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Unformatted text preview: $4.50 (1.30) / (1.20) + $4.50 (1.30)2 / (1.20)2 + $68.45 / (1.20)2 P0 = $57.69 Dividend yield = D1/P0 = $4.50(1.30)/$57.69 = .1014 or 10.14% Capital gains yield = .20 – .1014 = .0986 or 9.86% In all cases, the required return is 20 percent, but the return is distributed differently between current income and capital gains. High-growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time. 31. a. Using the constant growth model, the price of the stock paying annual dividends will be: P0 = D0(1 + g) / (R – g) = $3.60(1.05)/(.14 – .05) = $42.00 252 b. If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will be one-fourth of annual dividend, or: Quarterly dividend: $3.60(1.05)/4 = $0.9450 To find the equivalent annual dividend, we must assume that the quarterly dividends are reinvested at the required return. We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the quarterly dividend, we reinvest it at the required return on the stock. So, the effective quarterly rate is: Effective quarterly rate: 1.14.25 – 1 = .0333 The effective annual dividend will be the FVA of the quarterly dividend payments at the effective quarterly required return. In this case, the effective annual dividend will be: Effective D1 = $0.9450(FVIFA3.33%,4) = $3.97 Now, we can use the constant growth model to find the current stock price as: P0 = $3.97/(.14 – .05) = $44.14 Note that we cannot simply find the quarterly effective required return and growth rate to find the value of the stock. This would assume the dividends increased each quarter, not each year. 32. 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 as dividends, so, applying the perpetuity equation, we get: P = Dividend / R P = $6.25 / .13 P = $48.08 b. The investment occurs every year in the growth opportunity, so the opportunity is a growing perpetuity. So, we first need to find the growth rate. The growth rate is: g = Retention Ratio × Return on Retained Earnings g = 0.20 × 0.11 g = 0.022 or 2.20% Next, we need to calculate the NPV of the investment. During year 3, 20 percent of the earnings will be reinvested. Therefore, $1.25 is invested ($6.25 × .20). One year later, the shareholders receive an 11 percent return on the investment, or $0.138 ($1.25 × .11), in perpetuity. The perpetuity formula values that stream as of year 3. Since the investment opportunity will continue indefinitely and grows at 2.2 percent, apply the growing perpetuity formula to calculate the NPV of the investment as of year 2. Discount that value back two years to today. NPVGO = [(Investment + Return / R) / (R – g)] / (1 + R)2 NPVGO = [(–$1.25 + $0.138 / .13) / (0.13 – 0.022)] / (1.13)2 NPVGO = –$1.39 253 The value of the stock is the PV of the firm without making the investment plus the NPV of the investment, or: P = PV(EPS) + NPVGO P = $48.08 1.39 P = $46.68 c. Zero percent! There is no retention ratio which would make the project profitable for the company. If the company retains more earnings, the growth rate of the earnings on the investment will increase, but the project will still not be profitable. Since the return of the project is less than the required return on the company stock, the project is never worthwhile. In fact, the more the company retains and invests in the project, the less valuable the stock becomes. 33. Here we have a stock with differential growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be: P3 = $4.20(1.20)(1.15)(1.10)(1.05) / (.12 – .05) = $95.63 The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so: P0 = $4.20(1.20)/(1.12) + $4.20(1.20)(1.15)/1.122 + $4.20(1.20)(1.15)(1.10)/1.123 + $95.63/1.123 P0 = $81.73 34. Here we want to find the required return that makes the PV of the dividends equal to the current stock price. The equation for the stock price is: P = $4.20(1.20)/(1 + R) + $4.20(1.20)(1.15)/(1 + R)2 + $4.20(1.20)(1.15)(1.10)/(1 + R)3 + [$4.20(1.20)(1.15)(1.10)(1.05)/(R – .05)]/(1 + R)3 = $98.65 We need to find the roots of this equation. Using spreadsheet, trial and error, or a calculator with a root solving function, we find that: R = .1081 or 10.81% 35. In this problem, growth is occurring from two different sources: The learning curve and the new project. We need to separately compute the value from the two different sources. First, we will compute the val...
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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 Texas-Tyler.

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