### Calculate WACC for Natal Limited-Cost of Equity-Preference Shares and Debt

**Question:**

Natal Limited uses a combination of shares and debt in its capital structure.

**The details are given below:**

There are 3 million R4.20 ordinary shares in issue and the current market price is R5.90 per share. The latest dividend paid was 83 cents and an 8% average growth for the past six years was maintained. The company has 1 750 000 R2.50, 9% preference shares with a market price of R3.80 per share. Natal Limited has a publicly traded debt with a face value of R5 million. The coupon rate of the debenture is 8% and the current yield to maturity of 11%. The debenture has 7 years to maturity. They also have a bank overdraft of R 3 million due in 4 years and interest is charged at 16% per annum. Natal Limited has a beta of 2.3, a risk-free rate of 6%, and a return on the market of 16%. The company tax rate is 30%.

Calculate the weighted average cost of capital, using the Gordon Growth Model to calculate the cost of equity.

**To calculate the Weighted Average Cost of Capital (WACC) for Natal Limited, follow these steps:**

**1. Calculate the Cost of Equity using the Gordon Growth Model:**

The Gordon Growth Model (Dividend Discount Model) is used to determine the cost of equity. The formula is:

$Cost of Equity(r_{e})=PD +g$

Where:

- $D_{1}$ = Expected dividend next year
- $P_{0}$ = Current market price per share
- $g$ = Growth rate of dividends

**Given:**

- Latest Dividend ($D_{0}$) = R0.83
- Dividend Growth Rate ($g$) = 8% or 0.08
- Current Market Price per Share ($P_{0}$) = R5.90

Calculate $D_{1}$ (expected dividend next year):

$D_{1}=D_{0}×(1+g)$ $D_{1}=0.83×(1+0.08)$ $D_{1}=0.83×1.08$ $D_{1}=0.8964$

Then, use the Gordon Growth Model formula:

$r_{e}=PD +g$ $r_{e}=5.900.8964 +0.08$ $r_{e}=0.1512+0.08$ $r_{e}=0.2312or23.12%$

**2. Calculate the Cost of Preference Shares:**

The cost of preference shares is calculated using the formula:

$Cost of Preference Shares(r_{ps})=PD $

Where:

- $D_{ps}$ = Annual dividend per preference share
- $P_{ps}$ = Market price per preference share

**Given:**

- Annual Dividend ($D_{ps}$) = 9% of R2.50 = R0.225
- Market Price ($P_{ps}$) = R3.80

$r_{ps}=3.800.225 $ $r_{ps}=0.0592or5.92%$

**3. Calculate the Cost of Debt:**

The cost of debt is given by the yield to maturity for publicly traded debt.

**Given:**

- Yield to Maturity = 11%

The cost of debt, after tax adjustment, is:

$Cost of Debt(r_{d})=Yield to Maturity×(1−Tax Rate)$ $r_{d}=0.11×(1−0.30)$ $r_{d}=0.11×0.70$ $r_{d}=0.077or7.70%$

**4. Calculate the Weighted Average Cost of Capital (WACC):**

To calculate WACC, use the formula:

$WACC=VE ×r_{e}+VP ×r_{ps}+VD ×r_{d}$

Where:

- $E$ = Market value of equity
- $P$ = Market value of preference shares
- $D$ = Market value of debt
- $V$ = Total market value of the firm’s financing (equity + preference shares + debt)

**Market Values:**

- Market Value of Equity ($E$) = Number of shares × Price per share = 3,000,000 × 5.90 = R17,700,000
- Market Value of Preference Shares ($P$) = Number of shares × Price per share = 1,750,000 × 3.80 = R6,650,000
- Market Value of Debt ($D$) = R5,000,000 (Since the face value is used here)

Total Market Value ($V$):

$V=E+P+D$ $V=17,700,000+6,650,000+5,000,000$ $V=29,350,000$

Now, calculate WACC:

$WACC=,,,, ×0.2312+,,,, ×0.0592+,,,, ×0.077$ $WACC=0.603×0.2312+0.226×0.0592+0.170×0.077$ $WACC=0.1397+0.0134+0.0131$ $WACC=0.1662or16.62%$

**Summary: **The Weighted Average Cost of Capital (WACC) for Natal Limited is approximately **16.62%**.

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