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Solutions to Chapter 5

Valuing Bonds

Note: Unless otherwise stated, assume all bonds have $1,000 face (par) value.

1. a. The coupon payments are fixed at $60 per year. Coupon rate = coupon payment/par value = 60/1000 = 6%, which remains unchanged.

b. When the market yield increases, the bond price will fall. The cash flows are discounted at a higher rate.

c. At a lower price, the bond’s yield to maturity will be higher. The higher yield to maturity on the bond is commensurate with the higher yields available in the rest of the bond market.

d. Current yield = coupon payment/bond price. As coupon payment remains the same and the bond price decreases, the current yield increases.

2. When the bond is selling at a discount, $970 in this case, the yield to maturity is greater than 8%. We know that if the discount rate were 8%, the bond would sell at par. At a price below par, the YTM must exceed the coupon rate.

Current yield equals coupon payment/bond price, in this case, 80/970. So current yield is also greater than 8%.

3. Coupon payment = .08 x 1000 = $80

Current yield = 80/bond price = .075

Therefore, bond price = 80/.075 = $1,066.67

4. Par value is $1000 by assumption. Coupon rate = $80/$1000 = .080 = 8.0% Current yield = $80/$950 = .0842 = 8.42% Yield to maturity = 9.12% [n = 6; PV= (-)950; FV = 1000; PMT = 80)

5. To sell at par, the coupon rate must equal yield to maturity. Since Circular bonds yield 9.12%, this must be the coupon rate.

6. a. Current yield = annual coupon/price = $80/1050 = .0762 = 7.62%.

b. YTM = 7.2789%. On the calculator, enter PV = (-)1050, FV = 1000, n = 10, PMT = 80, compute i.

7. When the bond is selling at par, its yield to

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