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Unformatted text preview: = D0{1.30/1.13 + 1.302/1.132 + 1.303/1.133 + [(1.30)3(1.18) + 56.00] / 1.134} Reducing the equation even further by solving all of the terms in the braces, we get: $65 = $39.86D0 D0 = $65.00 / $39.86 = $1.63 This is the dividend today, so the projected dividend for the next year will be: D1 = $1.63(1.30) = $2.12 16. The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0 (1 + g) / (R – g) = $12(1 – .06) / [(.11 – (–.06)] = $66.35 17. We are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. Using the constant dividend growth model, we get: P0 = $49.80 = D0 (1 + g) / (R – g) Solving this equation for the dividend gives us: D0 = $49.80(.11 – .05) / (1.05) = $2.85 18. The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 5, so we can find the price of the stock in Year 4, one year before the first dividend payment. Doing so, we get: P4 = $7.00 / .06 = $116.67 The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = $116.67 / (1.06)4 = $92.41 244 19. The annual dividend is the dividend divided by the stock price, so: Dividend yield = Dividend / Stock price .016 = Dividend / $19.47 Dividend = $0.31 The “Net Chg” of the stock shows the stock decreased by $0.12 on this day, so the closing stock price yesterday was: Yesterday’s closing price = $19.47 – (–0.12) = $19.59 To find the net income, we need to find the EPS. The stock quote tells us the P/E ratio for the stock is 19. Since we know the stock price as well, we can use the P/E ratio to solve for EPS as follows: P/E = 19 = Stock price / EPS = $19.47 / EPS EPS = $19.47 / 19 = $1.025 We know that EPS is just the total net income divided by the number of shares outstanding, so: EPS = NI / Shares = $1.025 = NI / 25,000,000 NI = $1.025(25,000,000) = $25,618,421 20. To find the number of shares owned, we can divide the amount invested by the stock price. The share price of any financial asset is the present value of the cash flows, so, to find the price of the stock we need to find the cash flows. The cash flows are the two dividend payments plus the sale price. We also need to find the aftertax dividends since the assumption is all dividends are taxed at the same rate for all investors. The aftertax dividends are the dividends times one minus the tax rate, so: Year 1 aftertax dividend = $1.50(1 – .28) Year 1 aftertax dividend = $1.08 Year 2 aftertax dividend = $2.25(1 – .28) Year 2 aftertax dividend = $1.62 We can now discount all cash flows from the stock at the required return. Doing so, we find the price of the stock is: P = $1.08/1.15 + $1.62/(1.15)2 + $60/(1+.15)3 P = $41.62 The number of shares owned is the total investment divided by the stock price, which is: Shares owned = $100,000 / $41.62 Shares owned = 2,402.98 245 21. Here we have a stock paying a constant dividend for a fixed period, and an increasing dividend thereafter. We need to find the present value of the two different cash flows using the appropriate quarterly interest rate. The constant dividend is an annuity, so the present value of these dividends is: PVA = C(PVIFAR,t) PVA = $0.75(PVIFA2.5%,12) PVA = $7.69 Now we can find the present value of the dividends beyond the constant dividend phase. Using the present value of a growing annuity equation, we find: P12 = D13 / (R – g) P12 = $0.75(1 + .01) / (.025 – .01) P12 = $50.50 This is the price of the stock immediately after it has paid the last constant dividend. So, the present value of the future price is: PV = $50.50 / (1 + .025)12 PV = $37.55 The price today is the sum of the present value of the two cash flows, so: P0 = $7.69 + 37.55 P0 = $45.24 22. Here we need to find the dividend next year for a stock with nonconstant 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 constant dividend times the FVIF. The dividend in Year 3 will be: D3 = D(1.05) The equation for the stock price will be the present value of the constant dividends, plus the present value of the future stock price, or: P0 = D / 1.11 + D /1.112 + D(1.05)/(.11 – .05)]/1.112 $38 = D / 1.11 + D /1.112 + D(1.05)/(.11 – .05)]/1.112 We can factor out D0 in the equation. Doing so, we get: $38 = D{1/1.11 + 1/1.112 + [(1.05)/(.11 – .05)] / 1.112} Reducing the equation even further by solving all of the terms in the braces, we get: $38 = D(15.9159) D = $38 / 15.9159 = $2.39 246 23. The required return of a stock consists of two components, the capital gains yield and the dividend yield. In the constant dividend growth model (growing perpetuity equation), the capital gains yield is the same as the dividend growth rate, or algebraically: R = D1/P0 + g We can find the dividend growth rate by the growth rate equation, or: g = ROE × b g = .16 × .80 g = .1280 or 12.80% This is also the growth rate in dividends. To find the current dividend, we can use the i...
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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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