(Bond valuation) You are examining three bonds with a par value of $1 comma 000 (you receive $1 comma 000 at maturity) and are concerned with what would happen to their market value if interest rates (or the market discount rate) changed. The three bonds are Bond Along dasha bond with 5 years left to maturity that has an annual coupon interest rate of 8 percent, but the interest is paid semiannually. Bond Blong dasha bond with 10 years left to maturity that has an annual coupon interest rate of 8 percent, but the interest is paid semiannually. Bond Clong dasha bond with 15 years left to maturity that has an annual coupon interest rate of 8 percent, but the interest is paid semiannually. What would be the value of these bonds if the market discount rate were a. 8 percent per year compounded semiannually? b. 5 percent per year compounded semiannually? c. 15 percent per year compounded semiannually? d. What observations can you make about these

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:

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:

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:

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.

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