A newly issued bond pays its coupons once a year. Its coupon rate is 4.8%, its m

Question

A newly issued bond pays its coupons once a year. Its coupon rate is 4.8%, its maturity is 20 years, and its yield to maturity is 7.8%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.8% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Holding-period return             %_____________

b. If you sell the bond after one year when its yield is 6.8%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

After-tax holding-period return             %______________

d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 6.8% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.8% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Realized compound yield before taxes             %_______________

e. Use the tax rates in part (b) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

After-tax two-year realized compound yield             %_____________

Explanation / Answer

1 The initial price is: P0 = $70.10, for [n = 20; PMT = 4.8; FV = 100; i = 7.8] The next year’s price is: P1 = $79.02, for [n = 19; PMT = 4.8; FV = 100; i = 6.8] HPR = [$4.8 + ($79.02-70.10)]/$79.02 => 17.36% 2 Using OID tax rules, the price path of the bond under the constant yield method is obtained by discounting at an 7.8% yield, and reducing maturity by one year at a time: Constant yield prices: P0 = $70.10 P1 = $70.77 (implies implicit interest over first year = $0.67) P2 = $71.49 (implies implicit interest over second year = $1.39) Tax on explicit plus implicit interest in the first year = 0.40 x ($4.8 + $0.67) = $2.19 Capital gain in the first year = actual price – constant yield price $79.02 – 70.77= 8.25 Tax on capital gain = 0.30 x 8.25 = $2.48 Total taxes = $2.19+2.48 = $4.67 3 The after-tax HPR = [$4.8 + ($79.02-70.10) - $4.67]/$70.10 = 12.91%

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