Question

 

A newly issued bond pays its coupons once a year. Its coupon rate is 4.6%, its maturity is 10 years, and its yield to maturity is 7.6%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.6% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Holding-period return 14.9 %

b. If you sell the bond after one year when its yield is 6.6%, 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	$24.17
Tax on capital gain	$17.40
Total taxes	$41.57

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 9.67 %

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 6.6% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.6% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Realized compound yield before taxes 10.57 %

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.)

Answer 1

Answering Part E alone but whereever required doing calculations for previous items also. Also as per the OID guidelines the taxes should be paid on accrured interest even when the interest pay out has not happened i.e in Year 1 though the bond is not sold the amortisation of purchase discount should be reported and taxes should be paid on that - however basis feedback, we are working on the assumption that the taxes are paid only on actual interest credit.

Year 1 coupon on bond : 46 ; Taxes = 40%; Net of Tax = 46 * (1-40%) = 27.6

This is reinvested at 2.6% for one year and becomes : 27.6 * (1+2.6%) = 28.32 . The tax on interest for Year 2 (interest on interest) is (28.32-27.6) * 40%= 0.29 . Hence net at end of Year 2 = 28.03

Year 2 coupon = 46 and net of Tax = 27.6

At constant YTM of 7.6%, the price of the bond at end of Year 2 would be 824.95. Thus the interest portion of capital gains as per OID = (824.95 - 795.01) = 29.94. Net of tax will be = 29.94 * (1-40%) = 17.96

Capital Gains : Price of bond at 6.6% YTM at end of Year 2 is 878.70, hence capital gains = (878.70 - 795.01 - 29.94) = 53.75. Net of tax, capital gains = 53.75 * (1-30%) = 37.62

Now we have all the net of tax cash flows:

(28.03 + 17.96 +27.6 + 37.62 + 795.01) = 906.22

Hence if 2 year return is r, then we have : 906.22 = 795.01 * (1+r)²; solving we get r = 6.77%