Question

A newly issued bond pays its coupons once annually. Its coupon rate is 8%, its maturity is 20 years, and its yield to maturity is 10%.

a. Find the holding-period return for a 1-year investment period if the bond is selling at a yield to maturity of 9% 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, 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.)

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 2-year holding period, assuming that (1) you sell the bond after two years, (2) the bond yield is 9% at the end of the second year, and (3) the coupon can be reinvested for one year at a 3% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

e. Use the tax rates in (b) above to compute the after-tax 2-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, the question has multiple subparts, I have answered the first four.

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Part a)

Step 1: Calculate Bond Price Today

The bond price today can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, YTM), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 10%, Nper = 20, PMT = 1,000*8% = $80 an FV = $1,000

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

Bond Price Today = PV(10%,20,80,1000) = $829.73

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Step 2: Calculate Bond Price At the End of the Year

The bond price at the end of the year can again be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, YTM), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 9%, Nper = 20-1 = 19, PMT = 1,000*8% = $80 an FV = $1,000

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

Bond Price at the End of the Year = PV(9%,19,80,1000) = $910.50

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Step 3: Calculate Holding-Period Return

The value of holding-period return is determined as follows:

Holding-Period Return = (Bond Price at the End of the Year - Bond Price Today + Coupon Payment)/Bond Price Today*100 = (910.50 - 829.73 + 80)/829.73*100 = 19.38%

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Part b)

Step 1: Calculate Bond Price At the End of the Year with Original Yield to Maturity of 10%

The bond price at the end of the year can again be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, YTM), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 10%, Nper = 20-1 = 19, PMT = 1,000*8% = $80 an FV = $1,000

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

Bond Price at the End of the Year = PV(10%,19,80,1000) = $832.70

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Step 2: Calculate Tax on Capital Gain and Interest Income

The value of tax on capital gain and interest income is arrived as follows:

Tax on Capital Gain = Tax Rate*(Bond Price at the End of the Year with 10% YTM - Bond Price at the End of the Year with 9% YTM) = 30%*(910.50 - 832.70) = $23.34

Tax on Interest Income = Tax Rate*(Bond Price at the End of the Year with 10% YTM - Bond Price Today + Coupon Payment) = 40%*(832.70 - 829.73 + 80) = $33.19

Total Tax = Tax on Capital Gain + Tax on Interest Income = 23.34 + 33.19 = $56.53

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Part c)

The after-tax holding-period return on the bond is calculated as below:

After-Tax Holding Period Return = (Bond Price at the End of the Year with 10% YTM - Bond Price Today + Coupon Payment - Tax)/Bond Price Today*100 = (910.50 - 829.73 + 80 - 56.53)/829.73*100 = 12.56%

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Part d)

Step 1: Calculate Revised Bond Price with 2 Year Holding Period and YTM of 9%

The bond price can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, YTM), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 9%, Nper = 20-2 = 18, PMT = 1,000*8% = $80 an FV = $1,000

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

Revised Bond Price = PV(9%,18,80,1000) = $912.44

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Step 2: Calculate Earnings from Reinvestment of Coupon Payment

The earnings from reinvestment of coupon payment is derived as below:

Earnings from Reinvestment of Coupon Payment = Coupon Payment + Coupon Payment*(1+Reinvestment Rate) = 80 + 80*(1+3%) = $162.40

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Step 3: Calculate Realized Yield

The value of realized yield is arrived as follows:

Realized Yield = [(Revised Bond Price + Earnings from Reinvestment of Coupon Payment)/(Bond Price Today)]^(1/Period) - 1 = [(912.44 + 162.40)/(829.73)]^(1/2) - 1 = 13.82%