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

a). FV = 1,000; PMT (quarterly coupon payment) = coupon rate*par value/4 = (6%*1,000)/4 = 15; N (number of coupon payments) = 5*4 = 20; rate (quarterly rate) = annual rate/4 = 8%/4 = 2%, solve for PV.

Purchase price = 918.24 (Since price is less than par value of 1,000, this is a discount bond)

b-i). Since APR becomes equal to coupon rate of 6%, bond is selling at par so bond price = 1,000

Current yield = annual dividend/current price = (15*4)/1,000 = 6% (equals the coupon rate)

ii). Capital gains yield =(current price/purchase price) -1 = (1,000/918.24) -1 = 8.90%

iii). If coupons are reinvested at 2% per quarter then we have:

Total value after bond is sold = FV of coupons reinvested + value at maturity

= 15*(1+2%)^3 + 15*(1+2%)^2 + 15*(1+2%) + (1,000+15) = 1,061.82

Total rate of return = (total value/purchase price) -1 = (1,061.82/918.24) -1 = 15.64%

iv). Bond A's one year total rate of return cannot be calculated by summing up the current yield and the capital gains yield as it does not take into account the reinvestment income earned on the coupons.