You can invest in a​ risk-free technology that requires an upfront payment of $1.02 million and will provide a perpetual annual cash flow of $75,000. Suppose all interest rates will be either 10.2% or 5.5% in one year and remain there forever. The​ risk-neutral probability that interest rates will drop to 5.5% is 88%. The​ one-year risk-free interest rate is 7.8%​, and​ today's rate on a​ risk-free perpetual bond is 5.6%. The rate on an equivalent perpetual bond that is repayable at any time​ (the callable annuity​ rate) is 8.8%.
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.