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Chapter 13 Equity Valuation 1

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**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 2

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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 3

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**Dividend Discount Models: General Model**

D å t = V o + ( 1 k ) t t = 1 V0 = Value of Stock Dt = Dividend k = required return

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

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**No Growth Model: Example**

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

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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? 7

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**Constant Growth Model + D ( 1 g ) Vo = - k g**

g = constant perpetual growth rate

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**Constant Growth Model: Example**

+ D ( 1 g ) o Vo = - k g E1 = $5.00 b = 40% k = 15% g = 8% V0 = 3/( ) =

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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? 10

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**Estimating Dividend Growth Rates**

= g ROE b 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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**Shifting Growth Rate Model**

+ t + ( 1 g ) D ( 1 g ) å 1 T 2 = + V D o o + t - + ( 1 k ) ( k g ) ( 1 k ) T 2 t = 1 g1 = first growth rate g2 = second growth rate T = number of periods of growth at g1

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**Shifting Growth Rate Model: Example**

D0 = $ g1 = 20% for 3years g2 = 5% forever 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 13

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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? 14

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**Specified Holding Period Model**

+ P V = 1 + 2 . . . + N N + 1 + 2 + ( 1 k ) ( 1 k ) ( 1 k ) N PN = 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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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 Answer: B Difficulty: Medium Answer: C Difficulty: Medium Answer: C Difficulty: Hard 16

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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 $ 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 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 $ 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 Answer: B Difficulty: Medium Answer: B Difficulty: Hard Answer: C Difficulty: Hard 17

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**Partitioning Value: Growth and No Growth Components**

1 V + PVGO o = k + D ( 1 g ) E o 1 PVGO = - ( k - g ) k PVGO = Present Value of Growth Opportunities E1 = Earnings Per Share for period 1

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**Partitioning Value: Example**

ROE = 20% dy = 60% b = 40% E1 = $5.00 D1 = $3.00 k = 15% g = .20 x .40 = .08 or 8% 19

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**Partitioning Value: Example**

3 V = = $42 . 86 o (. 15 - . 08 ) 5 NGV = = $33 . 33 o . 15 PVGO = $42 . 86 - $33 . 33 = $9 . 52 Vo = value with growth NGVo = no growth component value PVGO = Present Value of Growth Opportunities 20

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

Required Rates of Return (k) Expected growth in Dividends Uses Relative valuation Extensive Use in industry 21

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**P/E Ratio: No expected growth**

1 = P k P 1 = E k 1 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 with Constant Growth**

D E ( 1 - b ) 1 1 P = = k - g k - ( b ROE ) P 1 - b = E k - ( b ROE ) 1 b = retention ration 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 24

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**Numerical Example with 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% PE=? 25

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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% 26

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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 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 What is the present value of growth opportunities for ART? A) $8.57 B) $9.29 C) $14.29 What price do you expect ART shares to sell for in 4 years? ? A) $53.96 B) $44.95 C) $41.68 27

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**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 28

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**Other Valuation Ratios & Approaches**

Price-to-book Price-to-cash flow Price-to-sales Present Value of Free Cash Flow Residual Income Model 29

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