Bonds of the Abel & Crawford Corporation with a par value of $1,000 sell for $96
ID: 2761832 • Letter: B
Question
Bonds of the Abel & Crawford Corporation with a par value of $1,000 sell for $960, mature in 5 years, and have a 7 percent semi-annual coupon rate. a. What is the bond’s current yield? b. What is the bond’s current yield-to-maturity (YTM)? c. What is the bond’s horizon yield (or annualized total return) for an investor with a 3-year holding period and a reinvestment rate of 6 percent over that period? (Assume that at the end of the 3 years, the yield-to-maturity for similar bonds with 2 years left to run is 7%.)
Explanation / Answer
a. The current yield = Annual Coupons/Current BOnd price = 70/960 = 0.0729 = 7.29%
b. YTM =rate(nper,pmt,pv,fv) nper = 5*2=10, PMT = 7%*1000 = 70(annual) ans semi annual = 70/2 =35
YTM (Semiannual) = rate(5*2,35,-960,1000) = 3.993%
Hence annual YTM = 3.993*2 = 7.986% = 7.99%
c. Return for three years is
Coupon in every 6 months for 3 years (6 periods) is 35.
The reinvestment rate for that period (semi - annual) = 0.06/2 = 0.03
Hence the future value of the coupon payments reinvested is =fv(rate,nper,pmt) =fv(0.06/2,6,35) = 226.39
Hence the total return = Selling price + Copon payments - Purchase price
Total return = 1000 +226.39 -960 = 266.39
Hence total return = 266.39/960 = 0.277489583
Annualized return =0.277489583/3 = 9.25%
Annualized (Horizon ) Yield = 9.25%