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Unformatted text preview: equired return changes twice. To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So: P6 = D6 (1 + g) / (R – g) = D0 (1 + g)7 / (R – g) = $2.75(1.06)7 / (.11 – .06) = $82.70 Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is: P3 = $2.75(1.06)4 / 1.14 + $2.75(1.06)5 / 1.142 + $2.75(1.06)6 / 1.143 + $82.70 / 1.143 P3 = $64.33 Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is: P0 = $2.75(1.06) / 1.16 + $2.75(1.06)2 / (1.16)2 + $2.75(1.06)3 / (1.16)3 + $64.33 / (1.16)3 P0 = $48.12 11. Here we have a stock that pays no dividends for 10 years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember that general form of the constant dividend growth formula is: Pt = [Dt × (1 + g)] / (R – g) This means that since we will use the dividend in Year 10, we will be finding the stock price in Year 9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation gives you the PV one period before the first payment. So, the price of the stock in Year 9 will be: P9 = D10 / (R – g) = $9.00 / (.13 – .055) = $120.00 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: P0 = $120.00 / 1.139 = $39.95 242 12. The price of a stock is the PV of the future dividends. This stock is paying five dividends, so the price of the stock is the PV of these dividends using the required return. The price of the stock is: P0 = $13 / 1.11 + $16 / 1.112 + $19 / 1.113 + $22 / 1.114 + $25 / 1.115 = $67.92 13. With differential 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 differential growth period. The stock begins constant growth in Year 5, so we can find the price of the stock in Year 4, one year before the constant dividend growth begins, as: P4 = D4 (1 + g) / (R – g) = $2.50(1.05) / (.13 – .05) = $32.81 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 4 stock price. So, the price of the stock today will be: P0 = $9 / 1.13 + $7 / 1.132 + $5 / 1.133 + ($2.50 + 32.81) / 1.134 = $38.57 14. With differential 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 differential 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: P3 = D3 (1 + g) / (R – g) = D0 (1 + g1)3 (1 + g2) / (R – g2) = $2.40(1.25)3(1.07) / (.12 – .07) = $100.31 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: P0 = $2.40(1.25) / 1.12 + $2.40(1.25)2 / 1.122 + $2.40(1.25)3 / 1.123 + $100.31 / 1.123 P0 = $80.40 15. Here we need to find the dividend next year for a stock experiencing differential growth. We know the stock price, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the current dividend times the FVIF. The dividend in Year 3 will be: D3 = D0 (1.30)3 And the dividend in Year 4 will be the dividend in Year 3 times one plus the growth rate, or: D4 = D0 (1.30)3 (1.18) The stock begins constant growth after the 4th dividend is paid, so we can find the price of the stock in Year 4 as the dividend in Year 5, divided by the required return minus the growth rate. The equation for the price of the stock in Year 4 is: P4 = D4 (1 + g) / (R – g) 243 Now we can substitute the previous dividend in Year 4 into this equation as follows: P4 = D0 (1 + g1)3 (1 + g2) (1 + g3) / (R – g3) P4 = D0 (1.30)3 (1.18) (1.08) / (.13 – .08) = 56.00D0 When we solve this equation, we find that the stock price in Year 4 is 56.00 times as large as the dividend today. Now we need to find the equation for the stock price today. The stock price today is the PV of the dividends in Years 1, 2, 3, and 4, plus the PV of the Year 4 price. So: P0 = D0(1.30)/1.13 + D0(1.30)2/1.132 + D0(1.30)3/1.133+ D0(1.30)3(1.18)/1.134 + 56.00D0/1.134 We can factor out D0 in the equation, and combine the last two terms. Doing so, we get: P0 = $65.00...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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