What is Making the Texas Vineyard Industry Tick?
A Real Options Analysis of Entry and Exit
Don Cyr
Associate Professor of Finance
Department of Finance, Operations and Information Systems
Brock University
dcyr@brocku.ca
Roger D. Hanagriff, PhD
Associate Professor in Agricultural Business
Texas A&M University - Kingsville
ABSTRACT
Over the past 30 to 40 years the Texas wine industry has grown at a phenomenal rate
and since the mid 1980’s the quality of Texas wines has been increasing and has received
significant recognition. Although the number of Texas wineries has greatly increased in
recent years a limiting factor in the industry has been the supply of grapes on the part of
Texas vineyards. Recently it has been estimated that the number of acres committed to wine
grape growing would have to increase almost four fold in order to meet the demand for Texas
grapes on the part of Texas wine makers. Many wine producers find themselves fortunate if
50 percent of their wine is comprised of Texas grapes and many wineries resort to importing
grapes from the state of California in order to meet their needs. This mixing of non-Texas
grape product has brought controversy and divided marketing strategy and cooperation to a
market that needs collective bargaining. The apparent lack of investment in grape producing
acreage in the state of Texas also is indicative of investment hysteresis whereby the
opportunity to invest in a vineyard represents an option which will only be rationally
exercised if a critical price level for wine grapes is achieved. Employing a real options
framework we model the critical entry and exit grape prices for Texas vineyard producers,
given estimates of the various investment and cost factors for a typical Texas vineyard and
uncertainty in prices. We find that current prices for Texas grapes would have to increase by
at least 30 percent before a significant investment in vineyard production would rationally
take place. Our results have implications not only for vineyard producers and the associated
wineries but also for state agencies eager to promote an expansion of the industry.
Key Words: Real options, Entry and Exit, Vineyard production, Texas, Wine grape supply
Language of the full paper and of the presentation: English
What is Making the Texas Vineyard Industry Tick?
A Real Options Analysis of Entry and Exit
Introduction
The Texas Grape and Wine Industry
Attempts to grow vitis vinifera grapes in the state of Texas date back to the 1700’s
with old world Spanish missionary settlements. Until the late 1970’s however, when a
commercially successful wine industry was finally established, earlier efforts were curtailed
due to a variety of factors including weather and disease. Any early history of the Texas wine
industry is of course not complete without mention of the major contribution to viticulture by
the Illinois born, Texan horticulturalist T.V. Munson for his extensive classification of grape
varieties in the late 1800’s and early 1900’s. He is also renowned for his work with the
French wine industry in developing phylloxera resistant rootstocks, which resulted in him
being awarded the Legion of Honor from the French government in 1888 (McEachern, 2003).
Phylloxera were unintentionally imported to Europe in the mid-1800s from North America
and about 75 percent of the vines of France were destroyed within 30 years of the
introduction.
Throughout the 1970’s and early 80’s the industry finally established itself and in
1985 Texas wines began receiving national and international recognition. In 1986, a Texas
wine was awarded Double Gold at the prestigious San Francisco Fair Wine Competition.
Since then the industry has been growing at a tremendous rate from only four wineries in
1986 (Cañada, 2008) to 54 in 2003 and 150 in 2008. Considering only 2008, the market for
Texas wines increased by 25 percent.
Although vineyards exist in almost all areas of Texas, the state consists of four
distinct geographic zones most suitable for viticulture. They are the High-Plains region, the
Trans-Pecos region, the Texas Hill country region and the East-Texas region with the most
favorable regions being the High Plains and Texas Hill country. High Plains and Texas Hill
Country comprise 80 percent of the Texas wine grape production with each representing
approximately 40 percent production share. Figure 1 provides a map of the state outlining the
prime grape growing areas.
Figure 1: Map of Texas Indicating Prime Wine Grape Growing Areas
In spite of the general suitability of many regions in the state for wine grape growing,
there are several limiting factors including disease and weather. Pierce's disease, in particular,
is a serious potential problem for vineyards and is considered by many to be the single
greatest threat to grape growing in Texas. Although the risk of Pierce’s disease is much lower
in areas that experience colder winter temperatures, such as in the Northern and Western
parts of the state, winter injury in such areas can result in major losses. Significant losses
occurred during severe winter temperatures of 1989, 1993 and again in 2006 and 2007
(Marshall, 2008). Winter injury due to late freezes and hail in 2006 and 2007 resulted in a
drop in average yield from 4.0 tons per acre in 2005 to only 1.68 tons in 2008 (USDA, 2009).
The Texas wine industry is 99 percent Vitis Vinifera with almost 2 million gallons of
wine currently being produced a year (Marshall, 2008). Considering the relative infancy of
the industry, a dominant grape variety has not been established and consequently a number of
varieties are still experimented with and produced. In 2008, production acres represented
white wine varieties at 38.3 percent and red wine varieties at 57.8 percent. The most popular
varieties in 2008 were Cabernet Sauvignon (18.4%), Chardonnay (14.4%), Chenin Blanc
(12%), Merlot (11.2%), Syrah (6%) and Black Spanish (Lenoir) (5.2%).
A major limiting factor faced by the Texas wine industry is that in spite of significant
growth of acres under wine grape production, the demand for Texas grapes far exceeds the
supply and has done so for several years. At 2 million gallons of wine production, the
estimated demand is approximately 11,500 tons of grapes while current production in the
state is only about 4,500 tons. The lower yields due to winter injury in 2006 and 2007 have
intensified the situation. It is estimated that to completely meet the demand of Texas wineries
for home grown grapes, the number of acres in production would have to increase to nearly
12,000 from the current 3,600.
A situation that results from lacking production translates into lower state wine
production. In comparing cases sold to Texans, demand in 2007 has risen to nearly 14
million cases representing Texas as the fourth highest consuming wine state (Dodd, 2008).
The decreasing level of production acres and the increasing numbers of Texas wineries
causes a rational loss in market share (Hanagriff, Lau and Rogers, 2009). Figure 2 illustrates
wine consumption and cases produced in Texas, which illustrates the loss of market share and
access to a potential growing consumer base. The numbers of Texas wineries have increased,
but Texas produced cases is decreasing likely related to decreasing acres and high producing
wineries cutting back on production to match grape supply.
Figure 2: Cases of Texas Wine Consumption and Production from 2001-2007
13,847,390
12,622,835
10,723,650
4.0%
732,890
6.8%
2001
6.6%
6.2%
704,135
6.8%
2002
4.7%
741,656
5.9%
5.4%
2003
2004
3.5%
Wine Cases Produced in
Texas (% Texas Market
Share)
565,799
5.6%
2005
1.2%
Wine Cases Sold in Texas
(% Annual Growth)
2006 (est.) 2007 (est.)
Source: Based on TABC Data July 2007 (updated August 2008)
Many wineries in Texas have also turned to alternative sources of supply such as
importing grapes from the state of California. Texas wineries consider themselves fortunate if
they have over 50 percent of their wine made from Texas grapes (Marshall, 2008). The
resulting excess demand has driven up Texas grape prices in recent years, although
substitutes such as California grapes have greatly aided in meeting the needs of the industry
often at significantly lower prices than those paid for Texas grapes. Figure 3 provides a graph
of recent average annual grape prices per ton, received for Texas grapes.
Average price per ton
Figure 3: Average Texas grape prices per ton (2002 through 2008)
$2,000
$1,800
$1,600
$1,400
$1,200
$1,000
$800
$600
$400
$200
$2002
2003
2004
2005
Year
2006
2007
2008
Despite rising demand and associated prices for Texas grapes, the lack of new acres
under production persists and is a significant deterrent to the industry. In spite of traditional
NPV analysis suggesting a profitable endeavor, potential grape growers appear hesitant to
invest. Part of the delay in production is due to the three to four year lag required before a
planted vineyard reaches productive capability. An analysis of non-bearing acres, however
still indicates a significant lack of investment. This apparent delay in investment is typical of
the concept of hysteresis and the purpose of this paper is to explore and model the critical
grape prices at which investment in Texas vineyard production will rationally take place
based upon real options analysis.
Investment Hysteresis and Real Options Analysis
The general topic of investment hysteresis, or the perpetuation of an economic
activity long after its initial cause has disappeared, has been recognized in many economic
decisions and endeavors. With respect to agriculture, Glen Johnson (1960) was the first to
note that supply elasticity appeared to be non-symmetrical and lower for a price decrease than
for a price increase. He postulated that the requirement of fixed investment in land and labor
led to a delay in entry, in response to price increases, as well as a delay in exit except at very
low prices.
Brennan and Schwartz (1985), McDonald and Siegel (1985, 1986) and Majd and
Pindyck (1987) were the first to model the real asset investment and abandonment decision
using financial option theory, commonly known as real options analysis.1 The explicit
application to the theory of industrial entry and exit, or investment hysteresis was
subsequently developed by Dixit (1989 and 1991) and Dixit and Pindyck (1994). The
1
It is generally believe that the term "real option" was first employed by Stewart Myers at the MIT Sloan
School of Management in 1977
approach recognizes that investment or disinvestment decisions, effectively requiring
irreversible financial commitment in the face of uncertain returns, results in the creation of
options. The critical prices at which these options may rationally be exercised would appear
to involve delay, compared to traditional investment theory. In particular the potential to
invest or enter production can be characterized as a call option where the decision to disinvest
or exit, a put option.
In terms of agriculture, it is generally recognized that the issue of hysteresis is a more
significant one for growers of perennial crops, such as tree and vine fruit, as their investment
is generally much greater and requires commitment for a longer period of time. Uncertainty
and significant sunk investment costs can combine to cause critical commodity prices, for
establishing or removing an orchard or vineyard, to diverge significantly from what
traditional net present value analysis would suggest.
One line of research in real options analysis has been to econometrically examine
historical commodity prices and investment levels for the implied statistical presence of real
options, leading to economic hysteresis. Applications include the decision to investment or
remove a peach orchard (Price and Wetzstein, 1999) hog production capacity (Hinrichs et al.,
2008) as well as grape variety selection on the Californian wine industry (Richards and
Green, 2003), Our goal however is use the Dixit (1989) and Dixit and Pindyck (1994) model
to estimate the critical grape prices at which entry and exit in vineyard production would
rationally take place. Examples of such an approach, specifically to agricultural production
include Isik et. al. (2003) for agribusiness endeavors, Tauer (2006) in terms of dairy farming
and Luong and Tauer (2006) with respect to Vietnamese coffee planting.
The basis of the model is that the potential investment in idle land, for subsequent
vineyard production, represents an option to investment with an exercise price equivalent to
the fixed costs of investing. The underlying asset that forms the basis of the option is the
value of a productive vineyard which also includes the value of the option to abandon or
disinvest. The assumption of uncertainty and irreversibility of investment is a reasonable
approximation in the case of vineyard production. Investment in vineyard production
involves fairly extensive sunk costs associated with the investment in land, planting of vines
and investment in infrastructure and equipment. This investment can also be characterized as
infinitely lived given that land has an infinite life and grape vines can and are replaced by
vineyard owners on a regular basis. Such depreciation of vines as well as equipment can be
added to the variable costs of production (Luong and Tauer, 2006).
The paper proceeds by first describing the model, followed by a description of the
data used to estimate the parameters required. Solutions of critical entry and exit grape price
are then provided, under varying assumptions regarding the opportunity cost of capital and
price volatility.
The Model
This study employs the framework developed by Dixit (1989) and Dixit and Pindyck
(1994) to model the entry and exit decision in the Texas wine industry and the following
notation, similar to Tauer (2006).
V0: the value of idle investment in a vineyard
V1: the value of an active investment in a vineyard
P: Market price per ton of grapes
µ: expected percent growth rate of the market price P of grapes.
σ2: Variance of the percentage change of the market price P.
C: Variable cost of a ton of grapes produced from the investment
K: Sunk costs of investment per ton of grapes produced
X: Net liquidation value, per ton of grapes produced
ρ: Opportunity cost of capital for the firm where ρ >µ.
H: Critical market price of grapes per ton at which investment occurs
L: Critical market price of grapes per ton at which abandonment occurs.
The model makes the traditional assumption that grape prices follow geometric Brownian
motion process, generating a lognormal price distribution specified as
dP = µPdt + σPdz
(1)
where dz follows a Wiener process (
) with ε representing a random draw from a
standardized normal distribution
If the cost of production is assumed to be relatively constant over time then the value
of the investment V(P,t) is a function of the price P and time t. However given that the case
considered is an infinite horizon problem, time is not a decision variable. Therefore through
Ito’s Lemma it can be written that
(2)
with
(3)
Functional Form of the Value of an Idle Project
An idle project
, with no previous investment, represents an option to invest. In
equilibrium the expected capital gain of an idle project should equal the normal return from
the value of the investment:
(4)
Equating equations (3) and (4) and dividing by dt yields the differential equation:
(5)
with the general solution shown (Dixit (1989) and Dixit and Pindyck (1994)) to be
(6)
where A and B are constants to be determined, and
(7)
(8)
are the two roots of a quadratic equation.
For an idle project, in the limit, the value of an investment should approach zero as
the price P approaches zero. Since
and
, option value of equation (6)
approaches zero when P approaches zero, only if A approaches zero. Consequently the
functional form of the value of an idle project is given by:
(9)
Functional Form of the Value of an Active Project
In equilibrium the normal return (ρ) to an active project
should equal the expected
capital gain plus net revenue flow, shown as:
(10)
where C is the variable cost per ton of grapes. Substituting equation (3) into (10) and dividing
by dt produces the differential equation:
(11)
With a general solution given by:
(12)
Where
is the present value of the net revenue and
the option to
abandon. As the price P approaches infinity, the option abandon goes to zero. This is true
only if B = 0. Consequently the functional form of the value of an active investment project is
given by:
(13)
Determining Critical Investment and Abandonment Prices
At the critical entry price point H, at which investment would take place, the value of
the option to invest (the value of the idle project V0) must equal the value obtained through
exercising the option (V1 ) less the sunk cost of investment (K). Consequently this value
matching condition results in:
(14)
In addition the smooth pasting condition requires that the two value functions meet
tangentially, resulting in:
(15)
Similarly, at the critical abandonment price (L) the value of the active project would be given
up in order to receive any net liquidation value (X) associated with abandoning the project,
plus the value of an idle project representing an option to invest. 2
(16)
and again the smooth pasting condition results in
(17)
Substituting the functional forms of V0 and V1, given by equations (9) and (13) respectively,
into equations (14), (15), (16) and (17) and rearranging produces the following system of
equations:
2
Dixit and Pindyck (1994) define X as the cost of abandonment and hence it takes a negative value. They
indicate that if there is salvage value to the investment after abandonment costs then X is a positive value.
Assuming that the net salvage of a vineyard investment is non-negative, we define X as a positive value.
(18)
(19)
(20)
(21)
The parameters ρ µ, and σ are estimated from empirical data while α and β are
provided by equations (7) and (8) respectively. The four unknown values of A, B, L and H are
then solved for simultaneously. Solving equation 18 through 21 is not a trivial task as they
are highly nonlinear and must be solved using iterative procedures. The optimal solutions are
highly sensitive to start values and multiple solutions may exist which must be checked for
economic rationality.
Parameter Estimates
Approximately 507 producing vineyards are in operation in Texas with 3,600 acres in
total and production currently valued at $38.4 million. The distribution of producing acres
among the vineyards is quite uneven though, with 41 percent of production coming from 5
vineyards of 100 acres or more and 13 percent from vineyards of less than 5 acres. Of the 507
producing vineyards, 81 percent are less than five acres in size and 42 percent are between
one and five acres (Watson, 2005). Although systematic historical data on the investment and
variable costs of establishing and operating a vineyard in Texas is not available, over the
years a number of estimates of such costs have been made are available from sources such as
the Texas Department of Agriculture.
Investment Cost per Ton (K)
The establishment or sunk cost of a typical vineyard includes the costs of purchasing
land, equipment costs including trellis systems, site preparation, planting etc. In addition a
new vineyard does not typically reach commercial production until the third year at the very
least. Any costs accrued up to that point represent the establishment or investment costs of
the vineyard. Table I provides a summary of the typical establishment costs arrived at from
data provided in the Texas Department of Agriculture’s Grape Growers Guide.
Although site preparation equipment and other related costs are fairly standard across
the state, in recent years the cost of vineyard-suitable land has varied greatly depending upon
the location. Prices range from $1,500 per area in the High-Plains region to as high as
$25,000 per acre in some parts of the Hill Country region, west of the city of Austin. Rural
areas near the city of Dallas command prices around $5,000 per acre (Marshall, 2008). We
assume a land price of $2,500 per acre based upon the Grape Grower’s Guide; however, the
required investment in land would clearly affect the critical entry and exit prices.
The yield in terms of ton of grapes produced per acre in the state of Texas varies
greatly by grape variety as well as location of the vineyard. In normal years, assuming no loss
due to winter injury a USDA report indicates that yields generally range from three to five
tons per acres. We will therefore assume an average yield of approximately four acres per
ton. Table I indicates the investment level K of $4,775 per ton, required.
Abandonment Value per Ton (X)
The abandonment value of the vineyard represents any residual value for land and
investment less any costs incurred by the vineyard owner to prepare the land for sale. We will
assume that land values does not decline in value however we will assume that equipment
investment is valued at 40 percent of initial cost. Land prices may actually increase over time
however by assuming no change in land value we remove the return to an investment in real
estate from the overall analysis, leaving only the return to the operation of a vineyard. In this
way significant rising real estate prices, perhaps due to other factors, do not bias the critical
entry and exit prices for vineyard operations. Although the trellis system and vines would
have to be removed, at a cost, to prepare the land for resale, it is assumed that firewood could
be salvaged for sale and consequently a zero net cost. Similarly any irrigation systems are
assumed to have a net zero value. Table I reports the subsequent assumed abandonment value
X as $825 per ton.
Table I: Average Investment (Per Acre) to Establish a Vineyard in Texas
Item
Year 1
Year 2
Year 3
Total
Land purchase
$
2,500
$
2,500
Equipment
$
2,000
$
2,000
Site Preparation & Planting
$
4,400
$
-
$
-
$
4,400
Trellis Construction
$
3,500
$
-
$
-
$
3,500
Drip Irrigation & Install
$
1,300
$
-
$
-
$
1,300
Cultural practices
$
1,800
$
1,800
$
1,800
$
5,400
Total Investment per Acre
$
15,500
$
1,800
$
1,800
$
19,100
$
4,775
$
3,300
K = Investment per ton
Net Abandonment Value per
Acre1
X = Abandonment Value per Ton
$
825
1
Net abandonment is comprised of 100% of the original cost of land and 40% of the original value of equipment.
Variable Costs (C)
Table II provides an estimate of the annual variable costs per acre associated with a 4
acre vineyard, consistent with the typical size of vineyard operations in the state (Watson,
2005). The model assumes that the investment in a vineyard is infinitely lived. This is
reasonably approximated by the fact that vineyards generally need to completely replant over
a 25 to 40 year period and that major equipment, trellis and irrigation systems and replaced
on a regular basis. Therefore we will assume a two percent replanting and depreciation rate of
the investment, not including land, which we add to the variable costs of operations. The
resulting variable costs are $822.75 per ton, assuming the yield of four tons per acre.
Table II: Average Annual Variable Costs per Acre and per Ton
Chemical Cost
Labor
Harvesting
Maintenance/Repairs
Irrigation/Fuel
Depreciation1
$
$
$
$
$
$
622.00
1,500.00
300.00
424.00
113.00
332.00
Total Variable Cost per Acre
Total Cost per Ton (4 tons per acre)
$
$
3,291.00
822.75
1
Annual depreciation consists of 2% of original investment value,
not including land.
Wine Grape Prices
The primary assumption underlying the model is that grape prices are lognormally
distributed. In order to estimate the input parameters of µ and σ the variable Ri = ln(Pt/Pt-1)
was calculated based on annual average grape prices. Unfortunately, a long time series of
Texas wine grape prices is relatively difficult to obtain. Systematic records of average prices
paid for Texas wine grapes does not seem to have been regularly recorded until the late
1990s. As a result, annually observed, average prices paid per ton, were only readily available
for 2002 through 2008. Based on the available data, a value 0.046 for µ of and 0.12 for σ was
estimated.
Given the lack of an extensive time series of Texas grape prices, however, the
behavior of average California grape prices over the period of 1988 through 2007 were also
analyzed with estimates for µ and σ of 0.034 and 0.093 respectively. Although both the Texas
and California grape prices have non-zero values for the drift term µ, both price series appear
to exhibit a onetime structural shift in mean prices that occurs in 2005, in the case of Texas
grape prices, and in 1997 with respect to California grape prices.3 Consequently we will make
the assumption, from a potential producers perspective that prices follow a random walk with
3
The results of the time series analysis identifying a structural shift in average annual grape prices are available
from the authors.
zero drift (µ = 0) at any point in time. Given different estimates for the price volatility
parameter, we will vary the estimate of σ in the analysis.
Finally the opportunity cost of capital must be estimated. Again exact estimates are
difficult to ascertain and so we a cost of capital ranging from 8 percent to 12 percent. The rate
of 8 percent represents a reasonable estimate of the average long term borrowing rate, while
12 percent is consistent with an estimate of long term average equity returns.
Results
The summary of parameter inputs, obtained from the data on average Texas vineyard
operations with respect to investment, variable production costs and wine grape prices are
provided in Table III
Table III: Summary of Parameter Estimates
Parameter
µ
σ
ρ
C
K
X
Value
0
.12 and .09
.08 to .12
$ 822.75
$ 4,775
$
825
After substituting the above parameter estimates into equations 18 through 21 the
solutions for the critical entry (H) and exit (L) prices are solved for simultaneously with
simultaneous equation software, employing iterative procedures. Table IV provides the
summary of critical prices obtained under varying assumptions with respect to the
opportunity cost of capital ρ, and the assumed volatility of grape prices. Figure 4 provides a
graph of the critical prices for opportunity cost of capital ranging from 8 percent to 12 percent
and also the estimated volatility values for σ of 0.12 and 0.09. In addition Figure 4 includes
the 2008 average price per ton obtained for Texas wine grapes of $1,200.
Table IV: Critical Entry (H) and Exit (L) Prices Under Varying Assumptions for ρ and
σ
σ=.12
ρ
12.00%
11.50%
11.00%
10.50%
10.00%
9.50%
9.00%
8.50%
8.00%
H
$1,762.59
$1,739.43
$1,716.28
$1,693.23
$1,669.95
$1,646.73
$1,623.61
$1,600.48
$1,577.46
σ=.09
L
$734.35
$728.37
$722.39
$716.33
$710.46
$704.54
$698.54
$692.53
$686.45
H
$1,667.10
$1,644.45
$1,620.79
$1,600.00
$1,576.97
$1,553.84
$1,531.14
$1,508.54
$1,485.62
L
$772.64
$766.68
$760.27
$755.13
$748.93
$742.85
$737.06
$730.93
$724.76
Figure 4: Graph of Critical Entry and Exit Prices versus opportunity cost (ρ) and for
estimates of σ = .12 and .09.
Figure 4 indicates that the range between critical entry and exit prices becomes
narrower, the lower is the estimated volatility of grape prices. The differences between entry
prices (H) with increased price volatility (σ = 0.12 versus 0.09) is particularly significant at
all levels of opportunity cost ρ.
It is clear from Table 4 and Figure 4 however, that the average price obtained for
Texas wine grapes in 2008, although above the critical exit price at which a producer may
abandon a vineyard, is below the critical entry price given reasonable estimates of the
opportunity cost of capital. Assuming an opportunity cost of capital of only eight percent and
an estimate of price volatility of σ = 0.09, the level of average Texas grape prices would have
to increase to $1,577.46 from $1,200 per ton, in order for the option to invest in a vineyard to
be rationally exercised, under typical operations. Such a price increase seems unlikely as the
impact on wine producers would require a significant increase in the price per bottle that
Texas wines would have to sell at. Although such increased prices may be achievable by
small boutique wineries selling their product in tasting rooms, it is not viable for the larger
wineries distributing to outlets such as grocery stores where they face the competition of
Californian, Chilean and Argentinean wines at much lower prices (Marshall, 2008).
In summary, given the current level of Texas grape prices our analysis shows that it is
unlikely that there will be a significant increase in the number of smaller vineyards, typical of
the industry as it now stands, without significant government investment incentives. It is
possible however that larger operations ranging in the size of 100 acres may face significantly
lower variable costs due to economies of scale and consequently lower critical entry prices.
Conclusions and possible Future Research
One question that arises is the impact of competition or industry wide reaction to
grape prices. If an investor waits rather than invest, competitors will enter and consequently
investment opportunities will gradually diminish. The results of Leahy (1993) indicate
however that the critical price that would trigger the option to invest is theoretically the same
for the investor who considers the effects of competitor interaction as the one who considers
industry-wide investment as fixed. The reason is that the critical price at which investment
takes place is when the value of the option to invest (the idle project) is equal to the value of
the active project. The impact of competition reduces both the option to invest as well as the
value of the active investment. The critical exercise price remains unaffected. This is
somewhat confirmed by the analysis of Metcalf and Hasset (1995) who found that
incorporating a mean reverting price process for the assumption of the underlying asset has
little impact on critical entry and exit prices. The more recent results of Levandorskii (2005)
would, however, suggest that incorporating mean reversion may result in substantial
differences in critical prices.
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