Question

A newly issued bond pays its coupons once annually. Its coupon rate is 9.2%, its maturity is 20 years, and its yield to maturity is 11%. a. Find the holding-period return for a 1-year investment period if the bond is selling at a yield to maturity of 10% 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, 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 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.) Aftar tav haldinn nariad return

Answer 1

a]

Issue price of bond

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 11% (YTM of bonds = market interest rate)

nper = 20 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 9.2% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $856.66

x fc A1 A A 1 ($856.66)! =PV(11%,20,1000*9.2%,1000) E F B C D

sale price of bond

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 10% (YTM of bonds = market interest rate)

nper = 19 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 9.2% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $933.08

А2 х v ft =PV (10%,19,1000*9.2%,1000) B C D E - A 2 | ($933.08) |

holding period return = (sale price - purchase price + annual coupon payment) / purchase price

annual coupon payment = face value * coupon rate = 1000 * 9.2% = $92

holding period return = ($933.08 - $856.66 + $92) / $856.66

holding period return = 19.66%

b]

With original issue tax discount treatment, the difference between issue price and face value is amortized over the life of the bond, and the amortization amount in each year is treated as interest income.

Interest amortized per year = (face value - issue price) / bond life in years

Interest amortized per year = ($1,000 - $856.66) / 20 = $7.17

tax on interest income = (interest amortized per year + annual coupon payment) * tax rate on interest income

tax on interest income = ($7.17 + $92) * 40% = $39.67

tax on capital gain = (sale price - purchase price) * tax rate on capital gain

tax on capital gain = ($933.08 - $856.66) * 30% = $22.93

total taxes = $39.67 + $22.93 = $62.59

c]

after tax holding period return = (sale price - purchase price + annual coupon payment - total taxes) / purchase price

after tax holding period return = ($933.08 - $856.66 + $92 - $62.59) / $856.66

after tax holding period return = 12.35%