Question1) Siemeh Funds Limited has invested in GHф 1,000 , five-year bonds with a coupon rate of $20 \%$ paid yearly. The bonds have three years to maturity and are currently trading with a yield to maturity of $21 \%$ on the fixed income market. What is the duration of the bonds? $y$ [8 marks]

Studdy Solution

STEP 1

1. The bond has a face value of GH₵ 1,000.
2. The coupon rate is $20\%$ , paid annually.
3. The bond has three years remaining to maturity.
4. The yield to maturity (YTM) is $21\%$ .

STEP 2

1. Calculate the annual coupon payment.
2. Determine the present value of each cash flow.
3. Calculate the weighted average time to receive each cash flow (duration).

STEP 3

Calculate the annual coupon payment:
$\text{Coupon Payment} = \text{Face Value} \times \text{Coupon Rate}$ $= 1000 \times 0.20$ $= 200$

STEP 4

Determine the present value of each cash flow:
For Year 1: $\text{PV}_1 = \frac{200}{(1 + 0.21)^1}$
For Year 2: $\text{PV}_2 = \frac{200}{(1 + 0.21)^2}$
For Year 3 (including face value): $\text{PV}_3 = \frac{200 + 1000}{(1 + 0.21)^3}$
Calculate each present value:
$\text{PV}_1 = \frac{200}{1.21} \approx 165.29$ $\text{PV}_2 = \frac{200}{1.21^2} \approx 136.58$ $\text{PV}_3 = \frac{1200}{1.21^3} \approx 821.93$

STEP 5

Calculate the weighted average time to receive each cash flow (duration):
$\text{Duration} = \frac{\sum (\text{Time} \times \text{PV of Cash Flow})}{\sum (\text{PV of Cash Flow})}$
$\text{Total PV} = 165.29 + 136.58 + 821.93 = 1123.80$
$\text{Weighted Time} = \frac{(1 \times 165.29) + (2 \times 136.58) + (3 \times 821.93)}{1123.80}$
$= \frac{165.29 + 273.16 + 2465.79}{1123.80}$
$= \frac{2904.24}{1123.80} \approx 2.58$
The duration of the bonds is approximately:
$\boxed{2.58 \text{ years}}$

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