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1 1 Chapter 13 Equity Valuation

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2 2 Fundamental Stock Analysis: Models of Equity Valuation Basic Types of Models Balance Sheet Models Dividend Discount Models Price/Earning Ratios Estimating Growth Rates and Opportunities

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3 3 Intrinsic Value and Market Price Intrinsic Value 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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44 4 Dividend Discount Models: General Model V D k o t t t ()1 1 V 0 = Value of Stock D t = Dividend k = required return

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55 5 No Growth Model V D k o Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

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66 6 No Growth Model: Example E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33 V D k o

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7 7 Exercise in class Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

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88 8 Constant Growth Model Vo Dg kg o ()1 g = constant perpetual growth rate

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99 9 Constant Growth Model: Example Vo Dg kg o ()1 E 1 = $5.00b = 40% k = 15% g = 8% V 0 = 3/(.15-.08) = 42.86.

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10 Exercise in class Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

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11 Estimating Dividend Growth Rates gROEb 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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12 Shifting Growth Rate Model VD g k Dg kgk oo t t t T T T () () () ()() 1 1 1 1 1 1 2 2 g 1 = first growth rate g 2 = second growth rate T = number of periods of growth at g 1

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13 Shifting Growth Rate Model: Example D 0 = $2.00 g 1 = 20% for 3years g 2 = 5% forever 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 V 0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

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14 Exercise in class Suppose a firm is expected to increase dividends by 20% in one year and by 15% in the next two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

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15 Specified Holding Period Model 0 1 1 2 2 111 V D k D k DP k NN 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

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16 Exercise in class 1.Gagliardi Way Corporation has an expected ROE of 15%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earning in the form of dividends. A)4.5% B)10.5% C)15.0% D)30.0% 2.Rose Hill Trading Company is expected to have EPS in the upcoming year of $8.00. The expected ROE is 18.0%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 70%, its dividend in the upcoming year should be __________. A)$1.12 B)$1.44 C)$2.40 D)$5.60 3.Rose Hill Trading Company is expected to have EPS in the upcoming year of $6.00. The expected ROE is 18.0%. An appropriate required return on the stock is 14%. If the firm has a plowback ratio of 70%, its intrinsic value should be __________. A)$20.93 B)$69.77 C)$128.57 D)$150.00

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17 Exercise in class 4. Cache Creek Manufacturing Company is expected to pay a dividend of $3.36 in the upcoming year. Dividends are expected to grow at 8% per year. The riskfree rate of return is 4% and the expected return on the market portfolio is 14%. Investors use the CAPM to compute the market capitalization rate, and the constant growth DDM to determine the value of the stock. The stock's current price is $84.00. Using the constant growth DDM, the market capitalization rate is __________. A)9% B)12% C)14% D)18% 5. Caribou Gold Mining Corporation is expected to pay a dividend of $6 in the upcoming year. Dividends are expected to decline at the rate of 3% per year. The risk-free rate of return is 5% and the expected return on the market portfolio is 13%. The stock of Caribou Gold Mining Corporation has a beta of -0.50. Using the constant growth DDM, the intrinsic value of the stock is __________. A)$50.00 B)$150.00 C)$200.00 D)$400.00 6. Lifecycle Motorcycle Company is expected to pay a dividend in year 1 of $2.00, a dividend in year 2 of $3.00, and a dividend in year 3 of $4.00. After year 3, dividends are expected to grow at the rate of 7% per year. An appropriate required return for the stock is 12%. Using the multistage DDM, the stock should be worth __________ today. A)$63.80 B)$65.13 C)$67.98 D)$85.60

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18 Partitioning Value: Growth and No Growth Components V E k PVGO Dg kg E k o o 1 1 1() () PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1

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19 Partitioning Value: Example ROE = 20% dy = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8%

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20 V NGV PVGO o o 3 1508 86 5 15 33 863352 (..) $42.. $33. $42.$33.$9. Partitioning Value: Example V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

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21 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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22 P/E Ratio: No expected growth P E k P Ek 0 1 0 1 1 E 1 - expected earnings for next year E 1 is equal to D 1 under no growth k - required rate of return

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23 P/E Ratio with Constant Growth P D kg Eb kbROE P E b kb 0 11 0 1 1 1 () () () b = retention ration ROE = Return on Equity

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24 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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25 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% PE=?

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26 Example 223 The market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. Its expected ROE is 12% and its expected EPS is $5.00. If the firm's plow-back ratio is 40%, its P/E ratio will be __________. A)8.33 B)11.54 C)19.23 D)50.00 Gagliardi Way Corporation has an expected ROE of 15%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earning in the form of dividends. A)4.5% B)10.5% C)15.0% D)30.0% Brevik Builders has an expected ROE of 25%. Its dividend growth rate will be __________ if it follows a policy of paying 30% of earning in the form of dividends. A)5.0% B)15.0% C)17.5% D)45.0%

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27 Example 2223 ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock. At what price would you expect ART to sell? A)$25.00 B)$34.29 C)$42.86 D)none of the above At what P/E ratio would you expect ART to sell? A)8.33 B)11.43 C)14.29 D)none of the above What is the present value of growth opportunities for ART? A)$8.57 B)$9.29 C)$14.29 D)none of the above What price do you expect ART shares to sell for in 4 years? ? A)$53.96 B)$44.95 C)$41.68 D)none of the above

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28 Pitfalls in Using PE Ratios Flexibility in reporting makes choice of earnings difficult Pro forma earnings may give a better measure of operating earnings Problem of too much flexibility

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29 Other Valuation Ratios & Approaches Price-to-book Price-to-cash flow Price-to-sales Present Value of Free Cash Flow Residual Income Model

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