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Unformatted text preview: nformation provided about the net income, shares outstanding, and payout ratio. The total dividends paid is the net income times the payout ratio. To find the dividend per share, we can divide the total dividends paid by the number of shares outstanding. So: Dividend per share = (Net income × Payout ratio) / Shares outstanding Dividend per share = ($10,000,000 × .20) / 2,000,000 Dividend per share = $1.00 Now we can use the initial equation for the required return. We must remember that the equation uses the dividend in one year, so: R = D1/P0 + g R = $1(1 + .1280)/$85 + .1280 R = .1413 or 14.13% 24. First, we need to find the annual dividend growth rate over the past four years. To do this, we can use the future value of a lump sum equation, and solve for the interest rate. Doing so, we find the dividend growth rate over the past four years was: FV = PV(1 + R)t $1.93 = $1.20(1 + R)4 R = ($1.93 / $1.20)1/4 – 1 R = .1261 or 12.61% We know the dividend will grow at this rate for five years before slowing to a constant rate indefinitely. So, the dividend amount in seven years will be: D7 = D0(1 + g1)5(1 + g2)2 D7 = $1.93(1 + .1261)5(1 + .07)2 D7 = $4.00 25. a. We can find the price of all the outstanding company stock by using the dividends the same way we would value an individual share. Since earnings are equal to dividends, and there is no growth, the value of the company’s stock today is the present value of a perpetuity, so: P=D/R P = $750,000 / .14 P = $5,357,142.86 247 The priceearnings ratio is the stock price divided by the current earnings, so the priceearnings ratio of each company with no growth is: P/E = Price / Earnings P/E = $5,357,142.86 / $750,000 P/E = 7.14 times b. Since the earnings have increased, the price of the stock will increase. The new price of the all the outstanding company stock is: P=D/R P = ($750,000 + 100,000) / .14 P = $6,071,428.57 The priceearnings ratio is the stock price divided by the current earnings, so the priceearnings with the increased earnings is: P/E = Price / Earnings P/E = $6,071,428.57 / $750,000 P/E = 8.10 times c. Since the earnings have increased, the price of the stock will increase. The new price of the all the outstanding company stock is: P=D/R P = ($750,000 + 200,000) / .14 P = $6,785,714.29 The priceearnings ratio is the stock price divided by the current earnings, so the priceearnings with the increased earnings is: P/E = Price / Earnings P/E = $6,785,714.29 / $750,000 P/E = 9.05 times 26. a. If the company does not make any new investments, the stock price will be the present value of the constant perpetual dividends. In this case, all earnings are paid dividends, so, applying the perpetuity equation, we get: P = Dividend / R P = $8.25 / .12 P = $68.75 b. The investment is a onetime investment that creates an increase in EPS for two years. To calculate the new stock price, we need the cash cow price plus the NPVGO. In this case, the NPVGO is simply the present value of the investment plus the present value of the increases in EPS. So, the NPVGO will be: NPVGO = C1 / (1 + R) + C2 / (1 + R)2 + C3 / (1 + R)3 NPVGO = –$1.60 / 1.12 + $2.10 / 1.122 + $2.45 / 1.123 NPVGO = $1.99 248 So, the price of the stock if the company undertakes the investment opportunity will be: P = $68.75 + 1.99 P = $70.74 c. After the project is over, and the earnings increase no longer exists, the price of the stock will revert back to $68.75, the value of the company as a cash cow. 27. a. The price of the stock is the present value of the dividends. Since earnings are equal to dividends, we can find the present value of the earnings to calculate the stock price. Also, since we are excluding taxes, the earnings will be the revenues minus the costs. We simply need to find the present value of all future earnings to find the price of the stock. The present value of the revenues is: PVRevenue = C1 / (R – g) PVRevenue = $6,000,000(1 + .05) / (.15 – .05) PVRevenue = $63,000,000 And the present value of the costs will be: PVCosts = C1 / (R – g) PVCosts = $3,100,000(1 + .05) / (.15 – .05) PVCosts = $32,550,000 Since there are no taxes, the present value of the company’s earnings and dividends will be: PVDividends = $63,000,000 – 32,550,000 PVDividends = $30,450,000 Note that since revenues and costs increase at the same rate, we could have found the present value of future dividends as the present value of current dividends. Doing so, we find: D0 = Revenue0 – Costs0 D0 = $6,000,000 – 3,100,000 D0 = $2,900,000 Now, applying the growing perpetuity equation, we find: PVDividends = C1 / (R – g) PVDividends = $2,900,000(1 + .05) / (.15 – .05) PVDividends = $30,450,000 This is the same answer we found previously. The price per share of stock is the total value of the company’s stock divided by the shares outstanding, or: P = Value of all stock / Shares outstanding P = $30,450,000 / 1,000,000 P = $30.45 249 b. The value of a share of stock in a company is the...
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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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