Question

A newly issued bond pays its coupons once a year. Its coupon rate is 5.1%, its maturity is 15 years, and its yield to maturity is 8.1%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7.1% 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 7.1%, 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 7.1% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3.1% 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.)

Answer 1

Since, there are multiple parts to the question, I have answered the first four with complete details.

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Part a)

To calculate holding period return, we need to find the bond price today (P0) and price after 1 Year (P1). The bond price can be calculated with the use of PV function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, Yield), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Bond Price Today

Here, Rate = 8.1%, Nper = 15, PMT = 1,000*5.1% = $51 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond Price Today (P0) = PV(8.1%,15,51,1000) = $744.78

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Bond Price after 1 Year

Here, Rate = 7.1%, Nper = 15 - 1 = 14, PMT = 1,000*5.1% = $51 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond Price After 1 Year (P1) = PV(7.1%,14,51,1000) = $826.13

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Now, we can calculate the holding period return as below:

Holding Period Return for 1 Year Investment = (Bond Price After 1 Year - Bond Price Today + Annual Coupon Payment)/Bond Price Today*100 = (826.13 - 744.78 + 51)/744.78*100 = 17.77%

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Part b)

We will have to calculate the bond price after 1 year at the original yield of 8.1% to determine the amount of implicit interest for the first year. The price can again be calculated with the use of PV function as specified in Part a).

Bond Price after 1 Year at 8.1% Yield

Here, Rate = 8.1%, Nper = 15 - 1 = 14, PMT = 1,000*5.1% = $51 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond Price After 1 Year (P1) = PV(8.1%,14,51,1000) = $754.10

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Now, we can determine the amount of implicit and total interest as below:

Implicit Interest = Bond Price after 1 Year at 8.1% Yield - Bond Price Today at 8.1% Yield = 754.10 - 744.78 = $9.33

Total Interest = Explicit Interest + Implicit Interest = 50 + 9.33 = $59.33

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The amount of capital gain is arrived as below:

Capital Gain = Bond Price after 1 Year at 7.1% Yield - Bond Price after 1 Year at 8.1% Yield = 826.13 - 754.10 = $72.03

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The amount of tax is calculated as below:

Tax on Interest Income (59.33*40%)	$23.73
Tax on Capital Gain (72.03*30%)	$21.61
Total Taxes (23.73 + 21.61)	$45.34

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Part c)

The after-tax holding period return is arrived as follows:

After-Tax Holding Period Return = (Bond Price After 1 Year - Bond Price Today + Annual Coupon Payment - Taxes)/Bond Price Today*100 = (826.13 - 744.78 + 51 - 45.34)/744.78*100 = 11.68%

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Part d)

The bond price after 2 years will again be calculated with the use of PV function/formula specified in Part a).

Bond Price After 2 Years at 7.1% Yield

Here, Rate = 7.1%, Nper = 15 - 2 = 13, PMT = 1,000*5.1% = $51 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Bond Price After 2 Years at 7.1% Yield (P2) = PV(7.1%,13,51,1000) = $833.79

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The value of total income from interest including reinvestment income is determined as below:

Total Income from Coupon Payment including Reinvestment Income = Coupon Payment for First Year*(1+Reinvestment Rate) + Coupon Payment for Second Year = 51*(1+3.1%) + 51 = $103.581

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Now, we can calculate the realized compound yield before taxes for a two-year holding period is calculated as below:

Realized Compound Yield Before Taxes for a Two-Year Holding Period = [(Bond Price After 2 Years at 7.1% Yield + Total Income from Coupon Payment including Reinvestment Income)/Bond Price Today (P0) at 8.1% Yield]^(1/2) - 1 = [(833.79 + 103.581)/744.78]^(1/2) - 1 = 12.19%