Question

Question 4

Gustavo Fring, a seasoned businessman, has a lot of liquidity (cash) at his disposal. Accordingly, he

decides to invest some of his earnings in a fixed income security. He has two Bonds to choose

from. Each has a maturity of 5 years, a par value of $500, and a yield to maturity of 15%. Bond

A has a coupon interest rate of 5% paid annually. Bond B has a coupon interest rate of 10% paid

annually.

a. Calculate the price of both the bonds.

b. Gustavo will be investing 10,000 USD. Approximately how many of each of the two

bonds could Gustavo purchase?

c. Calculate the yearly interest income of each bond based on its coupon rate and the

number of bonds that Gustavo could buy with his $10,000.

d. Assume that Gustavo will reinvest the interest payments as they are paid (at the end of

each year) and that his rate of return on the reinvestment is only 8%. For each bond,

calculate the value of the principal payment plus the value of Gustavo’s reinvestment

account at the end of the 5 years.

e. Why are the two values calculated in part d different? If Gustavo were worried that he

would earn less than the 15% yield to maturity on the reinvested interest payments, which

of these two bonds would be a better choice?

Answer 1

Particulars	Bond A	Bond B
Maturity Years	5	5
Par Value	$500	$500
Coupon Interest	5%	10%
YTM	15%	15%

(a) Price of Bonds is mentioned below

Interest = Par Value * Coupon Interest

Bond A
Particulars	1	2	3	4	5
Ineterst On Bond A	25	25	25	25	25
Par Value					500
Total	25	25	25	25	525
Discounting Factor @15%	1.15	1.3225	1.520875	1.749006	2.011357
Present Value	21.73913	18.90359	16.43791	14.29383	261.0178
Total	332.3922451

Bond B
Particulars	1	2	3	4	5
Ineterst On Bond A	50	50	50	50	50
Par Value					500
Total	50	50	50	50	550
Discounting Factor @15%	1.15	1.3225	1.520875	1.749006	2.011357
Present Value	43.47826	37.80718	32.87581	28.58766	273.4472
Total	416.1961225

(b)

For Bond A, Gustavo could Purchased = 10000/332.392 = 30.084 = 30units

For Bond B, Gustavo could Purchased = 10000/416.196 = 24.027 = 24units

(c)

Bond A
Particulars	1	2	3	4	5
Par Value	500
Total Number of Units	30
Total value	15000
Ineterst On Bond A	750	750	750	750	750

Bond B
Particulars	1	2	3	4	5
Par Value	500
Total Number of Units	24
Total value	12000
Ineterst On Bond A	1200	1200	1200	1200	1200

(d) Value of bond after 5 year spost reinvestment of ineterst @ 8% is as under

Value of Bond A = (750*(1.08^4))+(750*(1.08^3))+(750*(1.08^2))+(750*1.08)+(750+15000) = 19399.95

Value of Bond B = (1200*(1.08^4))+(1200*(1.08^3))+(1200*(1.08^2))+(1200*1.08)+(1200+12000) = 19039.92

(e) For calculating PV for bond, IRR is taken 15% while reinvesting rate is 8 %. so there is gap due to gap between reinvestment rate & YTM.

If reinvestment rate is less than 15%, bond A is better choice.