Answer:
Bond A, 5 years to maturity, semiannual coupons, 8%
Bond B, 10 years to maturity, annual coupon, 8%
Bond C, 15 years to maturity, semiannual coupon, 8%
a) market rate 8% semiannual
Bonds A and C will be worth $1,000 (par value)
price of bond B:
- effective interest rate = 1.04² - 1 = 8.16%
- PV of face value = $1,000 / 1.04²⁰ = $456.39
- PV of coupon payments = $80 x 6.66192 (PV ordinary annuity factor, 8.16%, 10 periods) = $532.95
market price = $989.34
b) price of bond A:
PV of face value = $1,000 / 1.025¹⁰ = $781.98
PV of coupon payments = $40 x 8.75206 (PV ordinary annuity factor, 2.5%, 10 periods) = $350.08
market price = $1,132.06
price of bond B:
- effective interest rate = 1.025² - 1 = 5.0625%
- PV of face value = $1,000 / 1.025²⁰ = $610.27
- PV of coupon payments = $80 x 7.69817 (PV ordinary annuity factor, 5.0625%, 10 periods) = $615.85
market price = $1,226.12
price of bond C:
PV of face value = $1,000 / 1.025³⁰ = $476.74
PV of coupon payments = $40 x 20.93029 (PV ordinary annuity factor, 2.5%, 30 periods) = $837.21
market price = $1,313.95
c) price of bond A:
PV of face value = $1,000 / 1.075¹⁰ = $485.19
PV of coupon payments = $40 x 6.86408 (PV ordinary annuity factor, 7.5%, 10 periods) = $274.56
market price = $759.75
price of bond B:
- effective interest rate = 1.075² - 1 = 15.5625%
- PV of face value = $1,000 / 1.075²⁰ = $235.41
- PV of coupon payments = $80 x 4.91292 (PV ordinary annuity factor, 15.5625%, 10 periods) = $393.03
market price = $628.44
price of bond C:
PV of face value = $1,000 / 1.075³⁰ = $114.22
PV of coupon payments = $40 x 11.81039 (PV ordinary annuity factor, 7.5%, 30 periods) = $472.42
market price = $586.64
d) If the market rate is lower than the coupon rate, then the bonds will sell at a premium. The longer the maturity date, the larger the variations in market price due to different interest rates. E.g. the 15 year bond is more affected than the 5 year bond.
