Thus the option to delay will have value even when project cash flows are riskless. This implies two things. On the one hand, since interest rates affect the value of all projects, the simple NPV rule cannot be applied to any investment that can be postponed regardless of the nature of the cash flows. On the other hand, since the effect of interest rates on project value is similar across projects, it should, in principle, be possible to derive a practical investment rule that, like simple NPV analysis, would apply to a wide range of projects.

The object of this paper is to derive a such a rule for two important classes of investment decisions that can be postponed. The first class isolates the effect of the interest rate option by restricting attention to projects for which no resolution of uncertainty about the distribution of the cash flows is expected. In this case the simple NPV rule needs only a small adjustment to incorporate the option to delay. The correct procedure, in a nutshell, is to multiply the discount rate by the ratio of the callable riskless rate to the non-callable riskless rate and then apply the rule as before. Since callable riskless rates (in the form of mortgage backed securities (GNMAs)) are almost as actively quoted as riskless rates themselves, this rule is as tractable as the standard NPV rule for projects that cannot be delayed.

As we have already pointed out, obtaining a widely applicable and simple rule outside this class is difficult because of the idiosyncratic nature of the resolution of cash flow uncertainty. Nevertheless, we derive such a rule for a particular class of investments — the option to expand. Specifically, we show that a firm should choose to expand whenever the time value of a particular (American) call option on its stock is zero.3 Since stock options are widely traded, this rule can be easily implemented. It also provides a theoretical basis for arguing, at least in this narrow context, for the importance of not ignoring the option component of value. Generally, only deep in the money stock options have zero time values. Since we show that the present value of the expansion itself is proportional to the intrinsic value of the option, the result implies that the option to expand will only be exercised early if the NPV of the expansion itself is very large. We also derive a simple rule, using stock options with differing strike prices, for deciding on the optimal size of the expansion.

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