Question

A newly issued bond pays its coupons once a year. Its coupon rate is 4%, its maturity is 10 years, and its yield to maturity is 7%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6% 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%, 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.)

Tax on interest income	$
Tax on capital gain	$
Total taxes	$

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% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2% 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             %

Answer 1

Issue price of the bond = Coupon payment x PVIFA _{7%, 10 years} + Maturity amount x PVIF _{7%, 10th year} = $ 40 x 7.0236 + $ 1,000 x 0.5083 = $ 789.24

a. Price at the end of the year = Coupon payment x PVIFA _{6%, 9 years} + Maturity amount x PVIF _{6%, 9th year} = $ 40 x 6.8017 + $ 1,000 x 0.5919 = $ 863.97

Holding period return = [$ ( 863.97 - 789.24) + $ 40] / $ 789.24 x 100 = $ 114.73 / $ 789.24 = 14.54%

b. As the bond is not held for more than one year, capital gains are short term capital gains, and would be treated as ordinary income.

Therefore total tax liability = $ ( 40 + 74.73) x 0.4 = $ 45.89

c. After-tax holding period return on the bond = $ ( 114.73 - 45.89) = $ 68.84 or $ 68.84 / $ 789.24 x 100 = 8.72%

d. After 2 years, price of the bonds = Coupon payment x PVIFA _{6.5%, 8 years} + Maturity amount x PVIF_{6.5%, 8th year} Coupon payment x ( 1+ r) x PVIF_{6.5%, 1 year} = $ 40 x 6.0888 + $ 1,000 x 0.6042 + $ 40 ( 1.025) / ( 1.065) = $ 243.552 + $ 604.20 + $ 38.50 = $ 886.25

Compound yield before taxes for a 2 -year period = $ ( 886.25 - 789.24) + $ 40 / $ 789.24 x 100 = 17.36 %

e. Tax on interest income= $ (40 + 41) x 0.4 = $ 32.4

Tax on capital gain = $ ( 886.25 - 789.24) x 0.30 = $ 29.10

Total tax liability = $ ( 32.4 + 29.10) = $ 61.5

After-tax 2 -year realised compound yield = $ ( 137.01 - 61.5) / $ 789.24 = 9.57%