Question

One bond has a coupon rate of 5.4%, another a coupon rate of 8.2%. Both bonds pay interest annually, have 13-year maturities, and sell at a yield to maturity of 7.5%.a. If their yields to maturity next year are still 7.5%, what is the rate of return on each bond? (Do not round intermediate calculations. Enter your answers as a percent to 1 decimal place.) rate or returnbond 1 __________bond 2 ___________b. Does the higer-coupon bond give a higher rate of return? (yes or no)

Answer 1

Answer:

a. rate or return bond 1 6.6% bond 2 7.71%

b. Does the higher-coupon bond give a higher rate of return? yes

Explanation:

bond 1 has a coupon rate of 5.4%

bond 2 has a coupon rate of 8.2%

yield to maturity formula = {C + [(Face value - market value) / n]} / [(Face value + market value) / 2]

assume bond 1's face value = $1,000

coupon = 54

n = 13

YTM = 7.5%

0.075 = {54 + [(1,000 - M) / 13]} / [(1,000 + M) / 2]

0.075 x  [(1,000 + M) / 2] = 54 +  [(1,000 - M) / 13]

0.075 x (500 + 0.5M) = 54 + 76.92 - 0.0769M

37.50 + 0.0375M = 130.92 - 0.0769M

0.0375M + 0.0769M = 130.92 - 37.50

0.1144M = 93.42

M = 93.42 / 0.1142 = $818.04

rate of return = $54 / $818.04 = 0.066 = 6.6%

assume bond 2's face value = $1,000

coupon = 82

n = 13

YTM = 7.5%

0.075 = {82 + [(1,000 - M) / 13]} / [(1,000 + M) / 2]

0.075 x  [(1,000 + M) / 2] = 82 +  [(1,000 - M) / 13]

0.075 x (500 + 0.5M) = 82 + 76.92 - 0.0769M

37.50 + 0.0375M = 158.92 - 0.0769M

0.0375M + 0.0769M = 158.92 - 37.50

0.1144M = 121.42

M = 121.42 / 0.1142 = $1,063.22

rate of return = $82 / $1,063.22 = 0.07712 = 7.71%