Subjects finance

Cost Of Capital 177A84

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1. **State the problem:** Calculate the cost of capital using the given market data for preferred stock, common stock, and retained earnings, considering the corporate tax rate. 2. **Formula and concepts:** The cost of capital (WACC) is the weighted average of the costs of each component of capital: preferred stock, common stock, and retained earnings. The formula is: $$\text{WACC} = w_p r_p + w_c r_c + w_r r_r$$ where: - $w_p$, $w_c$, $w_r$ are the weights of preferred stock, common stock, and retained earnings respectively (based on market values). - $r_p$, $r_c$, $r_r$ are the costs of preferred stock, common stock, and retained earnings respectively. Note: Cost of debt is not given, so we consider only these components. 3. **Calculate weights:** Total market value = $300,000 + 1,200,000 + 350,000 = 1,850,000$ $$w_p = \frac{300,000}{1,850,000} = 0.1622$$ $$w_c = \frac{1,200,000}{1,850,000} = 0.6486$$ $$w_r = \frac{350,000}{1,850,000} = 0.1892$$ 4. **Calculate cost of preferred stock $r_p$:** Preferred dividend = $4.50$ Price per share = $25.00$ $$r_p = \frac{4.50}{25.00} = 0.18 = 18\%$$ 5. **Calculate cost of common stock $r_c$ using Dividend Growth Model:** Current dividend yield = 8% (given) Average dividend growth rate $g = 15\%$ Cost of common stock: $$r_c = \text{dividend yield} + g = 0.08 + 0.15 = 0.23 = 23\%$$ 6. **Cost of retained earnings $r_r$:** Given as 21%. 7. **Calculate WACC:** $$\text{WACC} = (0.1622)(0.18) + (0.6486)(0.23) + (0.1892)(0.21)$$ $$= 0.0292 + 0.1492 + 0.0397 = 0.2181 = 21.81\%$$ **Final answer:** The cost of capital is approximately **21.81%**.