Mirtha Mudflat has sufficient funds to choose one of two investments. The same amount will be invested in either case. Choice one: ten year $100,000 5% Treasury bonds issued to yield 4% per annum, the market rate. Choice two: a risky bond of the same amount that has expected cash flows of $9,000 per year for the same period. What is the risk premium that makes Mirtha indifferent between the two investments?

Question

Quizplus · Accepted Answer

To find the risk premium that makes Mirtha indifferent between the two investments, we need to find the expected return of the risky bond and subtract the risk-free rate.

The expected return of the risky bond is:

($9,000/$100,000) x 100% = 9%

The risk-free rate is the yield on the Treasury bond issued. Since the bond yields 4% per annum and has a 10-year maturity, we can use the formula for the present value of an annuity to find its price:

PV = C x (1 - (1 + r)^-n)/r

where PV is the present value, C is the coupon payment, r is the yield (4% per annum), and n is the number of years (10).

Plugging in the numbers, we get:

PV = $100,000 x (1 - (1 + 0.04)^-10)/0.04 = $123,602.77

Therefore, the risk premium that makes Mirtha indifferent between the two investments is:

9% - 4% = 5%

So Mirtha should choose the risky bond only if the risk premium is greater than 5%. Since the only option greater than 5% is C, the answer is C.

Mirtha Mudflat Has Sufficient Funds to Choose One of Two