Question

A newly issued bond pays its coupons once a year. Its coupon rate is 5.5%, its maturity is 10 years, and its yield to maturity is 8.5%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7.5% 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 7.5%, 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 7.5% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3.5% 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

Hello

a) Let the face value of the bond be $1,000

Annual Coupon Payment = 5.5% of 1,000 = $55

P0 is equal to finding PV in a financial calculator with the following inputs:

N = 10, I/Y = 8.5, PMT = 55, FV = 1000

Compute PV = 803.16

P0 = 803.15955

P1 is the price of the bond after 1 year, so N = 9 and I/Y = 7.5

N = 9, I/Y = 7.5, PMT = 55, FV = 1000

Compute PV = 872.4222

P1 = $872.4222

(b) Based on ODI tax rules, the prices are obtained under constant yield method at 8.9% yield, then prices for first 2years will be:
P0 = $803.16
P1 = $816.43
That means differences in price = 816.43 - 803.16 = 13.27 is the implicit interest over first year.
Tax on interest = (55+13.27)*40% = $27.31

Capital gain = P1 - P0 = 872.4222 - 803.15955 = $69.2627

So, the tax on capital gain = 30% * 69.2627 = $20.78

Total tax = 27.31+ 20.78 = $48.09

(c) Computation of after tax HPR = (Ending price - beginning price+ Interest earned) - total taxes / Beginning price
= [(872.4222 - 803.15955 + 55) - 48.09]/803.15955 = 9.48%

After - tax HPR = 9.48%

(d) P2 = Selling price of the bond at the end of year 2 is calculated with the following inputs

N = 8, number of years to maturity at the end of year 2

I/Y = 7.5%, given

PMT = 55, coupon payment

FV = 1000

Compute PV = 882.8539

P2 = 882.8539

Total coupon received with reinvestment interest = 55 + 55 + 55*0.035 = $111.952

2 year holding period return = 23.861553%

Realized compound yield before taxes = 11.29%

(e) Based on ODI tax rules, the prices are obtained under constant yield method at 8.9% yield, then prices will be:
P0 = $803.16
P1 = $816.43
P2 = $830.82
That means differences in price = 830.82 - 803.16 = 27.66 is the implicit interest over two year.
Tax on interest = (55(1.035)+27.66)*40% = $33.834

Capital gain = Actual price - constant yield price
= $882.8539 - $830.82 = 52.0339
Tax on capital gain = 52.0339*30% = $15.61
Total taxes = 33.834 + 15.61 = $49.44

After tax HPR = (Ending price - beginning price+ Interest earned) - total taxes / Beginning price
= (882.8539- 803.16+111.952) - 49.44 / 803.16 = 17.7058%

After tax realized compound yield = square root of (after tax HPR+1) -1
= square root of (17.7058%+1) -1 = 8.49%

I hope this clears your query.

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