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

# 05 370 5280 012 005 007 rs g n rs g n this

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Unformatted text preview: rs  g n This is the price of the stock 5 years from now. The PV of this price, discounted back 5 years, is as follows: Ö PV of P5 = \$52.80(PVIF12%,5) = \$52.80(0.5674) = \$29.96. Step 3 The price of the stock today is as follows: Ö P0 Ö = PV dividends Years 1 through 5 + PV of P5 = \$9.46 + \$29.96 = \$39.42. This problem could also be solved by substituting the proper values into the following equation: Answers and Solutions: 7 - 11 Ö P0 = 5 § t !1 t 0 (1  g s )  ¨ 6 © ©r g t (1  rs ) n ªs 5 ¸¨ 1 ¸ ¹© ¹ ¹ ©1 r ¹ . sº ºª Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash flow register, input I = 12, PV = ? PV = \$39.43. c. First Year D1/P0 = \$2.01/\$39.42 Capital gains yield Expected total return = 5.10% = 6.90% = 12.00% Sixth Year D6/P5 = \$3.70/\$52.80 Capital gains yield Expected total return = 7.00% = 5.00 = 12.00% *We know that r is 12 percent, and the dividend yield is 5.10 percent; therefore, the capital gains yield must be 6.90 percent. The main points to note here are as follows: 1. The total yield is always 12 percent (except for rounding errors). 2. The capital gains yield starts relatively high, then declines as the supernormal growth period approaches its end. The dividend yield rises. 3. After t=5, the stock will grow at a 5 percent rate. The dividend yield will equal 7 percent, the capital gains yield will equal 5 percent, and the total return will be 12 percent. Answers and Solutions: 7 - 12 a. Part 1. Graphical representation of the problem: Supernormal growth 1 0 | 2 | D0 PVD1 PVD2 PV P0 | Ö (D2 + P2 ) D1 Normal growth 3 |  | D3 D ¤ ¥ 2 D1 = D0(1 + gs) = \$1.6(1.20) = \$1.92. D2 = D0(1 + gs)2 = \$1.60(1.20)2 = \$2.304. Ö P2 = Ö P0 D3 = rs  g n 2 (1  g n ) rs  g n \$2.304 (1 .06) = \$61.06. 0.10  0.06 = Ö = PV(D1) + PV(D2) + PV( P ) Ö P2 D1 D2 =   (1  rs ) (1  rs ) 2 (1  rs ) 2 = \$1.92(0.9091) + \$2.304(0.8264) + \$61.06(0.8264) = \$54.11. ¦ 7-18 Calculator solution: Input 0, 1.92, 63.364(2....
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