Question

You can invest in a risk-free technology that requires an upfront payment of 1,180,000 and will provide a perpetual annual cash flow of 114,000. Suppose all interest rates will be either 9.9% or 4.7% in one year and remain there forever. The risk-neutral probability that interest rates will drop to 4.7% is 89%. The one-year risk-free interest rate is 8.2% anid today's rate on a risk-free perpetual bond is 5.1%, the rate on an equivalent bond that is repayable at any time(the callable annuity rate is 8.5%.

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.

Answer 1

a)The risk free return on perpetual bond is given 5.1 % so we will consider it for calculation of NPV for investing today

NPV =Present value of inflows - Present value of outflows.

NPV=C/R-PV factor @5.1%* for 1st year *1180000

NPV=114000/.051-1180000

NPV=2235294-1180000

NPV=1055294.11

b)NPV will remain same for waiting and investing tomorrow as interest rate for one year remains the same.

c)NPV for 9.7%=1175257.73-1180000

NPV=-4742.26

NPV for 9.6%=1187500-1180000

NPV=7500

So IRR lies between 9.6% and 9.7 %

IRR=lower rate+(NPV at lower rate/NPV at lower-NPV at higher rate)*(higher rate-lower rate)

IRR=9.6+(7500/4742.26+7500)*(9.7-9.6)

IRR=9.6+.066126

IRR=9.66126