The Timing of Development Revealed by the Market:
An Options Approach
Dorothea M. Colwell
70 W. Burton Place (Apt. 3006)
Chicago, IL 60616
Phone: 312 988-7108 dorothea.colwell@accenture.com and
Peter F. Colwell
4005 Golf Creek Dr.
Champaign, IL 61822
Cell: 906 280-0555
Fax: 217 244-9867 pcolwell@uiuc.edu
January 28, 2004
Dorothea Colwell is a graduate of the University of Illinois College of Engineering with a major in General Engineering a minor in Germanic Studies, and a secondary field in Business Administration. She is a Manager in the Global Architecture and
Core Technologies Division of Accenture. Her consulting experience includes industries such as financial services, telecommunications, retail, and manufacturing.
She has extensive international experience in countries such as Finland, Austria,
Germany, Japan, and China.
Peter Colwell, Ph.D. is an Emeritus Professor of Finance at the University of Illinois and an Emeritus faculty member of the Weimer School of the Homer Hoyt Institute.
He was formerly an Honorary Professor at the University of Aberdeen in Scotland, a
Lecturer at Howard University, and an Assistant Professor at the University of
Georgia. He is a former President of the American Real Estate and Urban Economics
Association. In the area of real estate, he has published over fifty academic articles, over seventy five non-technical articles, and over 30 articles and book chapters aimed at a professional audience. He is on the editorial review boards of three academic and one professional journal. Currently, he does consulting in the area of property valuation and continues to do research and to publish.

The Timing of Development Revealed by the Market:
An Options Approach
ABSTRACT
The market provides an estimate of the time to development. This paper shows simple computations for the price of agricultural land with no development option, the price of the option to develop, and the payoff associated with the development option.
Given these sizes of these variables, it is possible to compute the expected time to development. Sensitivity analysis is used to explore probable alternatives. Finally, we confirm that the present value of the property is the value with the development option and show how to compute the present value of damages or benefits that will be realized at the time of development.
KEY WORDS: real option, timing of development, risky real rate, Fisher Effect, electric transmission lines, externalities

I.
The Timing of Development Revealed by the Market:
An Options Approach
Introduction
When will development occur? There are a number of reasons an analyst may have for predicting the time of development. For example, the present value of the land is found as the discounted net income from an agricultural use over the time prior to development plus the present value of the reversion value at the time of development.
Thus, development timing is critical in this computation. Alternatively, there may be some potentially negative feature (i.e., external diseconomy, negative externality, or whatever) such as an electrical transmission line, gas pipeline, or road that does not affect agricultural income but does affect reversion value (i.e., it affects the developed use). A computation of the present value of the damage from the negative feature requires an estimate of the time to development. Fortunately, the market provides an estimate of the time to development . . . if we can only recognize it.
The time to development of residential property is often at least as long as it takes for utilities (e.g., city water, sewer, gas, and perhaps fast internet service in the future) to reach the subject property. So estimating the prediction of the time to development that is implied in market prices is often more or less equivalent to estimating what the market (i.e., the investor at the margin) thinks regarding the time that will elapse before the subject property will have city services. Retail development often lags residential development. Whether residential, retail, or something else, the highest and best use of a site is not a constant. Rather it evolves over time controlled primarily by the pace, direction, and nature of urban growth and development.
In the next section, some of the more important terms and concepts in option pricing are explained. In following sections, this article shows simple computations for the price of agricultural land with no development option, the price of the option to develop, and the payoff associated with the development option.
1 Given these sizes of these variables, it is then possible to compute the expected time to development as revealed in the market. We illustrate how sensitivity analysis can proceed using monte carlo analysis. Finally, we confirm that the present value of the property is the value
1
For other real estate applications, see: R. A. Brealey, S. C. Myers, and A. J. Marcus, Fundamentals of
Corporate Finance , Irwin-McGraw-Hill, 1999: 665-666.
2

with the development option and show how to compute the present value of damages that will be realized in the future . . . at the time of development.
II.
Options
What is an option? An option is the right to do something in the future without the obligation to do it. For example, a person can buy an option to purchase someone else’s property in the future at some predetermined price called the strike price or exercise price. In this case, the purchaser of the option may buy the property but is not required to buy the property. So the purchaser of the option will only buy the property if the value of the property turns out to be above the previously agreed upon strike price (i.e., the option is “in the money”). The right to buy is a call option, and the right to sell is a put option. The value or price of the option itself, often referred to as the option premium, depends on the value of the underlying asset, the property. The fact that the value of one asset (i.e., the option) depends on the value of another asset, the property, is what makes the option a derivative security.
Those who first encounter contemporary thought about option pricing may wonder what all the fuss is about. The fuss is about a couple of things. First and foremost, option pricing models have been developed for certain types of options that are remarkably accurate and remarkably economical in terms of the kind of information they require. While we do not know for sure whether art is imitating life or life is imitating are, we suspect that art is imitating life (i.e., the markets are driving the models), because there are extreme cases in which the market deviates from the results of the models. This suggests that the market is marching to its own drummer.
These models may be “closed form” models such as the famous Black-Scholes model, or they may require complex computational methods (e.g., monte-carlo simulations of stochastic processes such as Brownian motion in which prices change randomly from one period to the next in addition to drifting up or down through time. Beyond providing some guidance for option traders, the second major contribution of option pricing is that insights have been gained that were initially counter intuitive. Among these insights is the idea that the value of a call option actually increases if the volatility in the price of the underlying asset increases. That is, the riskier the underlying asset, the higher the price of the call option.
A real option is a particular type of option. While there are a lot of examples of real options in real estate, the word “real” means different things in these two
3

terms. The word “real” in the term real estate harks back to early English common law in which “real” actions involved more than simply monetary damages. For example, these were actions in which someone might be ejected from certain lands by the court. In contrast, the word “real” in the term real option refers to the fact that the exercise of the right or option involves modifications of the physical capital so that the exercise is irreversible to some substantial degree. Real estate development is a real option, because it involves putting streets and utilities in place and constructing buildings. Real estate development can be reversed, but only at substantial cost. This is what is meant by irreversibility. The strike price for the development option is the cost of development plus the cost of getting the zoning changed and all the other permitting impediments to development. The development option is “in the money” if the value of the completed development is in excess of the strike price. One of the major ideas that has emerged from the study of real options is that the difference between the value of the completed development and the strike price may have to be substantial before the real option will be exercised. This is because the risky price of the underlying asset (i.e., the completed development) makes it possible for the investor to be hurt if price falls in the face of irreversibility. Another way to put this is that optimal exercise may be delayed with real options. This delay is called hysteresis.
There are other interesting ideas connected with the strategic exercise of real options.
For example, someone might want to develop a shopping center well before it is optimal in some isolated sense if this development keeps competitors from doing the same thing either by the influence of the existing center on zoning authorities or on the private decision making processes of other potential center developers.
In this article, we are focused on real option prices that are extracted from the market. We do not employ any normative model of option pricing (i.e., a model of what prices ought to be). Instead, we take a positivist point of view (i.e., we look a what prices actually are). The price of agricultural land, or any other land use that employs only a tiny value of physical capital such as a parking lot or some very old buildings, can usefully be divided into two components. One of these components is the value of the land in its existing use, agricultural or whatever. Another component is the value of the real option to develop (or redevelop) the land in some other use.
One of the central ideas of this article is that this second component, the price of the real option, can be observed. Appraisers might characterize this observation as a residual valuation method. The value of the agricultural land can be determined in the
4

usual way by observing and adjusting comparable sales. The value of the land strictly in the agricultural use can be determined by observing and adjusting sales of agricultural properties that clearly have no development potential but are otherwise comparable (e.g., in terms of fertility). Alternatively, we find the value of the land strictly in the agricultural use by the income approach (i.e., the present value of the net agricultural cash rent). The price of the real option to develop is then found as the residual, the difference between the total value of the agricultural land and the value strictly in the agricultural use. In this way, we discover the price of the real option which would be trivial in the world of financial options where the price is explicit but is far from obvious in the world of real estate development. The price of the real option to develop property has not previously been derived in this way.
III.
Price without the development option
As we have just indicated, the price of undeveloped property has two components.
One of these components is the price with no development option. This would be the price that would be observed if the property were completely beyond the path of development so that it would be unreasonable to imagine that it could be profitably developed in the foreseeable future. The second component is the price of the development option. It is the first of these two components that is developed in this section.
Imagine an 80 acre parcel that would sell for $5,000 per acre or $400,000 at the present time. The cash agricultural rent on this parcel is $160 per acre per annum.
2
Supposing that the cap rate, or the real (i.e., inflation-adjusted) risky rate, is 8%, the price of the property without any development option is the Present Value of the $160 in perpetuity or $2,000. This can be expressed several ways as follows: 3
(1) 2 , 000

160 * PVAF

8 %,


 t



1
( 1

160
.
08 ) t

160 / .
08 where PVAF

8 %,



1
.
08

the Present Value of an Annuity Factor at 8% for infinite years.
2 For simplicity, here and elsewhere in this paper we abstract from any tax issues.
3 The mathematics is standard throughout the paper. For those who need to review the time value of money formulas, see: P. F. Colwell, Derivation of Time Value of Money Formulas, The Illinois Real
Estate Letter , Spring, 1999, 10-11. Online: www.uiuc.edu/orer/V13-2-3 .
5

Of course, we do not expect that the cash rent will continue to be $160 into perpetuity.
Our best estimate however is that it would tend to grow at the rate of inflation. So we can use $160 as the constant real cash rent. Thus, we must use a real discount rate, one that is reduced by the expected rate of inflation. Let us say that the riskless real interest rate is about 2% (e.g., check the rate on government inflation-indexed bonds) and that the risk premium is about 6%. So the risky real rate is about 8%.
4
IV.
Price of the development option
Total price is the sum of the two components. Since we have the total price and one of the components, the remaining component is simply the difference. Thus, the price of the development option is the total price minus the price with no development option or $3,000.
(2) 3 , 000

5 , 000

2 , 000
If the total price were very large, the price of the development option would be large because development would be imminent. In contrast, if the total price were only slightly above $2,000 per acre, the price of the development option would be tiny because development would be distant in time.
V.
Payoff from the development option
It should be possible to observe the price of land today that is immediately developed for the use that is the ultimate highest and best use of the subject property (i.e., the 80 acre parcel worth $5,000). Suppose that the price of land that is immediately developed is $20,000 per acre assuming that the physical attributes (i.e., other than location or access) are very similar to those of the subject property. Of course, we do not imagine that the nominal price for developable property will be the same amount when the subject property is developed. Our best estimate is that the price of immediately developable property will grow at the rate of inflation. Thus, we estimate that the $20,000 will be the real value of our subject property when it is ripe for development. The payoff from the development option is the difference between this price and the real, pure agricultural price of $2,000. That is, the payoff will be
$18,000.
4
This reflects the well-known Fisher Effect. For a description of the Fisher Effect, see: T. M. Clauretie
& G. S. Sirmans, Real Estate Finance: Theory and Practice , 4th Edition, Thompson-Southwestern,
2003: 18.
6

(3) 18 , 000

20 , 000

2 , 000
VI.
The time to development
We have an option with a price of $3,000 and a payoff of $18,000 in real terms. Real prices may rationally grow at the risky real rate of interest. If prices were thought to grow faster, buyers would see the excess return, enter the market and bid up the price of the development option today. Similarly, if prices were thought to grow slower, buyers would be discouraged and more suppliers would see the excess profit in selling now driving down the price of the option. Another way of saying this is that if we were to expect an assets price to grow in real terms at a rate different than the risky real rate, there would be ex ante (i.e., before we invest) arbitrage opportunities.
Thus, we may ask the question, “What time interval is required to turn $3,000 into $18,000 if the rate of growth is at the risky real rate?” The answer to the question can be found on any financial calculator where
I = 8,
PV = -3000 (i.e., it is negative because it is an outflow),
FV = 18000, and
PMT = 0.
Computing N reveals that it will take 23.28 years for $3,000 to grow to $18,000 at a rate of 8% per annum. Perhaps less mechanistically,
(4) FV

PV * ( 1
 r )
N
Solving for N yields
(5) N

FV ln ln

1
PV
 r

Substituting the relevant sizes of FV , PV , and r into equation (4) yields the answer we seek as follows:
7

(6) 23 .
28
 ln ln


18 , 000

1
3 ,

000
.
08



So we would conclude that market participants (i.e., the marginal buyer and seller) expect that the subject property will be developed in about 23 years. The current price that they are willing to pay and receive, respectively, reflects this implicit forecast.
VII.
Sensitivity analysis
Several parameters have been used in the analysis. While these parameters may be our best estimates, we cannot be absolutely confident they are correct thus we should make reasonable assumptions about the distributions of these parameters and see the result using monte-carlo analysis.
5
In fact, the key problem with using present value analysis to evaluate an option is the problematic interest rate assumption, especially the risk premium. On the other hand, conventional option pricing models require knowledge of other problematic parameters (e.g., the instantaneous variance in the price of the asset). So the approach we have chosen is the low tech present value analysis approach with sensitivity analysis. This sensitivity analysis should not be confused with normative, computational option pricing models that also use montecarlo analysis. The sensitivity analysis here merely explores the impact of variation in the parameters used in the time-value-of-money calculation. As an additional caution, it should be noted that the parameters involved are assumed to be uncorrelated with each other, however it is a very simple matter to alter this assumption.
The key parameters are the total price of the property in the present, the cash rent, the risky real rate of interest, and the price of the property at the time of development. We will use distributions that are described with three attributes or
8

parameters: the maximum, the minimum, and the mode or most likely. This distribution is called a triangular distribution. It is chosen specifically because it will resonate with practitioners who are used to thinking about best-case, worst-case, and most-likely-case scenarios in the context of sensitivity analysis. These cases translate directly into the parameters of the triangular distribution. The assumptions for the monte carlo analysis are given in the table below.
Total price today
Maximum
$6,000
Minimum
$4,000
Most likely
$5,000
Cash rent today
Risky real rate
$170
9%
$150
7%
$160
8%
Development price $30,000 $15,000 $20,000
The reader will note that all the distributions are symmetrical with the exception of the distribution for development price, which is skewed to the right. The result of the monte-carlo analysis is summarized by the statistics for the time to development given in the table below.
5 The software used is Crystal Ball from Decisioneering.
9

Years to development
Mean
Median
Standard deviation
Maximum
24.48
24.38
3.03
36.73
15.11 Minimum
What we discover by the monte-carlo, sensitivity analysis is that the range in possible development times is from slightly more than 15 years to almost 37 years. However, we should realize that estimates of the years until development close to either of these extreme estimates are not very probable. The expected or mean number of years is between 24 and 25 years. Furthermore, it is about 66% probable that the development will occur within plus or minus 3 years from the expected time of development (i.e., one standard deviation).
VIII.
Applications
The Present Value of the income and the reversion value should equal the current price. That is,
(7) 5 , 000

160 * PVAF

8 %, 23 .
28


20 , 000 * PVF

8 %, 23 .
28

This can be written in other ways as well. For example,
5 , 000


160


1

.
08

.
08
1


23 .
28
.
08


23 .
28
1



20 , 000
( 1

.
08 )
23 .
28
 t
23 

1
160
( 1

.
08 ) t

20 , 000
( 1

.
08 )
23
10

Of course, this example is true by construction, but this could not be done without an estimate of the time to development. Also, equation (7) confirms that the algebra is correct given that what we have done explicitly is the following:
(8) 5 , 000

160 * PVAF

8 %,



18 , 000 * PVF

8 %, 23 .
28

Or rewriting,
5 , 000


160

1
.
08

18 , 000
( 1

.
08 )
23 .
28
 t



1
160
( 1

.
08 ) t

20 , 000
( 1

.
08 )
23
This is the present value of the perpetual income stream plus the payoff on the option.
Suppose that there is some positive or negative feature that is put in place in the present. Suppose further that it has no impact on the agricultural use but will positively or negatively affect the developed use in the future. That is, it doesn’t start to have an impact for 23.28 years. An imperfect example of a positive feature might be a pond that is a borrow pit for highway construction or a millpond before the age of steam power. After residential development, the pond benefits its neighbors directly, whereas before development it might convey no benefits. In fact, it might have negative features, and that is why it is not a perfect example for this analysis.
Utility easements provide possible examples of negative features. Specifically, suppose a 100 ft. easement is created for high voltage transmission wires along a quarter mile edge of an 80 acre parcel. This easement would be 3.0303… acres in area. For the sake of discussion, let us say that the easement reduces the value of the burdened acreage by half. It could be used for water detention, a walking path, sideyards, or backyards, so it will not be useless, but its uses may be diminished by the easement. Just for the sake of the argument, let us suppose that we have evidence of some stigma on the next 100 ft. strip (i.e., a second approximately 3 acre strip). Its value is reduced by one quarter because of the view or perhaps something else.
11

Suppose further that the impact does not extend beyond this second strip of land. The ultimate total damage would be computed to be $45,454 as follows:
(9) 45 , 454

3 .
03 * 20 , 000 * (.
5

.
25 )
The damage per acre on the entire parcel would be the total damage divided by the number of acres. This is $568 as follows:
(10) 568 .
18

45 , 454
80
But this impact does not hit for more than 23 years. Thus the present value of the impact per acre is
(11) 94 .
70

568 .
18 * PVF

8 %, 23 .
28

Thus the bottom line is that the damage from the transmission line is almost $95 per acre. This is almost 2% of the fee value of the parcel. The signs on these effects would be reversed if this were a positive feature like the pond.
IX.
Conclusions
As a result of decomposing the current price into a pure price of agricultural land without any development option and the price of the development option, we have been able to determine the market expectation for the time remaining prior to development. We have been able to apply sensitivity analysis to the problem in order to reveal the reasonable variability in our estimate. Finally, we have found two applications for this estimate. Our first application is a rather conventional income approach that requires the time to development. Our second application is for an advantage or a damage that appears to affect the developed land use. We find that the magnitude of the advantage or the damage is quite small due to the estimated time until development will occur.
12

We utilized the observed price of the real option along with the standard timevalue-of-money calculations to infer when the real option is likely to be exercised.
This approach is useful for a number of reasons. The approach provides insight into why agricultural land frequently sells for more than can be justified by the agricultural use. The approach also provides teachers of financial concepts with a realistic scenario for solving for time (i.e., instead of just PV, FV, and I) as well as a context in which to discuss modern option theory (e.g., the relationship between volatility and price) and institutions (e.g., why the real option to develop is an American and not a
European option). The approach provides researchers with a way to evaluate aspects of real options that have not been well explored (e.g., event studies of implied volatility in real estate markets). Finally, the approach allows practitioners the means to evaluate the present value of the positive or negative impacts that emerge at the time of development (e.g., ponds and utility easements).
13

BIBLIOGRAPHY
R. A. Brealey, S. C. Myers, and A. J. Marcus, Fundamentals of Corporate Finance ,
(Irwin-McGraw-Hill, 1999), 665-666.
T. M. Clauretie & G. S. Sirmans, Real Estate Finance: Theory and Practice , (4th
Edition, Thompson-Southwestern, 2003), 18.
P. F. Colwell, Derivation of Time Value of Money Formulas, The Illinois Real Estate
Letter , Spring, 1999: 10-11. On line: www.uiuc.edu/orer/V13-2-3 .
14