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e values can be obtained by projecting the FCFE at the mon rate. (Alternatively, the ponents of FCFE can be projected and aggregated for each year.)This table shows the process for estimating the current per share value:FCFE Base AssumptionsShares outstanding: 84 million, k = 14%Actual2011Projected2012Projected2013Projected2014Growth rate (g)27%27%13%TotalPer ShareEarnings after tax$80$$$$Plus: Depreciation expense23$Less: Capital expenditures38$Less: Increase in net working capital41$Equals: FCFE24$Terminal value$*Total cash flows to equity$$?Discounted value$? $?Current value per share$167。 = $D3 = E3 180。 = $E3 = E0 180。 = $ 180。 this year’s earnings plowback ratio now falls to and payout ratio = 3$$EPS grows by () (15%) = 6% and payout ratio = At time 2: At time 0: c. P0 = $11 and P1 = P0(1 + g) = $(Because the market is unaware of the changed petitive situation, it believes the stock price should grow at 10% per year.)P2 = $ after the market bees aware of the changed petitive situation.P3 = $ 180。 20% = 12%b. P1 = V1 = V0(1 + g) = $ 180。 $2 = $1g = b 180。 180。 (1 – ) = $1b. P3 = P0(1 + g)3 = $25()3 = $10. a. b. Leading P0/E1 = $$ = Trailing P0/E0 = $$ = c. The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).d. Now, you revise b to 1/3, g to 1/3 180。s growth prospects.9. a. g = ROE 180。Chapter 18 Equity Valuation ModelsCHAPTER 18: EQUITY VALUATION MODELSPROBLEM SETS 1. Theoretically, dividend discount models can be used to value the stock of rapidly growing panies that do not currently pay dividends。 b = 16% 180。 9% = 3%, and D1 to:E0 180。 (2/3) = $Thus:V0 = $( – ) = $V0 increases because the firm pays out more earnings instead of reinvesting a poor ROE. This information is not yet known to the rest of the market.11. a. b. The dividend payout ratio is 8/12 = 2/3, so the plowback ratio is b = 1/3. The implied value of ROE on future investments is found by solving:g = b 180。 ROE = 180。 = $14.Time:0156E t$$$$D t$ $ $ $bg%%%%The year6 earnings estimate is based on growth rate of () = . a. b. The price should rise by 15% per year until year 6: because there is no dividend, the entire return must be in capital gains.c. The payout ratio would have no effect on intrinsic value because ROE = k.15. a. The solution is shown in the Excel spreadsheet below:b., c. Using the Excel spreadsheet, we find that the intrinsic values are $ and $, respectively.16. The solutions derived from Spreadsheet are as follows:Intrinsic Value:FCFFIntrinsic Value:FCFEIntrinsic Value per Share: FCFFIntrinsic Value per Share: FCFEa.100,00075,128b.109,42281,795c.89,69366,01417.Time:0123D t$$$$g%%%%a. The dividend to be paid at the end of year 3 is the first installment of a dividend stream that will increase indefinitely at the constant growth rate of 5%. Therefore, we can use the constant growth model as of the end of year 2 in order to calculate intrinsic value by adding the present value of the first two dividends plus the present value of the price of the stock at the end of year 2.The expected price 2 years from now is:P2 = D3/(k – g) = $( – ) = $The PV of this expected price is $$The PV of expected dividends in years 1 and 2 isThus the current price should be: $ + $ = $b. Expected dividend yield = D1/P0 = $$ = , or %c. The expected price one year from now is the PV at that time of P2 and D2:P1 = (D2 + P2)/ = ($ + $)/ = $The implied capital gain is(P1 – P0)/P0 = ($ – $)/$ = = %The sum of the implied capital gains yield and the expected dividend yield is equal to the market capitalization rate. This is consistent with the DDM.18.Time:0145E t$$$$D t$$$$Dividends = 0 for the next four years, so b = (100% plowback ratio).a. (Since k=ROE, knowing the plowback rate is unnecessary)b. Price should increase at a rate of 15% over the next year, so that the HPR will equal k.19. Beforetax cash flow from operations $2,100,000Depreciation 210,000Taxable Ine 1,890,000Taxes ( 35%) 661,500Aftertax unleveraged ine 1,228,500Aftertax cash flow from operations(Aftertax unleveraged ine + depreciation) 1,438,500New investment (20% of cash flow from operations) 420,000Free cash flow(Aftertax cash flow from operations – new investment) $1,018,