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CHAPTER 8 B-145 The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P 0 = \$111.11 / 1.14 9 = \$34.17 12. The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends using the required return. The price of the stock is: P 0 = \$10 / 1.11 + \$14 / 1.11 2 + \$18 / 1.11 3 + \$22 / 1.11 4 + \$26 / 1.11 5 = \$63.45 13. With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at the beginning of the constant dividend growth, as: P 4 = D 4 (1 + g ) / ( R g ) = \$2.00(1.05) / (.12 – .05) = \$30.00 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 3 stock price. So, the price of the stock today will be: P 0 = \$11.00 / 1.11 + \$8.00 / 1.11 2 + \$5.00 / 1.11 3 + \$2.00 / 1.11 4 + \$30.00 / 1.11 4 = \$40.09 14. With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the futures stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3, one year before the constant dividend growth begins as: P 3 = D 3 (1 + g ) / ( R g ) = D 0 (1 + g 1 ) 3 (1 + g 2 ) / ( R g ) P 3 = \$1.80(1.30) 3 (1.06) / (.13 – .06) P 3 = \$59.88 The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. The price of the stock today will be: P 0 = \$1.80(1.30) / 1.13 + \$1.80(1.30) 2 / 1.13 2 + \$1.80(1.30) 3 / 1.13 3 + \$59.88 / 1.13 3 P 0 = \$48.70 We could also use the two-stage dividend growth model for this problem, which is: P 0 = [D 0 (1 + g 1 )/(R – g 1 )]{1 – [(1 +

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