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**Equity Valuation Models**

CHAPTER 18

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**Valuation Methods Valuation by comparables**

Price/Earning Ratios Balance Sheet Models Book Value Expected Returns vs. Required Return CAPM Intrinsic Value vs. Market price Dividend Discount Models

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**Table 18.1 Financial Highlights for Microsoft Corporation, October 25, 2007**

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**Limitations of Book Value**

Book value is an application of arbitrary accounting rules Can book value represent a floor value? Better approaches Liquidation value Replacement cost Tobin’s q ratio

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**Expected Holding Period Return**

The return on a stock investment comprises cash dividends and capital gains or losses Assuming a one-year holding period

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**Required Return CAPM gave us required return:**

If the stock is priced correctly Required return should equal expected return

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**Intrinsic Value and Market Price**

Self assigned Value Variety of models are used for estimation Market Price Consensus value of all potential traders Trading Signal IV > MP Buy IV < MP Sell or Short Sell IV = MP Hold or Fairly Priced

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**Specified Holding Period**

PH = the expected sales price for the stock at time H H = the specified number of years the stock is expected to be held

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**Dividend Discount Models: General Model**

V0 = Value of Stock Dt = Dividend k = required return

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No Growth Model Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

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**No Growth Model: Example**

E1 = D1 = $5.00 k = .15 V0 = $5.00 /.15 = $33.33

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Constant Growth Model g = constant perpetual growth rate

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**Constant Growth Model: Example**

E1 = $5.00 b = 40% k = 15% (1-b) = 60% D1 = $3.00 g = 8% V0 = 3.00 / ( ) = $42.86

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**Estimating Dividend Growth Rates**

g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate (1- dividend payout percentage rate)

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**Figure 18.1 Dividend Growth for Two Earnings Reinvestment Policies**

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**Present Value of Growth Opportunities**

If the stock price equals its IV, growth rate is sustained, the stock should sell at: If all earnings paid out as dividends, price should be lower (assuming growth opportunities exist)

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**Present Value of Growth Opportunities Continued**

Price = No-growth value per share + PVGO (present value of growth opportunities)

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**Partitioning Value: Example**

ROE = 20% d = 60% b = 40% E1 = $5.00 D1 = $3.00 k = 15% g = .20 x .40 = .08 or 8%

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**Partitioning Value: Example Continued**

Vo = value with growth NGVo = no growth component value PVGO = Present Value of Growth Opportunities

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**Life Cycles and Multistage Growth Models**

g1 = first growth rate g2 = second growth rate T = number of periods of growth at g1

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**Multistage Growth Rate Model: Example**

D0 = $ g1 = 20% g2 = 5% k = 15% T = 3 D1 = 2.40 D2 = D3 = D4 = 3.63 V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 + D4 / ( ) ( (1.15)3 V0 = = $30.40

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**Table 18.2 Financial Ratios in Two Industries**

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**Figure 18.2 Value Line Investment Survey Report on Honda Motor Co.**

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**Price Earnings Ratios P/E Ratios are a function of two factors**

Required Rates of Return (k) Expected growth in Dividends Uses Relative valuation Extensive Use in industry

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**P/E Ratio: No Expected Growth**

E1 - expected earnings for next year E1 is equal to D1 under no growth k - required rate of return

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**P/E Ratio: Constant Growth**

b = retention ratio ROE = Return on Equity

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**Numerical Example: No Growth**

E0 = $ g = 0 k = 12.5% P0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8

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**Numerical Example: Growth**

b = 60% ROE = 15% (1-b) = 40% E1 = $2.50 (1 + (.6)(.15)) = $2.73 D1 = $2.73 (1-.6) = $1.09 k = 12.5% g = 9% P0 = 1.09/( ) = $31.14 PE = 31.14/2.73 = 11.4 PE = ( ) / ( ) = 11.4

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**Table 18.3 Effect of ROE and Plowback on Growth and the P/E Ratio**

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**P/E Ratios and Stock Risk**

Holding all else equal Riskier stocks will have lower P/E multiples Higher values of k; therefore, the P/E multiple will be lower

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**Pitfalls in P/E Analysis**

Use of accounting earnings Earnings Management Choices on GAAP Inflation Reported earnings fluctuate around the business cycle

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**Figure 18.3 P/E Ratios of the S&P 500 Index and Inflation**

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**Figure 18.4 Earnings Growth for Two Companies**

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**Figure 18.5 Price-Earnings Ratios**

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**Figure 18.6 P/E Ratios for Different Industries, 2007**

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**Other Comparative Value Approaches**

Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio

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**Figure 18.7 Market Valuation Statistics**

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**Free Cash Flow Approach**

Discount the free cash flow for the firm Discount rate is the firm’s cost of capital Components of free cash flow After tax EBIT Depreciation Capital expenditures Increase in net working capital

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**Comparing the Valuation Models**

In practice Values from these models may differ Analysts are always forced to make simplifying assumptions

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**The Aggregate Stock Market**

Explaining Past Behavior Forecasting the Stock Market

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**Figure 18.8 Earnings Yield of S&P 500 versus 10-Year Treasury-Bond Yield**

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**Table 18.4 S&P 500 Price Forecasts Under Various Scenarios**

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The McGraw-Hill Companies, Inc., 2000

The McGraw-Hill Companies, Inc., 2000

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