Let's break down the information and calculate **Lidiya Ltd’s Weighted Average Cost of Capital (WACC)** step by step. --- ## 1. **Cost of Equity (Ke) – Gordon Growth Model** The **Gordon Growth Model** is: \[ K_e = \frac{D_1}{P_0} + g \] Where: - \( D_1 \) = Dividend expected next year = \( D_0 \times (1+g) \) - \( D_0 \) = Most recent dividend = 30 cents = R0.30 - \( P_0 \) = Current market price = R4.50 - \( g \) = Dividend growth rate = 13% = 0.13 So: \[ D_1 = 0.30 \times (1 + 0.13) = 0.30 \times 1.13 = 0.339 \] \[ K_e = \frac{0.339}{4.50} + 0.13 = 0.0753 + 0.13 = 0.2053 = \boxed{20.53\%} \] --- ## 2. **Cost of Preference Shares (Kp)** \[ K_p = \frac{D_{ps}}{P_{ps}} \] Given: - Preference dividend = 14% of R3.00 = R0.42 - Market price = R5.00 So: \[ K_p = \frac{0.42}{5.00} = 0.084 = \boxed{8.4\%} \] --- ## 3. **Cost of Debentures (Kd)** - Given: **Yield to maturity = 6%** - Debenture interest is tax deductible, so after-tax cost: \[ K_d = 6\% \times (1 - 0.3) = 6\% \times 0.7 = \boxed{4.2\%} \] --- ## 4. **Cost of Bank Loan (Kb)** - Given: **Interest rate = 13%** - After-tax cost: \[ K_b = 13\% \times (1 - 0.3) = 13\% \times 0.7 = \boxed{9.1\%} \] --- ## 5. **Market Values of Each Component** ### **Ordinary Shares** - 2,000,000 shares × R4.50 = **R9,000,000** ### **Preference Shares** - 1,500,000 shares × R5.00 = **R7,500,000** ### **Debentures** - Face value = **R800,000** (no market value given, assume at par) ### **Bank Loan** - **R900,000** ### **Non-distributable Reserves** - **R2,000,000** (these are part of equity) #### **Total Market Value (V)** \[ V = 9,000,000 \text{ (ordinary)} + 7,500,000 \text{ (preference)} + 2,000,000 \text{ (reserves)} + 800,000 \text{ (debentures)} + 900,000 \text{ (loan)} \] \[ V = 20,200,000 \] --- ### **Proportion of Each Component** | Component | Value (R) | Proportion (W) | |-------------------|------------|---------------| | Ordinary shares | 9,000,000 | 0.4455 | | Preference shares | 7,500,000 | 0.3713 | | Reserves | 2,000,000 | 0.0990 | | Debentures | 800,000 | 0.0396 | | Bank loan | 900,000 | 0.0446 | | **Total** | 20,200,000 | 1.000 | --- ## 6. **Assigning Costs** - **Ordinary shares + Reserves** = All equity = Use \( K_e \) - Value = 9,000,000 + 2,000,000 = **11,000,000** - Proportion = 11,000,000 / 20,200,000 = **0.5446** - **Preference shares** = Use \( K_p \) = 8.4% - Value = 7,500,000 / 20,200,000 = **0.3713** - **Debentures** = Use \( K_d \) = 4.2% - Value = 800,000 / 20,200,000 = **0.0396** - **Loan** = Use \( K_b \) = 9.1% - Value = 900,000 / 20,200,000 = **0.0446** --- ## 7. **WACC Calculation** \[ WACC = (W_{e} \times K_{e}) + (W_{p} \times K_{p}) + (W_{d} \times K_{d}) + (W_{l} \times K_{l}) \] Where: - \( W_{e} = 0.5446 \), \( K_e = 20.53\% \) - \( W_{p} = 0.3713 \), \( K_p = 8.4\% \) - \( W_{d} = 0.0396 \), \( K_d = 4.2\% \) - \( W_{l} = 0.0446 \), \( K_l = 9.1\% \) Calculation: - \( 0.5446 \times 0.2053 = 0.1119 \) - \( 0.3713 \times 0.084 = 0.0312 \) - \( 0.0396 \times 0.042 = 0.0017 \) - \( 0.0446 \times 0.091 = 0.0041 \) Sum: \[ WACC = 0.1119 + 0.0312 + 0.0017 + 0.0041 = 0.1489 = \boxed{14.89\%} \] --- ## **Final Answer** ### **The weighted average cost of capital (WACC) for Lidiya Limited is:** \[ \boxed{14.89\%} \] **(rounded to 2 decimal places)** --- **If you need a more detailed breakdown or explanation of any step, let me know!**