Question

A 7.20 percent coupon bond with 23 years left to maturity is priced to offer a 6.1 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.7 percent. What would be the total return of the bond in dollars? (Assume interest payments are semiannual.) What would be the total return of the bond in percent? (Assume interest payments are semiannual.)

Answer 1

Coupon = (0.072 * 1000) / 2 = 36

Rate = 6.1% / 2 = 3.05%

Number of periods = 23 * 2 = 46

Current price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Current price = 36 * [1 - 1 / (1 + 0.0305)⁴⁶] / 0.0305 + 1000 / (1 + 0.0305)⁴⁶

Current price = 36 * 24.55513 + 251.06847

Current price = $1,135.0532

Coupon = (0.072 * 1000) / 2 = 36

Rate = 6.7% / 2 = 3.35%

Number of periods = 22 * 2 = 44

Current price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Current price = 36 * [1 - 1 / (1 + 0.0335)⁴⁴] / 0.0335 + 1000 / (1 + 0.0335)⁴⁴

Current price = 36 * 22.84759 + 234.60585

Current price = $1,057.1190

total return of the bond in dollars = Ending value + coupon - beginning value

total return of the bond in dollars = $1,057.1190 + 72 - $1,135.0532

total return of the bond in dollars = -5.9342

Total return in percent = (-5.9342 / 1,135.0532) * 100

Total return in percent = -0.5228%