1. **Problem Statement:** Estimate the cost of capital for National using the given market data and financial information. 2. **Formula and Concepts:** The cost of capital is the weighted average cost of capital (WACC), calculated as: $$\text{WACC} = \frac{E}{V}r_e + \frac{P}{V}r_p + \frac{D}{V}r_d(1 - T_c)$$ where $E$ = market value of equity, $P$ = market value of preferred stock, $D$ = market value of debt, $V = E + P + D$, $r_e$ = cost of equity, $r_p$ = cost of preferred stock, $r_d$ = cost of debt, and $T_c$ = corporate tax rate. 3. **Calculate Market Values:** - Bonds (Debt) = $300,000 + 350,000 = 650,000$ - Preferred Stock = $25.00 \times 25,000 = 625,000$ - Common Stock = $46.75 \times 150,000 = 7,012,500$ - Retained Earnings = $1,500,000$ (already market value) Total Equity $E = 7,012,500 + 1,500,000 = 8,512,500$ Total Preferred $P = 625,000$ Total Debt $D = 650,000$ Total Value $V = 8,512,500 + 625,000 + 650,000 = 9,787,500$ 4. **Calculate Cost of Debt $r_d$:** Given yields: 10-year bonds 14%, 15-year bonds 17%, 1-year bonds 21%, and 19% bonds. Assuming average cost of debt $r_d = \frac{14 + 17 + 21 + 19}{4} = 17.75\%$ 5. **Calculate Cost of Preferred Stock $r_p$:** $$r_p = \frac{\text{Preferred Dividend}}{\text{Price}} = \frac{4.50}{25.00} = 0.18 = 18\%$$ 6. **Calculate Cost of Equity $r_e$:** Using Dividend Growth Model: $$r_e = \frac{D_1}{P_0} + g$$ Where $D_1$ = next dividend, $P_0$ = current price, $g$ = growth rate. Given current dividend yield 8%, growth 15%, so: $$r_e = 0.08 + 0.15 = 0.23 = 23\%$$ 7. **Calculate WACC:** $$\text{WACC} = \frac{8,512,500}{9,787,500} \times 0.23 + \frac{625,000}{9,787,500} \times 0.18 + \frac{650,000}{9,787,500} \times 0.1775 \times (1 - 0.40)$$ Calculate each term: - Equity portion: $0.87 \times 0.23 = 0.2001$ - Preferred portion: $0.0638 \times 0.18 = 0.0115$ - Debt portion: $0.0664 \times 0.1775 \times 0.60 = 0.0071$ Sum: $$0.2001 + 0.0115 + 0.0071 = 0.2187 = 21.87\%$$ 8. **Assumptions:** - Market values accurately reflect true values. - Growth rate and dividend yield remain constant. - Debt yields are representative of cost of debt. - Tax rate is constant at 40%. 9. **Qualifications:** - Estimates depend on market conditions and may vary. - Growth rates and yields are historical averages. - Different projects may have different risk profiles. - WACC assumes constant capital structure. - Inflation and market volatility can affect costs. Final estimate of cost of capital is approximately **21.87%**.