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Chapter 13 Equity Valuation

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13-2 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Fundamental Stock Analysis: Models of Equity Valuation Basic Types of Models Basic Types of Models –Balance Sheet Models –Dividend Discount Models –Price/Earning Ratios Estimating Growth Rates and Opportunities Estimating Growth Rates and Opportunities

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13-3 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Intrinsic Value and Market Price Intrinsic Value Intrinsic Value –Self assigned Value –Jason: $14, Jamie: $16, Katie: $18 –Variety of models are used for estimation Market Price Market Price –Consensus value of all potential traders ($16) Trading Signal Trading Signal –IV > MP Buy –IV < MP Sell or Short Sell –IV = MP Hold or Fairly Priced

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13-4 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Dividend Discount Models: General Model V 0 = Value of Stock V 0 = Value of Stock D t = Dividend D t = Dividend k = required return k = required return

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13-5 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 No Growth Model Stocks that have earnings and dividends that are expected to remain constant Stocks that have earnings and dividends that are expected to remain constant Preferred Stock Preferred Stock

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13-6 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 No Growth Model: Example E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33

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13-7 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Constant Growth Model g = constant perpetual growth rate g = constant perpetual growth rate Note: D 1 = D 0 (1+g)

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13-8 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Constant Growth Model: Example E 1 = $5.00b = 40% k = 15% (1-b) = 60%D 1 = $3.00 g = 8% V 0 = 3.00 / (.15 -.08) = $42.86

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13-9 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Estimating Dividend Growth Rates g = growth rate in earnings g = growth rate in earnings ROE = Return on Equity for the firm ROE = Return on Equity for the firm b = plowback or retention percentage rate b = plowback or retention percentage rate – (1- dividend payout percentage rate) d = dividend payout = 1 - b d = dividend payout = 1 - b

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13-10 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Constant growth Rankin Corporation earns a constant 20% on new equity investment (ROE) and pays out a constant 60% of earnings as dividends. EPS for the year just ended = $3.00. Rankin Corporation earns a constant 20% on new equity investment (ROE) and pays out a constant 60% of earnings as dividends. EPS for the year just ended = $3.00. The beta of the stock is.90, the expected return on the market is 13 percent and Rf = 4 percent. The beta of the stock is.90, the expected return on the market is 13 percent and Rf = 4 percent. Calculate earnings and dividends for the next 4 years. Calculate earnings and dividends for the next 4 years.

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13-11 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Rankin

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13-12 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Rankin continued Calculate the growth (percentage change) in earnings and dividends. Calculate the growth (percentage change) in earnings and dividends. Calculate the required return Calculate the required return –R = Rf + Beta*(Rm-Rf) –R =.04 +.9*(.13-.04) =.121 Calculate the price (or value) Calculate the price (or value) –P t = D t+1 /(k-g)

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13-13 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Rankin continued Calculate the percentage change in the stock price. Calculate your HPR if you buy today and hold for one period.

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13-14 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Shifting Growth Rate Model g 1 = first growth rate g 1 = first growth rate g 2 = second growth rate g 2 = second growth rate T = number of periods of growth at g 1 T = number of periods of growth at g 1

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13-15 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Shifting growth Value at t = 0 D1D1 D2D2 D3D3 Value at time T DTDT ……... Note: value at T = D T+1 /(k-g)

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13-16 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Lang Company The Lang Company just paid a dividend of $2 The Lang Company just paid a dividend of $2 Dividends are expected to grow at a rate of 20% for 3 years and then at a constant rate of 5 percent. Dividends are expected to grow at a rate of 20% for 3 years and then at a constant rate of 5 percent. If your required return is 15%, how much would you pay for a share of Lang Company stock? If your required return is 15%, how much would you pay for a share of Lang Company stock?

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13-17 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Shifting Growth Rate Model: Example D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 = 2.40 D 2 = 2.88 D 3 = 3.46 D 4 = 3.63 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 + D 3 /(1.15) 3 + D 4 / (.15 -.05) ( (1.15) 3 D 4 / (.15 -.05) ( (1.15) 3 V 0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

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13-18 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Multistage or nonconstant growth The Wade Company just paid a dividend of $1.20 per share. Dividends are expected to grow at a rate of 10% for 2 years, 9 percent for the next 2 years and a constant 8 percent thereafter. If the required return is 13 percent, find value of a share of Wade. The Wade Company just paid a dividend of $1.20 per share. Dividends are expected to grow at a rate of 10% for 2 years, 9 percent for the next 2 years and a constant 8 percent thereafter. If the required return is 13 percent, find value of a share of Wade.

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13-19 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Specified Holding Period Model P N = the expected sales price for the stock at time N P N = the expected sales price for the stock at time N N = the specified number of years the stock is expected to be held N = the specified number of years the stock is expected to be held

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13-20 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Partitioning Value: Growth and No Growth Components PVGO = Present Value of Growth Opportunities PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1 E 1 = Earnings Per Share for period 1

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13-21 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Partitioning Value: Example ROE = 20% d = 60% b = 40% ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8% g =.20 x.40 =.08 or 8%

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13-22 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Partitioning Value: Example V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

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13-23 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Price Earnings Ratios P/E Ratios are a function of two factors P/E Ratios are a function of two factors –Required Rates of Return (k) –Expected growth in Dividends Uses Uses –Relative valuation –Extensive Use in industry

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13-24 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 P/E Ratio: No expected growth E 1 - expected earnings for next year E 1 - expected earnings for next year –E 1 is equal to D 1 under no growth k - required rate of return k - required rate of return

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13-25 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 P/E Ratio with Constant Growth b = retention ration b = retention ration ROE = Return on Equity ROE = Return on Equity

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13-26 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Numerical Example: No Growth E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8

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13-27 Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1998 Numerical Example with Growth b = 60% ROE = 15% (1-b) = 40% E 1 = $2.50 (1 + (.6)(.15)) = $2.73 D 1 = $2.73 (1-.6) = $1.09 k = 12.5% g = 9% P 0 = 1.09/(.125-.09) = $31.14 PE = 31.14/2.73 = 11.4 PE = (1 -.60) / (.125 -.09) = 11.4

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