Use the following information to answer the question(s)below.
Rearden Metal can invest in a risk-free technology that requires an up-front investment of $1 million.Rearden's managers are hesitant to invest because of uncertainty over future interest rates.Suppose that all interest rates will be either 8% or 4% in one year and remain there forever.The risk-neutral probability that interest rates will drop to 4% is 40%.The one-year risk-free interest rate is 5% and today's rate on a risk-free perpetual bond is 6%.The rate on an equivalent perpetual bond that is repayable at any time (the callable annuity rate)is 7.65%.
-Assuming that this project will provide Rearden with perpetual annual cash flows of $65,000,the NPV of investing in the project today is closest to:
A)-$281,000.
B)-$83,000.
C)+$46,000.
D)+$83,000.
E)+$143,000.

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to discount the perpetual cash flow of $65,000 by the appropriate discount rate. Since the project is risk-free, the appropriate discount rate is the risk-free rate, which is 6%. Therefore, the value of the perpetual cash flow is: 
    
    $65,000 / 0.06 = $1,083,333.33

Next, we need to determine the probability-weighted average of the two discount rates, using the risk-neutral probabilities. The weighted average is:

0.4 x 4% + 0.6 x 8% = 6%

Since the risk-neutral probability-weighted average discount rate is equal to the risk-free rate, there is no risk premium and the NPV is equal to the present value of the perpetual cash flows, which is:

-$1,000,000 + $1,083,333.33 = +$83,333.33

Therefore, the closest answer is D, +$83,000.

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