Question

Bond A is a $1,000, 6% quarterly coupon bond with 5 years to maturity.

(a) If you bought Bond A today at a yield (APR) of 8%, what is your purchase price? Is this a premium or discount bond? Why?

(b) One year later, Bond A's YTM (APR) has gone down to 6% and you sell it immediately after receiving the coupon.

(i) What is the current yield?

(ii) What is the capital gains yield?

(iii) What is the one-year total rate of return (in APR) if the coupons are reinvested at 2% per quarter during the holding period?

(iv) Can Bond A’s one-year total rate of return be determined correctly by simply adding up the current yield and the capital gains yield? Explain your answer without calculations.

Answer 1

1.
=6%*1000/8%*(1-1/1.02^20)+1000/1.02^20
=918.24283
Discount bond as price is less than par of 1000

2.
As coupon rate is equal to ytm, price is equal to par=1000
current yield=6%

3.
capital gains yield=1000/918.24283-1=8.904%

4.
=(6%*1000/8%*(1.02^4-1)+1000)/(918.24283)-1
=15.637%

5.
No as reinvestment rate is not the same as purchase yield

Formulas used above:
1.
=Present value of coupons+Present value of par
=coupon rate*par value/yield*(1-1/(1+yield/4)^(4*t))+Par value/(1+yield/4)^(4*t)

2.
=Coupon rate

3.
=Price now/Price one year ago-1

4.
=(Future value of coupons+Price one year later)/Purchase Price-1