I POSTED THIS SAME QUESTION EARLIER AND THE ANSWER IS INCORRECT. DO NOT COPY AND

Question

I POSTED THIS SAME QUESTION EARLIER AND THE ANSWER IS INCORRECT. DO NOT COPY AND PASTE IT HERE! THANKS.

A newly issued bond pays its coupons once a year. Its coupon rate is 4.5%, its maturity is 20 years, and its yield to maturity is 7.5%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.5% 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 6.5%, 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.)

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 6.5% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.5% 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             %

Tax on interest income $ Tax on capital gain $ Total taxes $

Explanation / Answer

Since, there are multiple parts to the question, I have answered the first four parts (part a to part d) with all the details.

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Part a)

Step 1: Calculate Initial Bond Price

The initial 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 = 7.5%, Nper = 20, PMT = 1,000*4.5% = $45 and FV = $1,000

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

Initial Bond Price = PV(7.5%,20,45,1000) = $694.17

____

Step 2: Calculate Bond Price after 1 Year

We will have to use the the same PV formula/function as specified in Step 1 to determined bond price after 1 year with the following variables:

Here, Rate = 6.5%, Nper = 20 -1 = 19, PMT = 1,000*4.5% = 45, and FV = 1,000

Bond Price after 1 Year = PV(6.5%,19,45,1000) = $785.31

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Step 3: Calculate Holding Period Return

The value of holding period return is arrived as below:

Holding Period Return = [(Bond Price after 1 Year - Initial Bond Price) + Annual Coupon Payment]/Initial Bond Price*100

Using the values calculated in Step 1 and Step 2, we get,

Holding Period Return = [(785.31 - 694.17) + 45]/694.17*100 = 19.61%

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Part b)

We will have to calculate the price of bond after 1 year at a constant yield of 7.5% with the use of PV function/formula specified in part a).

Here, Rate = 7.5%, Nper = 19, PMT = 1,000*4.5% = $45 and FV = $1,000

Bond Price after 1 Year = PV(7.5%,19,45,1000) = $701.23

Now, we can calculate tax on interest income, capital gain and total taxes as below:

Interest on Tax Income = Tax Rate*[Coupon Payment + (Bond Price after 1 Year based on Constant Yield - Initial Bond Price)] = 40%*[45 + (701.23 - 694.17)] = $20.82

____

Tax on Capital Gain = Tax Rate*(Actual Bond Price after 1 Year - Bond Price after 1 Year based on Constant Yield) = 30%*(785.31 - 701.23) = $25.22

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Total Taxes = Tax on Interest Income + Tax on Capital Gain = 20.82 + 25.22 = $46.05

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Tabular Representation:

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Part c)

The value of after-tax holding period return is calculated as follows:

After-Tax Holding-Period Return =  [(Bond Price after 1 Year - Initial Bond Price) + Annual Coupon Payment - Total Taxes]/Initial Bond Price*100 = [(785.31 - 694.17) + 45 - 46.04]/694.17*100 = 12.98%

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Part d)

Step 1: Calculate Bond Price after 2 Years

Here, Rate = 6.5%, Nper = 18, PMT = 1,000*4.5% = $45 and FV = $1,000

Using these values in the PV function/formula specified in Part a), we get,

Bond Price after 2 Years = PV(6.5%,18,45,1000) = $791.35

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Step 2: Calculate Reinvested Coupon Income

The reinvested coupon income is calculated as below:

Reinvested Coupon Income = 45*1.025 + 45 = $91.13

____

Step 3: Calculate Value of Total Funds and Realized Compound Yield after 2 Years

The value of total funds is calculated as below:

Total Funds = Bond Price after 2 Year + Reinvested Coupon Income = 791.35 + 91.13 = $882.48

Now, we can calculate realized compound yield after 2 years with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Payment (if any), PV = Present Value and FV = Future Value.

Here, Nper = 2, PMT = 0, PV = $694.17 and FV = $882.48

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

Realized Compound Yield = Rate(2,0,-694.17,882.48) = 12.75%

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Notes:

There can be a slight difference in final answers on account of rounding off values.

Tax on interest income 20.82 Tax on capital gain 25.22 Total taxes 46.04

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