Question

A newly issued bond pays its coupons once a year. Its coupon rate is 5.7%, its maturity is 15 years, and its yield to maturity is 8.7%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7.7% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. If you sell the bond after one year when its yield is 7.7%, 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.)

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 7.7% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3.7% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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

a.) If the Face value of Bond is $1000

Present Value (PV) of Bond at Year 0= $753.84

where,

Period = 15 Years

YTM = 8.7%

Coupon Rate = 5.7% annually

PV of Bond At end of Year 1 = $832.20

Holding Period Gain = Capital gain after Year 1 and Coupon Received

Holding period Gain = (832.20-753.84) +57= $135.36

Holding Period Return = 135.36/753.84 = 17.95%

Tax on Interest Income = 57* 0.4 = $22.8

Tax on Capital Gains = (832.20-753.84) * 0.3 = $23.508

Total Taxes = 22.80+ 23.508 = $46.308

c.

After Tax Holding Period Return = (Holding Period Gain - Total Tax Paid)/PV of Bond at Year 0

After Tax Holding Period Return = (135.36-46.308)/753.84

After Tax Holding Period Return = 0.1181 = 11.81%

d.

After Year 2 Value of Bond = $839.28

2 Year Holding period Gain on Bond = Capital Gain for 2 years + Coupon payment and Year 1 and Year 2 + Reinvestment Return of Coupoun of Year 1 at 3.7%

2 Year Holding Period Gain = (839.28-753.84) + 57*2 + 57(0.037)

2 Year Holding Period Gain = 85.44 + 114 +2.109 = $201.55

CAGR =

CAGR =

CAGR = 0.1256 = 12.56%

2 Year Compound yield = 201.55/753.84 = 0.2673 = 26.73%