To calculate the Weighted Average Cost of Capital (WACC) for Barnyard Traders, we must determine the cost of equity using the Capital Asset Pricing Model (CAPM) and the cost of each component of the firm's capital: ordinary shares, preference shares, debentures, and bank overdraft.
### 3.1 Weighted Average Cost of Capital (WACC) Calculation
**Step 1: Calculate Cost of Equity using CAPM**
The Capital Asset Pricing Model (CAPM) formula is:
\[ \text{Cost of Equity} (r_e) = r_f + \beta (r_m - r_f) \]
Where:
- \(r_f\) is the risk-free rate
- \(\beta \) is the beta of the company
- \(r_m\) is the return on the market
Given:
- Risk-free rate (\(r_f\)): 6.5% (0.065)
- Beta (\(\beta\)): 1.2
- Market return (\(r_m\)): 11.5% (0.115)
Plugging in the values:
\[ r_e = 0.065 + 1.2 \times (0.115 - 0.065) \]
\[ r_e = 0.065 + 1.2 \times 0.05 \]
\[ r_e = 0.065 + 0.06 \]
\[ r_e = 0.125 \text{ or } 12.5\% \]
**Step 2: Calculate Cost of Preference Shares**
The cost of preference shares (\(r_{ps}\)) is calculated as:
\[ r_{ps} = \frac{D_{ps}}{P_{ps}} \]
Where:
- \(D_{ps}\) is the dividend on preference shares, which is 8% of R9
- \(P_{ps}\) is the market price of the preference share, which is R8.80
\[ D_{ps} = 0.08 \times R9 = R0.72 \]
\[ r_{ps} = \frac{R0.72}{R8.80} = 0.08182 \text{ or } 8.182\% \]
**Step 3: Calculate Cost of Debt**
The cost of debt must consider the current market price and YTM (yield to maturity) of the debenture.
Given:
- Face value of debenture: R18,000,000
- Current price of debenture: R7,144,200
- Coupon rate: 7%
- YTM: 15%
The cost of debt \(r_d\) before tax is the YTM, which is 15%. After-tax cost of debt:
\[ r_d \text{(after tax)} = r_d \times (1 - \text{Tax Rate}) = 0.15 \times (1 - 0.30) = 0.15 \times 0.70 = 0.105 \text{ or } 10.5\% \]
**Step 4: Calculate Cost of Bank Overdraft**
The interest is charged at 12%, and it's fully interest-bearing, so the after-tax cost of the overdraft is:
\[ r_{od} \text{ (after tax)} = 0.12 \times (1 - 0.30) = 0.12 \times 0.70 = 0.084 \text{ or } 8.4\% \]
**Step 5: Determine the Market Value of Each Component**
1. **Ordinary Shares**
\[ \text{Market Value of Ordinary Shares} (E) = 20,000,000 \times 8.50 = R170,000,000 \]
2. **Preference Shares**
\[ \text{Market Value of Preference Shares} (PS) = 10,500,000 \times 8.80 = R92,400,000 \]
3. **Debentures**
\[ \text{Market Value of Debentures} (D) = R7,144,200 \]
4. **Bank Overdraft**
\[ \text{Market Value of Bank Overdraft} = R8,000,000 \]
**Step 6: Calculate Total Market Value**
\[ \text{Total Market Value} = 170,000,000 + 92,400,000 + 7,144,200 + 8,000,000 = R277,544,200 \]
**Step 7: Calculate WACC**
WACC is calculated as:
\[ \text{WACC} = \left( \frac{E}{V} \times r_e \right) + \left( \frac{PS}{V} \times r_{ps} \right) + \left( \frac{D}{V} \times r_d \right) + \left( \frac{Bank Overdraft}{V} \times r_{od} \right) \]
Where \(V\) is the total market value:
- \(V = R277,544,200 \)
- \(E = R170,000,000 \)
- \(PS = R92,400,000 \)
- \(D = R7,144,200 \)
- \(Bank Overdraft = R8,000,000 \)
\[ \text{WACC} = \left( \frac{170,000,000}{277,544,200} \times 0.125 \right) + \left( \frac{92,400,000}{277,544,200} \times 0.08182 \right) + \left( \frac{7,144,200}{277,544,200} \times 0.105 \right) + \left( \frac{8,000,000}{277,544,200} \times 0.084 \right) \]
\[ \text{WACC} = \left( 0.612 \times 0.125 \right) + \left( 0.333 \times 0.08182 \right) + \left( 0.026 \times 0.105 \right) + \left( 0.029 \times 0.084 \right) \]
\[ \text{WACC} = 0.0765 + 0.02723 + 0.00273 + 0.00243 \]
\[ \text{WACC} = 0.10889 \text{ or } 10.889\% \]
### 3.2 Cost of Equity using the Gordon Growth Model
The Gordon Growth Model formula is:
\[ r_e = \frac{D_0 (1 + g)}{P_0} + g \]
Where:
- \(D_0\) is the latest dividend paid
- \(P_0\) is the current market price of the share
- \(g\) is the growth rate
Given:
- Latest dividend paid (\(D_0\)): R0.99
- Current market price (\(P_0\)): R8.50
- Growth rate (\(g\)): 11% (0.11)
\[ r_e = \frac{0.99 (1 + 0.11)}{8.50} + 0.11 \]
\[ r_e = \frac{0.99 \times 1.11}{8.50} + 0.11 \]
\[ r_e = \frac{1.0989}{8.50} + 0.11 \]
\[ r_e = 0.12929 \text{ or } 12.929\% \]
In conclusion:
- **The cost of equity, using the CAPM, is 12.5%**
- **The cost of equity, using the Gordon Growth Model, is 12.929%**
- **The WACC is approximately 10.889%**
Barnyard Traders uses a combination of shares and debt in their capital structure.
The details are given below:
ü There are 20 million R10.80 ordinary shares in issue and the current market price is R8.50 per share. The latest dividend paid was 99 cents and 11% average growth for the past six years was maintained.
ü The company has 10 500 000 R9, 8% preference shares with a market price of R8.80 per share.
ü Barnyard Traders has a public traded debt with a face value of R18 000 000. The coupon rate of the debenture is 7% and the current yield to maturity of 15%. The debenture has 8 years to maturity. Note that the security is currently trading at : R7 144 200
ü They also have a bank overdraft of R8 000 000 due in 4 years’ time and interest is charged at 12% per annum.
Additional Information:
ü Barnyard Traders has a beta of 1.2, a risk-free rate of 6.5% and a return on the market of 11.5%.
ü Company tax rate is 30%.
Required:
3.1 Calculate the weighted average cost of capital, using the Capital Asset Pricing Model to calculate the cost of equity. (22 Marks)
3.2 Calculate the cost of equity, using the Gordon Growth Model. (3 Marks)
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