To calculate the cost of equity and the weighted average cost of capital (WACC), we'll follow these steps:
Step 1: Calculate the Cost of Equity
The cost of equity can be estimated using the Gordon Growth Model (Dividend Discount Model), which is given by the formula:
\[ \text{Cost of Equity} = \frac{D_1}{P_0} + g \]
Where:
- \(D_1\) = next year's expected dividend
- \(P_0\) = current share price
- \(g\) = growth rate of dividends
Given:
- Last dividend paid (\(D_0\)) = 4.1 gwe
- Current share price (\(P_0\)) = 97.5 gwe
- Dividend has grown from 2 gwe (2 years ago) to 4.1 gwe over 2 years.
Calculate the Growth Rate \(g\)
To find the growth rate, we can calculate the annual growth rate over the last 2 years:
Using the formula for compound annual growth rate (CAGR): \[ g = \left( \frac{D_0}{D_{-2}} \right)^{\frac{1}{n}} - 1 \] Where:
- \(D_0\) = 4.1 gwe
- \(D_{-2}\) = 2 gwe
- \(n\) = number of years = 2
\[ g = \left( \frac{4.1}{2} \right)^{\frac{1}{2}} - 1 \]
Calculating this value: \[ g = \left( 2.05 \right)^{0.5} - 1 = 1.43 - 1 = 0.43 \quad (\text{or } 43%) \]
Calculate \(D_1\), the expected dividend next year:
\[ D_1 = D_0 \times (1 + g) = 4.1 \times (1 + 0.43) = 4.1 \times 1.43 \approx 5.87 \text{ gwe} \]
Now substitute back into the cost of equity formula:
\[ \text{Cost of Equity} = \frac{5.87}{97.5} + 0.43 \] Calculating: \[ \text{Cost of Equity} = 0.0601 + 0.43 \approx 0.4901 \quad (\text{or } 49.01%) \]
Step 2: Calculate the After-Tax Cost of Debt
The after-tax cost of debt is calculated using the formula: \[ \text{After-Tax Cost of Debt} = r_d \times (1 - T) \] Where:
- \(r_d\) = cost of debt before tax = 0.10
- \(T\) = tax rate = 0.3
Calculating: \[ \text{After-Tax Cost of Debt} = 0.10 \times (1 - 0.3) = 0.10 \times 0.7 = 0.07 \quad (\text{or } 7%) \]
Step 3: Calculate the Weighted Average Cost of Capital (WACC)
WACC is given by the formula: \[ \text{WACC} = \left( \frac{E}{V} \times r_e \right) + \left( \frac{D}{V} \times r_d \times (1 - T) \right) \] Where:
- \(E\) = Market value of equity = 60 million
- \(D\) = Market value of debt = 40 million
- \(V = E + D\) = Total value = 100 million
- \(r_e\) = Cost of equity = 49.01% (or 0.4901)
- \(r_d\) = Cost of debt = 10% (or 0.10)
Calculate the Proportions of Equity and Debt:
\[ \frac{E}{V} = \frac{60}{100} = 0.6 \] \[ \frac{D}{V} = \frac{40}{100} = 0.4 \]
Substitute values into the WACC formula:
\[ \text{WACC} = \left( 0.6 \times 0.4901 \right) + \left( 0.4 \times 0.10 \times (1 - 0.3) \right) \]
Calculating: \[ \text{WACC} = (0.6 \times 0.4901) + (0.4 \times 0.07) \] \[ \text{WACC} = 0.29406 + 0.028 = 0.32206 \quad (\text{or } 32.21%) \]
Summary
- Cost of Equity: 49.01%
- WACC: 32.21%
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