Question

Last year, you bought a bond with face value $1000, maturity 20 years, coupon rate of 7% per year payable semi-annually and yield to maturity of 5.5% per year. Currently the bond sells for $900. How much would be your total yield if you sell this bond today? (17.84%) (15.79%) 13.71% 10.78%.

Answer 1

First of all we have to calculate the price at which bond was purchased last year.

Purchase Price of Bond = Semi Annual Interest Rate* PVAF (r%, n period), + Maturity Amount* PVF (r%, n period)

PVAF (r%, n period) is the annuity factor where r% is semi annual rate and n period refers to number of semi annual period.

PVF (r%, n period) is the present value factor of 40th period,where r% is semi annual rate and n period refers to 40th semi annual period.

PVAF (2.75%, 40 period)= (1+r%)ⁿ-1/ (r%*(1+r%)ⁿ)

= (1+0.0275)⁴⁰-1/ (0.0275*(1+0.0275)⁴⁰)

=2.959873987-1/(0.0275*2.959873987)

=1.959873987/0.081396535

=24.078

Semi Annual Interest Payment = 1000*3.5% = $35

Maturity Amount = $ 1000 (As it is assumed that they are redeemed at par)

Therefore Purchase price of Bond = 35*24.078 + 1000*0.338

=842.73 + 338

= $ 1180.73

Capital Gain from sale of bond after 1 year = 900-1180.73

= $-280.73

Interest received from holding bond = $ 70 ( 2 semi annual payments of $35 )

Total Yield =(Capital Gain+ Interest)*100/ Purchase Price

= (-280.73+70)*100/1180.73

= (-210.73*100)/1180.73

= -17.847% or (17.84%)