Question

A 30-year maturity bond has a 6% coupon rate, paid annually. It sells today for $877.42. A 20-year maturity bond has a 5.5% coupon rate, also paid annually. It sells today for $889.5. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 7% and that 15-year maturity bonds will sell at yields of 6.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 5%. a. Calculate the expected rate of return of the 30-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 20-year bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Expected rate of return

Answer 1

SOLUTION:

(a) Calculate the annual return for the 30-year maturity bond over the next five years.

The value of 30-year maturity bond after 5-years can be calculated using PV function

N = 25, PMT = 60, FV = 1000, I/Y = 7%

=> PV = $883.46

Expected annual rate of return can be calculated using I/Y function

N = 5, PV = - 877.42, PMT = 60, FV = $883.46

=> Rate of return = I/Y = 6.79%

(b) What is the expected return of the 20-year bond.

Similarly, price of the 20-year bond in five years

N = 15, PMT = 55, FV = 1000, I/Y = 6.5%

=> PV = $905.97

Expected annual rate of return can be calculated using I/Y function

N = 5, PV = - 889.5, PMT = 75, FV = $905.97

=> Rate of return = I/Y = 6.51%