Assume that the project in Example 22.5 pays an annual cash flow of $100,000 (instead of $90,000).
a. What is the NPV of investing today?
b. What is the NPV of waiting and investing tomorrow?
c. Verify that the hurdle rate rule of thumb gives the correct time to invest in this case.
Example 22.5:
Problem
You can invest in a risk-free technology that requires an upfront payment of $1 million and will provide a perpetual annual cash flow of $90,000. Suppose all interest rates will be either 10% or 5% in one year and remain there forever. The risk-neutral probability that interest rates will drop to 5% is 90%. The one-year risk-free interest rate is 8%, and todayâs rate on a risk-free perpetual bond is 5.4%. The rate on an equivalent perpetual bond that is repayable at any time (the callable annuity rate) is 9%.9 Should you invest in the technology today, or wait and see if rates drop and then invest?
Solution
Because the investment is risk free, the cost of capital is the risk-free rate. Thus, Eq. 22.4 suggests using a hurdle rate equal to the callable annuity rate of 9%. With that rate,
The hurdle rate rule implies that you are indifferent. Letâs see if this is correct. The actual cost of capital is 5.4% (the rate offered on a risk-free perpetuity), so the investment opportunity clearly has a positive NPV:
90,000 NPV= 1,000,000 = 0 0.09 90,000 NPV= .054 1,000,000 = $666,667
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