CHAPTER 18: EQUITY VALUATION MODELS 1.P0= D1/(k – g) = $2.10/(0.11 – 0) = $19.09 2.I and II 3. a. k = D1/P0+ g 0.16 = $2/$50 + g ⇒g = 0.12 = 12% b. P0= D1/(k – g) = $2/(0.16 – 0.05) = $18.18 The price falls in response to the more pessimistic dividend forecast. The forecast for currentyear earnings, however, is unchanged. Therefore, the P/E ratio falls. The lower P/E ratio is evidence of the diminished optimism concerning the firm's growth prospects. 4. a. g = ROE ×b = 16% ×0.5 = 8% D1= $2(1 – b) = $2(1 – 0.5) = $1 P0= D1/(k – g) = $1/(0.12 – 0.08) = $25 b. P3= P0(1 + g)3= $25(1.08)3= $31.49 5. a. This director is confused. In the context of the constant growth model [i.e., P0= D1/(k – g)], it is true that price is higher when dividends are higher holding everything else including dividend growth constant. But everything else will not be constant. If the firm increases the dividend payout rate, the growth rate gwill fall, and stock price will not necessarily rise. In fact, if ROE > k, price will fall. b.(i) An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate (i.e., ROE ×plowback) will fall as plowback ratio falls. (ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason -- less funds are reinvested in the firm. 18-1
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