## The Option to Delay a Project

Projects are typically 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. Expected cash flows and discount rates change

Real Option: A real option is an option on a non-traded asset, such as a investment project or a gold mine.

over time, however, and so does the net present value. Thus, a project that has a negative net present value now may have a positive net present value in the future. In a competitive environment, in which individual firms have no special advantages over their competitors in taking projects, this may not seem significant. In an environment in which a project can be taken by only one firm (because of legal restrictions or other barriers to entry to competitors), however, the changes in the project's value over time give it the characteristics of a call option.

In the abstract, assume that a project requires an initial investment of X (in real dollars) and that the present value of expected cash inflows computed right now is PV. The net present value of this project is the difference between the two:

Now assume that the firm has exclusive rights to this project for the next n years, and that the present value of the cash inflows may change over that time, because of changes in either the cash flows or the discount rate. Thus, the project may have a negative net present value right now, but it may still be a good project if the firm waits. Defining V as the present value of the cash flows, the firm's decision rule on this project can be summarized as follows:

If V > X Project has positive net present value

V < X Project has negative net present value

This relationship can be presented in a payoff diagram of cash flows on this project, as shown in Figure 6.8, assuming that the firm holds out until the end of the period for which it has exclusive rights to the project:

Figure 6.8: The Option to Delay a Project

Project has negative npv in this range

Initial Inve

Initial Inve

Project's NPV turns positive in this range

Present Value of Expected Cash Flows

PV of Cash Flows

Project's NPV turns positive in this range

Note that this payoff diagram is that of a call option — the underlying asset is the project, the strike price of the option is the investment needed to take the project; and the life of the option is the period for which the firm has rights 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.

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