· This article is start from issue of “traditional net present value approach cannot capture the value of the options to a project”.
· In recent years, an argument has been made that the traditional net present value approach cannot capture the value of the options to a project. Conventionally, the net present value of a project is the measure of the value adding to the firm if it takes the project. However, the limitation of the model is that it analyzes projects only on the basis of expected cash flows and discount rates.
· It fails to fully consider the options associated with the project or the investment.
· The real options approach is the modern approach to project evaluation. It considers the value of the options for the decision makers. It is dynamic because it considers the effect of possible uncertainty along the whole cycle of the project, and what/how/when the relevant real options shall be exercised
· The objective of the article is to introduce how to apply the real options approach to the evaluation of the real world projects.
· The real options approach is relatively straightforward when looking at a single project. Furthermore, this approach is even more powerful when being applied to multiple investment choices, like a large multi-stage oil project.
· In the net present value approach, uncertainty usually depresses the value of the investment, but the real options approach expands the opportunity of the investment when considering the flexibility of decisions in the future
· Projects are often analyzed based upon their expected cash flows and discount rates at the time of the analysis; the net present value computed on that basis is a measure of its value and acceptability at that time. When expected cash flows and discount rates change, the net present value changes. Therefore, a project that has a negative net present value now may have a positive net present value in the future. The option to delay the project has value.
Real Options Model
In this article, the Black Scholes Real Options model will be used in doing the analysis.
Value of Call = S Exp (-y t) N (dl) - K Exp (-r t) N (d2)
(equation 1)
S = Current Value of the Underlying Asset
K = Strike Price of the Option
t = Life to Expiration of the Option
r = Risk free interest rate corresponding to the life of the option
s^sup 2^ = Variance in the Value of the Underlying Asset
y = Dividend Yield (Dividends/Current Value of the Asset)
Option to Delay a Project
Sometimes, because of legal restrictions or other barriers to competitors, only one firm can take a specific project. The changes in value of such a project give it the characteristics of an American Call Option, which is an asset that gives the holder the right (not the obligation) to buy an asset for a fixed exercise price, until a certain date.
It is assumed that a project requires an initial investment of A and the present value ofthe expected cash inflows is Z. The net present value of this project is the difference between the two:
NPV = Z – A
It is also assumed that the firm has exclusive rights to this project for the next n years and the present value of the cash inflows may change with the changes in either the cash flows or the discount rate over time. Therefore, the project may have a negative net present value right now, but it may have positive net present value in the future.
Defining Z again as the present value of the cash flows, the firm's decision rule on this project can be summarized as follows: if Z is larger than A, the firm will take the project because of its positive net present value; if Z is smaller than A, the firm will give up the project because ofthe negative net present value.
If the firm chooses not to take the project, there are no additional cash flows and the firm will lose the initial investment A.
This relationship can be presented in a payoff diagram of cash flows on this project, as shown in figure 1. The assumption is that the firm holds out until the end of the period for which it has exclusive rights to the project.
This payoff diagram is that of an American call option-the underlying asset is the project, the strike price of the option is the investment needed to take on the project; and the life of the option is the period for which the firm has the exclusive right to the project. The present value of the cash flows on this project, and the expected variance in this present value, represent the value and variance of the underlying asset-the project.
Inputs for Valuing the Option to Delay
To value any options, people need the inputs including the value of the underlying asset, the variance in that value, the time to expiration on the option, the strike price, the risk free rate, and the equivalent of the dividend yield (cost of delay).
Value of the Underlying Asset
To a specific project, the underlying asset is the project itself. The present value of this asset is the present value of expected cash flows from the project, not including the initial investment, which can be obtained by doing a capital budgeting analysis.
In fact, the cash flow estimate will change over the time, as well as the present value of the project. However, this uncertainty should be viewed as the reason for why the project delay option has value. If the expected cash flows on the project were known with certainty and were not expected to change, there would be no need to adopt the real options approach because there would be no value to the option.
Variance in the Value of the Asset
It is known that the price of crude oil will affect the value of an oil project while technological shifts will change the cost structure and profitability of an IT project.
However, the prices of crude oil or the new technology five years later are not known at this point of time. These uncertainties are associated with the cash flows, as well as the present value.
The variance in the cash flows from the project can be obtained in one of the following three ways.
* Adopt the variance in the firm value of firms involved in the same business. Therefore, the average variance in the firm value of firms like Imperial Oil, Petro-Canada, Suncor and Shell, involved in oil and gas industry can be used as the variance in present value of an oil and gas project.
* Calculate the variance of cash flow based on the probabilities of a variety of market scenarios. Alternatively, the probability distributions can be estimated for each of the inputs into the project analysis-the supply and demand, the market share, and the profit margin, for instance-and simulations used to estimate the variance in the present values that emerge. If there are only one or two variables of uncertainty about cash flow from the project, the approach works best [5].
* Use the variance in the cash flow from similar projects, which have been done by that firm or its competitors. This may be the way that a consumer product company like Toyota might estimate the variance associated with introducing a new generation of Camry.
The variance in cash flows has a great impact on the value of the option-the higher the variance, the higher the value of the project delay option [3]. Therefore, the value of an option to do a project in a stable business will be less than the value of one in an environment where product price, technology, and markets, are all changing dramatically.
Exercise Price on Option
A project delay option will be exercised when the firm owning the rights decides to take on the project. The cost of the project is the exercise price of the option. It is assumed that the cost of the project remains the same in present value and uncertainty in the project has been included in the variance of the present value of the cash flows from the project.
Expiration of the Option
The project delay option will expire when the firm's rights to the project expire. It is assumed that any investments after the project rights expire have no present value. The risk free rate to use in pricing the option should be the rate that corresponds to the expiration of the option. When firms have the right to a project through a license or a lease contract, for instance, the rate can be obtained easily. When firms only have a competitive advantage to take a project, it becomes far more difficult to obtain. Since competitive advantages fade over time, the number of years for which the firm can be expected to have these advantages is the life of the option.
Cost of Delay (Dividend Yield)
There is a cost to delay, taking on a project once the net present value turns positive. Because firm's rights to a project expire after a period of time and the possible positive net present value will disappear after this period of time, each year of delay in taking on a project will result in one less year of value adding cash flows. If the cash flows are evenly distributed over time, and the life of the patent is n years, the cost of delay can be written as:
Annual cost of delay = 1/n
(equation 3)
Therefore, if the project rights are for 20 years, the annual cost of delay will be 5 percent a year. However, the cost of delay is not consistent over the time. It rises along the time, for instance, to 1/19 in year two, 1/18 in year three and so on, making the cost of delaying the right to exercise the option larger over time.
Valuing an Oil Reserve
Consider an offshore oil property with an estimated oil reserve of 100 million barrels of oil; the cost of developing the reserve is expected to be $1.2 million dollars, and the development lag is two years.
The firm has the rights to exploit this reserve for the next 20 years, and the marginal value per barrel of oil is $12 currently (price per barrel - marginal cost per barrel). For simplicity, it is assumed that while this marginal value per barrel of oil will grow over time, the present value of the marginal value will remain unchanged at $12 per barrel. Once developed, the net production revenue each year will be five percent of the value of the reserves. The risk free rate is eight percent.
Please note that if development is started today, the oil will not be available for sale until two years from now. The estimated opportunity cost of this delay is the lost production revenue over the delay period.
NPV of Project = $1200 million + $12 x 100 million /(1+5%)^sup 2^
= -$1200 million + $1088.44 million
= -$111.56 million
This project has a negative net present value currently. However, it does not mean that the rights to the project does not have value, which is the value of the delay option. The biggest source of uncertainty on this project is the price of crude oil. From the historical data, the variance in crude oil price is 0.03.
Current Value of the Project S = $12 x 100 million / (1 + 5 percent)^sup 2^ =$1,088.44 million.
Exercise Price K = Present Value of Development Cost = $1,200 million.
Variance in the Value of the Underlying Asset s^sup 2^ = 0.03.
Risk free Rate r = 8 percent.
Dividend Yield y = Net Product Revenue / Value of Reserve = 5 percent.
Time to Expiration on the Option t = 20 years.
Based upon these inputs, the Black-Scholes model provides the following value for the call option:
d1 = 1.0359 N(d1) = 0.8498
d2 = 0.2613 N(d2) = 0.6030
Call Value = 1088.22(exp(-0.05)(20) (0.8498) -1200 (exp(-0.08)(20) (0.6030)
= $194.16 million
Therefore, at this crude oil price, the project is not an acceptable project but it would be a valuable one if the crude oil price goes up. The project should be delayed rather than abandoned.
Application Considerations
It is no doubt that the option to delay exists in many projects. When the real options pricing model is being applied to real world projects, there are several considerations that need to be considered, including the following.
Cash flows over time may not follow the price path established by the real options pricing models. The price path used in the real options is based on the variance of past historical data or stimulations. However, the variance can change dramatically due to new events.
For example, based on the variance in crude oil prices between 1991 to 2000, it was hard to predict the crude oil price reach of US$ 70/barrel in 2006.
To accurately predict the price path, the best way is to include the up-to-date data into the calculation. Therefore, the variance keeps changing.
Also consider the price of the underlying asset in this option. To a specific project, the price of the underlying asset is the value of the project itself.
Because the project is not publicly traded like stock, the value and variance will not be obtained easily.
Also consider the expiration to the option. In fact, there may be no specific period for which the firm has rights to the project.
Unlike the example above, in which the firm had exclusive rights to the oil reserves for 20 years, often the firm's rights may be less clearly defined, both in terms of exclusivity and time. For instance, a firm may have significant advantages over its competitors, which may, in turn, provide it with the virtually exclusive rights to a project for a period of time. However, the rights are not legal restrictions and could erode faster than expected.
Alternatively, the barriers to entry may turn out to be greater than expected, and allow the firm to earn excess returns for a longer period of time. Uncertainty about the expected life of the option can increase the variance in present value and the expected value of the rights to the project.
Conclusion
* A project may have a negative net present value based upon expected cash flows currently, but it may still be a good project because of the option characteristics. Therefore, it should not conclude that the rights to a project are worthless only because of a negative net present value.
* Though a project has a positive net present value now, it may not be taken on right away because the firm may earn more if it waits and accepts the project at a later time. This is more likely to happen if the firm has the rights to the project for a long time and the variance in the project inflows is high like the oil and gas projects.
Uncertainty of a project makes the rights to the project more valuable. In a net present value analysis, increasing this uncertainty increases the risk of the project and may make it less attractive. When a project is viewed as an option, an increase in the uncertainty may actually make the option more valuable.
The real options theory has great potential to project evaluation applications. Even though real options' wide applications have not been realized because of its complexity, it is certainly true that there are options embedded in many projects. The real options approach is one of the methods that can be used to evaluate those options.
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