bkmsol_ch18

# Time 0 1 2 3 d t 10000 12500 15625 1953125 g 250 250

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Time: 0 1 2 3 D t \$1.0000 \$1.2500 \$1.5625 \$1.953125 g 25.0% 25.0% 25.0% 5.0% a. The dividend to be paid at the end of year 3 is the first installment of a dividend stream that will increase indefinitely at the constant growth rate of 5%. Therefore, we can use the constant growth model as of the end of year 2 in order to calculate intrinsic value by adding the present value of the first two dividends plus the present value of the price of the stock at the end of year 2. The expected price 2 years from now is: P 2 = D 3 /(k – g) = \$1.953125/(0.20 – 0.05) = \$13.02 The PV of this expected price is: \$13.02/1.20 2 = \$9.04 The PV of expected dividends in years 1 and 2 is: 13 . 2 \$ 20 . 1 5625 . 1 \$ 20 . 1 25 . 1 \$ 2 = + Thus the current price should be: \$9.04 + \$2.13 = \$11.17 b. Expected dividend yield = D 1 /P 0 = \$1.25/\$11.17 = 0.112 = 11.2% c. The expected price one year from now is the PV at that time of P 2 and D 2 : P 1 = (D 2 + P 2 )/1.20 = (\$1.5625 + \$13.02)/1.20 = \$12.15 The implied capital gain is: (P 1 – P 0 )/P 0 = (\$12.15 – \$11.17)/\$11.17 = 0.088 = 8.8% The sum of the implied capital gains yield and the expected dividend yield is equal to the market capitalization rate. This is consistent with the DDM. 26. Time: 0 1 4 5 E t \$5.000 \$6.000 \$10.368 \$12.4416 D t \$0.000 \$0.000 \$0.000 \$12.4416 Dividends = 0 for the next four years, so b = 1.0 (100% plowback ratio). a. 944 . 82 \$ 15 . 0 4416 . 12 \$ k D P 5 4 = = = 42 . 47 \$ 15 . 1 944 . 82 \$ ) k 1 ( P V 4 4 4 0 = = + = b. Price should increase at a rate of 15% over the next year, so that the HPR will equal k. 18-16

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27. Before-tax cash flow from operations \$2,100,000 Depreciation 210,000 Taxable Income 1,890,000 Taxes (@ 35%) 661,500 After-tax unleveraged income 1,228,500 After-tax cash flow from operations (After-tax unleveraged income + depreciation) 1,438,500 New investment (20% of cash flow from operations) 420,000 Free cash flow (After-tax cash flow from operations – new investment) \$1,018,500 The value of the firm (i.e., debt plus equity) is: 000 , 550 , 14 \$ 05 . 0 12 . 0 500 , 018 , 1 \$ 1 0 = = = g k C V Since the value of the debt is \$4 million, the value of the equity is \$10,550,000. 18-17
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