Question

A bond has an annual coupon of 8% with semiannual frequency. The maturity leftover is 9 years and the bond is callable in 3 years with a 20% call premium. The face value is $1000. The current market price of the bond is $1,071.

Now assume, investor held bought the bond today at the current market price and held the bond for 4 years. Each coupon he reinvested at 6%. Then he sold the bond exactly after 4 years from today when the YTM was 9%.
a) Calculate the selling price after 4 years.
b) Calculate the future value of reinvested coupons (FVRC) after 4 years from today.
c) Calculate his holding period return (HPR). Then using that calculate his annualized realized HPR.

Answer 1

Purchase price (P) = 1,071.

Yield to Call (YTC) of the bond: FV (call price) = par value*(1+call premium) = 1,000*(1+20%) = 1,200; PMT (semi-annual coupon) =

(coupon rate*par value)/2 = (4%*1,000)/2 = 40; N = 3*2 = 6; PV = 1,071, CPT RATE,

Semi-annual YTC = 5.48% so annual YTC = 5.48%*2 = 10.97%

Yield to Maturity (YTM) of the bond: FV (par value) = 1,000; PMT = 40; N = 9*2 = 18; PV = 1,071, CPT RATE.

Semi-annual YTM = 3.46% so annual YTM = 6.93%

The YTC is greater than the YTM so the bond will not be called. Even after 4 years, the YTM of 9% is less than the YTC so it will not be called even then.

a). Selling price of the bond after 4 years: FV = 1,000; PMT = 40; N = 5*2 = 10; rate = 9%/2 = 4.5%, CPT PV.

PV = 960.44 (Selling price after 4 years)

b). Future Value (FV) of reinvested coupons: PMT = 40; N = 8 (as in 4 years, the investor will get 8 coupons); rate (semi-annual reinvestment rate) = 6%/2 = 3%, CPT FV.

FV = 355.69

c). Total amount that the investor gets when bond is sold (TA) = 960.44 + 355.69 = 1,316.13

Total HPR = (TA/P) -1 = (1,316.13/1,017)-1 = 22.89%

Annualized HPR = [(1+22.89%)^(1/4)] -1 = 5.29%