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(re)=D1P0+g\text{Cost of Equity} (r_e) = \frac{D_1}{P_0} + gCost of Equity(re​)=P0​D1​​+g

Where:

• D1D_1D1​ = Expected dividend next year
• P0P_0P0​ = Current market price per share
• $g$ = Growth rate of dividends

Given:

• Latest Dividend (D0D_0D0​) = R0.83
• Dividend Growth Rate ($g$) = 8% or 0.08
• Current Market Price per Share (P0P_0P0​) = R5.90

Calculate D1D_1D1​ (expected dividend next year):

D1=D0×(1+g)D_1 = D_0 \times (1 + g)D1​=D0​×(1+g) D1=0.83×(1+0.08)D_1 = 0.83 \times (1 + 0.08)D1​=0.83×(1+0.08) D1=0.83×1.08D_1 = 0.83 \times 1.08D1​=0.83×1.08 D1=0.8964D_1 = 0.8964D1​=0.8964

Then, use the Gordon Growth Model formula:

re=D1P0+gr_e = \frac{D_1}{P_0} + gre​=P0​D1​​+g re=0.89645.90+0.08r_e = \frac{0.8964}{5.90} + 0.08re​=5.900.8964​+0.08 re=0.1512+0.08r_e = 0.1512 + 0.08re​=0.1512+0.08 re=0.2312 or 23.12%r_e = 0.2312 \text{ or } 23.12\%re​=0.2312 or 23.12%

2. Calculate the Cost of Preference Shares:

The cost of preference shares is calculated using the formula:

Cost of Preference Shares(rps)=DpsPps\text{Cost of Preference Shares} (r_{ps}) = \frac{D_{ps}}{P_{ps}}Cost of Preference Shares(rps​)=Pps​Dps​​

Where:

• DpsD_{ps}Dps​ = Annual dividend per preference share
• PpsP_{ps}Pps​ = Market price per preference share

Given:

• Annual Dividend (DpsD_{ps}Dps​) = 9% of R2.50 = R0.225
• Market Price (PpsP_{ps}Pps​) = R3.80

rps=0.2253.80r_{ps} = \frac{0.225}{3.80}rps​=3.800.225​ rps=0.0592 or 5.92%r_{ps} = 0.0592 \text{ or } 5.92\%rps​=0.0592 or 5.92%

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(rd)=Yield to Maturity×(1−Tax Rate)\text{Cost of Debt} (r_d) = \text{Yield to Maturity} \times (1 – \text{Tax Rate})Cost of Debt(rd​)=Yield to Maturity×(1−Tax Rate) rd=0.11×(1−0.30)r_d = 0.11 \times (1 – 0.30)rd​=0.11×(1−0.30) rd=0.11×0.70r_d = 0.11 \times 0.70rd​=0.11×0.70 rd=0.077 or 7.70%r_d = 0.077 \text{ or } 7.70\%rd​=0.077 or 7.70%

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

To calculate WACC, use the formula:

WACC=EV×re+PV×rps+DV×rd\text{WACC} = \frac{E}{V} \times r_e + \frac{P}{V} \times r_{ps} + \frac{D}{V} \times r_dWACC=VE​×re​+VP​×rps​+VD​×rd​

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=17,700,00029,350,000×0.2312+6,650,00029,350,000×0.0592+5,000,00029,350,000×0.077\text{WACC} = \frac{17,700,000}{29,350,000} \times 0.2312 + \frac{6,650,000}{29,350,000} \times 0.0592 + \frac{5,000,000}{29,350,000} \times 0.077WACC=29,350,00017,700,000​×0.2312+29,350,0006,650,000​×0.0592+29,350,0005,000,000​×0.077 $\text{WACC}=0.603\times 0.2312+0.226\times 0.0592+0.170\times 0.077$ $\text{WACC}=0.1397+0.0134+0.0131$ $\text{WACC}=0.1662\text{ or }16.62\%$

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