Question

A 25-year maturity bond has a 8% coupon rate, paid annually. It sells today for $887.42. A 15-year maturity bond has a 7.5% coupon rate, also paid annually. It sells today for $899.5. A bond market analyst forecasts that in five years, 20-year maturity bonds will sell at yields to maturity of 9% and that 10-year maturity bonds will sell at yields of 8.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 7%.

a. Calculate the expected rate of return of the 25-year bond over the five-year period. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expected rate of return% ?

b. What is the expected return of the 15-year bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expected rate of return% ?

Answer 1

a]

First, we calculate the price of the bond after 5 years from now.

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 9% (Yield of 20-year bonds after 5 years from now)

nper = 20 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 8% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $908.71

Now, we calculate the expected rate of return using MIRR function in Excel with the following cash flows :

cash outflow in Year 1 = $887.42 (price paid to buy bond today)

cash inflow in Years 1 to 4 = annual coupon payment = face value * coupon rate =  1000 * 8% = $80

cash inflow in Year 5 = annual coupon payment + price of the bond after 5 years =  $80 + $908.71 =  $988.71

In MIRR function, we use 7% as the finance rate and reinvest rate, as that is the rate at which coupons will be invested.

MIRR is calculated to be 9.05%

The expected rate of return is 9.05%

b]

First, we calculate the price of the bond after 5 years from now.

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 8.5% (Yield of 10-year bonds after 5 years from now)

nper = 10 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 7.5% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $934.39

Now, we calculate the expected rate of return using MIRR function in Excel with the following cash flows :

cash outflow in Year 1 = $899.50 (price paid to buy bond today)

cash inflow in Years 1 to 4 = annual coupon payment = face value * coupon rate =  1000 * 7.5% = $75

cash inflow in Year 5 = annual coupon payment + price of the bond after 5 years =  $75 + $934.39 =  $1009.39

In MIRR function, we use 7% as the finance rate and reinvest rate, as that is the rate at which coupons will be invested.

MIRR is calculated to be 8.71%

The expected rate of return is 8.71%