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## CHAPTER FIFTEEN

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**CHAPTER FIFTEEN**DIVIDEND DISCOUNT MODELS 1**CAPITALIZATION OF INCOME METHOD**• THE INTRINSIC VALUE OF A STOCK • represented by present value of the income stream 2**CAPITALIZATION OF INCOME METHOD**• formula where Ct = the expected cash flow t = time k = the discount rate 3**CAPITALIZATION OF INCOME METHOD**• APPLICATION TO COMMON STOCK • substituting determines the “true” value of one share 7**CAPITALIZATION OF INCOME METHOD**• A COMPLICATION • the previous model assumes can forecast dividends indefinitely • a forecasting formula can be written Dt = Dt -1 ( 1 + g t ) where g t = the dividend growth rate 8**THE ZERO GROWTH MODEL**• ASSUMPTIONS • the future dividends remain constant such that D1 = D2 = D3 = D4 = . . . = DN 9**THE ZERO GROWTH MODEL**• Applying to V 12**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? 13**THE ZERO GROWTH MODEL**• Example(continued) If the current market price is $65, the stock is underpriced. Recommendation: BUY 14**THE CONSTANT-GROWTH MODEL**• ASSUMPTIONS: • growth rate in dividends is constant • earnings per share is constant • payout ratio is constant ***CONSTANT GROWTH MODEL**• In General Dt = D0 (1 + g)t 16**CONSTANT GROWTH MODEL**• Using the infinite property series, if k > g, then 18**CONSTANT GROWTH MODEL**• since D1= D0 (1 + g) 20**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 ***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 ***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 21**THE MULTIPLE-GROWTH MODEL**• Finding PV of all forecast dividends paid after time t • next period dividend Dt+1 and all thereafter are expected to grow at rate g 23**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 ***Two-Stage Growth Model Example**Suppose D(0) = $2; k = 12%; g1 = 11%; g2 = 6%; and g1 continues for 4 years. V(0) = $41.90 ***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 ***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. ***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 ***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 26**MODELS BASED ON P/E RATIO**• PRICE-EARNINGS RATIO MODEL • EARNINGS MULTIPLIER: = PRICE - EARNINGS RATIO = Current Market Price following 12 month earnings 27**PRICE-EARNINGS RATIO MODEL**• The P/E Ratio is a function of • the expected payout ratio ( D1 / E1 ) • the required return (k) • the expected growth rate of dividends (g) 30**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 ***PRICE-EARNINGS RATIO MODEL**• The Model is derived from the Dividend Discount model: 28**PRICE-EARNINGS RATIO MODEL**• Dividing by the coming year’s earnings 29**SOURCES OF EARNINGS GROWTH**• What causes growth? • assume no new capital added • retained earnings used to pay firm’s new investment • Ifpt = the payout ratio in year t • 1-pt = the retention ratio 35**SOURCES OF EARNINGS GROWTH**• Growth rate depends on • the retention ratio • average return on equity 42**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) ***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% ***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 *