8. Three coupon bonds with a 10% coupon rate all just sell for their face value

Question

8. Three coupon bonds with a 10% coupon rate all just sell for their face value of $1,000. The three bonds will mature in one, two, and five years, respectively. Interest rates on all these bonds are 10% when they are bought, but decline to 5% after they are purchased. Calculate the one-year rates of return on these bonds. What are the initial current yields and the one-year rates of capital gain on these bonds? Which of the three bonds would be the best choice for an investor who has a one-year holding period? Why?

Explanation / Answer

Bonds A B C Face Value $1,000.00 $1,000.00 $1,000.00 Coupon Rate 10.00% 10.00% 10.00% Coupon Payment $100.00 $100.00 $100.00 Rate 10.00% 10.00% 10.00% Period 1 2 5 PV $1,000.00 $1,000.00 $1,000.00 After 1 year Bonds A B C Face Value $1,000.00 $1,000.00 $1,000.00 Coupon Rate 10.00% 10.00% 10.00% Coupon Payment $100.00 $100.00 $100.00 Rate 5.00% 5.00% 5.00% Period 0 1 4 PV $1,000.00 $1,047.62 $1,177.30 A B C ROR = (PV after 1 year + coupon payment - PV at initial year)/PV at initial year 10.00% 14.76% 27.73% Current Yield = Coupon Payment/ Initial PV 10.00% 10.00% 10.00% Capital Gain Yield = (PV after 1 year + coupon payment - PV at initial year)/PV at initial year 10.00% 14.76% 27.73% Bond C because it has a highest capital gain yield and ROR.

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