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Besley: Chapter 7 Assignment 5

Besley: Chapter 7 Assignment 5. Pg. 324 7-3; 7-4 Pg. 325 7-6 Pg. 327 7-11. Pg 324 7-3.

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Besley: Chapter 7 Assignment 5

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  1. Besley: Chapter 7Assignment 5 Pg. 324 7-3; 7-4 Pg. 325 7-6 Pg. 327 7-11

  2. Pg 324 7-3 Your broker offers to sell you some shares of Wingler & Co. common stock that paid a dividend of $2 yesterday. You expect the dividend to grow at the rate of five percent per year for the next three years, and if you buy the stock you plan to hold it for three years and then sell it. • Find the expected dividend for each of the next three years; that is, calculate D^1, D^2, and D^3. Note that D0 = $2.

  3. Pg 324 7-3 continued • Given that the appropriate discount rate is 12 percent and that the first of these dividend payments will occur one year from now, find the present value of the dividend stream; that is, calculate the PV of D^1, D^2, and D^3, and then sum these PVs. PV = $2.10(0.8929)+$2.21(0.7972)+$2.32(0.7118) = $5.29

  4. Pg 324 7-3 continued • You expect the price of the stock three years from now to be $34.73; that is you expect P^3 to equal $34.73. Discount at a 12 percent rate, what is the present value of this expected future stock price? In other words, calculate the PV of $34.73 PV of P^3 = $34.72(0.7118) = $24.72

  5. Pg 324 7-3 continued • If you plan to buy the stock, hold it for three years, and then sell it for $34.73, what is the most you should pay for it? P^0 = $24.72 + $5.29 = $30.01 • Use Equation 7-6 to calculate the present value of this stock. Assume that g = 5%, and it is constant.

  6. Pg 324 7-3 continued • Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period were two years or five years rather than three years, would this affect the value of the stock today, P^0? The value of the stock is not dependent on the holding period, but rather is dependent on the cash flow stream.

  7. Pg 324 7-4 You buy a share of Damanpour Corporation stock for $21.40. You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in Years 1,2, and 3, respectively, and you expect to sell it at a price of $26.22 at the end of three years. • Calculate the growth rate in dividends. g1 =(1.1449-1.07)/1.07 = 7% g2 =1.2250/1.1449 – 1.0 = 7%

  8. Pg 324 7-4 continued • Calculate the expected dividend yield. $1.07/$21.40 = 5% • Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to get the expected total rate of return. What is this stock’s expected total rate of return?

  9. Pg 325 7-6 Bayboro Sails is expected to pay dividends of $2.50, $3.00, and $4.00 in the next three years-D^1, D^2, and D^3, respectively. After three years, the dividend is expected to grow at a constant rate equal to four percent per year indefinitely. Stockholders require a return of 14% to invest in the common stock of Bayboro Sails.

  10. Pg 325 7-6 continue • Compute the present value of the dividends Bayboro is expected to pay over the next three years. PV = $2.50(0.8772) + $3.00(0.7695) + $4.00(0.6750) = $7.20 • For what price should investors expect to be able to sell the common stock of Bayboro at the end of three years? (Hint: The dividend will grow at a constant 4 percent in Year 4, Year 5, and every year thereafter, so Equation 7-6 can be used to find P^3-the appropriate dividend to use in the numerator is D^4.)

  11. PV of dividends + PV of price = $7.20 + $41.60(0.6750) = $35.28 Pg 325 7-6 continue • Compute the value of Bayboro’s common stock today, P^0.

  12. Pg 327 7-11 Suppose Sartoris Chemical Company’s management conducts a study and concludes that if Sartoris expanded its consumer products division (which is less risky that its primary business, industrial chemicals), the firm’s beta would decline from 1.2 to 0.9. However, consumer products have a somewhat lower profit margin, and this would cause Sartoris’s constant growth rate in earnings and dividends to fall from seven to five percent.

  13. Pg 327 7-11 continued • Should management make the change? Assume the following: km = 12%; krf = 9%’ D0 = $2. ks NEW = kRF + (ks-kRF)bs = 9%+(12%-9%)0.9 = 11.7% ks OLD = kRF + (ks-kRF)bs = 9%+(12%-9%)1.2 = 12.6% P0NEW = $2(1.05)/(.117-.05) P0OLD = $2(1.07)/(.126-.07) = $31.34 = $38.21 Since the New price is lower than the Old price, the expansion into the less risky consumer products market.

  14. Pg 327 7-11 continued • Assume all the facts as given above expect the change in the beta coefficient. How low would the beta have to fall to cause the expansion to be a good one? (Hint: Set P^0 under the new policy equal to P^0 under the old one, and find the new beta that will produce this equality. Solve for ks $2.10 = $38.21(ks)-1.9105 $4.0105 = $38.21(ks) ks = 0.10496 10.496% = 9% + 3%(bs) Solve for bs 1.496% = 3%(bs) bs = 0.49865

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