Answer:
a. rate or return bond 1 <u>6.6%</u> bond 2 <u>7.71%</u>
b. Does the higher-coupon bond give a higher rate of return? <u>yes</u>
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%
