Question

A bond that pays coupons annually is issued with a coupon rate of 4 percent, maturity of 30 years, and a yield to maturity of 7 percent. What annual rate of return will be earned in the following situations by an investor who purchases the bond and holds it for 4 year if the bond’s yield to maturity when the investor sells is 8 percent? a) All coupons were immediately consumed when received. b) All coupons were reinvested in your bank account, which pays 2 percent interest until the bond is sold. c) All coupons were reinvested at 10.88 percent until the bond is sold.

Answer 1

a. If all the coupons are received and consumed. the gain will only be the capital gain from the bond

Price at purchase =PV(rate,nper,pmt,fv) =PV(0.07,30,40,1000) = 627.73

Price at sale =PV(0.08,26,40,1000) = $567.60

Annual rate of return = (1+ (567.60-627.73)/627.73)^(1/4)-1 = -0.0249 = -2.49%

Annual rate of return = -2.49%

b. Value of Coupons = 40*1.02^3 +40*1.02^2 +40*1.02 + 40 = 164.86

Total return = (567.60-627.73+164.86) = 104.73

Annual rate of return = (1+104.73/627.73)^(1/4) -1 = 0.0393 = 3.93%

Annual rate of return = 3.93%

c.Value of Coupons = 40*1.1088^3 +40*1.1088^2 +40*1.1088 + 40 = 188.06

Total return = (567.60-627.73+188.06) = 127.93

Annual rate of return = (1+127.93/627.73)^(1/4) -1 = 0.0475 = 4.75%

Annual rate of return = 4.75%