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11 CHAPTER FIFTEEN DIVIDEND DISCOUNT MODELS

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22 CAPITALIZATION OF INCOME METHOD THE INTRINSIC VALUE OF A STOCK –represented by present value of the income stream

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33 CAPITALIZATION OF INCOME METHOD formula where C t = the expected cash flow t = time k = the discount rate

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74 CAPITALIZATION OF INCOME METHOD APPLICATION TO COMMON STOCK –substituting determines the “true” value of one share

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85 CAPITALIZATION OF INCOME METHOD A COMPLICATION –the previous model assumes can forecast dividends indefinitely –a forecasting formula can be written D t = D t -1 ( 1 + g t ) where g t = the dividend growth rate

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96 THE ZERO GROWTH MODEL ASSUMPTIONS –the future dividends remain constant such that D 1 = D 2 = D 3 = D 4 =... = D N

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127 THE ZERO GROWTH MODEL Applying to V

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138 THE ZERO GROWTH MODEL Example –If Zinc Co. is expected to pay cash dividends of $8 per share and the firm has a 10% required rate of return, what is the intrinsic value of the stock?

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149 THE ZERO GROWTH MODEL Example(continued) If the current market price is $65, the stock is underpriced. Recommendation: BUY

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*10 THE CONSTANT-GROWTH MODEL ASSUMPTIONS: growth rate in dividends is constant earnings per share is constant payout ratio is constant

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1611 CONSTANT GROWTH MODEL In General D t = D 0 (1 + g) t

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1812 CONSTANT GROWTH MODEL Using the infinite property series, if k > g, then

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2013 CONSTANT GROWTH MODEL since D 1 = D 0 (1 + g)

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*14 Constant Perpetual Growth Model Example Suppose D(0) = $2; k = 12%; g = 6%. D(1) = ($2.00 x 1.06) = $2.12 V(0) = $2.12 / (.12 -.06) = $35.33

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*15 Constant Perpetual Growth Advantage –easy to compute Disadvantages –not usable for firms paying no dividends –not usable when g > k –sensitive to choice of g and k –k and g may be very difficult to estimate –constant perpetual growth is often unrealistic

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2116 THE MULTIPLE-GROWTH MODEL ASSUMPTION: –future dividend growth is not constant Model Methodology –to find present value of forecast stream of dividends –divide stream into parts (lifecycle stage) –each representing a different value for g

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2317 THE MULTIPLE-GROWTH MODEL Finding PV of all forecast dividends paid after time t –next period dividend D t+1 and all thereafter are expected to grow at rate g

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*18 Two-Stage (any number) Dividend Growth Model If you have two different growth rates, one for an early period and one for a later period, you would use the two-stage model

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*19 Two-Stage Growth Model Example Suppose D(0) = $2; k = 12%; g 1 = 11%; g 2 = 6%; and g 1 continues for 4 years. V(0) = $41.90

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*20 Two-Stage Growth Advantage –allows for two different growth rates –g can be greater than k during period 1 Disadvantages –not usable for firms paying no dividends –sensitive to choice of g and k –k and g may be difficult to estimate

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*21 Estimating the Discount Rate Start with the CAPM (covered later): Discount rate = Risk-free rate + (Stock beta x Market risk premium) where: Risk-free rate = U.S. T-bill rate, which is the wait component or time value of money. Stock beta measures the individual stock’s risk relative to the market. Market risk premium measures the difference in return between investing in the market and investing in T- bills.

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*22 Discount Rate Example Assume T-bills yield 4.5%; KO’s beta is 1.15; and the market risk premium = 8% Discount rate = 4.5% + (1.15 x 8%) = 13.70% Using the CPGM with D(0) = $2 and g = 6%: V(0) = $2(1.06)/(.1370 -.06) = $27.53 What if the MRP were 9%? DR = 4.5% + (1.15 x 9%) = 14.85% V(0) = $2(1.06)/(.1485 -.06) = $23.95 What if g = 7%? V(0) = $2(1.07)/(.1370 -.07) = $31.94

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2623 MODELS BASED ON P/E RATIO PRICE-EARNINGS RATIO MODEL –Many investors prefer the earnings multiplier approach since they feel they are ultimately entitled to receive a firm’s earnings

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2724 MODELS BASED ON P/E RATIO PRICE-EARNINGS RATIO MODEL –EARNINGS MULTIPLIER: = PRICE - EARNINGS RATIO = Current Market Price following 12 month earnings

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3025 PRICE-EARNINGS RATIO MODEL The P/E Ratio is a function of –the expected payout ratio ( D 1 / E 1 ) –the required return (k) –the expected growth rate of dividends (g)

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*26 High vs. Low P/Es A high P/E ratio: –indicates positive expectations for the future of the company –means the stock is more expensive relative to earnings –typically represents a successful and fast-growing company A low P/E ratio: –indicates negative expectations for the future of the company –may suggest that the stock is a better value or buy

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2827 PRICE-EARNINGS RATIO MODEL The Model is derived from the Dividend Discount model:

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2928 PRICE-EARNINGS RATIO MODEL Dividing by the coming year’s earnings

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3529 SOURCES OF EARNINGS GROWTH What causes growth? assume no new capital added retained earnings used to pay firm’s new investment If p t = the payout ratio in year t 1-p t = the retention ratio

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4230 SOURCES OF EARNINGS GROWTH Growth rate depends on –the retention ratio –average return on equity

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*31 Sustainable Growth Rate Using the sustainable growth rate to estimate g: Sustainable growth rate = ROE x retention ratio ROE = return on equity ROE = net income / book equity Payout ratio = Dividends per share / EPS Retention ratio = 1 - payout ratio Sustainable growth rate = ROE x (1 - Payout ratio)

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*32 Sustainable Growth Rate Example Assume ROE = 11%; EPS = $3.25; and D(0) = $2.00 SGR =.11 x (1 - 2.00/3.25) = 4.23%

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*33 Price Ratio Analysis Price/Cash flow ratio –cash flow = net income + depreciation = cash flow from operations or operating cash flow Price/Sales –current stock price divided by annual sales per share

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