Homework 4 Answer Key

Homework 4 Answer Key - ENGR 111 ­ Fall 2011 ...

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Unformatted text preview: ENGR 111 ­ Fall 2011 Nov 25, 2011 HOMEWORK 4 ANSWER KEY 1. (2 points) 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) = 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 = 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 2. (2 points) The discount rate 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 information 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% 3. a. (0.7 points) 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. (0.7 points) The investment is a one ­time 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 So, the price of the stock if the company undertakes the investment opportunity will be: P = $68.75 + 1.99 P = $70.74 c. (0.6 points) 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. 4. a. (1 point) Earnings Per Share and Stock Price Source: Google Finance. Amazon EPS: 1.90 Price: 195.97 NPVGO=195.97 ­(1.90/.15) = 183.30 Apple EPS: 27.67 Price: 385.40 NPVGO=385.40 ­(27.67/.15)= 200.93 Netflix EPS: 4.40 Price: 66.02 NPVGO=66.02 ­(4.40/.15)= 36.69 IBM EPS: 12.64 Price: 188.10 NPVGO=188.10 ­(12.64/.15)= 103.83 EPS: 2.75 Price: 25.35 NPVGO=25.35 ­(2.75/.15)=7.02 Microsoft b. (1 point) If in each of the years he holds the stock the return on the stock was R1, R2, and R3 respectively, then; (1+R1)(1+R2)(1+R3) ­1=.60 Geometric Average Return =  ­1 = 1.1696 ­1= 17% For the Arithmetic Average Return we need to know the returns for each year but we do not have that information. (We have one equation and three unknowns.) If we assume that each year had the same return then we can say that the Arithmetic and Geometric Average Returns coincide, that is, they are both 17%. 5. (2 points) See the Excel File “Homework 4, Question 5” ...
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This note was uploaded on 12/05/2011 for the course ENGINEERIN 111 taught by Professor Melihabulu-taciroglu during the Fall '11 term at UCLA.

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