Cost of Equity

The Cost of Equity (Ke) represents the expected rate of return that a company's shareholders require for investing their capital. It's the opportunity cost of equity capital, reflecting what investors could earn elsewhere for a comparable risk. In finance, the cost of equity is vital when making capital budgeting decisions, setting hurdle rates, and evaluating financing options. Firms that underestimate this cost may accept projects that reduce shareholder value, while overestimation can lead to missed growth opportunities. The cost of equity not only guides investment selection but also determines a firm's capital structure and influences market perception.

Dividend Discount Model (DDM)

a. DDM Concept

The Dividend Discount Model calculates the cost of equity by equating a stock's current price to the present value of all its expected future dividends. The underlying premise is that the intrinsic value of a share equals the sum of discounted dividends, assuming dividends are the sole cash flows to equity holders.

b. DDM Formula and Steps

The most common form is the Gordon Growth Model, suitable for firms with stable dividend growth:

\[ k_e = \frac{D_1}{P_0} + g \] Where:

• k_e: Cost of equity
• D₁: Expected dividend next year
• P₀: Current market price per share
• g: Constant growth rate of dividends

c. Example

Suppose ABC Ltd. is expected to pay a dividend of ₹5 next year, its shares trade at ₹100, and dividends are projected to grow by 6% annually:

1. Identify variables: D₁ = ₹5, P₀ = ₹100, g = 0.06
2. Apply the formula: k_e = (5 / 100) + 0.06 = 0.05 + 0.06 = 0.11
3. Cost of equity = 11%

Capital Asset Pricing Model (CAPM)

a. CAPM Concept

CAPM estimates the cost of equity based on systematic risk, as measured by beta. It presumes that investors require compensation for both time value (risk-free rate) and market risk, which is unique to each security.

b. CAPM Formula and Interpretation

\[ k_e = R_f + \beta (R_m - R_f) \] Where:

• k_e: Cost of equity
• R_f: Risk-free rate (typically government securities)
• β: Beta (volatility of the stock relative to market)
• R_m: Expected market return
• (R_m - R_f): Market risk premium

c. Example

Assume:

• Risk-free rate (R_f) = 7%
• Expected market return (R_m) = 13%
• Beta (β) = 1.2

1. Calculate market risk premium: 13% - 7% = 6%
2. Apply the formula: k_e = 7% + 1.2 × 6% = 7% + 7.2% = 14.2%
3. Cost of equity = 14.2%

Earnings Yield Approach

Earnings Yield Concept and Application

The earnings yield approach provides a straightforward method, relating earnings to market price. This approach is especially relevant for firms that retain much of their earnings or don't pay regular dividends.

\[ k_e = \frac{E}{P_0} \] Where:

• E: Earnings per share
• P₀: Current market price per share

Example: If XYZ Ltd. has earnings per share of ₹8 and the share price is ₹80:

1. k_e = 8 / 80 = 0.10
2. Cost of equity = 10%

Growth Rate Estimation and Relevance in Valuation

a. Estimating Growth Rate

Growth rate (g) is critical for equity valuation models like DDM. Estimation methods include:

• Historical dividend growth: Calculate average past increase in dividends.
• Sustainable growth rate: g = Retention ratio × Return on equity (ROE)

b. Relevance in Valuation

Growth rate influences the present value of future dividends and, consequently, the calculated cost of equity. A higher g increases valuation, but assumptions must be realistic. Overestimating growth can distort investment decisions, so it's wise to analyze stable historical data and future prospects.

Risk-Free Rate, Beta, and Market Risk Premium Interpretation

a. Risk-Free Rate

The risk-free rate is the return on government securities, considered default-free. It anchors the minimum required return for any investment.

b. Beta

Beta measures the sensitivity of a stock's returns to movements in the overall market.

• β = 1: Stock moves in line with market.
• β > 1: Stock is more volatile than market.
• β < 1: Stock is less volatile than market.

c. Market Risk Premium

The market risk premium is the expected excess return over the risk-free rate. It's a reward for taking market risk, and forms the backbone of CAPM's risk adjustment.

Estimating the cost of equity is central to sound financial decision-making. Whether you use DDM, CAPM, or earnings yield, the key is understanding assumptions behind each model and carefully interpreting risk and growth parameters.