Chapter 12: The Cost of Capital (Essentials of Corporate Finance)

Cost of Capital: Concepts and Overview

Introduction to Cost of Capital

The cost of capital is a fundamental concept in corporate finance, representing the minimum return a firm must earn on its investments to satisfy its investors and remain profitable. It reflects the market's perception of the risk associated with the firm's assets and is used as the discount rate for evaluating investment projects.

• Definition: The cost to a firm for capital funding, or the return required by providers of funds (debt and equity).

• Required Return: The firm must earn at least the required return to compensate investors for the financing provided.

• Discount Rate: The required return is used as the discount rate for computing Net Present Value (NPV).

• Risk: The return earned on assets depends on the risk of those assets.

Components of Cost of Capital

Cost of Equity (rcs)

The cost of equity is the return required by equity investors given the risk of the firm's cash flows. It can be estimated using two major methods:

• Dividend Growth Model (DGM): Assumes dividends grow at a constant rate.

• Security Market Line (SML) or Capital Asset Pricing Model (CAPM): Relates expected return to systematic risk (beta).

Dividend Growth Model (DGM)

The DGM estimates the cost of equity using the formula:

• $P_0 = \frac{D_1}{R_E - g}$

• Rearranged: $R_E = \frac{D_1}{P_0} + g$

• Where: $D_1$ = expected dividend next period, $P_0$ = current stock price, $g$ = growth rate of dividends.

Example: If a company expects to pay a $4.24 dividend next year, dividends grow at 6% per year, and the current stock price is $60:

• $R_E = \frac{4.24}{60} + 0.06 = 0.1307$ or 13.07%

Security Market Line (SML) / CAPM

The SML approach uses the CAPM formula:

• $R_E = R_f + \beta (E(R_M) - R_f)$

• Where: $R_f$ = risk-free rate, $E(R_M)$ = expected market return, $\beta$ = systematic risk of the asset.

Example: If $\beta = 1.15$, $R_f = 7\%$, and market risk premium $= 6\%$:

• $R_E = 0.07 + 1.15 \times 0.06 = 0.139$ or 13.9%

Advantages and Disadvantages

• DGM: Easy to use, but only applicable to firms paying dividends at a constant growth rate; sensitive to growth rate estimates; does not explicitly consider risk.

• SML/CAPM: Explicitly adjusts for systematic risk; applicable to all companies with a known beta; requires estimates of market risk premium and beta, which can vary over time.

Cost of Debt (rd)

The cost of debt is the required return on a company's debt, typically measured by the yield to maturity (YTM) on existing debt or similar rated bonds. The coupon rate is not relevant for new issues.

• Formula: After-tax cost of debt: $r_d (1 - T)$, where $T$ is the corporate tax rate.

• Example: If YTM is 7.37% and tax rate is 21%: $r_d (1 - T) = 0.0737 \times (1 - 0.21) = 0.0582$ or 5.82%

Cost of Preferred Stock (rp)

Preferred stock pays a constant dividend and is valued as a perpetuity:

• $r_p = \frac{D}{P}$

• Example: If annual dividend is $1.25 and stock price is $25.85:$r_p = \frac{1.25}{25.85} = 0.0484$ or 4.84%

Weighted Average Cost of Capital (WACC)

Definition and Calculation

The WACC is the average cost of capital for the firm, weighted by the proportion of each capital component (equity, debt, preferred stock). It represents the minimum return required on the firm's assets.

• $\text{WACC} = w_E R_E + w_P R_P + w_D R_D (1 - T)$

• Where: $w_E$, $w_P$, $w_D$ are the weights (market value proportions) of equity, preferred stock, and debt, respectively.

Determining Capital Structure Weights

• Market Value of Equity: Number of shares outstanding × price per share.

• Market Value of Debt: Number of bonds × bond price.

• Market Value of Firm: $V = E + P + D$

• Weights: $w_E = E/V$, $w_P = P/V$, $w_D = D/V$

Example Calculation

• Common equity: $150M$, Preferred stock: $25M$, Debt: $75M$, Total: $250M$

• Weights: $w_E = 0.6$, $w_P = 0.1$, $w_D = 0.3$

• WACC: $0.6 \times 14\% + 0.1 \times 9\% + 0.3 \times 10\% \times (1 - 0.4) = 8.4\% + 0.9\% + 1.8\% = 11.1\%$

Factors Influencing WACC

• Market conditions (interest rates, tax rates, risk premium)

• Firm's capital structure and dividend policy

• Investment policy (riskiness of projects)

Divisional and Project Costs of Capital

Risk-Adjusted WACC

Different divisions or projects may have different risk profiles. The WACC should be adjusted to reflect the appropriate risk and capital structure for each project.

• Subjective Approach: Assign projects to risk categories and adjust the discount rate accordingly.

• Pure Play Approach: Use betas from comparable companies to estimate project risk.

Example: Subjective Approach

Risk Level	Discount Rate
Low Risk	6%
Moderate Risk	10%
Risk as Firm	14%
High Risk	20%

Company Valuation with WACC

Valuing the Firm

The value of the firm can be estimated using the WACC as the discount rate for free cash flows:

• $\text{Value} = \frac{\text{CFA}^*}{\text{WACC} - g}$

• Where: CFA* = free cash flow, $g$ = growth rate

• Example: If CFA* = $120M$, $g = 5\%$, WACC = 9%: $\text{Value} = \frac{120}{0.09 - 0.05} = 3,000$ (in millions)

Summary Table: Key Formulas

Component	Formula	Description
Cost of Equity (DGM)	$R_E = \frac{D_1}{P_0} + g$	Dividend growth model
Cost of Equity (CAPM)	$R_E = R_f + \beta (E(R_M) - R_f)$	Security market line
Cost of Debt	$r_d (1 - T)$	After-tax cost of debt
Cost of Preferred Stock	$r_p = \frac{D}{P}$	Perpetuity formula
WACC	$w_E R_E + w_P R_P + w_D R_D (1 - T)$	Weighted average cost of capital
Firm Value	$\frac{\text{CFA}^*}{\text{WACC} - g}$	Valuation using WACC

Key Takeaways

• The cost of capital is essential for investment decisions and company valuation.

• WACC reflects the firm's overall risk and capital structure.

• Different projects may require risk-adjusted discount rates.

• Accurate estimation of component costs and weights is crucial for reliable WACC calculation.

Additional info: These notes expand on the original slides and text by providing full definitions, formulas, and examples for each concept, as well as a summary table for quick reference.