Question

Calculate the yield to maturity on the following bonds:

A 9.1 percent coupon (paid semiannually) bond, with a $1,000 face value and 16 years remaining to maturity. The bond is selling at $980.

An 8.1 percent coupon (paid quarterly) bond, with a $1,000 face value and 10 years remaining to maturity. The bond is selling at $910.

An 11.1 percent coupon (paid annually) bond, with a $1,000 face value and 6 years remaining to maturity. The bond is selling at $1,060.

Answer 1

The yield to maturity(YTM), coupon payments, time to maturity (N), bond market price and bond par value are all linked to each other by the following equation:

Bond Market Price = Periodic Bond Coupon x (1/YTM) x [1-{1/(1+YTM)^(N)}] + Bond Par Value / (1+YTM)^(N)

(1) Bond Market Price = $ 980, Bond Par Value = $ 1000, Periodic Coupon = 0.091 x 0.5 x 1000 = $ 45.5, N = 16 years or 32 half-years, YTM = 2R

Therefore, 980 = 45.5 x (1/R) x [1-{1/(1+R)^(32)}] + 1000 / (1+R)^(32)

Using a financial calculator/excel/trial and error to solve the above equation we get:

R = 0.0467 or YTM = 9.34 %

(2) Bond Market Price = $ 910, Bond Par Value = $ 1000, Periodic Coupon = 0.081 x 0.25 x 1000 = $ 20.25, N = 10 years or 40 quarters, YTM = 4R

Therefore, 910 = 20.25 x (1/R) x [1-{1/(1+R)^(40)}] + 1000 / (1+R)^(40)

Using a financial calculator/excel/trial and error to solve the above equation we get:

R = 0.0238 or YTM = 9.52 %

(3)

Bond Market Price = $ 1060, Bond Par Value = $ 1000, Periodic Coupon = 0.111 x 1000 = $ 111, N = 6 years , YTM = R

Therefore, 1060 = 111 x (1/R) x [1-{1/(1+R)^(6)}] + 1000 / (1+R)^(6)

Using a financial calculator/excel/trial and error to solve the above equation we get:

R = 0.0973 or YTM = 9.73 %