Question

Bond valuation and yield to maturity  Personal Finance Problem   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 6.20 %6.20%.The first bond is issued by Crabbe Waste Disposal and has a coupon interest rate of 6.334​% paid annually. The second ​ bond, issued by Malfoy​ Enterprises, has a coupon interest rate of 8.90​% paid annually.

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

b.  Mark has ​$18,000 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?

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 9​%. 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 6.20​%.

​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.

Bond price of Crabbe Waste Disposal:

=

n = 5

C = 6.334% = $63.34

F = 1000

r = 6.20%

Price as calculated is = $1005.614 (price of Crabbe Waste Disposal)

Similarly price as calculated for Malfoy​ Enterprises is = $1113.19

b. Bonds that can be bought of Crabbe Waste Disposal = $18000/1005.614 = 17.89 i.e. maximum 17 bonds

Bonds that can be bought of Malfoy​ Enterprises = $18000/1113/19 = 16.17 i.e. maximum 16 bonds

c. Total interest income that Mark could earn each year if he invested only in Crabbe​ Waste Disposal bonds = 17*63.34 = $1076.78

Total interest income that Mark could earn each year if he invested only in Malfoy​ Enterprises​ bonds = 16*89 = $1424

d. Total amount received at the end of five years = principal of $ 1000 plus the cumulative return of the all coupons payments reinvested at 9% per annum i.e.

F (par value) + C1*(1+9%)^4 + C2*(1+9%)^3 + C3*(1+9%)^2 + C4*(1+9%)^1 + (C5+F)

For Crabbe Wabble Disposal = 89.40+75.25+69.04+1063.34 = $1379.07

Now if, he invests in total 17 Crabbe bonds which can be bought for $18000, his total income would be = 17*1379 = $23443

For Malfoy​ Enterprises = 125.63+115.25+105.74+97.01+1089 = $1532.63

Now, if he invests in total 16 Malfoy bonds which can be bought for $18000, his total income would be = 16*1532.63 = $24378.08

e. As can be seen from total income from part d, total income is greater for  Malfoy​ Enterprises bonds which is due to increased coupon payments each year received in Malfoy​ Enterprises bonds.