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

Assume $1000 is the face value.

FV = 1000, PMT = 40, N = 10, YTM = 7%

PV = (PMT/YTM) * [1 - 1/(1 + YTM)^N] + FV/(1 + YTM)^N

Use above formula or financial calculator, PV = $789.29

A: when N = 9, YTM = 6%; compute PV = $863.97

HPR = 863.97/789.29 - 1 = 0.0946 = 9.46%

B:

Tax on interest income = 40*0.40 = $16

Tax on capital gain = (863.97 - 789.29)*0.30 = $22.40

C:

After-tax HPR = (863.97 - 16 - 22.40) / 789.29 - 1 = 0.045965 = 4.60%

D: After 2-year of holding, N = 8

When N = 8, YTM = 6%; compute PV = 875.80

Proceed from selling and coupons = 875.80 + 40 + 40*1.02 = 956.60

(1 + r)^2 = 956.60/789.29

r = 0.1009 = 10.09%