Question

QUESTION 1 (30 marks)

Jo-Anne just bought 200 bonds at a purchase price of R1 043.70 each. The bonds will mature in 7 years' time and have a face value of

R1 000.00. The coupon rate is 11% and is paid semi-annually. Answer the questions that follow:

1.1 Calculate the prevailing interest rate.

1.2 If the prevailing interest rate is 12%, what would happen to the price of the bond?

1.3 If Lee-Anne bought the bonds at R1 043.70 and the prevailing interest rate changes to 12%, what would the capital gains yield be?

1.4 Lee-Anne bought the bonds at R1 043.70 and after four years she decides to sell the bonds while the prevailing interest rate is 9%. Answer the following questions relating to this scenario:

1.4.1 Calculate the capital gains yield.

1.4.2 Calculate the current yield.

1.4.3 Calculate the total Rand return

1.5 Explain in your own words the relationship between prevailing interest rates and bond prices and why the prices of bonds can change.

[30 marks]

Answer 1

Solution:

1.1

Calculation of prevailing interest rate:

Price of Bond (B_o) = Cashflows x PVIFA ( i %, r years) + Redemption value x PVIF ( i %, r years)

where,
i = interest rate
r = Period in years
PVIFA = Present Value Interest Factor Annuity
PVIF = Present Value Interest Factor

As per QuestionL

- Cash flows or Interest = Face Value x Coupon Rate = 1,000 x 11% = 110

- Redemption Value is assumed to be at par as no is given.

- Substituting the above in formula:
B_o = 1043.70
Cash flows (Semi - annually) = 110/ 2 = 55
r (annually) = 7 yrs
Semi - Annually = 14 periods

By formula
1043.70 = 55 x PVIFA ( i %, 14) + 1000 x PVIF ( i %, 14)
By interpolation, we can calculate i % = 10.11 % (approximately)

- Since the coupon rate is higher than the interest rate (YTM), the Bond price is more than face value and Bond is trading at a premium.

1.2

If the prevailing interest rate is 12% which is 1% more than the current interest rate i.e 11% the Bond price increases slightly higher.

Bond price = Coupon rate x PVIFA (i %, r) + Redemption Value PVIF ( i %, r)
                  = (120 / 2 ) x PVIFA ( 10.11 %, 14) + 1000 x PVIF ( 10.11%, 14)
                  = $ 1,094.21

1.3

Price of Bond at i = 10.11% and interest (coupon) = 11% is $1043.70

Keeping the Bond price to be constant and interest rate to change at 12%, YTM (i) can be calculated as 11.08%

Hence, Capital gain in yield = (11.08 - 10.11) / 10.11 = 9.59%

1.5

Relationship between Bond price and interest rate:

1. Bonds have an inverse relationship to interest rates; when interest rates rise, bond prices fall, and vice-versa.

2. Most bonds pay a fixed interest rate, if interest rates in general fall, the bond's interest rates become more attractive, so people will bid up to the price of the bond.

3. Likewise, if interest rates rise, people will no longer prefer the lower fixed interest rate paid by a bond, and their price will fall.

4. Zero-coupon bonds provide a clear example of how this mechanism works in practice.