Question

General Electric bonds have a par value of $1,000, sell for $1,070, mature in 6 years, and have a 7% coupon rate paid annually.

a. Calculate the current yield and yield to maturity for this bond.

b. Calculate the realized compound yield for an investor with a 4-year horizon and a reinvestment rate of 5% over the period. At the end of the 4 years, assume that the coupon bonds will sell at a YTM of 6%.

c. Explain why the initial YTM is higher or lower than the realized compound yield. Would the initial YTM be higher or lower than the realized compound yield if the investor held the bond until maturity (and the reinvestment rate remained at 5%)? (Hint: Consider how the holding period length affects price risk and reinvestment risk.)

Answer 1

a). Current yield = annual coupon/current price = 70/1,070 = 6.54%

FV = 1,000; PV = 1,070; PMT = 70; N = 6, solve for RATE. Annual YTM = 5.59%

b). Total value from the bond after 4 years will be the sum of present value (PV) of reinvested coupons + price of the bond

Bond price after 4 years: FV = 1,000; PMT = 70; N = 2; rate = 6%, solve for PV. Bond price = 1,018.33

1st coupon: PV1 = 70*(1+5%)^3 = 81.03

2nd coupon: PV2 = 70*(1+5%)^2 = 77.18

3rd coupon: PV3 = 70*(1+5%)^1 =73.50

4th coupon + principal = 70 + 1,018.33 = 1,088.33

Total value = 81.03 + 77.18 + 73.50 + 1,088.33 = 1,320.44

Annual return on the bond = [(Final value/initial value)^(1/holding period)] -1

= [(1,320.44/1,070)^(1/4)] -1 = 5.39%

c). Initial YTM is higher than the realized compound yield because the reinvestment rate is less than the YTM. The yield would be equal to the initial YTM only if the coupons are reinvested at the YTM rate. So, even if the bond is held till maturity but the reinvestment rate is less than the YTM, the realized yield would still be lower than the YTM.