Equity Valuation

Equity Valuation Notes

13.1 Valuation by Comparables

• Valuation Models Using Comparables

  • Involves assessing a firm's value by comparing it to similar firms.

  • This comparative analysis looks at the relationship between price and various determinants of value for those firms.

  • The internet facilitates easy access to firm data, with resources including:

  • EDGAR

  • Finance.yahoo.com

13.2 Intrinsic Value versus Market Price

• Definitions:

  • Expected Dividend per Share (E(D1)): Represents the anticipated dividends an investor expects to receive at the end of the period.

  • Current Share Price (P): The price at which a share currently trades on the market.

  • Expected End-of-Year Price (P1): The price expected to be realized at the end of the year.

• Capital Asset Pricing Model (CAPM)

  • Provides the required return on investment.

  • Condition for Proper Pricing: If the stock is priced correctly, the required return should equal the expected return.

• Intrinsic Value:

  • Calculated as the present value of the firm’s expected future net cash flows, discounted at the required rate of return (RoR).

• Market Capitalization Rate:

  • Represents the market consensus estimate of the appropriate discount rate for the firm’s cash flows.

• Intrinsic Value Formula:

  $V<em>o = \frac{E(D</em>1) + E(P_1)}{1 + k}$

  • For a holding period H:

  $V<em>o = \frac{D</em>1}{(1+k)} + \frac{D<em>2}{(1+k)^{2}} + … + \frac{D</em>H + P_H}{(1+k)^{H}}$

• Dividend Discount Model (DDM):

  • The formula for intrinsic value of a firm is equivalent to the present value of all expected future dividends.

13.3 Dividend Discount Models

• No Growth Case:

  • Stocks that have earnings and dividends expected to remain constant.

  • Preferred Stock Value:

  $V = \frac{D}{k}$

• No Growth Model Example:

  • Given:

  • E1 = D1 = $5.00

  • k = 0.15

  • Calculated:

  V_0 = \frac{5.00}{0.15} = $33.33

• Constant-Growth DDM:

  • This model assumes dividends will grow at a constant rate.

  • Value of Stock Formula:

  $V<em>0 = \frac{D</em>1}{k - g}$

  • Implications for stock values:

  • Larger dividend per share increases value.

  • Lower market capitalization rate (k) increases value.

  • Higher expected growth rate of dividends increases value.

• Example of Constant Growth Model:

  • Given:

  • k = 15%

  • D1 = $3.00

  • g = 8%

  • Calculated:

  V_0 = \frac{3.00}{(0.15 - 0.08)} = $42.86

• Holding Period Return:

  • For a stock priced equal to its intrinsic value, the expected holding period return is given by:

  $E(r) = \frac{D<em>1}{P</em>0} + g$

• Growth Rate Calculation:

  • Growth rate (g) determined by the formula:

  $g = ROE \times b$

  • Where:

  • ROE = Return on Equity for the firm.

  • b = Plowback or retention percentage rate (1 - Dividend Payout Ratio).

• Growth Scenario Implications:

  • If a stock price equals its intrinsic value and the growth rate is sustained, the stock should maintain its price.

  • If all earnings are paid out as dividends, the price should be lower assuming growth opportunities exist.

• Price Calculation with Growth Opportunities:

  • The formula is given by:

  $P = \text{No-growth value per share} + \text{PVGO}$

  • Where PVGO = Present Value of Growth Opportunities.

• Partitioning Value Example:

  • Given:

  • ROE = 20%

  • d = 60%

  • b = 40%

  • E1 = $5.00

  • D1 = $3.00

  • k = 15%

  • g = 0.20 * 0.40 = 0.08 or 8%

• Calculating Different Components:

  • Price with growth (Po) and no growth components calculated using respective formulas.

13.4 Price-Earnings Ratios

• P/E Ratios:

  • Dependent on:

  • Required Rates of Return (k)

  • Expected growth in Dividends

  • Applications include:

  • Relative valuation techniques

  • Extensively used in various industries

• Calculation of P/E ratio:

  $P/E = \frac{E_1}{k}$

  • Where:

  • E1 = Expected earnings for next year.

  • Under no growth, E1 is equal to D1.

• P/E Ratio with Constant Growth:

  • Calculated as:

  $P/E = \frac{(1 - b)}{(k - g)}$

  • Where:

  • b = retention ratio

  • ROE = Return on Equity

• Numerical Example for No Growth:

  • Given:

  • E0 = $2.50

  • g = 0

  • k = 12.5%

  • Calculated:

  P_0 = \frac{D}{k} = \frac{2.50}{0.125} = $20.00

  • P/E Ratio = $\frac{1}{0.125} = 8$

• Numerical Example for With Growth:

  • Given:

  • b = 60%

  • ROE = 15%

  • (1 - b) = 40%

  • E1 = $2.50(1 + (0.6*0.15)) = $2.73

  • D1 = $2.73(1 - 0.6) = $1.09

  • k = 12.5%

  • g = 9%

  • Calculated:

  P_0 = \frac{1.09}{(0.125 - 0.09)} = $31.14

• Risks Projections in P/E Ratios:

  • Riskier stocks exhibit lower P/E multiples due to higher required rates of return (high k values).

13.5 Free Cash Flow Valuation Approaches

• Free Cash Flow for Firm (FCFF):

  • Defined as:

  $FCFF = EBIT(1 - t_c) + \text{Depreciation} - \text{Capital Expenditures} - \text{Increase in NWC}$

  • Where:

  • EBIT = Earnings Before Interest and Taxes

  • t_c = Corporate tax rate

  • NWC = Net Working Capital

• Free Cash Flow to Equity Holders (FCFE):

  • Defined as:

  $FCFE = FCFF - \text{Interest Expense} \times (1 - t_c) + \text{Increases in Net Debt}$

• Estimating Terminal Value Using Constant Growth Model:

  • Firm value given by:

  $PV = \sum<em>{t=1}^{T} \frac{FCFF</em>t}{(1 + WACC)^t} + \frac{FCFF_{T + 1}}{(WACC - g)}$

  • Where:

  • WACC = Weighted Average Cost of Capital

• Market Value of Equity:

  • Determined as:

  $MV = \sum<em>{t=1}^{T} \frac{FCFE</em>t}{(1 + k<em>E)^t} + \frac{FCFE</em>{T + 1}}{(k_E - g)}$

  • Where:

  • k_E = Required Rate of Return for Equity Holders