In: Finance
You can invest in a risk-free technology that requires an upfront payment of $1.13
million and will provide a perpetual annual cash flow of $115,000.
Suppose all interest rates will be either 9.7% or 4.7% in one year and remain there forever. The risk-neutral probability that interest rates will drop to 4.7% is 93%. The one-year risk-free interest rate is 8.1%,
and today's rate on a risk-free perpetual bond is 5.5%. The rate on an equivalent perpetual bond that is repayable at any time (the callable annuityrate) is 8.6%.
What is the NPV of investing today?
What is the NPV of waiting and investing tomorrow? The NPV if the rate goes up is $? The NPV if the rate goes down is $? The PV is?
Verify that the hurdle rate rule of thumb gives the correct time to invest in this case. The hurdle rule is $?
The NPV is >0 so should you invest now or wait?
What is the NPV of investing today?
Here the appropriate cost of capital to be used for capitalization of perpetual cash flows is todays's rate on a risk free perpetual bond = 5.5 %
NPV = Annual CIF / r - Upfornt Investment = 115,000 / (0.055) - 1130,000 = 960,909
What is the NPV of waiting and investing tomorrow?
Here we have to use discount rate in computing the present value = The one-year risk-free interest rate i= 8.1%, For capitalizing the cash flows, we have use the rates as they were after one year ( i.e either 9.7 % or 4.7% )
The NPV if the rate goes up is $?
NPV rate go up = 115,000 / (0.097) - 1130,000 = 55567
The NPV if the rate goes down is $? The PV is?
NPV rate goes down = 115,000 / (0.047) - 1130,000 = 1316809
PV = Present value = [ 55567 * (0.07) + 1316809 * (0.93) ] / (1.081)
= [ 3889.69 + 1224632 ] / (1.081) = 1,136,467.80
Verify that the hurdle rate rule of thumb gives the correct time to invest in this case.
Here we have apply r = callable bond annuity rate = 8.6% for computing the NPV
NPV = 115000 / 0.086 - 1130,000 = 207,209.30
The hurdle rule is $? .......... = 207,209.30 The NPV > 0 so should Invest now
Explanation. Hurdle rate method shall provide only an approximation. As seen in the above calulations the present value to invest after one year is 1,136,467.80 as against investing now of 960,909. Thus we should wait and invest after one year, but hurdle rate suggest immediate investment.