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Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 1
COMPOUND OPTIONS: A REAL OPTIONS APPLICATION TO
A FOOD BUSINESS
BRIAN C. BRIGGEMAN, JOSHUA D. DETRE, AND ALLAN W. GRAY1
Real options analysis integrates uncertain outcomes of investment decisions. This framework is used to analyze a new product launch from an agricultural business to a market with multiple uncertainties. Findings indicate a more accurate valuation of the investment when real options and their interactions with the investment are considered. Key words: real options, simulation, uncertainty, strategic management
Introduction
The changing landscape of agriculture has forced those businesses that have a direct linkage
to the agriculture sector to reassess the manner in which they make operational decisions. These
decisions include but are not limited to the following: what is the appropriate price to license a
new technology or a brand, what is the maximum or optimal amount of money that should be
invested in the research and development of a new product, what is the value of being able to
switch input suppliers and/or outsourcers at any time, and how do you value the flexibility of
having the option to defer entry into market.
In today’s agriculture, these operational decisions can no longer be made using the traditional
Net Present Value (NPV) analysis that once dominated corporate strategy. Trigeorgis (1988)
outlines two key areas of value which are not accounted for within a NPV analysis: (1) the
ability of the manager to make operational decisions throughout time or the value of flexibility
1 Brian C. Briggeman and Joshua D. Detre are graduate students in the Department of Agricultural Economics, Purdue University. Allan W. Gray is an associate professor Department of Agricultural Economics, Purdue University. Paper presented during the August 1st - 4th 2004 AAEA meetings in Denver, Colorado. Copyright © 2004 by Brian C. Briggeman, Joshua D. Detre, and Allan W. Gray. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 2
(e.g. defer, abandon, or expand a given project), and (2) the interdependencies of these decisions
on the investment throughout time (e.g. entrance of competition into the market). The
framework needed to address the shortcomings of a traditional NPV analysis must be an
integrated framework that incorporates multiple forms of uncertainty in conjunction with the
flexibility to exercise decisions at any point in time. This examines a simulation approach to real
options, which serves as the integrated framework giving an agribusiness the capabilities to make
these types of decisions. In particular, the decision by Fresh Juice Inc. to either launch a new
product today or wait and see how the market unfolds. In addition to this decision, Fresh Juice
Inc. must also decide whether to bottle the new juice product with a facility built and operated by
Fresh Juice Inc. or to out-source bottling with a co-packer.
Real options are an integrated approach to options theory using financial theory,
economic analysis, management and decision science, statistics, and econometrics. An
important aspect of real options theory is the ability to account for the dynamics and uncertainty
of business decisions. Traditional NPV analyses typically assume a static decision making
process with no recourse in changing those decisions while real options allow the business to
make strategic decisions under uncertainty. Real options give the management flexibility to
assimilate and process these uncertainties over time. One can think of real options as a learning
model that allows the management to make informed and accurate strategic decisions over the
course of time.
Trigeorgis (1988) defines real options as being the owner of a discretionary investment
opportunity who has the right to the investment’s present value of cash flows by making some
initial outlay on or before the termination date of that investment. He later develops a theoretical
framework in which he demonstrates the value of managerial flexibility when strategic decisions
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 3
are made throughout time. Bernake (1983) developed a framework to account for the effects of
irreversibility and uncertainty on investments when those investments are cyclical in nature. He
posits that incorporating the flow of information throughout time can create a positive incentive
to undertake the investment; in essence the manager takes a “learning-by-doing” approach to the
investment. Dixit (1989) and McDonald and Siegel (1986) consider a real options approach to
investment under uncertainty wherein they look at optimal trigger values indicating when a firm
should enter or exit the given investment. Copeland and Keenan (1998) employ real options to a
case study which looks at the decision to build or not to build a factory which has a significant
amount of uncertainty surrounding its profits. Luehrman (1998) introduces a NPV metric that
links corporate discounted cash flow (DCF) methods to the classic (Black-Scholes) Model. The
motivation for Luehrman’s NPV metric is to circumvent the complex mathematical calculations
necessary for a real options analysis by allowing managers a way to introduce uncertainty into
their preexisting DCF models. Each of these contributions to the real options literature
highlights the importance of agribusinesses adopting a real options framework or at least the
mentality of real options when making investment decisions.
Fresh Juice Inc., adopted from Gray (2000), is in the process of launching a new GMO
juice into the marketplace. In launching this new product, Fresh Juice Inc. has many questions
about that product or real options theory is applied to disentangle this web of uncertainty. Two
areas of uncertainty are considered given their importance to a new product launch. 1) The time
of entry of the product into the market. A growth or expansion option allows Fresh Juice Inc. to
place a value on first mover advantages within the given market. Conversely, Fresh Juice Inc.
potentially has value in waiting for some of the uncertainties to be revealed which is captured by
the option to defer. 2) The ability of Fresh Juice Inc. to use alternative technologies, which
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 4
directly affect the product. An example would be a flexible production contract. The firm can
terminate the production contract and move to a least cost method of production at any time.
Valuation of this is done through the use of a switching option.
Although these options can be valued independently, there exist interdependences
between these options. These interactions create additional option value to the firm and must be
accounted for. The flexibility of altering production processes, i.e. switching option, has a direct
effect upon the valuation of the option to grow or defer. This relationship can be viewed as a
staged investment problem, which revolves around the asset specificity of the capital outlay.
Initial design choice of the production processes allows management to choose outsourcing or
in-house production when dealing with large amounts of uncertainty and asset specificity.
Without this initial design choice, the sequential interdependences among the options are
overlooked and can lead to incorrect investment decisions by the Fresh Juice Inc.
From here we look at the methodology used to analyze the decision faced by Fresh Juice
Inc. Next is a discussion of the data collected from Fresh Juice Inc. followed by the results of
the real options analysis. Finally, the conclusions of the analysis are addressed and their
implications towards further use in the agribusiness literature.
Methodology/Data
Option to Defer
Options are widely used within financial markets so as to allow uncertainty surrounding
the given stock/commodity to unfold over time while maintaining the option to enter the market
at a specified price. It is apparent when financial options should be utilized in a firm’s risk
management strategy however, real options are not as noticeable and can be applied in situations
in which a financial option does not exist. Dixit and Pindyck (1994), state that real options are
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 5
applicable in situations where uncertainty, irreversibility, and the owner of the real option can
delay entry. Thus the option to defer can be thought of as a strategic option that gives the owner
or decision maker the ability to hedge their investment decision against any downside risk.
In keeping with the analogy between financial options and real options, the option to
defer can be thought of as a call option. (Mun 2002) presents a slightly adjusted Black-Scholes
model so as to use the model as an option to defer:
(1) ( )
Option to defer S d Xe d
d
S
XT r
T
d d T
tr T
of
f= −
=
+ +
= −
−Φ Φ( ) ( )
ln
1 2
1
2
2 1
12σ
σσ
Where S is the value of the underlying asset and is indexed on time t; Φ is the cumulative
standard normal distribution function; X is the cost of developing the intangible asset; rf is the
risk free rate; σ is the standard deviation or volatility of cash flows throughout the life of the
investment; T is the economic life of the option to defer.
A limitation of modeling the option to defer via the Black-Scholes model is seen in the
underlying assumptions of the Black-Scholes model. The main assumption is that the price
structure of the intangible asset follows a Geometric-Brownian Motion with a constant drift and
volatility parameters. A Markov-Wiener stochastic process is assumed to represent the motion
portion with the following derivation:
(2) dS uSdt SdZ
dZ dt
= +
=
σε
dZ is a Weiner process; u is the drift rate; σ is the volatility measure. Other assumptions of the
Black-Scholes model are an efficient market with no riskless arbitrage opportunities, no
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 6
transaction cost, no taxes, and price changes are continuous and instantaneous. All of these
assumptions are subject to scrutiny especially when applied to a real options context.
Figure 1 provides a graphical demonstration on how a final analysis would appear if the
Black-Scholes model were applied to an option to defer. Given the uncertain fluctuations
surrounding an investment, the option to defer brings additional value to the investment as
shown in the Figure 1. The standard DCF approach has more risk, measured as the standard
deviation (σ) of returns, and a lower average percentage return (µ) when compared to the real
options approach. Elimination of downside risk is highlighted here through the real options
approach because the owner of the option to defer would not execute the option if the returns of
the investment were a worst case scenario over time.
By construction of the Black-Scholes model, the option value cannot take on a negative
value. This is an issue that could cause an owner of an option to defer to “over-value” his or her
investment. For example, an industry leader may feel that a given investment has too much
uncertainty surrounding its success. Therefore, an option to defer is calculated and the results
indicate that there is value in waiting to see how the market unfolds. By waiting to proceed with
the investment, the company may have missed out on any first mover advantages and thus are
now following the market if they do decide to go forward with the investment.
Switching Option
As technology or terms of production change, agribusinesses must reassess if their
current production methods are the least cost method. Mun (2002) addresses this issue via a
switching option. This method puts a value on the firm’s ability to change from one technology
to the next throughout time. Calculating this option is as follows:
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 7
(3)
−
+Φ−
−
+Φ−
+
+Φ
T
T
SX
S
XST
T
SX
S
ST
T
SX
S
Sσ
σ
σ
σ
σ
σ2)1(
ln(2)1(
ln(2)1(
ln(2
1
2
1
2
1
2
1
2
1
2
2
S2 represents the new technology asset value; S1 is the current technology asset value; X is a
proportional cost relative to S1; all other notation holds from the option to defer discussion.
Hence, the switching option is interpreted as the optimal time to switch is when the new
technology asset value is greater than the current technology asset value plus any associated
costs with switching. It is interesting to note that as the volatility of S2 increases relative to S1,
the value of the switching option increases. That is as the uncertainty of the cash flows
surrounding the new technology increases; value is created for the switching option owner to
have the ability to change technologies over time.
Compound Option
A compound option considers the value of an option being contingent upon other options
that are executed prior to or during the valuation of the current option. Prior decisions affect the
value of the underlying investment and therefore making future options conditional on exercised
past options. Simply adding up the values of all options considered can dramatically overstate
the total value of the investment and result in incorrect strategic decisions being made.
Trigeorgis (1993) models multiple real options and finds that the interactions of real options
depend on the type, separation of when the options occur, and order in which the options occur.
These interactions can have a positive or negative impact upon the valuation of the investment,
i.e. one option may dominate and actually negate the value of another option we examined in the
context of a compound option. Combining different real options gives management the
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 8
flexibility to see the economic value that their decisions will have on the investment throughout
time.
Data and Empirical Model
Fresh Juice Inc. (Fresh Juice Inc. is a fictitious name, but the data underlying the case is
true, the name of the company is change to protect the confidentiality of the firm) is a leader in
the finished consumer juice industry and has been producing and distributing competitively
priced high quality fruit juices to leading national grocery chains for a number of years. While
demand for fruit juice has remained steady over the last 10 years, the increase in the number of
competitors continues to place pressure on Fresh Juice Inc.’s leader status. The intense
competition for shelf space and the continuing fragmentation of consumer’s tastes and
preferences has kept competitors battling each other on price, advertising, and packaging just to
maintain their market share. The product development team’s latest product, GMO Juice (this is
an internal name for the product, the actual name for the product has not been finalized), just
may be the ticket to give Fresh Juice Inc. the new competitive advantage they need in an industry
that has not seen an innovative product in fifteen years.
To analyze the decision of introducing the new GMO Juice to the market a spreadsheet
model was developed in Microsoft Excel to incorporate the uncertainty surrounding the decision.
The @Risk add-in for Microsoft Excel is utilized to run Monte Carlo simulations, with 5,000
iterations for each scenario. Therefore, the model calculates the likelihood of profitability and
the NPV of the project over a ten-year period to determine which alternative produces the
highest payoff for the firm under scenario analysis. This approach to valuing an investment
through simulation techniques was employee by Hyde, Stoke, and Engel (2003).
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 9
- Market Size
The current fruit juice market is about 10,000,000 cases annually. Management believes
there is a 90% chance the market for GMO Juice is between 2,250,000 and 2,750,000 cases
annually. Initial analysis assumes 2,500,000 cases as the most likely but the aforementioned
interval recognizes the uncertainty in this estimate of market size. To further supplement these
estimates, Fresh Juice Inc. recently launched a product (ENER Juice) which has similar
characteristics, both in type of juice and market acceptance, to the GMO Juice being considered.
Table 1 outlines the historical information of ENER Juice.
How many cases of GMO juice will be demanded in the market place in each year is
estimated by using ENER Juice data. To calculate GMO Juice demand we take what each
historical year’s sales were for ENER Juice as a percent of the estimated total market size of
2,500,000 of ENER Juice. We use percentages to estimate the following regression equation:
(4) 2
21 ttyt ββα ++=
where yt is the percentage of the total market for each historical year’s sales, t is time, α is a
constant, β1 is a slope coefficient on time, and β2 is a slope coefficient on time squared. This
quadratic regression equation fits the data and produces the classic product adoption curve shape.
- Market Share
Market share is certainly a critical variable in determining the profitability of GMO juice.
It is understood that market share is closely related to the actions of your competitors. The
question is how much impact does each competitor have? Table 2 contains Fresh Juice Inc.’s
estimates for both the relative powers of each competitor and the likelihood (by year for the first
5 years) of each competitor entering the market for GMO Juice.
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 10
Competitor number one is a relatively small company with a power rating of only 0.27.
Fresh Juice Inc. believes that this company does not have the products in place to enter this
market in the first year; however they expect the company to be moving fairly rapidly with a 30
percent increase in the probability of entering the market in each of years 2 through 4 with a
certain entry into the market by year 5. Competitor number 2 is the smallest of the competitors
with a power rating of 0.25. This competitor’s focus does not seem to fit the GMO juice market
and thus the likelihood of their entry into the market is not nearly as strong as the other
competitors. Of primary interest are competitors 3 and 5. These are the two strongest
competitors that Fresh Juice Inc. faces and both of them are actively pursuing the market for
GMO juice. Competitive intelligence has discovered that competitor 3 is gearing up and will
enter the market at the same time Fresh Juice Inc. plans to enter the market. Apparently,
competitor 5 has been a little slower in developing their product but still has a good chance of
entering the market in year 1 (80% probability of entering the market) and will certainly enter the
market by the second year. The final competitor, number 4, will likely be later in entering the
market but is expected to compete by year 5.
Using the competitor information from Table 1 which contains the historical market share
for ENER Juice, we model the future market share of GMO Juice. Conjoint analysis is utilized
to estimate competitor strength relative to our strength (which is set at 1.0). The following
method for modeling market share’s response to competition is described in Powell (1997).
(5)
tt
11
Market in the companies ofstrength Total
1
Market in the companies ofstrength Total
StrengthOur
))(1(
==
−−+= −−
t
tttt
L
MLcMM
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 11
where Mt is our firm’s share of the market in time period t; Lt is our firm’s long-term share of
the market, which is base on our market power relative to the power of all firms in the market
place; (1-c) is a parameter, which measures, in rough terms, the amount of time it takes our firm
to “slide” towards its long-term share given the market share it encountered during the last
period. In order to estimate the aforementioned parameter we estimate the following regression
equation based on ENER Juice information:
(6) ))(1( 11 −− −−=− tttt MLcMM - Prices
To determine the prices to be received for each case of GMO Juice from the retailers, we
use the information on ENER Juice to forecast the price for GMO juice. The following elasticity
equations are used to estimate the price of any product:
(7) 1%,1%
)%%1(
11
1
−=∆−=∆
∆+∆+=
−−
−
t
t
t
t
dstt
S
SS
D
DD
SeDePP
( ) ( )SeDeP
Pds
t
t ∆+∆=
−
−
%ˆ%ˆ11
Pt is the price in period t; es is the elasticity of supply; ed is the elasticity of demand; D is
Demand; S is Supply. Po is given in Table 1, D is calculated in equation 4 and S is based on the
capacity of the industry which is calculated in equations 5 and 6. By using ENER Juice data, the
demand and supply elasticities are estimated through a regression analysis.
- Costs
GMO Juice will require a $150,000 investment in new extractor equipment so as to
extract the juice from the specialized fruit and mix in the necessary ingredients for enhanced
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 12
taste and shelf life. In addition, the cost of a new line to bottle and label the juice has been
estimated to cost $1,225,000 for an initial investment cost of $1,375,000. Variable costs per unit
for bottling the GMO Juice ourselves are determined based on the following cost equation:
(9) 2000006.0007.073.2 qqAVCq +−=
Here q is in 1,000 units so to get the variable cost per unit we take the volume sold and divide by
1000 and then use the above equation. For the Co-packing option, variable costs per unit are
$3.05 per bottle constantly. For the “in-house” option, fixed costs are $285,000. For the co-pack
option, there are no fixed costs. Advertising costs have been estimated by the marketing
department and are independent of volume and the type of bottling operation chosen.
Results
The results of the base model for both the bottling and co-packing scenarios yield a
negative expected NPV, of -$540,635 and -$44,823 respectively (Table 1). Analysis also
indicates that the Co-Pack option will have at least a 25% chance of an NPV exceeding
$765,014, while the Bottling option will generate an NPV $292,177 or less 75% of the time. This
provides an indication that the GMO Juice project, with the options currently available to Fresh
Juice Inc. Inc., is a project that is not worth undertaking regardless of the bottling method
chosen.
The next result concerns the introduction of the switching option. The switching option
allows Fresh Juice Inc. to switch bottling methods from the Co-Pack option to the Bottling
option anytime over the 10-year production period. It should be noted that we begin with the
assumption that neither investment has been made therefore there are no sunk costs of
production. The switch in production methods occurs when the expected cost of producing a
case via the Co-Pack option exceeds the expected cost of producing a case with the Bottling
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 13
Option. The switching option does not allow for Fresh Juice Inc. to switch back to the Co-Pack
option once they begin producing GMO Juice in-house. When examining the results of the
switching option, production is shifted to the Bottling option in all 5000 iterations by the fifth
year of production. In the second year of production approximately 44% of the iterations
indicate that the production has shifted to the Bottling option, in both years 3 and 4 of production
over 90% of the iterations suggest that production should be done by the Bottling option. These
results support our a priori expectations that as the total market size increases and our share of
the total market grows, the large fixed production costs associated with the Bottling option are
spread out over more cases driving costs per case below that of the Co-Pack option. Thus, in the
beginning the low volume of GMO Juice being purchased in conjunction with the cost structure
of the co-packer and bottling in house makes the Co-Pack option the most attractive for the first
two years of production.
The ability to switch production methods now makes GMO Juice a profitable project
with an expected NPV of $22,265 as shown in Table 4. Having the ability to switch production
methods allows Fresh Juice Inc. to utilize a production method that aligns more tightly with the
total market size and GMO juices share of the market. The question then becomes what is the
value of switching, or put another way, what is the value of the option associated with switching
production methods. The answer is the difference between the expected NPV for a fixed
production method and the NPV of being able to switch production methods. For Bottling, the
switching option is worth $563,200 and for Co-Pack the switching option is worth $67,388. The
value of this option can be equated to what Fresh Juice Inc. would be willing to pay the co-
packer to get out of their contract. In essence, once the information is revealed (market demand,
competitor capacity, and market share) that bottling GMO Juice in house is less expensive the
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 14
relying on a co-packer to bottle GMO Juice, Fresh Juice Inc. would terminate the aforementioned
contract and begin in-house production.
The next set of results concern the option of deferring entry into the market. A firm
typically defers entry into a market because there is a degree of uncertainty surrounding the
market that they are uncomfortable with. By waiting the firm is hoping that information will be
revealed that addresses the uncertainties in the market providing the firm with a go or no go
decision on entering the market. The value of the deferment or delay option can be thought of as
the amount of money the firm would be willing to pay someone i.e. the co-packer to guarantee
the contract parameters that are available for entering the market from the beginning and/or a
guaranteed price on the equipment that will be used in the production of GMO Juice.
Our results for the deferment option are rather intriguing and do not agree with our a
priori expectations which is based upon previous real options literature which says there is value
in waiting when uncertainty is present in the market. However, the simulation model indicates
that for Fresh Juice Inc. this assumption is incorrect. Tables 5 and 7 indicate that the expected
NPV although negative for both the Co-Pack and Bottling option is negative for entry at the
initial start of the market; it is higher than that of entering in any other year. This result arises
because GMO Juice controls a dominate market share and is one of the leading producers in the
juice market. By entering into the market at the initial stages, Fresh Juice Inc. is able to capture
first mover advantages. These first mover advantages can be attributed to the large initial market
share of 49% and the capacity power of Fresh Juice Inc. By grabbing such a large initial market
share, well above Fresh Juice Inc.’s 33% expected long term share, Fresh Juice Inc. is able
survive even though there is very little expected demand in the first few years of the market.
When entering anytime between years 1 through 4 expected NPV is over a one million dollar
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 15
loss, and only entering in year nine and ten does the expected NPV greater than entry at time
zero for the bottling option (Table 5). This occurs for two reasons: (1) the market has reached
maturity which creates a large and stable demand for the product and (2) Fresh Juice Inc. is able
sell off investments for a large salvage value. GMO Juice is unable to earn a positive NPV
because being a follower into the market GMO Juice enters below their long term market share,
i.e. they can not enter the market and automatically gain their market share, they must gradually
take market share away from the competition. The same results occur for the co-pack option
(Table 7).
The option value for deferment is negative for both the bottling and co-pack options until
the 9th and 10th year, when the option values are positive (Table 6 and 8). Furthermore, Fresh
Juice Inc. would never choose to enter the market because the NPV is still negative, even when
utilizing a deferment option. Although, if Fresh Juice Inc. was forced to enter or had already
make the commitment to contract with a co-packing company or purchased the equipment to
produce GMO Juice, they would wait to enter in year 10, which has the highest expected NPV.
The next option examined is the compound option, which is the combination of the
switching and delay option. It should be noted that a compound option, is not an additive option
i.e. one cannot simply add up the option values of the switching option and the deferment option
to get the value of the compound option. The compound option is dominated by the first mover
advantages associated with Fresh Juice Inc's market power and the switching option. Table 9
shows that the best time for GMO Juice to enter the market is at time zero. This where expected
NPV is $22,256 which is the same expected NPV as the switching option only. As with the
deferment option, it is observed that there are no advantages to waiting to enter the market for
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 16
Fresh Juice Inc., because of their dominant market position, however the ability to switch
production processes still maintains value.
Conclusions
Our results demonstrate that real options have value as a strategic proactive approach to
investment management, but it is not an analysis tool that is meant to be used blindly. The
results from our model indicate that there is value to having the ability to switch production
process i.e., Fresh Juice Inc. would be willing to pay to have flexibility in their production
process. However, the value of deferring entry is not valuable to Fresh Juice Inc. until year nine
or ten, because of the market position of Fresh Juice Inc. This result is in contrast to what is
often obtained through real options analysis using calculus which almost always indicates that
the value of waiting is positive when there is uncertainty in the market. By being able to capture
the effects of market power and first mover advantages in the simulation model, we have been
able to demonstrate that real options analysis has value but the value is not always positive as
traditional literature has indicated.
The real options analysis using simulation as a method to determine the true value of the
option is fruitful for further research. One possible extension of this research would be to
compare the results from the simulation model to that of a real options analysis that uses a
calculus based approach to solve for the values of the switching, delay, and compound options.
Another possible extension to this research would be to conduct real options analysis with other
data sets to test for the robustness of real options analysis conducted via simulation.
There are two key limitations to our research: the first is that we model supply as a
capacity system and that the firms can meet all demand market. These limitations are the result
of the data that was available for the model since the simulation model uses historical and
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 17
propriety information. The supply capacity is measured relative to Fresh Juice Inc. which is a
power of 1 and is not an actual capacity number for each firm.
Briggeman, Detre, and Gray Compound Options: A Real Options Application to a Food Business 18
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ggem
an, D
etre
, and
Gra
y
C
ompo
und
Opt
ions
: A
Rea
l Opt
ions
App
lica
tion
to a
Foo
d B
usin
ess
19
Tab
le 1
: H
isto
rica
l inf
orm
atio
n fo
r E
NE
R J
UIC
E
Tot
al A
nnua
l O
ur F
irm
's
Our
Fir
m's
N
umbe
r of
C
apac
ity/
Pow
er
Yea
r M
arke
t Sal
es
Sale
s Sh
are
Com
petit
ors
of a
ll C
ompe
titor
s P
rice
1985
42
9,88
5 42
9,88
5 1.
00
0 0.
00
2.88
19
86
719,
087
719,
087
1.00
0
0.00
3.
30
1987
97
0,38
0 97
0,38
0 1.
00
0 0.
00
3.62
19
88
1,04
9,53
7 1,
011,
850
0.96
1
0.27
2.
84
1989
1,
600,
187
1,45
1,47
7 0.
91
1 0.
27
2.73
19
90
1,78
8,93
3 1,
479,
509
0.83
2
0.52
2.
49
1991
1,
716,
579
1,26
4,33
3 0.
74
3 1.
12
1.55
19
92
1,58
5,35
9 1,
069,
566
0.67
3
1.12
1.
58
1993
1,
888,
628
1,19
3,08
8 0.
63
4 1.
48
1.46
19
94
1,68
9,30
9 89
2,34
4 0.
53
4 1.
48
1.49
19
95
1,65
4,92
0 84
6,66
8 0.
51
4 1.
48
1.64
19
96
998,
333
391,
218
0.39
5
2.03
1.
17
1997
1,
163,
044
447,
395
0.38
5
2.03
1.
31
1998
90
4,73
6 29
7,39
7 0.
33
5 2.
03
1.37
19
99
685,
750
226,
397
0.33
5
2.03
1.
49
Bri
ggem
an, D
etre
, and
Gra
y
C
ompo
und
Opt
ions
: A
Rea
l Opt
ions
App
lica
tion
to a
Foo
d B
usin
ess
20
Tab
le 2
: R
elat
ive
Pow
er o
f C
ompe
tito
rs a
nd P
roba
bilit
y of
Com
peti
tor
Ent
ry
R
elat
ive
Prob
abili
ty A
ssig
ned
to E
ntry
in Y
ear:
Fi
rm
Pow
er
1 2
3 4
5 1
0.27
0.
00
0.30
0.
60
0.90
1.
00
2 0.
25
0.00
0.
10
0.20
0.
30
0.40
3
0.60
1.
00
1.00
1.
00
1.00
1.
00
4 0.
36
0.00
0.
25
0.55
0.
75
1.00
5
0.55
0.
80
1.00
1.
00
1.00
1.
00
Tab
le 3
: N
PV
for
Bas
e Sc
enar
ios
and
the
Swit
chin
g O
ptio
n
B
ottl
ing
Co-
Pac
k Sw
itch
ing
Opt
ion
Stat
isti
cs
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
M
ean
($54
0,63
5)
($44
,823
) $2
2,56
5
Stan
dard
D
evia
tion
$1
,297
,314
$1
,232
,898
$1
,262
,909
5%
($2,
495,
005)
($
1,90
5,13
0)
($1,
861,
560)
25
%
($1,
465,
734)
($
922,
617)
($
888,
854)
50
%
($65
3,56
3)
($14
8,96
0)
($89
,112
) 75
%
$292
,177
$7
65,0
14
$831
,268
95
%
$1,7
93,2
81
$2,1
92,8
65
$2,2
74,1
36
Bri
ggem
an, D
etre
, and
Gra
y
C
ompo
und
Opt
ions
: A
Rea
l Opt
ions
App
lica
tion
to a
Foo
d B
usin
ess
21
Tab
le 4
: V
alue
of
the
Swit
chin
g O
ptio
n fo
r th
e C
o-P
ack
and
Bot
tlin
g Sc
enar
io
Val
ue o
f t
he
Dif
fere
nce
of t
he
Sw
itch
ing
Opt
ion
Sw
itch
ing
Opt
ion
at t
he M
ean
fr
om a
Zer
o N
PV
B
ottl
ing
$5
63,2
00
$22,
565
C
o-P
ack
$67,
388
$2
2,56
5
Tab
le 5
: N
PV
for
the
Def
erm
ent
Opt
ion
Und
er t
he B
ottl
ing
Scen
ario
B
ottl
ing
Bot
tlin
g B
ottl
ing
Bot
tlin
g B
ottl
ing
Bot
tlin
g B
ottl
ing
Bot
tlin
g B
ottl
ing
Bot
tlin
g B
ottl
ing
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
E
ntry
Yea
r M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
0
1 2
3 4
5 6
7 8
9 10
Mea
n ($
540,
635)
($
3,10
6,84
6)
($2,
984,
794)
($
2,44
5,96
1)
($1,
932,
314)
($
1,46
8,60
9)
($1,
086,
093)
($
776,
431)
($
543,
491)
($
329,
478)
($
134,
427)
Std
. Dev
$1
,297
,314
$7
62,3
61
$865
,498
$6
10,3
54
$437
,062
$3
22,3
03
$234
,862
$1
56,7
60
$91,
550
$4
3,17
2
$12,
982
5%
($2,
495,
005)
($
4,24
7,62
9)
($4,
560,
386)
($
3,48
9,73
2)
($2,
620,
826)
($
1,95
0,86
6)
($1,
434,
658)
($
1,00
7,45
4)
($67
6,90
3)
($39
2,37
8)
($15
3,67
2)
25%
($
1,46
5,73
4)
($3,
648,
234)
($
3,46
8,02
3)
($2,
851,
680)
($
2,25
1,69
2)
($1,
704,
023)
($
1,25
9,09
4)
($88
9,09
1)
($60
9,41
1)
($36
0,42
2)
($14
3,59
8)
50%
($
653,
563)
($
3,18
1,26
3)
($2,
893,
414)
($
2,42
6,87
2)
($1,
948,
156)
($
1,49
5,41
7)
($1,
107,
333)
($
791,
414)
($
551,
591)
($
333,
562)
($
135,
555)
75%
$2
92,1
77
($2,
613,
721)
($
2,41
0,99
1)
($2,
037,
345)
($
1,65
0,94
4)
($1,
265,
609)
($
941,
522)
($
680,
858)
($
488,
283)
($
303,
666)
($
126,
703)
95%
$1
,793
,281
($
1,75
0,92
9)
($1,
680,
224)
($
1,46
1,12
5)
($1,
174,
872)
($
898,
623)
($
661,
943)
($
492,
888)
($
376,
517)
($
250,
192)
($
111,
002)
Bri
ggem
an, D
etre
, and
Gra
y
C
ompo
und
Opt
ions
: A
Rea
l Opt
ions
App
lica
tion
to a
Foo
d B
usin
ess
22
Tab
le 6
: V
alue
of
the
Def
erm
ent
Opt
ion
Und
er t
he B
ottl
ing
Scen
ario
V
alue
of
the
V
alue
of
the
Def
erm
ent
Opt
ion
D
efer
men
t O
ptio
n
at
the
Mea
n
at t
he M
ean
B
ottl
ing
Yea
r 0
$0
($54
0,63
5)
Bot
tlin
g Y
ear
1 ($
2,56
6,21
1)
($3,
106,
846)
B
ottl
ing
Yea
r 2
($2,
444,
160)
($
2,98
4,79
4)
Bot
tlin
g Y
ear
3 ($
1,90
5,32
6)
($2,
445,
961)
B
ottl
ing
Yea
r 4
($1,
391,
679)
($
1,93
2,31
4)
Bot
tlin
g Y
ear
5 ($
927,
974)
($
1,46
8,60
9)
Bot
tlin
g Y
ear
6 ($
545,
459)
($
1,08
6,09
3)
Bot
tlin
g Y
ear
7 ($
235,
797)
($
776,
431)
B
ottl
ing
Yea
r 8
($2,
856)
($
543,
491)
B
ottl
ing
Yea
r 9
$211
,156
($
329,
478)
B
ottl
ing
Yea
r 10
$4
06,2
08
($13
4,42
7)
Tab
le 7
: N
PV
for
the
Def
erm
ent
Opt
ion
Und
er t
he C
o-P
ack
Scen
ario
C
o-P
ack
Co-
Pac
k C
o-P
ack
Co-
Pac
k C
o-P
ack
Co-
Pac
k C
o-P
ack
Co-
Pac
k C
o-P
ack
Co-
Pac
k C
o-P
ack
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
E
ntry
Yea
r M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
0
1 2
3 4
5 6
7 8
9 10
Mea
n ($
44,8
23)
($2,
103,
905)
($
1,80
1,50
3)
($1,
398,
532)
($
1,00
4,14
4)
($65
5,93
7)
($38
9,38
5)
($20
1,29
2)
($10
2,74
9)
($41
,651
) ($
11,0
47)
Std.
Dev
$1
,232
,898
$7
28,3
59
$870
,216
$6
03,7
89
$429
,892
$3
16,2
60
$230
,530
$1
54,3
47
$90,
706
$4
3,02
9
$13,
000
5%
$0
($3,
205,
236)
($
3,43
8,84
1)
($2,
455,
703)
($
1,70
7,94
9)
($1,
141,
984)
($
738,
838)
($
434,
796)
($
239,
188)
($
106,
252)
($
30,1
06)
25%
$3
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
($
938,
540)
50%
$0
($
2,15
0,73
3)
($1,
664,
903)
($
1,35
0,21
3)
($1,
007,
633)
($
671,
936)
($
401,
761)
($
211,
156)
($
110,
083)
($
45,2
67)
($12
,338
)
75%
($
527,
420)
($
1,64
2,43
7)
($1,
217,
571)
($
990,
031)
($
715,
496)
($
452,
375)
($
241,
801)
($
104,
776)
($
47,6
73)
($15
,814
) ($
3,33
9)
95%
($
1,90
5,13
0)
($84
0,22
1)
($54
6,42
1)
($44
6,61
2)
($28
2,74
9)
($10
4,81
8)
$21,
738
$7
4,68
0
$59,
048
$3
6,45
6
$12,
629
Bri
ggem
an, D
etre
, and
Gra
y
C
ompo
und
Opt
ions
: A
Rea
l Opt
ions
App
lica
tion
to a
Foo
d B
usin
ess
23
Tab
le 8
: V
alue
of
the
Def
erm
ent
Opt
ion
for
the
Co-
Pac
k Sc
enar
io
Val
ue o
f th
e
Dif
fere
nce
of t
he
D
efer
men
t O
ptio
n
Def
erm
ent
Opt
ion
at t
he M
ean
fr
om a
Zer
o N
PV
B
ottl
ing
Yea
r 0
$0
($44
,823
) B
ottl
ing
Yea
r 1
($2,
059,
082)
($
2,10
3,90
5)
Bot
tlin
g Y
ear
2 ($
1,75
6,68
0)
($1,
801,
503)
B
ottl
ing
Yea
r 3
($1,
353,
709)
($
1,39
8,53
2)
Bot
tlin
g Y
ear
4 ($
959,
321)
($
1,00
4,14
4)
Bot
tlin
g Y
ear
5 ($
611,
114)
($
655,
937)
B
ottl
ing
Yea
r 6
($34
4,56
2)
($38
9,38
5)
Bot
tlin
g Y
ear
7 ($
156,
469)
($
201,
292)
B
ottl
ing
Yea
r 8
($57
,926
) ($
102,
749)
B
ottl
ing
Yea
r 9
$3,1
72
($41
,651
) B
ottl
ing
Yea
r 10
$3
3,77
6
($11
,047
)
Tab
le 9
: N
PV
for
the
Com
poun
d O
ptio
n
Sw
itch
ing
Swit
chin
g Sw
itch
ing
Swit
chin
g Sw
itch
ing
Swit
chin
g Sw
itch
ing
Swit
chin
g Sw
itch
ing
Swit
chin
g Sw
itch
ing
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
Net
Pre
sent
V
alue
N
et P
rese
nt
Val
ue
E
ntry
Yea
r M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
M
ain
Mod
el
Mai
n M
odel
Stat
isti
cs
0 1
2 3
4 5
6 7
8 9
10
Mea
n $2
2,56
5
($2,
136,
428)
($
1,91
8,35
0)
($1,
748,
708)
($
1,49
2,36
9)
($1,
238,
411)
($
1,03
4,19
5)
($88
1,43
2)
($78
8,28
7)
($73
6,12
8)
($71
1,91
9)
Stan
dard
D
evia
tion
$1
,262
,909
$7
35,7
31
$871
,241
$6
06,0
56
$433
,532
$3
18,1
62
$234
,745
$1
56,3
15
$90,
730
$4
3,02
9
$13,
000
5%
$0
($3,
247,
318)
($
3,54
1,19
6)
($2,
822,
698)
($
2,20
0,17
1)
($1,
728,
574)
($
1,40
0,11
6)
($1,
123,
804)
($
924,
984)
($
800,
729)
($
730,
978)
25%
$3
($
2,65
7,87
5)
($2,
365,
504)
($
2,13
2,23
2)
($1,
799,
917)
($
1,46
3,54
0)
($1,
199,
381)
($
991,
988)
($
852,
979)
($
766,
791)
($
721,
186)
50%
$0
($
2,19
0,22
5)
($1,
799,
669)
($
1,71
3,42
9)
($1,
498,
394)
($
1,25
4,41
6)
($1,
047,
199)
($
889,
917)
($
795,
570)
($
739,
743)
($
713,
211)
75%
$8
1,61
4
($1,
668,
428)
($
1,33
9,03
2)
($1,
341,
094)
($
1,20
3,74
4)
($1,
034,
976)
($
885,
336)
($
781,
166)
($
733,
288)
($
710,
291)
($
704,
211)
95%
($
1,86
1,56
0)
($81
6,70
0)
($65
1,34
7)
($76
6,50
4)
($76
2,77
9)
($69
4,01
5)
($62
1,63
6)
($60
5,78
8)
($62
6,43
8)
($65
8,02
1)
($68
8,24
4)
Bri
ggem
an, D
etre
, and
Gra
y
C
ompo
und
Opt
ions
: A
Rea
l Opt
ions
App
lica
tion
to a
Foo
d B
usin
ess
24
µ 1
µ 2
Tab
le 1
0: V
alue
of
the
Com
poun
d O
ptio
n
Val
ue o
f th
e
Dif
fere
nce
of t
he
C
ompo
und
Opt
ion
C
ompo
und
Opt
ion
at t
he M
ean
fr
om a
Zer
o N
PV
B
ottl
ing
Yea
r 0
$67,
388
$2
2,56
5
Bot
tlin
g Y
ear
1 ($
2,09
1,60
5)
($2,
136,
428)
B
ottl
ing
Yea
r 2
($1,
873,
527)
($
1,91
8,35
0)
Bot
tlin
g Y
ear
3 ($
1,70
3,88
5)
($1,
748,
708)
B
ottl
ing
Yea
r 4
($1,
447,
546)
($
1,49
2,36
9)
Bot
tlin
g Y
ear
5 ($
1,19
3,58
8)
($1,
238,
411)
B
ottl
ing
Yea
r 6
($98
9,37
2)
($1,
034,
195)
B
ottl
ing
Yea
r 7
($83
6,60
9)
($88
1,43
2)
Bot
tlin
g Y
ear
8 ($
743,
464)
($
788,
287)
B
ottl
ing
Yea
r 9
($69
1,30
5)
($73
6,12
8)
Bot
tlin
g Y
ear
10
($66
7,09
6)
($71
1,91
9)
P
roba
bilit
y
R
eal O
ptio
ns
D
CF
App
roac
h
Sour
ce:
Mun
F
igur
e 1.
DC
F a
nd R
eal O
ptio
ns:
Ris
k-R
etur
n C
ompa
riso
ns
% R
etur
ns
σ 1
σ 2
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