A 30-year maturity bond has a 9% coupon rate, paid annually. It sells today for

Question

A 30-year maturity bond has a 9% coupon rate, paid annually. It sells today for $897.42. A 20-year maturity bond has a 8.5% coupon rate, also paid annually. It sells today for $909.5. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 10% and that 15-year maturity bonds will sell at yields of 9.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 8%. a-1. Calculate the annual return for the 30-year maturity bond over the next five years. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return % a-2. Calculate the annual return for the 20-year maturity bond over the next five years. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual rate of return % b. Which bond offers the higher expected rate of return over the five-year period? 30-year maturity bond 20-year maturity bond

Explanation / Answer

a1) Current Value of of bond = $897.42

Annual Coupon = 9% * 1000 =$90

Reinvestment Rate = 8%

Value of the bomd after 5 years =PV(10%,25,90,1000) = $909.23

The cash flows of this bond will be as follows:

Let Annual Rate of Return be r.

897.42 * (1 + r)5 = 1437.22

(1 + r)5 = 1437.22/897.42 = 1.6015

1 + r = 1.60151/5

r = 1.0988 -1 = 0.0988 = 9.88%

a2) Current Value of of bond = $909.5

Annual Coupon = 8.5% * 1000 =$85

Reinvestment Rate = 8%

Value of the bomd after 5 years =PV(9.5%,15,85,1000) = $921.72

The cash flows of this bond will be as follows:

Let Annual Rate of Return be r.

909.5 * (1 + r)5 = 1420.38

(1 + r)5 = 1420.38/909.5 = 1.5617

1 + r = 1.56171/5

r = 1.0933 - 1 = 0.0933 = 9.33%

b) Expected rate of return over the five-year period for 30-year maturity bond is greater than that of 20-year maturity bond ( 9.88% for 30-year maturity bond as compared to 9.33% for 20-year maturity bond).

Year Cash Flow Cash InFlows at the end of year 5 0 -897.42 1 90 122.44 2 90 113.37 3 90 104.98 4 90 97.20 5 999.23 999.23 Sum of Cash Inflows in year 5 $1437.22

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