Question

 

Personal Finance Problem | LG 2, 5, 6
P6–23 Bond valuation and yield to maturity Mark Goldsmith’s broker has shown him two bonds issued by different companies. Each has a maturity of 5 years, a par value of $1,000, and a yield to maturity of 7.5%. The first bond is issued by Crabbe Waste Disposal Corporation and has a coupon rate of 6.324% paid annually. The second bond, issued by Malfoy Enterprises, has a coupon rate of 8.8% paid annually.

Calculate the selling price for each bond.

Mark has $20,000 to invest. If he wants to invest only in bonds issued by Crabbe Waste Disposal, how many of those bonds could he buy? What if he wants to invest only in bonds issued by Malfoy Enterprises? Round your answers to the nearest integer.

What is the total interest income that Mark could earn each year if he invested only in Crabbe bonds? How much interest would he earn each year if he invested only in Malfoy bonds?

Assume that Mark will reinvest all the interest he receives as it is paid, and his rate of return on reinvested interest will be 10%. Calculate the total dollars that Mark will accumulate over 5 years if he invests in Crabbe bonds or Malfoy bonds. Your total dollar calculation will include the interest Mark gets, the principal he receives when the bonds mature, and all the additional interest he earns from reinvesting the coupon payments that he receives.

The bonds issued by Crabbe and Malfoy might appear to be equally good investments because they offer the same yield to maturity of 7.5%. Notice, however, that your answers to part d are not the same for each bond, suggesting that one bond is a better investment than the other. Why is that the case?

Answer 1

Part 1)

The current price of the bond 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).

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Selling Price of Crabbe Waste Disposal Corporation

Here, Rate = 7.5%, Nper = 5, PMT = 1,000*6.324% = $63.24 and FV = $1,000

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

Selling Price of Crabbe Waste Disposal Corporation = PV(7.5%,5,63.24,1000) = $952.42

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Selling Price of Malfoy Enterprises

Here, Rate = 7.5%, Nper = 5, PMT = 1,000*8.8% = $88 and FV = $1,000

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

Selling Price of Malfoy Enterprises = PV(7.5%,5,88,1000) = $1,052.60

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Part 2)

The number of bonds that can be bought are calculated as below:

Number of Bonds (Crabbe Waste Disposal Corporation) = Amount to be Invested/Current Selling Price of Bonds = 20,000/952.42 = 21 bonds

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Number of Bonds (Malfoy Enterprises) = 20,000/1,052.60 = 19 bonds

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Part 3)

The total amount of interest income that will be earned year is determined as below:

Total Interest Income (Crabbe Waste Disposal Corporation) = Number of Bonds*Annual Coupon Payment = 21*63.24 = $1,328.04

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Total Interest Income (Malfoy Enterprises) = Number of Bonds*Annual Coupon Payment = 19*88 = $1,672

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Part 4)

We will have to calculate the future value of annual coupon payments at 10% rate of interest and add it to $1,000 (the amount at which the bonds will sell on maturity). The future value of an annuity can be calculated with the use of FV (Future Value) function/formula of EXCEL/Financial Calculator. The function/formula for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Payment and PV = Present Value (if any)

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Total Dollar Amount Accumulated with Bonds Issued by Crabbe Waste Disposal Corporation

Here, Rate = 10%, Nper = 5, PMT = $63.24 and PV = 0

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

Future Value of Annual Coupon Payments = FV(10%,5,63.24,0) = $386.09

Now, we can calculate the total amount that will get accumulated at the end of 5 Years as below:

Total Amount Accumulated at End of 5 Years (Crabbe Waste Disposal Corporation) = Future Value of Annual Coupon Payments + Par Value = 386.09 + 1,000 = $1,386.09

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Total Dollar Amount Accumulated with Bonds Issued by Malfoy Enterprises

Here, Rate = 10%, Nper = 5, PMT = $88 and PV = 0

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

Future Value of Annual Coupon Payments = FV(10%,5,88,0) = $537.25

Now, we can calculate the total amount that will get accumulated at the end of 5 Years as below:

Total Amount Accumulated at End of 5 Years (Malfoy Enterprises) = Future Value of Annual Coupon Payments + Par Value = 537.25 + 1,000 = $1,537.25

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Part 5)

The difference is on account of the annual interest payments associated with each bond. The amount of annual interest is $63.24 for bonds issued by Crabbe Waste Disposal Corporation and $88 for bonds issued by Malfoy Enterprises. As the reinvestment rate is same for both the bonds at 10%, the bond providing higher coupon payment will result in more dollars getting accumulated at the end of 5 years. However, the decision to invest in bonds should not be based solely on the accumulated of dollar value at the end of 5 years. it would be more appropriate to calculate the YTM of the bonds at reinvestment rate of 10% to determine which bond is better to invest.