Question

Mark Goldsmith’s broker has shown him two bonds. Each has a maturity of five years, a par value of $1,000, and a yield to maturity of 12%. Bond A has a coupon interest rate of 6% paid semi-annually. Bond B has a coupon interest rate of 14% paid semi-annually.

1. Calculate the selling price for each of the bonds.
2. Mark has $20,000 to invest. Judging on the basis of the price of the bonds, how many of either one could Mark purchase if he were to choose it over the other? (Mark cannot really purchase a fraction of a bond, but for purposes of this question, pretend that he can.)
3. Calculate the yearly interest income of each bond on the basis of its coupon rate and the number of bonds that mark could buy with his $20,000.
4. Assume that Mark will reinvest the interest payments as they are paid (semi-annually) and that his rate of return on the reinvestment is only 10% (compounded semi-annually). For each bond, calculate the value of the principal payment plus the value of Mark’s reinvestment account at the end of the 5 years.

Answer 1

a. Calculating selling price of Bond A

Par value = 1000, Yield to maturity = 12%, Years to maturity = 5, Coupon rate = 6%

Semi annual coupon = (Coupon rate x par value) / 2 = (6% x 100)/2 = 30

Semi annual YTM = YTM/2 = 12%/2 = 6%

No of half years to maturity = 2 x no of years to maturity = 2 x Years to maturity = 2 x 5 = 10

We will use pv function in excel to calculate selling price

Formula to be used in excel: =pv(rate,nper,-pmt,-fv)

Using pv function in excel we get selling price of bond A = 779.20

Calculating selling price of Bond B

Par value = 1000, Yield to maturity = 12%, Years to maturity = 5, Coupon rate = 14%

Semi annual coupon = (Coupon rate x par value) / 2 = (14% x 100)/2 = 70

Semi annual YTM = YTM/2 = 12%/2 = 6%

No of half years to maturity = 2 x no of years to maturity = 2 x Years to maturity = 2 x 5 = 10

We will use pv function in excel to calculate selling price

Formula to be used in excel: =pv(rate,nper,-pmt,-fv)

Using pv function in excel, we get selling price of Bond B = 1073.60

b. Amount with Mark = 20000

No of bond A Mark can Purchase = Amount / Price of Bond A = 20000 / 779.20 = 25.66 Bonds

No of bond B Mark can Purchase = Amount / Price of Bond B = 20000 / 1073.60 = 18.62 Bonds

c. Yearly interest income = 2 x semi annual coupon x No of bonds Purchased

Yearly income from Bond A = 2 x 30 x 25.66 = 1539.60

Yearly income from Bond B = 2 x 70 x 18.62 = 2606.80

d. Calculating value of principal and reinvestment account at end of 5 years for Bond A

Reinvestment rate = 10% (compounded semi annually)

Semi - annual reinvestment rate = Reinvestment rate / 2 = 10% / 2 = 5%

Value of reinvestment account at end of 5 years = 30(1+5%)⁹ + 30(1+5%)⁸ + 30(1+5%)⁷ + .................................30(1+5%)² + 30(1+5%) + 30

Value of reinvestment account can be found out by finding future value of above annuity

This can be done using fv function in excel

Formula to be used in excel: =fv(rate,nper,-pmt)

Using fv function in excel , we get value of reinvestment account for Bond A = 377.34

Value of Principal and Value of reinvestment account at the end of 5 years for Bond A = Principal + Value of reinvestment account = 1000 + 377.34 = 1377.34

Calculating value of principal and reinvestment account at end of 5 years for Bond B

Reinvestment rate = 10% (compounded semi annually)

Semi - annual reinvestment rate = Reinvestment rate / 2 = 10% / 2 = 5%

Value of reinvestment account = 70(1+5%)⁹ + 70(1+5%)⁸ + 70(1+5%)⁷ + ............................................70(1+5%)² + 70(1+5%) + 70

Value of reinvestment account can be found out by finding future value of above annuity

This can be done using fv function in excel

Formula to be used in excel: =fv(rate,nper,-pmt)

Using fv function in excel , we get value of reinvestment account for Bond B = 880.45

Value of Principal and Value of reinvestment account at the end of 5 years for Bond B = Principal + Value of reinvestment account = 1000 + 880.45 = 1880.45