Question

Suppose an investor can purchase a 6-year 9% coupon bond with a par value of $100 that pays interest semi-annually. The yield to maturity for this bond is 10% on a bond-equivalent yield basis. What is the coupon interest, capital gain/loss and reinvestment income associated with this bond over its 6-year life? Assume that the reinvestment rate is equal to the yield to maturity.

Answer #1

Coupon rate (annual) = 9%; N (number of years) = 6; Par value = 100; semi-annual coupon payment = coupon rate*par value/2 = 9%*100/2 = 4.5; annual yield = 10%, so semi-annual yield = 10%/2 = 5%

FV = 100; N = 6*2 = 12; PMT = 4.5; rate = 5%, solve for PV. Current bond price = 95.57

Now total future dollars at maturity = current price*(1+semi-annual yield)^12 = 95.57*(1+5%)^12 = 171.63

Total dollar returns = total future dollars - current price = 171.63 - 95.57 = 76.06

Coupon interest = semi-annual coupon*number of payments = 4.5*12 = 54

Capital gain = par value - current price = 100 - 95.57 = 4.43

Reinvestment income = total dollar returns - coupon interest - capital gain

= 76.06 - 54 - 4.43 = 17.63

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