) 1130 Medium 50,000 $868.06 No/Yes
DTA (WACC) 2130 High 55,000 $1,103.97 No/Yes
DTA
(riskfree rate)
1130 Low 50,000 $257.78 Yes/Yes
DTA
(riskfree rate)
1130 Medium 50,000 $868.75 No/Yes
DTA
(riskfree rate)
2130 High 55,000 $1,111.02 No/Yes
ROA Figure 5.19 Low 52,500 $351.75 Figure 5.19
ROA Figure 5.22 Medium 52,500 $509.35 Figure 5.22
ROA Figure 5.25 High 60,000 $796.22 Figure 5.25
147
CHAPTER 6
CONCLUDING REMARKS AND FUTURE RESEARCH
6.1 Concluding Remarks
The fiercest competition today is in the automotive and high technology industries
due to globalization, rapid technological improvements, and the need for new energy
resources. OEM's in the aforementioned industries exert their power mostly over their
firsttier suppliers. Moreover, high market demand volatility, short product life cycles,
long design and production lead times, high capital investment requirements, and
irreversibility of the investments require extremely intelligent decision making.
Controlling fuel prices, interest rates, investments in other industries and/or
competitors, tax system, and insurance costs is impossible. Thus warehousing and
obsolescence costs become the most accessible targets for industries in terms of logistics
costs. Controlling warehousing costs starts with accurate warehouse sizing, adequate
floor space allocation, and, thus accurate inventory allocation, and streamlining the
relevant processes which can be translated as waste removal from the warehousing
activities.
148
Companies that can control the aforementioned costs can also control immediate
internal extensions. Such inhouse logistics operations as inbound delivery scheduling,
inventory planning and analysis, process streamlining, and waste elimination can be
considered as natural resource acquisition and exploitation activities depending on their
revenue generating potentials.
Similarly, any operation that does not require corecompetency of the enterprises
can either be handled inhouse or contracted out to effectively utilize the existing floor
space depending on the generated value. The bottom line is to effectively utilize the
existing floor space in order to obtain the greatest return for an investment, and thus to
compete in today's environment.
Effective floor space utilization provides in the flexibility to manage the capacity
needed to generate more revenue or more cost savings, thereby contributing to the
competitive advantage. Thus making capital investment decisions without taking floor
space valuation into account might be premature.
This research study is unique in its nature. The value of floor space in electronics
manufacturing is discussed in detail for the first time in the literature through different
techniques, and the decision recommendations are utilized by a realworld business entity
for capital investment decisions. The scope of this research study is limited to plant level
capital investment decisions of a global publicly held highvolume highmix automotive
electronics manufacturer. A method using traditional DCF techniques supported by
Monte Carlo simulation, decisiontree analysis, and ROA is developed in order to capture
the floor space value by including the stochastic behavior of the input variables, the
private risk, and the market risk, respectively.
149
The proposed method is applied to a realworld practical business application using real
data, where decisions made using the aforementioned techniques are compared to each
other. Numerical results obtained through the aforementioned techniques intuitively
indicate that, as additional business volume increases, the decision recommendation shifts
from alternative combinations offering less floor space toward the ones offering larger
floor space.
From the timing perspective, DCF approach suggests making the investments at
Year 0 by not considering the stochastic behavior of the input variables, especially the
revenues generated through additional business volume. Meanwhile DTA and ROA
suggest taking advantage of the arrival of the new information about the private and
market risks involved regarding the additional business volume by emboldening the
"waitandsee" approach.
Finally, the value of the floor space exhibits a very wide spectrum depending
upon the diversity of the solution methodology applied to the practical business
application and the associated features of each technique. It sounds unrealistic to assign
such low values as $25.60 to floor space without considering any revenuegenerating
potential. Thus valuation efforts that do not take into account the opportunities mislead
practitioners.
The floor space value calculated through the aforementioned techniques indicates
that, when the floor space is not utilized for nonrevenue generating activities, the
associated value is expressed in hundreds or thousands of US dollars.
150
Hence, aside from analyzing purely from a capital investment justification perspective
through DCF techniques, it is important to take into account the revenuegenerating
potential of the floor space generated by the investment. As discussed in this practical
business application, the most attractive capital investment alternatives may turn out to be
the least attractive ones when the revenuegenerating potential of the corresponding floor
space is taken into account, together with the timing aspects. The floor space valuation
utilizing an ROA framework allows decision makers to include market risk into the
valuation more realistically since it estimates the market volatility utilizing historical data
instead of a subjectively assessed probability distribution and it is easy to understand
each course of action under all possible circumstances with strong emphasis on revenue
generating opportunities with the value of additional information. This method can be
used as a practical way to evaluate business decisions for highvolume highmix
electronics manufacturing facilities if the associated decision alternatives offer floor
space with revenuegenerating potential. The aforementioned method is considered as a
useful tool for this specific practical business application since corporate planners do not
have a thorough method to understand and value the floor space in order to make
business decisions regarding future product allocations to manufacturing plants. Such
decisions are too complicated to be made by just dividing the overall budget by the total
floor space.
6.2 Future Research Areas
Irreversible capital investments generally require a significant amount of
implementation time.
151
The cash flow structure pertaining to implementation time lags might effect the decision.
The implementation time lag is assumed to be zero for this research study since the
required resolution negatively impacts the mathematical tractability. The magnitude of
the model becomes unmanageable if high resolution is required. Further research efforts
utilizing combinatorial optimization techniques might help implementation time lags
when used with ROA in order to enhance the mathematical tractability, especially for
complex realworld models regardless of the size of the model.
The useful project life for this research study is assumed to be fixed as five years.
It would be more realistic to assume dynamic project life, which would change the
planning horizon by reflecting realworld situations such as early contract terminations.
The impact of dynamic project life might lead to the optimum product type and facility
pair selection associated with available floor space alternatives. Then the research
question becomes which floor space alternative to allocate to which product at which
facility. Bayesian learning real options might be a valuable tool to tackle the dynamic
project life challenge.
In this research study lost sales are assumed to have zero impact on the cash flow
structure of the decision alternatives. The reason for that assumption is that the customer
demand is assumed to be satisfied by other facilities of the corporation in case the
selected facility is not capable of meeting the aforementioned demand. However, the
inclusion of the lost sales might be considered as an addon to the future research
opportunity, since finding the optimum product allocation for different manufacturing
plants within to the same corporation by taking the lost sales into consideration might be
another valuable tool for corporate decision makers.
152
Including the effects of volatility in oil price, exchange rates, labor costs, and
transportation costs might take the former opportunity one step further in terms of
understanding the business decisions regarding the transfer of business towards low cost
countries.
Corporate level business decisions such as expansions, contractions, plant
closings, and acquisitions might be better understood via game theory in the existence of
competition in the automotive electronics industry. Future research utilizing game theory
combined with options pricing theory might help decision makers to better understand,
analyze, and improve the aforementioned decisions as well as the associated behaviors of
the corresponding actors during the decisionmaking process.
Although WACC is treated as an input variable due to the acquisition that Plant I
went through, the riskfree interest rate is assumed to be fixed in order to control the
scope of this research study. However, with the ongoing uncertainty in the global
economy stemming from increasingly fluctuating oil prices, the effect of the dynamic
riskfree interest rate, together with the inflation on business valuation is worth
researching, especially for automotive industry decision makers and strategists.
Binomial lattices are easy to understand, manageable, and mathematically
tractable. A combination of decisiontree and binomial lattices are utilized in this
research study in order to reflect the multinomial nature of the practical business
application. The aforementioned scheme might not always fit the decision problem on
hand. Multinomial lattices, on the other hand, become error prone and intractable,
especially for large models. Further research might be valuable in order to make
multinomial lattices mathematically tractable and attractive for practitioners.
153
Finally, since an analogy between financial options and real options is made in
order to establish a real options analysis framework, a similar analogy can be made
between trading strategies of the financial options and trading strategies of floor space
options in the existence of extra office space for lease and valueadded floor space
requirements or in the existence of facilities for sale and facilities that require expansion.
154
BIBLIOGRAPHY
[1] ALFORD, L.P., and J. BANGS, Production Handbook, The Ronald Press, New
York, 1953.
[2] ANONYMOUS, "Welcome to the Office "Hotel"," Facilities, Vol. 14, No. 9, Sep
1996, pp. 78.
[3] BIERMAN, H., C. BONINI, and W. HAUSMAN, Quantitative Analysis for Business
Decisions, 6
th
[8] BROWN, C., and K. DAVIS, "Options in Mutually Exclusive Projects of Unequal
Lives," The Quarterly Review of Economics and Finance, Vol. 38, Special Issue, 1998,
pp. 569577.
ed., Richard D. Irwin, Homewood, IL, 1981.
[4] BLACK, F., and M. SCHOLES, "The Pricing of Options and Corporate Liabilities,"
Journal of Political Economy, Vol. 81, MayJun 1973, pp. 637659.
[5] BOER, F., The Real Options Solution: Finding Total Value in a HighRisk World,
John Wiley & Sons, Inc., New York, 2002.
[6] BOLLEN, N., "Real Options and Product Life Cycles," Management Science, Vol.
45, No. 5, May 1999, pp. 670684.
[7] BOYLE, P., "A Lattice Framework for Option Pricing with TwoState Variables,"
Journal of Financial and Quantitative Analysis, Vol. 23, 1988, pp. 112.
155
[9] BURNETAS, A., and P. RITCHKEN, "Option Pricing with DownwardSloping
Demand Curves: The Case of Supply Chain Options," Management Science, Vol. 51, No.
4, April 2005, pp. 566580.
[10] CANADA, J.R., and W.G. SULLIVAN, Economic and Multiattribute Evaluation of
Advanced Manufacturing Systems, Prentice Hall, Edgewood Cliffs, NJ, 1989.
[11] CARR, P., "The Valuation of Sequential Exchange Opportunities," The Journal of
Finance, Vol. 43, No.5, Dec 1988, pp. 12351256.
[12] CHEN, A.H., J.W. KENSINGER, and J.A. CONOVER, "Valuing Flexible
Manufacturing Facilities," The Quarterly Review of Economics and Finance, Vol. 38,
Special Issue, 1998, pp. 651674.
[13] CHILDS, P., and A. TRIANTIS, "Dynamic R&D Investment Policies," Management
Science, Vol. 45, No. 10, Oct 1999, pp. 13591377.
[14] CHUNG, K., "Output Decision under Demand Uncertainty with Stochastic
Production Function: A Contingent Claims Approach," Management Science, Vol. 36,
No.11, Nov 1990, pp. 13111324.
[15] COPELAND, T., T. KOLLER, and J. MURRIN, Valuation: Measuring and Managing
the Value of Companies, John Wiley & Sons, Inc., New York, 1996.
[16] COPELAND, T., and T.V. ANTIKAROV, Real Options: A Practitioner's Guide,
Texere, New York, 2003.
[17] CORTAZAR, G., and E. SCHWARTZ, "A Compound Option Model of Production
and Intermediate Inventories," Journal of Business, Vol. 66, No. 4, Oct 1993, pp. 517
540.
156
[18] COX, J., S. ROSS, and M. RUBINSTEIN, "Option Pricing: A Simplified Approach,"
Journal of Financial Economics, Vol. 7, 1979, pp. 229263.
[19] CUCCHIELLA, F., and M. GASTALDI, "Risk Management in Supply Chain," Journal
of Manufacturing Technology Management, Vol. 17, No. 6, 2006, pp. 700720.
[20] DETEMPLE, J., and S. SUNDERESAN, "Nontraded Asset Valuation with Portfolio
Constraints: A Binomial Approach," The Review of Financial Studies, Vol. 12, No. 4,
1999, pp. 835872.
[21] DIXIT, A., and R. PINDYCK, "The Options Approach to Capital Investment,"
Harvard Business Review, Vol. 73, Issue 3, MayJune 1995, pp. 105115.
[22] EVANS, J.L., D. ZHANG, N. VOGT, and J.R. THOMPSON, "Investment Analysis for
Automotive Electronics Manufacturing: A Case Study," The Engineering Economist,
Vol. 49, No. 2, 2004, pp. 159183.
[23] FISCHER, S., "Call Option Pricing When the Exercise Price is Uncertain, and the
Valuation of Index Bonds," The Journal of Finance, Vol. 33, No.1, Mar 1978, pp. 169
176.
[24] GESKE, R., "The Valuation of Compound Options," Journal of Financial
Economics, Vol. 7, No.1, Mar 1979, pp. 6381.
[25] GROOVER, M.P., Automation, Production Systems, and ComputerIntegrated
Manufacturing, 2
nd
ed., Prentice Hall, Upper Saddle River, NJ, 2001.
[26] HERAGU, S., Facilities Design, PWS Publishing Company, Boston, MA, 1997.
[27] HERATH, H.S.B., and C.S. PARK, "MultiStage Capital Investment Opportunities
as Compound Real Options," The Engineering Economist, Vol. 47, No. 1, 2002, pp. 127.
157
[28] HULL, J., Options, Futures, and Other Derivatives, 6
th
ed., Prentice Hall, Upper
Saddle River, NJ, 2006.
[29] KELLY, S., "A Binomial Lattice Approach for Valuing a Mining Property IPO,"
The Quarterly Review of Economics and Finance, Vol. 38, Special Issue, 1998, pp. 693
709.
[30] KEMNA, C., "Case Studies on Real Options," Financial Management, Vol. 22, No.
3, Autumn 1993, pp. 259270.
[31] KESTER, A., "Today's Options for Tomorrow's Growth," Harvard Business
Review, MarApr 1984, pp. 153160.
[32] KODUKULA, P., and C. PAPUDESU, Project Valuation Using Real Options, J. Ross
Publishing, Inc., Florida, 2006.
[33] KOGUT, B., and N. KULATILAKA, "Options Thinking and Platform Investments:
Investing in Opportunity," California Management Review, Vol. 36, No. 2, Winter 1994,
pp. 5267.
[34] KULATILAKA, N., "The Value of Flexibility: The Case of a DualFuel Industrial
Steam Boiler," Financial Management, Vol. 22, No. 3, Autumn 1993, pp. 271280.
[35] KUMAR, R., "A Note on Project Risk and Option Values of Investments in
Information Technology," Journal of Management Information Systems, Vol. 13, No. 1,
Summer 1996, pp. 187193.
[36] LINT, O., and E. PENNINGS, "An Option Approach to the New Product
Development Process: A Case Study at Phillips Electronics," R&D Management, Vol. 31,
No. 2, Winter 2001, pp. 5267.
158
[37] LUEHRMAN, T.A., "What's It Worth: A General Manager's Guide to Valuation,"
Harvard Business Review, MayJune 1997, pp. 105115.
[38] MADAN, D., R. MILNE, and H. SHEFRIN, "The Multinomial Option Pricing Model
and its Brownian and Poisson Limits," The Review of Financial Studies, Vol. 2, No. 2,
1989, pp. 251265.
[39] MARGRABE, W., "The Value of an Option to Exchange One Asset for Another,"
The Journal of Finance, Vol. 33, No. 1, Mar 1978, pp. 177186.
[40] MAUER, D., and S. OTT, "Investment under Uncertainty: The Case of Replacement
Investment Decisions," The Journal of Financial and Quantitative Analysis, Vol. 30,
Issue 4, Dec 1995, pp. 581605.
[41] MCLAUGHLIN, R., and R. TAGGART, "The Opportunity Cost of Using Excess
Capacity," Financial Management, Vol. 21, No. 2, Summer 1992, pp. 1223.
[42] MILLER, L., "Development of a Bayesian Real Options Framework and its
Application to Capital Budgeting Problem," Doctoral Dissertation, Auburn University,
May 2004.
[43] MILLER, L., and C.S. PARK, "Decision Making Under Uncertainty ? real Options
to the Rescue?," The Engineering Economist, Vol. 47, No.2, 2002, pp. 105150.
[44] MYERS, S., "Determinants of Capital Borrowing," Journal of Financial
Economics, Vol. 5, 1977.
[45] NEMBHARD, H.B., L. SHI, and M. AKTAN, "A RealOptionsBased Analysis for
Supply Chain Decisions," IIE Transactions, Vol. 37, 2005, pp. 945956.
159
[46] OTTOO, R., "Valuation of Internal Growth Opportunities: The Case of a
Biotechnology Company," The Quarterly Review of Economics and Finance, Vol. 38,
Special Issue, 1998, pp. 615633.
[47] PANAYI, S., and, L. TRIGEORGIS, "MultiStage Real Options: The Cases of
Information Technology Infrastructure and International Bank Expansion," The Quarterly
Review of Economics and Finance, Vol. 38, Special Issue, 1998, pp. 675692.
[48] PARK, C.S., and H.S.B. HERATH, "Exploiting UncertaintiesInvestment
Opportunities as Real Options: A New Way of Thinking in Engineering Economics," The
Engineering Economist, Vol. 45, No. 1, 2000, pp. 136.
[49] PARK, C.S., Contemporary Engineering Economics, Prentice Hall, Upper Saddle
River, NJ, 2002.
[50] PICKLES, E., and, J. SMITH, "Petroleum Property Valuation: A Binomial Lattice
Implementation of Option Pricing Theory," Energy Journal, Vol. 14, No. 2, 1993, pp. 1
26.
[51] RASMUSEN, E., Games and Information: An Introduction to Game Theory, 2
nd
ed.,
Blackwell Publishers, Cambridge, MA, 1994.
[52] REES, R., "Smooth Landing at Air Canada for 140,000 Aircraft Parts," Industrial
Engineering, Vol. 26, No. 6, Jun 1994, pp. 2829.
[53] RENDLEMAN, R., and, B. BARTER, "TwoState Option Pricing," The Journal of
Finance, Vol. 34, No. 5, 1979, pp. 10931110.
[54] RITCHKEN, P., and, C. TAPIERO, "Contingent Claims Contracting for Purchasing
Decisions in Inventory Management," Operations Research, Vol. 34, No. 6, NovDec
1986, pp. 864870.
160
[55] SAATY, T.L., and L.G. VARGAS, Models, Methods, Concepts & Applications of the
Analytical Hierarchy Process, Kluwer Academic Publishers, Norwell, MA, 2001.
[56] SMITH, J., and, R. NAU, "Valuing Risky Projects: Options Pricing Theory and
Decision Analysis," Management Science, Vol. 41, No. 5, May 1995, pp. 795816.
[57] SRINIVASAN, M.M., Streamlined: 14 Principles for Building & Managing the
Lean Supply Chain, Texere, Mason, OH, 2004.
[58] STOWE, J., and, T. SU, "A Contingent Claims Approach to the InventoryStocking
Decision," Financial Management, Vol. 26, No. 4, Winter 1997, pp. 4255.
[59] TAUDES, A., "Software Growth Options," Journal of Management Information
Systems, Vol. 15, No. 1, Summer 1998, pp. 165185.
[60] TIAN, Y., "A Modified Lattice Approach to Option Pricing," The Journal of
Future Markets, Vol. 13, No. 5, 1993, pp. 563577.
[61] THOMPSON, R., "Industrial Employment Densities," The Journal of real Estate
Research, Vol. 14, No. 3, 1997, pp. 309319.
[62] TRIGEORGIS, L., "Real Options and Interactions with Financial Flexibility," The
Financial Management, Vol. 22, No. 3, Autumn 1993, pp. 202224.
[63] VON NEUMANN, O., AND J. MORGENSTERN, Theory of Games and Economic
Behavior, John Wiley & Sons, Inc., 3
rd
ed., New York, 1967.
[64] WU, S.D., M. ERKOC, and S. KARABUK, "Managing Capacity in the HighTech
Industry: A Review of Literature," The Engineering Economist, Vol. 50, No. 2, 2005, pp.
125158.
[65] ZIMMERMAN, J.L., Accounting for Decision making and Control, McGrawHill,
3
rd
ed., Boston, MA, 2000.
161
APPENDIX A
ADVANTAGES OF ROA OVER TRADITIONAL TECHNIQUES
Decision makers, analysts, and other finance professionals use DCF analysis,
DTA, and MCS analysis for valuation purposes. Although those may very well serve the
purpose for many applications, their limitations still leave some holes from the valuation
perspective. Miller and Park (2002) define the main limitations of the traditional methods
as follows:
? Selecting an appropriate discount rate poses problems. If the project involves
high uncertainty, a high discount rate, which reflects a high risk premium, is
used.
? Traditional methods ignore the flexibility to modify decisions along the value
chain as new information arrives.
? Investment decisions are typically viewed as nowornever or gonogo type
decisions rather than decisions that may be delayed.
Traditional methods use deterministic cash flows, adjusting them for risk utilizing
a constant and riskadjusted discount rate all along the decision horizon, and subtract the
aforementioned cash flows from the investment outlays for NPV calculation. It should
also be noted that the risks are often hedged by high discount rates and the downswings
are always taken into account undervaluing opportunities.
162
ROA, on the other hand, captures the upside potential only by not exercising the
option when the circumstances are unfavorable. ROA only needs the riskfree interest
rate since the risk can be perfectly hedged, and thus there is no need for discount rate
adjustment. In other words, the risk behavior of the decision maker, thus his or her utility
function is not required. Hence it is possible to eliminate subjectivity from the valuation
process.
Traditional methods are unrealistically deterministic, whereas ROA accounts for
managerial flexibility, which is about understanding and managing the risk, as well as
capturing the embedded opportunities or switching between multiple options in a
financial decision problem as new information arrives and resolves uncertainty. Thus,
instead of steering away from uncertainty, decision makers, analysts, and other finance
professionals treat uncertainty as a profit opportunity since ROA enables them to make
intelligent decisions through uncertain market circumstances. In addition to uncertainty,
the length of the decision horizon increases the value of the real options, as well.
However, traditional methods often consider that the long decision horizons have
negative impact on NPV due to increasing uncertainty over time. Kodukula and Papudesu
(2006) argue that ROA accounts for the whole range of uncertainty using stochastic
processes and calculates a "composite" options value for a project, considering only those
outcomes that are favorable (i.e., options are exercised) and ignoring those that are not by
letting the options expire.
Future cash flows that can be generated by uncertain opportunities are often
ignored through valuation since traditional methods unrealistically require perfect
certainty to evaluate projects. ROA, however, is capable of evaluating projects with
163
uncertain payoffs that may occur at uncertain points in time. ROA is more valuable when
embedded options are about delaying, abandoning, and expanding commitments before
making a final decision. Hence, riskier projects become more favorable under uncertain
circumstances especially when they are marketdriven. In other words, as new
information arrives and the uncertainty resolves, waitandsee approach boils down all
possible outcomes into a single scenario, where decision maker may switch to a more
favorable alternative instead of following an irreversible and predetermined decision path
that may end up with a financial loss.
The value of ROA is illustrated with a simple numerical example below. Suppose
that you have a choice between investing $1M in a project today expecting to yield either
$1.6M or $0.8M with 50 percent probability each and delaying that investment by one
year, where the payoff uncertainty clears. The discount rate is given as 10 percent. Using
traditional DCF method, the NPV for the first choice is:
()
MM
M
NPV 0909.0$1$
10.01
2.1$
1
=?
+
=
On the other hand, since the uncertainty is expected to clear in one year, the investment
will be made only if the outcome is favorable, which is $1.6M with 50 percent
probability. Thus, the expected NPV for the delayed investment is calculated as follows:
()()
M
MM
NPV 207.0$
10.01
6.1$
10.01
1$
5.0
21
=
?
?
?
?
?
?
+
+
+
?
=
The value of delaying the decision is the difference between the two NPV's calculated
above: $0.207M$0.0909M = $0.1161M.
164
Also suppose that the uncertainty is increased. Thus the same project is now
expected to yield either $1.9M or $0.3M with 50 percent probability each and delaying
that investment by one year, where the payoff uncertainty clears. The discount rate is
given as 10 percent. Then the expected NPV for the delayed investment is calculated as
follows:
()()
M
MM
NPV 3306.0$
10.01
9.1$
10.01
1$
5.0
21
=
?
?
?
?
?
?
+
+
+
?
=
The value of delaying the decision when the uncertainty is increased is calculated as:
$0.3306M$0.0909M = $0.2397M. The value of the option is increased by $0.1236M
demonstrating that the ROA generates more favorable results under uncertainty.
.
165
APPENDIX B
TRADITIONAL DCF TECHNIQUES FOR VALUATION
In today's business environment strategic decisions are mostly multiperiod
decisions. Valuation of these decisions is a function of three fundamental factors: cash,
timing, and risk (Luehrman, 1997). Capital investments in real assets such as equipment,
machinery, plants, and buildings are being valued by the traditional approach known as
the NPV method. The NPV of a capital investment project is calculated by discounting
expected future incremental cash flows at a riskadjusted discount rate. The NPV
represents a measure of cash flow relative to the time point "now" with provisions that
account for earning opportunities (Park, 2002). The NPV formulation with discrete (Park,
2002) and continuous (Hull, 2006) compounding is respectively as follows:
()
()
?
=
+
=
N
n
n
n
i
A
iPW
0
1
(B1)
()
?
=
??
=
N
n
ni
n
eAiPW
0
(B2),
where i is the minimum attractive rate of return or cost of capital, n is the service life of
the project, PW(i) is the net present value calculated at the interest rate i, and A
n
is the net
cash flow at the end of period n.
166
Suppose that company ABC invests $500,000 in a new machine, where annual
labor savings with a 3year project life are $300,000; $350,000; and $400,000,
respectively. If the minimum attractive rate of return is 15 percent, the NPV of this
project using equations (B1) and (B2) are:
() k
kkkk
PW 5.288$
15.1
400$
15.1
350$
15.1
300$
15.1
500$
%15
3210
=+++
?
=
()
() ( ) ( )()
kekekekekPW 5.272$400$350$300$500$%15
315.0215.0115.0015.0
=?+?+?+??=
????????
Within the framework of the NPV method, other DCF techniques such as the
internal rate of return (hereafter IRR), the payback method, and the economic value
added (hereafter EVA) are commonly used by corporate managements to value strategic
capital investment projects.
The IRR is the interest rate charged on the unrecovered project balance of the
investment such that, when the project terminates, the unrecovered project balance will
be zero (Park, 2002). Suppose Company ABC invests $2.5 million in a new automated
material handling system with a 5year useful life and annual equivalent labor savings of
$500,000. The cash flow transaction is given in the following Table A1.
Table B.1 Sample Cash Transaction
Period Ending Cash Payment
0 $2,500,000
1 $800,000
2 $800,000
3 $800,000
4 $800,000
5 $800,000
167
The internal rate of return of this project is 18 percent. As indicated in Park (2002), if the
investing firm and the project are viewed as the lender and borrower, respectively, the
amortized loan transaction is as follows:
Table B.2 Sample Amortized Loan Transaction
Period
Beginning
Project Balance
Return on
Invested Capital
Ending Cash
Payment
Project
Balance
0 $0 $0 $2,500,000 $2,500,000
1 $2,500,000 $450,767 $800,000 $2,150,767
2 $2,150,767 $387,798 $800,000 $1,738,564
3 $1,738,564 $313,475 $800,000 $1,252,039
4 $1,252,039 $225,751 $800,000 $677,790
5 $677,790 $122,210 $800,000 $0
The IRR is a relative measure and depending on the project cash flow structure, it may
exhibit inconsistencies with other profitability measures since it does not provide
absolute monetary values. Hence it fails to measure the scale of the investment (Park,
2002).
The payback method screens projects on the basis of how long it takes for net
receipts to equal investment outlays. Conventional payback method ignores time value of
money whereas discounted payback method includes time value of money (Park, 2002).
Suppose Company ABC invests $1 million in a stateoftheart automated data capture
system with 3year useful life and generates annual equivalent net benefits of $500,000.
The conventional payback period (hereafter CPP) is calculated as follows:
Years 2
000,500$
000,000,1$
Benefit Equivalent Annual
Amount Investment
CPP ===
168
If Company ABC requires an internal rate of return of 10 percent, the following Table B3
is constructed to determine the discounted payback period to recover the capital
investment and the cost of funds required to support the project.
Table B.3 Sample Cash Flow Transaction for Discounted Payback Period
Calculation
Period Cash Flow Cost of Funds Cumulative Cash Flow
0 $1,000,000 $0 $1,000,000
1 $500,000 $100,000 $600,000
2 $500,000 $60,000 $160,000
3 $500,000 $16,000 $324,000
If the cash flows are assumed to be continuous the discounted payback period is
approximately 2 years and 3 months, or, if the endofyear approach is adopted, then the
discounted payback period is 3 years. The payback method determines how fast the
investor can restore the initial position so that additional investment opportunities that
may come along can be evaluated. Hence it is a supplementary component of the decision
making process. However, it is not a profitability measure and, since it ignores the timing
of the cash flows, it is not possible to determine the contribution of the investment.
EVA is a financial performance measure developed and defined by Stern Stewart
& Co. as the amount by which earnings exceed or fall short of the required minimum rate
of return, which shareholders and lenders could get by investing in other securities of
comparable risk (Zimmerman, 2000). It is calculated by taking adjusted accounting
earnings and subtracting the WACC multiplied by total capital employed. It is focused on
shareholder value and measures the economic value of an investment.
169
Suppose Company ABC invests $100,000 in a new assembly line and they can generate
$250,000 in sales revenue. The annual operating cost is $200,000, the tax rate is 30
percent, and the cost of capital is 7 percent. EVA is calculated as follows:
()
,000,28$000,7$000,35$
000,7$07.0000,100$
000,35$70.0000,50$ 1
000,50$000,200$000,250$
=?=?=
=?=?=
=?=??=
=?=?=
CostsCapitalNOPATEVA
CapitalofCostInvestmentCostsCapital
RateTaxEBITNOPAT
CostsOperatingSalesEBIT
where EBIT represents earnings before interest expenses and income taxes. EVA has
limited use for valuation because defining the cost of capital of an investment is
complicated in terms of determining the comparable risk of other securities. In other
words, the riskiness of the "other securities" may not always be truly comparable.
Park (2002) indicates that the equivalent present worth (hereafter PW), together
with its variations; the equivalent future worth (hereafter FW); and the equivalent annual
worth are the three common measures based on cash flow equivalence that establish a
foundation for accepting or rejecting a capital investment.
The future worth (hereafter FW) measures the NPV of an investment at a time
period other than 0. In other words it computes the value of an investment at the end of
any period rather than at the beginning (Park, 2002). The FW formulation is given as
follows:
() ( )
?
=
?
+=
N
n
nN
n
iAiFW
0
1 (B3)
The annual equivalent worth (hereafter AEW) criterion provides a basis for
measuring investment worth by determining equal payments on an annual basis.
170
The AEW is calculated by multiplying the NPV by the capital recovery factor. The
capital recovery and AEW formulations are given respectively as follows (Park, 2002):
()
( )
()11
1
,,/
?+
+
=
N
N
i
ii
NiPA (B4)
( )NiPANPVAEW ,,/= (B5),
where P represents the NPV, and N is the service life of the investment. Suppose the
NPV of an investment is $500,000 and the service life is 5 years. If the minimum
attractive rate of return is 15 percent, the FW and the AEW of this project are calculated
as follows:
()
( )
()
() 6.678,005,1$15.1000,500$%)15(
8.157,149$298.0000,500$
298.0
115.1
15.115.0
5%,15,/
5
5
5
=?=
=?=
=
?
=
FW
AEW
PA
The AEW is considered as a useful method especially for comparing mutually exclusive
projects with unequal service lives and for annual financial reporting including unit
profit/cost analysis. However McLaughlin and Taggart (1992) discuss that AEW relies on
stringent assumptions about the timing of future investment expenditures. By assuming
that all future investment will take place with certainty at particular dates, it ignores the
option component of the investment decision. According to their research even if the
AEW is implemented with a riskadjusted discount rate, it cannot capture the option
component embedded in the investments, since riskadjusted discounting at a constant
rate is illequipped to handle situations in which decisions will be postponed until more
uncertainty is resolved.
171
APPENDIX C
OPTIONS PRICING THEORY AND TRADING STRATEGIES
C1 Introduction
Black and Scholes developed a model based on riskfree arbitrage by providing a
closed form solution for the equilibrium price of a European call option. An investor can
create a hedged position, consisting of a long position in the stock and a short position in
the option, whose value does not depend on the price of the stock, but depends only on
time and the values of known constants under the following assumptions (Black and
Scholes 1973):
? The short term interest rate is known and is constant through time.
? The stock price follows a random walk in continuous time with a variance rate
proportional to the square of the stock price. Thus the distribution of possible
stock prices at the end of the finite interval is lognormal. The variance rate of
the return on the stock is constant.
? The stock pays no dividend or other distributions.
? The option is "European", that is, it can only be exercised at maturity.
? There are no transaction costs in buying or selling the stock or the option.
? It is possible to borrow any fraction of the price of a security to buy it or to
hold it, at the short term interest rate.
172
? There are no penalties to short selling. A seller who does not own a security
will simply accept the price of the security from a buyer and will agree to
settle with the buyer on some future date by paying him an amount equal to
the price of the security on that date.
The above ideal conditions do not hold for real world investment decisions,
therefore relaxing one or maybe more of these assumptions is required to make realistic
analysis. Their valuation formulation for a European call option is as follows:
() ( )
( )
( )
21
*
, dNcedxNtxw
ttr ??
?= (C1), where
() ()
ttv
ttvrcx
d
?
?
?
?
?
?
?
?
++
=
*
*2
1
2
1
/ln
(C2)
() ()
ttvd
ttv
ttvrcx
d ??=
?
?
?
?
?
?
?
?
?+
=
*
1
*
*2
2
2
1
/ln
(C3)
In the above expressions, x is the stock price or the price of the underlying asset,
c is the exercise price of the option, t is the current date, ( )txw , is the value of the
option as a function of the stock price x and time t ,
*
t is the maturity date, r is the
continuously compounded risk free rate,
2
v is the variance rate of the return on the stock,
v is the stock price volatility, and ( )dN is the cumulative probability distribution
function for a standardized normal distribution. ( )
1
dxN is the expected value of the stock
price, and
()
()
2
*
dNce
ttr ??
represents the expected riskfree value of the exercise price.
The value of a put option by the same token is calculated as follows (Hull, 2006):
()
( )
( ) ( )
12
*
, dxNdNcetxw
ttr
???=
??
(C4)
173
The graphical representation of Black and Scholes formulation in terms of the
relation between the option value and the stock price for a European call option is
illustrated in the following diagram (Black and Scholes, 1973):
Figure C.1 The Relation Between Option Value And Stock Price
In the above figure, Line A represents the maximum value of the option, where
Line B represents the minimum value of the option. The rationale is that the value option
can neither exceed the value of stock nor be less than the stock price minus the exercise
price, hence it can not be negative for a call option. The respective curves T
1
, T
2
, and T
3
represent the value of the option for successively shorter maturity dates.
It is obvious that
? As the stock price increases the value of the option increases.
? If the time to maturity is very long, then the value of the option is
approximately equal to the stock price (See Line A in Figure C1).
174
? If the time to maturity is very short, then the value of the option will be very
low or zero.
? As the time to maturity decreases the resulting decline in the option value
means an increase in the equity in the hedged position, hence possible losses
are offset by a large change in the stock price.
Hull (2006) discusses that the only problem in implementing equations (C5) and (C13) is
in calculating the cumulative normal distribution function. Although the NORMDIST
function of Microsoft Excel software calculates, he proposes a polynomial approximation
that gives sixdecimalplace accuracy:
()
()
() 0when
0when
1
1
5
5
4
4
3
3
2
21
'
<
?
?
?
?
??
++++?
=
x
x
xN
kakakakakaxN
xN (C5).
where
1
1
x
k
?+
= (C6)
2316419.0=? (C7)
31938153.0
1
=a (C8)
356563782.0
2
?=a (C9)
781477937.1
3
=a (C10)
821255978.1
4
?=a (C11)
330274429.1
5
=a (C12)
()
2/'
2
2
1
x
exN
?
=
?
(C13)
175
The Black and Scholes valuation formulation implies that the stock price fits to a
lognormal distribution since it can not be negative and the return on stock, which is
continuously compounded, is normally distributed. It should also be noted that creating a
riskfree position is always possible since the source of uncertainty for both the stock
price and the option value is the same. The Black and Scholes equations can be derived
by either solving their differential equations or by using the risk neutral valuation,
assuming that the world is risk neutral.
C2 Wiener Processes
The closed form solution referred to as BlackScholesMerton in the previous
chapter generates a hedging portfolio depending on the stock price. Thus both the
movement of the stock price and the change in the value of the stock price require further
investigation.
Any variable whose value changes over time in an uncertain way is said to follow
a stochastic process, which can be classified as discrete time or continuous time (Hull,
2006). The value of the variable changes only at certain fixed points in time through a
discrete time stochastic process, whereas the value of the variable can change at any time
through a continuous time stochastic process.
Stock prices are assumed to follow a specific type of stochastic process, where the
memoryless property of the underlying distribution plays a significant role. The future
price of a stock should not be influenced by its price one month ago, but by the present
price.
176
Suppose we know that the current value and the change in the value for a stock
price follows a standard normal distribution ( )??? , with 0=? and 1=? for one
period. Estimating the change in the value for two periods is the sum of two normal
distributions since two periods follow independent processes because of the Markov
process. The change in the value for two periods will follow a normal
distribution ( )2,0? because the variance of the changes in Markov processes is additive.
As the multiplier of the time period or the length of the consecutive time intervals
decreases and the size of the change in value is proportional to the length of the time
period, the standard deviation becomes much larger than the variance. This stochastic
calculus property translates itself into increased resolution in the pattern of the change in
the variable value as the length of time interval approaches zero.
Hull (2006) defines two intriguing properties of Wiener processes related to the
aforementioned property as follows:
? The expected length of the path followed by the variable z in any time interval
is infinite.
? The expected number of times z equals any particular value in any time
interval is infinite.
The variable z is the formal expression of a variable following a Wiener process,
which is also referred to as Brownian motion. The variable z has the following properties
(Hull, 2006):
? The change z? during a small period of time t? is tz ?=? ? , where ? has a
standard normal distribution ( )1,0? .
177
? The values of z? for any two different short intervals of time, t? , are
independent.
Due to the aforementioned properties, the change in the value of z during a
relatively long period of time, T, consisting of N small time intervals of t? , can be
expressed as follows (Hull, 2006):
() ()
?
=
?=?
N
i
i
tzTz
1
0 ? (C14)
Since ?z follows a Wiener process, ( ) ( )0zTz ? also follows a Wiener process and
is normally distributed with
? Mean of () ( )[]00 =? zTz
? Variance of () ( )[]TtNzTz =?=? 0
? Standard deviation of ( ) ( )[ ] TzTz =? 0
The mean change per unit of time for a stochastic process is known as the drift
rate and the variance per unit of time is known as the variance rate (Hull, 2006). So far
the drift rate of the variable z has been given as zero and the variance rate as 1.0. The
drift rate being zero means that the expected future value of z is equal to its current value.
However a zero drift rate is not realistic. Hence a more generalized Wiener process for a
variable x is defined by Hull (2006) as follows:
bdzadtdx += (C15),
where a and b are constants. If bdz equals zero then the change in the value of x with
respect to the change in time is equal to a. Integrating that equation gives
atxx +=
0
(C16)
178
Hence the generalized Wiener process can be expressed as follows(Hull, 2006):
tbtax ?+?=? ? (C17)
The generalized Wiener process is graphically represented by Hull (2006) as follows:
Figure C.2 Generalized Wiener Process
The only drawback of the above model is that the shareholders are reluctant to expect the
assumption of constant drift rate. Whatever the stock price is, the target increase expected
by the shareholders does not change. Hence Hull (2006) proposes to replace the former
assumption with the assumption that the expected return (i.e., expected drift divided by
the stock price) is constant. Thus Hull (2006) suggests the following continuous time and
discrete time models, respectively:
SdzSdtdS ?? += (C18)
tStSS ?+?=? ??? (C19),
where S is the stock price, ?S is the expected drift rate for some constant parameter ?.
With Hull's (2006) suggested assumption the equation (C18) and (C19) can be expressed
respectively as follows:
179
dzdt
S
dS
?? += (C20)
tt
S
S
?+?=
?
??? (C21)
C3 Trading Strategies
The profit pattern of the portfolios heavily depends on the relationship established
between the options and the underlying assets. Hull (2006) discusses trading strategies
involving both a single option with a stock and combinations of different options with the
underlying assets.
C3.1 Trading Strategies Involving a Single Option and a Stock
The profit patterns generalized by Hull (2006) consist of
? Long position in a stock combined with short position in a call
? Short position in a stock combined with long position in a call
? Long position in a put combined with long position in a stock
? Short position in a put combined with short position in a stock
Suppose there are two portfolios A and B, where portfolio A consists of one European
call option and an amount of cash equal to Ke
rT
and portfolio B consists of one European
put option and a share. Since both have a value of max(S
T
, K) the portfolios have the
same value, where the relationship can be expresses by the putcall parity defined by Hull
(2006):
DKecSp
rT
++=+
?
0
(C22)
180
Where p is the price of a European put, S
0
is the present value of the stock price, c is the
price of a European call, K is the strike price of both call and put, r is the risk free interest
rate, T is the time to maturity of both call and put, and D is the present value of the
dividends anticipated during the life of the options. The shapes of the general profit
patterns described above are respectively as follows:
Figure C.3 The Profit Pattern of a Long Position in a Stock Combined with Short
Position in a Call (Hull 2006)
Figure C.4 The Profit Pattern of a Short Position in a Stock Combined with Long
Position in a Call (Hull 2006)
Profit
S
TK
Profit
S
T
K
181
Figure C.5 The Profit Pattern of a Long Position in a Put Combined with Long
Position in a Stock (Hull 2006)
Figure C.6 The Profit Pattern of a Short Position in a Put Combined with Short
Position in a Stock (Hull 2006)
The profit pattern of a long position in a put combined with long position in a stock
(Figure C.5 by Hull (2006)) is very similar to the profit pattern of a long call option,
which is also explained by equation (C22). The similarity between the profit pattern of
long position in a stock combined with short position in a call and the profit pattern of a
short put can be expressed by the following equation using equation (C23) (Hull 2006):
pDKecS
rT
?+=?
?
0
(C23)
Profit
S
T
K
Profit
S
T
K
182
C3.2 Spreads
Hull (2006) explains the spread trading strategy as the combination of two or
more options of the same type.
A bull spread consists of buying an option with a certain strike price and selling
another option with a higher strike price on the same stock, where the expiration date is
the same for both options. Since a call price always decreases as the stock price increases,
the value of the option sold is always less than the value of the option bought. A bull
spread created from calls requires an initial investment, while the one created from put
options involves a positive upfront cash flow to the investor. Three types of bull spreads
are
? Both options are initially out of the money.
? One option is initially in the money, the other is initially out of the money.
? Both options are initially in the money.
An investor who enters a bull spread expects that the stock price will increase, hence the
bull logic is "buy cheap sell expensive." Thus the bull spread limits the investor's upside
profit as well as the downside risk (Hull 2006).
183
Figure C.7 The Profit Pattern of a Bull Spread Using Call Options (Hull 2006)
Table C.1 Payoff from a Bull Spread Using Call Options (Hull 2006)
Stock Price Range
Payoff from Long
Call Option
Payoff from Short
Call Option
Total
Payoff
S
T
?K
2
S
T
? K
1
(S
T
? K
2
) K
2
? K
1
K
1
< S
T
K
3
S
T
? K
1
S
T
? K
3
2(S
T
? K
2
) 0
K
1
K
3
Profit
S
T
K
2
187
Figure C.12 The Profit Pattern of a Butterfly Spread Using Put Options (Hull
2006)
Table C.6 Payoff from a Butterfly Spread Using Call Options (Hull 2006)
Stock Price Range
Payoff from
First Long
Put Option
Payoff from
Second Long
Put Option
Payoff
from
Short Puts
Total
Payoff
S
T
K
3
K
1
? S
T
K
3
? S
T
0 K
1
+ K
3
? 2S
T
A calendar spread is created by selling an option with a certain strike price and
buying a longer maturity option of the same type with the same strike price. The
important feature is that options have the same strike price but different maturity dates. A
calendar spread requires an initial investment since the option becomes more expensive
as the maturity date gets longer. A calendar spread is profitable if the strike price of the
option with the shorter maturity date is close to the strike price of the option with the
longer maturity date. A neutral calendar spread involves a strike price close to the current
strike price, a bullish calendar spread involves a higher strike price, and a bearish
calendar spread involves a lower strike price (Hull 2006).
K
1
K
3
Profit
S
T
K
2
188
A reverse calendar spread involves buying a short maturity option and selling a long
maturity option. It is profitable only if the stock price of the short maturity option is well
above or well below its strike price (Hull 2006).
Figure C.13 The Profit Pattern of a Calendar Spread Using Call Options (Hull
2006)
Table C.7 Payoff from a Calendar Spread Using Call Options (Hull 2006)
Stock Price Range Payoff from Long Call Payoff from Short Call Total Payoff
S
T
K S
T
? K 0 S
T
? K
Figure C.14 The Profit Pattern of a Calendar Spread Using Put Options (Hull
2006)
Profit
K
Profit
K
S
T
S
T
189
Table C.8 Payoff from a Calendar Spread Using Put Options (Hull 2006)
Stock Price Range Payoff from Long Put Payoff from Short Put Total Payoff
S
T
K K ? S
T
0 K ? S
T
The final spread is called a diagonal spread, which involves buying and selling
options with different strike prices and maturity dates (Hull 2006). Thus the profit ranges
can be extended.
C3.3 Combinations
A popular combination is a straddle, which involves buying a call and a put with
the same strike price and maturity date. A straddle is profitable if the stock price is well
above or well below the strike price. An investor enters a straddle if bidirectional large
moves in the stock price are expected. A spread can also be created by selling a call and a
put, which is called a top straddle or straddle write, whereas the former is called a bottom
straddle or straddle purchase. A top straddle is very risky since the loss is unlimited (Hull
2006).
Figure C.15 The Profit Pattern of a Bottom Straddle (Hull 2006)
Table C.9 Payoff from a Straddle (Hull 2006)
Profit
S
T
K
190
Stock Price Range Payoff from Call Payoff from Put Total Payoff
S
T
K S
T
? K 0 S
T
? K
A strip consists of a long position in one call and two puts with the same strike
price and maturity date. The investor expects that a big stock price decrease is more
likely than a big stock price increase (Hull 2006).
Figure C.16 The Profit Pattern of a Strip (Hull 2006)
A strap consists of a long position in two calls and one put with the same strike
price and maturity date. The investor expects that a big stock price increase in more likely
than a big stock price decrease (Hull 2006).
Profit
K S
T
191
Figure C.17 The Profit Pattern of a Strap (Hull 2006)
A strangle or a bottom vertical combination involves buying a put option and a
call option with the same maturity date and different strike prices. An investor who enters
a strangle expects a large bidirectional price move. A strangle is similar to a straddle,
where the downside risk is less than the straddle (Hull 2006). It should be noted that as
the strike prices get further apart the downside risk decreases, and as the stock price
increases the profit increases. If the combination involves selling a put option and a call
option with the same maturity date and different strike prices, it is called a top vertical
combination. It is profitable when the investor does not expect large stock price moves.
However it is a risky trading strategy involving unlimited potential losses (Hull 2006).
Figure C.18 The Profit Pattern of a Bottom Vertical Combination (Hull 2006)
Profit
K S
T
K
1
K
2
Profit
S
T
192
Table C.10 Payoff from a Bear Spread Using Call Options (Hull 2006)
Stock Price Range Payoff from Call Payoff from Put
Total
Payoff
S
T
?K
1
0 K
1
? S
T
K
1
? S
T
K
1
< S
T