Question 24.4: The Investment Timing Decision A project costs $200 and has ...
The Investment Timing Decision
A project costs $200 and has a future cash flow of $42 per year forever. If we wait one year, the project will cost $240 because of inflation, but the cash flows will be $48 per year forever. If these are the only two options, and the relevant discount rate is 12 percent, what should we do? What is the value of the option to wait?
In this case, the project is a simple perpetuity. If we take it today, the NPV is:
NPV = −$200 + $42/.12 = $150
If we wait one year, the NPV at that time will be:
NPV = −$240 + $48/.12 = $160
So, $160 is the NPV one year from now, but we need to know the value today. Discounting back one period, we get:
NPV = $160/1.12 = $142.86
If we wait, the NPV is $142.86 today compared to $150 if we start immediately, so the optimal time to begin the project is now.
What’s the value of the option to wait? It is tempting to say that it is $142.86 − 150 = −$7.14, but that’s wrong. Why? Because, as we discussed earlier, an option can never have a nega-tive value. In this case, the option to wait has a zero value.