Question

Calculate the yield to maturity on the following bonds:

A. A 9.9 percent coupon (paid semiannually) bond, with a $1000 face value and 24 years remaining to maturity. The bond is selling at $940.

B. A 10.4 percent coupon (paid quarterly) bond, with a $1000 face value and 10 years remaining to maturity. The bond is selling at $906.

C. An 9.4 percent coupon (paid annually) bond, with a $1000 face value and 10 years remaining to maturity. The bond is selling at $1056

Please round all answers to 3 decimal places.

Answer 1

Yield to maturity (YTM) is the total return on the bond if the bond is held until maturity.

YTM = [C + (FV - PP/n)] / (FV+PP)/2

where C = coupon payment

FV= Face value of bond

PP = price of bond

a) Case of Semi-annual bond

FV = $1000

PP = $940

n = 24 years * 2 = 48 years

C = 9.9%/2 * $1000 = $49.5

YTM = $49.5 + (1000-940/48) / (1000+940)/ 2

YTM = [$49.5 + $1.25]/ 970 = 0.0523 or 5.23%

b) Case of quarterly bond

FV = $1000

n = 10 years * 4 = 40 years

PP = $906

C = 10.4%/ 4 * 1000 = $52

YTM = [$52 + (1000-906/40) ] / (1000+906/2)

YTM = ($52 + $2.35)/ $953

YTM = 0.057 or 5.70%

c) Case of annual bond

FV = $1000

PP = $1056

n = 10 years

C= 9.4% * 1000 = $94

YTM = [$94 + (1000-1056/10)] / (1000+1056/2)

YTM = $88.4/ 1028 = 0.085 or 8.59%