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Unformatted text preview: Solutions to Chapter 6 Valuing Bonds 1. a. Coupon rate = 6%, which remains unchanged. The coupon payments are fixed at $60 per year. 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 for the bond is commensurate with the higher yields available in the rest of the bond market. d. Current yield = coupon rate/bond price As coupon rate 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 yield to maturity were 8%, the bond would sell at par. At a price below par, the yield to maturity exceeds the coupon rate. Current yield = coupon payment/bond price = $80/$970 Therefore, current yield is also greater than 8%. 3. Coupon payment = 0.08 × $1,000 = $80 Current yield = $80/bond price = 0.07 Therefore: bond price = $80/0.07 = $1,142.86 4. Coupon rate = $80/$1,000 = 0.080 = 8.0% Current yield = $80/$950 = 0.0842 = 8.42% To compute the yield to maturity, use trial and error to solve for r in the following equation: 6 6 ) r 1 ( 000 , 1 $ r) (1 r 1 r 1 $80 $950 + + + × × = ⇒ r = 9.119% Using a financial calculator, compute the yield to maturity by entering: n = 6; PV = ( )950; FV = 1000; PMT = 80, compute i = 9.119% 61 Verify the solution as follows: 98 . 949 $ 09119 . 1 000 , 1 $ ) 09119 . 1 ( 09119 . 1 09119 . 1 80 $ PV 6 6 = +  × = (difference due to rounding) 5. In order for the bond to sell at par, the coupon rate must equal the yield to maturity. Since Circular bonds yield 9.119%, this must be the coupon rate. 6. a. Current yield = coupon/price = $80/$1,100 = 0.0727 = 7.27% b. To compute the yield to maturity, use trial and error to solve for r in the following equation: 10 10 ) r 1 ( 000 , 1 $ r) (1 r 1 r 1 $80 $1,100 + + + × × = ⇒ r = 6.602% Using a financial calculator, compute the yield to maturity by entering: n = 10; PV = ( )1100; FV = 1000; PMT = 80, compute i = 6.602% Verify the solution as follows: 02 . 100 , 1 $ 06602 . 1 000 , 1 $ ) 06602 . 1 ( 06602 . 1 06602 . 1 80 $ PV 10 10 = +  × = (difference due to rounding) 7. When the bond is selling at face value, its yield to maturity equals its coupon rate. This firm’s bonds are selling at a yield to maturity of 9.25%. So the coupon rate on the new bonds must be 9.25% if they are to sell at face value. 8. The bond pays a coupon of 7.125% which means annual interest is $71.25. The bond is selling for: 130 5/32 = $1,301.5625. Therefore, the current yield is: $71.25/$1301.5625 = 5.47% The current yield exceeds the yieldtomaturity on the bond because the bond is selling at a premium. At maturity the holder of the bond will receive only the $1,000 face value, reducing the total return on investment....
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 Fall '11
 GingerWagner
 Finance, Corporate Finance

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