Question

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 and has a coupon interest rate of 6.324% paid annually. The second ​ bond, issued by Malfoy​Enterprises, has a coupon interest rate of 8.8​% paid annually. PLEASE ANSWER USING EXCEL FORMULAS WHERE APPLICABLE.

a. Calculate the selling price for each of the bonds.

b. 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 answer to the nearest integer.

c. 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?

d. Assume that Mark will reinvest all the interest he receives as it is paid and that his rate of return on the 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 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 he receives.

e. 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

a. For the Crabbe bond

FV = 1000

NPER = 5

PMT = 1000 * 6.324% = 63.24

rate = 7.5%

In excel = PV(7.5%, 5, 63.24, 1000)

PV = -952.42

The selling price of the Crabbe bond is $952.42

For the Malfoy bond

FV =1000

NPER = 5

PMT = 1000 * 8.8% = 88

rate = 7.5%

In excel, = PV(7.5%, 5, 88, 1000)

PV = -1052.597

The selling price of the Malfoy bond is $1,052.597

b. If he invested only in Crabbe bonds, he could buy 20000/952.42 = 20.99 or 21 bonds

If he invested only in Malfoy bonds, he could buy 20000/1052.597 = 19 bonds

c. Total interest income = annual coupon payment * number of years

For the Crabbe bonds, total interest income = 63.24 * 5 = $316.2

For the Malfoy bonds, total interest income = 88 * 5 = $440

d. To find the accumulated interest reinvested at 10%, we have to find the future value of all the interest payments reinvested at 10%.

For the Crabbe bond,

NPER = 5

PMT = 63.24

PV = 0

Rate = 10%

In excel =FV(10, 5, 63.24, 0)

FV = -386.087

The sum of all the accumulated interest is $386.087

All the dollars mark will accumulate = 386.087 + 1000 = $1,386.087

For the Malfoy bond,

NPER = 5

PMT = 88

PV = 0

Rate = 10%

In excel =FV(10, 5, 88, 0)

FV = -537.249

The sum of all the accumulated interest is $537.249

All the dollars mark will accumulate = 537.249 + 1000 = $1,537.249

e. A YTM of 7.5% means that all the coupons are reinvested at 7.5% . Since the coupons are reinvested at a different rate in part d. , we get a different value.