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Unformatted text preview: present value of its current operations, plus the present value of growth opportunities. To find the present value of the growth opportunities, we need to discount the cash outlay in Year 1 back to the present, and find the value today of the increase in earnings. The increase in earnings is a perpetuity, which we must discount back to today. So, the value of the growth opportunity is: NPVGO = C0 + C1 / (1 + R) + (C2 / R) / (1 + R) NPVGO = –$22,000,000 – $8,000,000 / (1 + .15) + ($7,000,000 / .15) / (1 + .15) NPVGO = $11,623,188.41 To find the value of the growth opportunity on a per share basis, we must divide this amount by the number of shares outstanding, which gives us: NPVGOPer share = $11,623,188.41 / $1,000,000 NPVGOPer share = $11.62 The stock price will increase by $11.62 per share. The new stock price will be: New stock price = $30.45 + 11.62 New stock price = $42.07 28. a. If the company continues its current operations, it will not grow, so we can value the company as a cash cow. The total value of the company as a cash cow is the present value of the future earnings, which are a perpetuity, so: Cash cow value of company = C / R Cash cow value of company = $85,000,000 / .12 Cash cow value of company = $708,333,333.33 The value per share is the total value of the company divided by the shares outstanding, so: Share price = $708,333,333.33 / 20,000,000 Share price = $35.42 b. To find the value of the investment, we need to find the NPV of the growth opportunities. The initial cash flow occurs today, so it does not need to be discounted. The earnings growth is a perpetuity. Using the present value of a perpetuity equation will give us the value of the earnings growth one period from today, so we need to discount this back to today. The NPVGO of the investment opportunity is: NPVGO = C0 + C1 / (1 + R) + (C2 / R) / (1 + R) NPVGO = –$18,000,000 – 7,000,000 / (1 + .12) + ($11,000,000 / .12) / (1 + .12) NPVGO = $57,595,238.10 c. The price of a share of stock is the cash cow value plus the NPVGO. We have already calculated the NPVGO for the entire project, so we need to find the NPVGO on a per share basis. The NPVGO on a per share basis is the NPVGO of the project divided by the shares outstanding, which is: NPVGO per share = $57,595,238.10 / 20,000,000 250 NPVGO per share = $2.88 This means the per share stock price if the company undertakes the project is: Share price = Cash cow price + NPVGO per share Share price = $35.42 + 2.88 Share price = $38.30 29. 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 = $7 / .11 P = $63.64 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 = 0.30 × 0.20 g = 0.06 or 6% Next, we need to calculate the NPV of the investment. During year 3, 30 percent of the earnings will be reinvested. Therefore, $2.10 is invested ($7 × .30). One year later, the shareholders receive a 20 percent return on the investment, or $0.42 ($2.10 × .20), in perpetuity. The perpetuity formula values that stream as of year 3. Since the investment opportunity will continue indefinitely and grows at 6 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 = [(–$2.10 + $0.42 / .11) / (0.11 – 0.06)] / (1.11)2 NPVGO = $27.89 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 = $63.64 + $27.89 P = $91.53 251 Challenge 30. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 20 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield. W: P0 = D0(1 + g) / (R – g) = $4.50(1.10)/(.20 – .10) = $49.50 Dividend yield = D1/P0 = 4.50(1.10)/$49.50 = .10 or 10% Capital gains yield = .20 – .10 = .10 or 10% X: P0 = D0(1 + g) / (R – g) = $4.50/(.20 – 0) = $22.50 Dividend yield = D1/P0 = $4.50/$22.50 = .20 or 20% Capital gains yield = .20 – .20 = 0% Y: P0 = D0(1 + g) / (R – g) = $4.50(1 – .05)/(.20 + .05) = $17.10 Dividend yield = D1/P0 = $4.50(0.95)/$17.10 = .25 or 25% Capital gains yield = .20 – .25 = –.05 or –5% Z: P2 = D2(1 + g) / (R – g) = D0(1 + g1)2(1 + g2)/(R – g2) = $4.50(1.30)2(1.08)/(.20 – .08) P2 = $68.45 P0 =...
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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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