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In their book Investment Under Uncertainty, Dixit and Pindyck use a simple example to illustrate the difference between NPV and option pricing methods.2
1 Empirical evidence indicates that executive stock options are exercised suboptimally. This must be taken into account in their valuation.
2 A. Dixit and R. Pindyck, Investment Under Uncertainty (Princeton, NJ: Princeton University Press, 1994).
Suppose you are deciding whether to invest $1,600 in a new project that makes widgets. The cash flow per widget is $200 but will change to either $300 or $100 at the end of the year with equal probability. After that it will stay at its new level forever. Note that the expected future cash flow is $200, the weighted average of the risky outcomes, $300 and $100. The cost of capital is 10 percent. Assuming that one widget can be sold immediately, and one per year thereafter, the net present value of the project would be estimated as follows:
The NPV approach discounts the expected project cash flows at the weighted average cost of capital. The decision rule is to take the maximum of the discounted expected cash flows or zero (meaning don't do the project). The NPV rule is the maximum (determined today) of the expected values. It also makes the implicit assumption that the project should be undertaken immediately or not at all, because the maximum must be decided right now. This assumption rules out the possibility of deferring the investment one year until the uncertainty about the price per widget is resolved. If we look at the project given the option to defer, the economics look better:
With the option to defer you can wait one period to invest, then decide whether to do so, based on the arrival of information about the long-term cash flow per widget. If the cash flow is only 100 per unit you will not exercise the option to invest, but if the cash flow is 300 per unit, you will. Although the NPV of investing immediately is $600, the NPV should you decide to defer is even higher at $733. Therefore, you will defer.
The value of this call option (with an exercise price of 1,600, a one-year life, a variance determined by the cash-flow spread of $200 per unit, and an underlying risky asset that has a value without flexibility of $600) is the
difference between the value of the project with flexibility and its value without flexibility, $733 - $600 = $133. Note also that the NPV is the maximum, decided today, of the expected discounted cash flows or zero, while the option value is the expected value of the maximums, decided when information arrives, of the discounted cash flows in each future state of nature, or zero:
The two methods use information quite differently. NPV forces a decision based on today's expectation of future information, while option valuation allows the flexibility of making decisions in the future contingent on the arrival of information. Option-pricing methods capture the value of flexibility while NPV does not. The value of a project using option pricing will always be greater than the value of the project using NPV. Sometimes the difference in value between the two approaches is small. This is usually the case when the project has such a high NPV that the flexibility is unlikely to be used, or conversely when the NPV is very negative. The biggest differences (see Exhibit 20.1) occur when the NPV is close to zero, that is, when the decision about whether to undertake the project is a close call. We have found differences in value of more than 100 percent in such situations. These were cases where senior management had often overruled the NPV results and accepted the project for ''strategic reasons." As you begin to feel
Exhibit 20.1 When Is Managerial Flexibility Valuable?
Likelihood of receiving new information
Low Uncertainty High
In every scenario flexibility value is greatest when the project's value without flexibility is close to break even
Flexibility value greatest when:
1. High uncertainty about the future Very likely to receive new information overtime
2. High room for managerial flexibility Allows management to respond appropriately to this new information
3. NPV without flexibility near zero
If a project is neither obviously good nor obviously bad. flexibility to change course is more likely to be used and therefore is more valuable
Under these conditions, the difference between options valuation and other decision tools is substantial
more comfortable with real options, you will see that the concept fits intuition better than the rigid assumptions of NPV.
To extend Dixit and Pindyck's example, let's see what happens if the variability of cash flows per unit increases from $300 versus $100 to $400 versus $0. Notice that the NPV is the same because the expected cash flows remain unchanged and we also assume that the new risk is uncorrelated with the economy, so the capital asset pricing model beta and the cost of capital are unchanged. But the value of the deferral option will increase because it is based on decisions that are contingent on the way that uncertainty is resolved. The algebra looks like this: