1. **State the problem:** We need to compute costs of different capital components for ABC Limited and then find the weighted average cost of capital (WACC). Finally, comment on the importance of cost of capital. 2. **Given data:** - Bank loan: sh. 3,000,000 at 15%, tax rate 30% - Corporate bonds: sh. 2,000,000 at 3% coupon, price sh. 105 - Preferred stock: sh. 3,000,000, dividend sh. 5 (5% of 120), flotation cost 3, price 118 - Common stock: sh. 5,000,000, dividend last year sh. 4, growth rate 2.5%, flotation cost 2, price 48.50 - Retained earnings: sh. 2,000,000 --- ### (i) Compute costs of capital components **Cost of Debt (after tax):** $$k_d = r_d (1 - T_c)$$ Where $r_d = 15\%$, $T_c = 30\%$ $$k_d = 0.15 \times (1 - 0.3) = 0.15 \times 0.7 = 0.105 = 10.5\%$$ **Cost of Corporate Bonds:** - Coupon payment = $3\% \times 100 = sh. 3$ (assumed for sh.100 bonds) - Market price = sh. 105 - Yield to maturity approx: $$k_b \approx \frac{Coupon}{Price} = \frac{3}{105} = 0.02857 = 2.857\%$$ **Cost of Preferred Stock:** - Dividend = $5$ (5% of sh.120 par) - Price net of flotation = $118 - 3 = 115$ $$k_{ps} = \frac{Dividend}{Price - Flotation} = \frac{5}{115} = 0.0435 = 4.35\%$$ **Cost of New Common Stock:** - Dividend next year: $$D_1 = D_0 (1 + g) = 4 \times 1.025 = 4.10$$ - Price net flotation: $$48.50 - 2 = 46.5$$ - Growth rate, $g = 2.5\% = 0.025$ $$k_{cs} = \frac{D_1}{P_0 - F} + g = \frac{4.10}{46.5} + 0.025 = 0.08817 + 0.025 = 0.11317 = 11.317\%$$ **Cost of Retained Earnings:** - Same as common stock but no flotation cost $$k_{re} = \frac{D_1}{P_0} + g = \frac{4.10}{48.50} + 0.025 = 0.0845 + 0.025 = 0.1095 = 10.95\%$$ --- ### (ii) Compute WACC Calculate market values: - Debt (Bank Loan): 3,000,000 (assumed at face value) - Bonds: Market price $= 2,000,000 \times \frac{105}{100} = 2,100,000$ - Preferred stock: $3,000,000 \times \frac{118}{120} = 2,950,000$ - Common stock: $5,000,000 \times \frac{48.50}{50} = 4,850,000$ - Retained earnings: 2,000,000 Total market value: $$MV = 3,000,000 + 2,100,000 + 2,950,000 + 4,850,000 + 2,000,000 = 14,900,000$$ Weights: $$W_d = \frac{3,000,000}{14,900,000} = 0.2013$$ $$W_b = \frac{2,100,000}{14,900,000} = 0.1409$$ $$W_{ps} = \frac{2,950,000}{14,900,000} = 0.1980$$ $$W_{cs} = \frac{4,850,000}{14,900,000} = 0.3255$$ $$W_{re} = \frac{2,000,000}{14,900,000} = 0.1342$$ Now calculate WACC: $$WACC = W_d \times k_d + W_b \times k_b + W_{ps} \times k_{ps} + W_{cs} \times k_{cs} + W_{re} \times k_{re}$$ $$= 0.2013 \times 0.105 + 0.1409 \times 0.02857 + 0.1980 \times 0.0435 + 0.3255 \times 0.11317 + 0.1342 \times 0.1095$$ $$= 0.0211 + 0.0040 + 0.0086 + 0.0368 + 0.0147 = 0.0852 = 8.52\%$$ --- ### (iii) Importance of Cost of Capital - It acts as a **hurdle rate** for evaluating investment projects; projects must earn returns greater than this to add value. - Helps in determining the **optimal capital structure** minimizing overall cost and maximizing firm value. - Essential for **budgeting, performance evaluation**, and strategic financial planning. - Affects decisions on **financing** (debt vs equity) and dividend policies. --- **Final answers:** - Cost of Debt (after tax): 10.5% - Cost of Corporate Bonds: 2.86% - Cost of Preferred Stock: 4.35% - Cost of New Common Stock: 11.32% - Cost of Retained Earnings: 10.95% - Weighted Average Cost of Capital (WACC): 8.52%