You can invest in a risk-free technology that requires an upfront payment of

$1.01

million and will provide a perpetual annual cash flow of

$84,000.

Suppose all interest rates will be either

9.9%

or

4.8%

in one year and remain there forever. The risk-neutral probability that interest rates will drop to

4.8%

is

88%.

The one-year risk-free interest rate is

8.2%,

and today's rate on a risk-free perpetual bond is

5.3%.

The rate on an equivalent perpetual bond that is repayable at any time (the callable annuity rate) is

9.1%.

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.