Cost of Capital

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1. Definition of Cost of Capital

Cost of Capital is the minimum required rate of return a firm must earn on its investments to maintain its market value and attract funds. It represents the firm's cost of financing and is used as a benchmark for evaluating investment opportunities.

Key Concepts

• Opportunity Cost: Return an investor could earn elsewhere with a similar risk.

• Weighted Average Cost of Capital (WACC): Average cost considering all sources of capital (equity, debt, and preferred stock).

Example 1

If a firm uses only equity financing and investors expect a 12% return, then the cost of capital is:

$$\text{Cost of Capital} = 12\%$$

Example 2

A company uses 60% equity (cost 10%) and 40% debt (cost 6%), then:

$$\text{WACC} = 0.6(10\%) + 0.4(6\%) = 6\% + 2.4\% = 8.4\%$$

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2. Components of Cost of Capital

1. Cost of Equity (Ke) – Return required by equity investors.

2. Cost of Debt (Kd) – Effective rate paid on firm’s borrowings.

3. Cost of Preferred Stock (Kp) – Return expected by preferred shareholders.

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3. Importance of Cost of Capital

• Investment Decision: Acts as a hurdle rate in capital budgeting.

• Financing Decision: Helps in choosing between debt, equity, or hybrid.

• Performance Evaluation: Determines economic value added (EVA).

• Valuation: Used as the discount rate in DCF analysis.

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4. Cost of Equity

A. Dividend Growth Model (DGM)

$$Ke = \frac{D_1}{P_0} + g$$

Where:
$D_1$ = expected dividend next year
$P_0$ = current market price
$g$ = growth rate of dividends

Example 1
$D_1 = 2.5$, $P_0 = 50$, $g = 5\%$

$$Ke = \frac{2.5}{50} + 0.05 = 0.05 + 0.05 = 10\%$$

Example 2
$D_1 = 3$, $P_0 = 60$, $g = 6\%$

$$Ke = \frac{3}{60} + 0.06 = 0.05 + 0.06 = 11\%$$

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B. Capital Asset Pricing Model (CAPM)

$$Ke = R_f + \beta (R_m - R_f)$$

Where:
$R_f$ = risk-free rate
$\beta$ = beta of the stock
$R_m$ = expected market return

Example 1
$R_f = 4\%$, $\beta = 1.2$, $R_m = 10\%$

$$Ke = 4\% + 1.2(10\% - 4\%) = 4\% + 7.2\% = 11.2\%$$

Example 2
$R_f = 3\%$, $\beta = 1.5$, $R_m = 12\%$

$$Ke = 3\% + 1.5(12\% - 3\%) = 3\% + 13.5\% = 16.5\%$$

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5. Cost of Debt

A. Irredeemable Debt (Perpetual)

$$Kd = \frac{I (1 - T)}{P}$$

Where:
$I$ = annual interest
$T$ = tax rate
$P$ = market price of debt

Example 1
$I = 80$, $P = 1,000$, $T = 30\%$

$$Kd = \frac{80(1 - 0.30)}{1,000} = \frac{56}{1,000} = 5.6\%$$

Example 2
$I = 100$, $P = 1,100$, $T = 25\%$

$$Kd = \frac{100(1 - 0.25)}{1,100} = \frac{75}{1,100} ≈ 6.82\%$$

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B. Redeemable Debt

$$Kd = \frac{I(1 - T) + \frac{(RV - P)}{N}}{\frac{(RV + P)}{2}}$$

Where:
$RV$ = redeemable value
$P$ = issue price
$N$ = number of years

Example 1
$I = 80$, $RV = 1,000$, $P = 950$, $N = 5$, $T = 30\%$

$$Kd = \frac{80(1 - 0.30) + \frac{(1,000 - 950)}{5}}{\frac{(1,000 + 950)}{2}} = \frac{56 + 10}{975} ≈ 6.77\%$$

Example 2
$I = 90$, $RV = 1,000$, $P = 920$, $N = 4$, $T = 25\%$

$$Kd = \frac{90(0.75) + 20}{960} = \frac{67.5 + 20}{960} ≈ 9.11\%$$

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6. Cost of Preferred Stock

$$Kp = \frac{D}{P}$$

Where:
$D$ = fixed dividend
$P$ = market price

Example 1
$D = 8$, $P = 100$

$$Kp = \frac{8}{100} = 8\%$$

Example 2
$D = 10$, $P = 120$

$$Kp = \frac{10}{120} = 8.33\%$$

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7. Calculation of Weights in Capital Structure

Weights are based on market value, not book value.

Weight of Equity (We)

$$We = \frac{E}{E + D}$$

Weight of Debt (Wd)

$$Wd = \frac{D}{E + D}$$

Where:
$E$ = market value of equity
$D$ = market value of debt

Example 1
Equity = $600,000; Debt = $400,000

$$We = \frac{600,000}{1,000,000} = 0.6;\quad Wd = \frac{400,000}{1,000,000} = 0.4$$

Example 2
Equity = $800,000; Debt = $200,000

$$We = 0.8;\quad Wd = 0.2$$

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8. Weighted Average Cost of Capital (WACC)

$$WACC = Ke \cdot We + Kd \cdot Wd \cdot (1 - T) + Kp \cdot Wp$$

Where:
$Wp$ = weight of preferred stock

Example
$Ke = 12\%, We = 0.6$
$Kd = 8\%, Wd = 0.3, T = 30\%$
$Kp = 9\%, Wp = 0.1$

$$WACC = 0.6(12\%) + 0.3(8\%)(1 - 0.3) + 0.1(9\%) = 7.2\% + 1.68\% + 0.9\% = 9.78\%$$

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9. Additional Concepts (Optional)

A. Marginal Cost of Capital (MCC)

Cost of obtaining one additional unit of capital.

B. Flotation Costs

Costs incurred when issuing new securities.

$$\text{Adjusted Ke} = \frac{D_1}{P_0(1 - F)} + g$$

Where $F$ is the flotation cost as a percentage.

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