Yield to maturity A bonds market price is 875 It has a 1000

(Yield to maturity) A bond\'s market price is $875. It has a $1,000 par value, will mature in 10 years, and has a coupon interest rate of 9 percent annual interest, but makes its interest payments semiannually. What is the bond\'s yield to maturity? What happens to the bond\'s yield to maturity if the bond matures in 20 years? What if it matures in 5 years?

Solution

a. Yield to maturity 10.93% Working: Market Price $           875 Par Value $       1,000 Semi annual period 10*2 = 20 Semi annual coupon 1000*9%*6/12 = $             45 Yield to maturity = Average Income / Average Investment (Semi annual) = (Coupon+(Par Value-Current Price)/Semi annual period)/((Current Price+Par Value)/2) = (45+(1000-875)/20)/((875+1000)/2) = 5.47% Annual Yield to maturity = 5.47% x 2 = 10.93% b. Yield to maturity 10.27% Working: Market Price $           875 Par Value $       1,000 Semi annual period 20*2 = 40 Semi annual coupon 1000*9%*6/12 = $             45 Yield to maturity = Average Income / Average Investment (Semi annual) = (Coupon+(Par Value-Current Price)/Semi annual period)/((Current Price+Par Value)/2) = (45+(1000-875)/40)/((875+1000)/2) = 5.13% Annual Yield to maturity = 5.13% x 2 = 10.27% c. Yield to maturity 12.27% Working: Market Price $           875 Par Value $       1,000 Semi annual period 5*2 = 10 Semi annual coupon 1000*9%*6/12 = $             45 Yield to maturity = Average Income / Average Investment (Semi annual) = (Coupon+(Par Value-Current Price)/Semi annual period)/((Current Price+Par Value)/2) = (45+(1000-875)/10)/((875+1000)/2) = 6.13% Annual Yield to maturity = 6.13% x 2 = 12.27%