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59533341-FM11-Ch-07-Instructors-Manual-1

5 412 123 step 2 calculate the expected dividends d0

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Unformatted text preview: = 7.5% + (4%)1.2 = 12.3%. Step 2: Calculate the expected dividends: D0 = $2.00 D1 = $2.00(1.20) = $2.40 D2 = $2.00(1.20)2 = $2.88 D3 = $2.88(1.07) = $3.08 Step 3: Calculate the PV of the expected dividends: PVDiv = $2.40/(1.123) + $2.88/(1.123)2 = $2.14 + $2.28 = $4.42. Ö Step 4: Calculate P2 : Ö P2 = D3/(rs - g) = $3.08/(0.123 - 0.07) = $58.11. Ö Step 5: Calculate the PV of P2 : PV = $58.11/(1.123)2 = $46.08. Step 6: Sum the PVs to obtain the stock¶s price: Ö P0 = $4.42 + $46.08 = $50.50. Alternatively, using a financial calculator, input the following: CF0 = 0, CF1 = 2.40, and CF2 = 60.99 (2.88 + 58.11) and then enter I = 12.3 to solve for NPV = $50.50. Answers and Solutions: 7 - 5 7-6 The problem asks you to determine the constant growth rate, given the following facts: P0 = $80, D1 = $4, and rs = 14%. Use the constant growth rate formula to calculate g: › rs= 1 +g 0 $4 +g $80 g = 0.09 = 9%. 0.14 = 7-7 Ö The problem asks you to determine the value of P3 , given the following facts: D1 = $2, b = 0.9, rRF = 5.6%, RPM = 6%, and P0 = $25. Proceed as follows: Step 1: Calculate the required rate of return: rs = rRF + (rM - rRF)b = 5.6% + (6%)0.9 = 11%. Step 2: Use the constant growth rate formula to calculate g: › rs 1 = +g 0 $2 +g $25 = 0.03 = 3%. 0.11 = g Step 3: Calculate Ö 3 : Ö3 = 0(1 + g)3 = $25(1.03)3 = $27.3182 § $27.32. Alternatively, you could calculate solve for Ö 3 : 4 and then use the constant growth rate formula to = 1(1 + g)3 = $2.00(1.03)3 = $2.1855. Ö 3 = $2.1855/(0.11 - 0.03) = $27.3188 } $27.32. 4 Answers and Solutions: 7 - 6 7-8 Vps = Dps/rps; therefore, rps = Dps/Vps. a. rps = $8/$60 = 13.3%. b. rps = $8/$80 = 10%. c. rps = $8/$100 = 8%. d. rps = $8/$140 = 5.7%. D 0 (1  g) $5[1  ( 0.05)] $5( 0.95) $4.75 = = = = $23.75. rs  g 0.15  ( 0.05)] 0.15  0.05 0 .20 7-9 Ö P0 = 7-10 a. ri = rRF + (rM - rRF)bi. rC = 9% + (13% - 9%)0.4 = 10.6%. rD = 9% + (13% - 9%)-0.5 = 7%. 1 rs  g = Note that rD is below the risk-free rate. But since this stock is like an insurance policy because it ³pays off´ when something bad happens (the market falls), the low return is not unreasona...
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