You can invest in a risk-free technology that requires an upfront payment of $1.

Question

You can invest in a risk-free technology that requires an upfront payment of $1.16

million and will provide a perpetual annual cash flow of $113,000.

Suppose all interest rates will be either 10.5% or 4.7%

in one year and remain there forever. The risk-neutral probability that interest rates will drop to 4.7%

is 85%. The one-year risk-free interest rate is 8.3%,

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.

Explanation / Answer

a) NPV = - initial investment + Present value of cash flow Initial Investment -$1,160,000 Present Value Annual Cash Flow perpetuity = $113,000/5.6% $2,017,857.14 NPV of investing today = -$1,160,000 +$2017857.14 $857,857.14 b) NPV up = - initial investment + Present value of cash flow Initial Investment -$1,160,000 Present Value Annual Cash Flow perpetuity = $113,000/10.5% $1,076,190.48 NPV -$83,809.52 NPV down = - initial investment + Present value of cash flow Initial Investment -$1,160,000 Present Value Annual Cash Flow perpetuity = $113,000/4.7% $2,404,255.32 NPV $1,244,255.32 NPV of waiting and investing tomorrow PV = 85% x $1,160,000/1.083 $910,433.98 c) Hurdle rate rule = NPV =-$1,160,000 + $113,000/8.8% $124,090.91 > 0 The rule of thumb suggests that you should not delay the investment.

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