- 15 Marks
Question
a. Prices of zero-coupon bonds reveal the following pattern of forward rates:
| Year | Forward rates |
|---|---|
| 1 | 4% |
| 2 | 6% |
| 3 | 8% |
| 4 | 10% |
A bond with face value of N1,000 pays annual coupon of 7.5% with maturity of three years.
i. What is the price of the bond? (3 Marks)
ii. Estimate the yield to maturity (YTM) of the bond. Explain why an investor holding the bond may not realise the calculated YTM. (5 Marks)
b. i. Calculate the duration of the bond. What does duration measure? (4 marks)
ii. As a bond portfolio manager, you are to make a choice between the following two bonds.
| Bond A | Bond B | |
|---|---|---|
| Maturity (Years) | 6 | 8 |
| Duration (Years) | 6 | 7.2 |
If it is generally believed that interest rates in the market will increase, which of the two bonds would you select and why?
No calculations are required (3 Marks)
Answer
a) i) Calculation Price
| Year 1 | 75/(1.04) | = | 72.115 |
|---|---|---|---|
| 2 | 75/(1.04 × 1.06) | = | 68.033 |
| 3 | 1,075/(1.04 × 1.06 × 1.08) | = | 902.912 |
| Current price | 1,043.060 |
ii) Calculation of YTM
| Year | CF | PV at 5% | PV at 6% |
|---|---|---|---|
| 0 | -1043.060 | -1043.060 | -1043.060 |
| 1 | 75 | 71.429 | 70.755 |
| 2 | 75 | 68.027 | 66.150 |
| 3 | 1,075 | 928.625 | 902.591 |
| NPV | 25.021 | – 3.564 |
YTM = IRR = 5 + 25.021 / 25.021+3.564 × (6 −5) = 5.89%
The YTM of 5.89% is a promised yield that may not be realised if:
The investor does not receive the related cash flows as and when due;
The bond is not held to maturity; and
The coupons cannot be reinvested at the yield to maturity of 5.89%.
b) i) Calculation of duration
| Year (n) | CF | PV at 5.89% (PV) | (PV) (n) |
|---|---|---|---|
| 1 | 75 | 70.828 | 70.828 |
| 2 | 75 | 66.889 | 133.777 |
| 3 | 1,075 | 905.407 | 2,716.220 |
| 1,043.124 | 2,920.825 |
Duration = 2,920.825/1,043.124 = 2.80 years
Duration is a measure of the sensitivity of a bond to a change in interest rates. In general, the higher the duration, the higher the sensitivity, and the higher the price risk.
ii) When interest rates increase, prices of bond fall. Bonds with lower durations will suffer price drop the least. Therefore, I will select Bond A with lower duration in order to minimise loss in the value of my portfolio.
- Topic: Business Valuation Techniques, Portfolio Management
- Series: MAY 2025
- Uploader: Samuel Duah