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1、文档供参考，可复制、编制，期待您的好评与关注！ CHAPTER 18: EQUITY VALUATION MODELSPROBLEM SETS 1.Theoretically, dividend discount models can be used to value the stock of rapidly growing companies that do not currently pay dividends; in this scenario, we would be valuing expected dividends in the relatively more distant f
2、uture. However, as a practical matter, such estimates of payments to be made in the more distant future are notoriously inaccurate, rendering dividend discount models problematic for valuation of such companies; free cash flow models are more likely to be appropriate. At the other extreme, one would
3、 be more likely to choose a dividend discount model to value a mature firm paying a relatively stable dividend.2.It is most important to use multistage dividend discount models when valuing companies with temporarily high growth rates. These companies tend to be companies in the early phases of thei
4、r life cycles, when they have numerous opportunities for reinvestment, resulting in relatively rapid growth and relatively low dividends (or, in many cases, no dividends at all). As these firms mature, attractive investment opportunities are less numerous so that growth rates slow.3.The intrinsic va
5、lue of a share of stock is the individual investors assessment of the true worth of the stock. The market capitalization rate is the market consensus for the required rate of return for the stock. If the intrinsic value of the stock is equal to its price, then the market capitalization rate is equal
6、 to the expected rate of return. On the other hand, if the individual investor believes the stock is underpriced (i.e., intrinsic value price), then that investors expected rate of return is greater than the market capitalization rate.4.First estimate the amount of each of the next two dividends and
7、 the terminal value. The current value is the sum of the present value of these cash flows, discounted at 8.5%.5.The required return is 9%. 6.The Gordon DDM uses the dividend for period (t+1) which would be 1.05.7.The PVGO is $0.56:8.a.b.The price falls in response to the more pessimistic dividend f
8、orecast. The forecast for current year earnings, however, is unchanged. Therefore, the P/E ratio falls. The lower P/E ratio is evidence of the diminished optimism concerning the firms growth prospects.9.a.g = ROE b = 16% 0.5 = 8%D1 = $2 (1 b) = $2 (1 0.5) = $1b.P3 = P0(1 + g)3 = $25(1.08)3 = $31.491
9、0.a. b.Leading P0/E1 = $10.60/$3.18 = 3.33Trailing P0/E0 = $10.60/$3.00 = 3.53c.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 9% = 3%, and D1 to:E0 (1 + g) (2/3)$3 1.03 (2/3) = $2.06Thus:V0
10、 = $2.06/(0.16 0.03) = $15.85V0 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 inves
11、tments is found by solving:g = b ROE with g = 5% and b = 1/3 ROE = 15%c. Assuming ROE = k, price is equal to:Therefore, the market is paying $40 per share ($160 $120) for growth opportunities.12.a.k = D1/P0 + gD1 = 0.5 $2 = $1g = b ROE = 0.5 0.20 = 0.10Therefore: k = ($1/$10) + 0.10 = 0.20, or 20%b.
12、Since k = ROE, the NPV of future investment opportunities is zero:c.Since k = ROE, the stock price would be unaffected by cutting the dividend and investing the additional earnings.13.a.k = rf + E(rM ) rf = 8% + 1.2(15% 8%) = 16.4%g = b ROE = 0.6 20% = 12%b.P1 = V1 = V0(1 + g) = $101.82 1.12 = $114.
13、0414.Time:0156E t$10.000$12.000$24.883$27.123D t$ 0.000$ 0.000$ 0.000$10.849b1.001.001.000.60g20.0%20.0%20.0%9.0%The year-6 earnings estimate is based on growth rate of 0.15 (1-.0.40) = 0.09. a.b. The price should rise by 15% per year until year 6: because there is no dividend, the entire return mus
14、t 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 $33.80 and $32.80, respectively.16.The solutions derived from Spreadshee
15、t 18.2 are as follows:Intrinsic Value:FCFFIntrinsic Value:FCFEIntrinsic Value per Share: FCFFIntrinsic Value per Share: FCFEa.100,00075,12838.8941.74b.109,42281,79544.1245.44c.89,69366,01433.1636.6717.Time:0123D t$1.0000$1.2500$1.5625$1.953g25.0%25.0%25.0%5.0%a.The dividend to be paid at the end of
16、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 presen
17、t 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) = $1.953125/(0.20 0.05) = $13.02The PV of this expected price is $13.02/1.202 = $9.04The PV of expected dividends in years 1 and 2 isThus the current price should be: $9.04 + $2.13 = $11.17b.
18、Expected dividend yield = D1/P0 = $1.25/$11.17 = 0.112, or 11.2%c.The expected price one year from now is the PV at that time of P2 and D2:P1 = (D2 + P2)/1.20 = ($1.5625 + $13.02)/1.20 = $12.15The implied capital gain is(P1 P0)/P0 = ($12.15 $11.17)/$11.17 = 0.088 = 8.8%The sum of the implied capital
19、 gains yield and the expected dividend yield is equal to the market capitalization rate. This is consistent with the DDM.18.Time:0145E t$5.000$6.000$10.368$10.368D t$0.000$0.000$0.000$10.368Dividends = 0 for the next four years, so b = 1.0 (100% plowback ratio).a. (Since k=ROE, knowing the plowback
20、rate is unnecessary)b.Price should increase at a rate of 15% over the next year, so that the HPR will equal k.19.Before-tax cash flow from operations$2,100,000Depreciation210,000Taxable Income1,890,000Taxes ( 35%)661,500After-tax unleveraged income1,228,500After-tax cash flow from operations(After-t
21、ax unleveraged income + depreciation)1,438,500New investment (20% of cash flow from operations)420,000Free cash flow(After-tax cash flow from operations new investment)$1,018,500The value of the firm (i.e., debt plus equity) is:Since the value of the debt is $4 million, the value of the equity is $1
22、0,550,000.20.a.g = ROE b = 20% 0.5 = 10%b.TimeEPSDividendComment0$1.0000$0.500011.10000.5500g = 10%, plowback = 0.5021.21000.7260EPS has grown by 10% based on last years earnings plowback and ROE; this years earnings plowback ratio now falls to 0.40 and payout ratio = 0.603$1.2826$0.7696EPS grows by
23、 (0.4) (15%) = 6% and payout ratio = 0.60At time 2: At time 0: c.P0 = $11 and P1 = P0(1 + g) = $12.10(Because the market is unaware of the changed competitive situation, it believes the stock price should grow at 10% per year.)P2 = $8.551 after the market becomes aware of the changed competitive sit
24、uation.P3 = $8.551 1.06 = $9.064 (The new growth rate is 6%.)YearReturn12 3Moral: In normal periods when there is no special information, the stock return = k = 15%. When special information arrives, all the abnormal return accrues in that period, as one would expect in an efficient market.CFA PROBL
25、EMS1.a. This director is confused. In the context of the constant growth modeli.e., P0 = D1/ k g), it is true that price is higher when dividends are higher holding everything else including dividend growth constant. But everything else will not be constant. If the firm increases the dividend payout
26、 rate, the growth rate g will fall, and stock price will not necessarily rise. In fact, if ROE k, price will fall.b. (i) An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate (i.e. ROE plowback) will fall as plowb
27、ack ratio falls.(ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason - less funds are reinvested in the firm.2.Using a two-stage dividend discount model, the current value of a share of Sundanci is calculated as follows.where:E0 = $0.952D0 = $0.286E1
28、= E0 (1.32)1 = $0.952 1.32 = $1.2566D1 = E1 0.30 = $1.2566 0.30 = $0.3770E2 = E0 (1.32)2 = $0.952 (1.32)2 = $1.6588D2 = E2 0.30 = $1.6588 0.30 = $0.4976E3 = E0 (1.32)2 1.13 = $0.952 (1.32)2 1.13 = $1.8744D3 = E3 0.30 = $1.8743 0.30 = $0.56233.a.Free cash flow to equity (FCFE) is defined as the cash
29、flow remaining after meeting all financial obligations (including debt payment) and after covering capital expenditure and working capital needs. The FCFE is a measure of how much the firm can afford to pay out as dividends but, in a given year, may be more or less than the amount actually paid out.
30、Sundancis FCFE for the year 2008 is computed as follows:FCFE = Earnings + Depreciation - Capital expenditures - Increase in NWC = $80 million + $23 million - $38 million - $41 million = $24 millionFCFE per share = At this payout ratio, Sundancis FCFE per share equals dividends per share.b.The FCFE m
31、odel requires forecasts of FCFE for the high growth years (2012 and 2013) plus a forecast for the first year of stable growth (2014) in order to allow for an estimate of the terminal value in 2013 based on perpetual growth. Because all of the components of FCFE are expected to grow at the same rate,
32、 the values can be obtained by projecting the FCFE at the common rate. (Alternatively, the components 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%Actual2011P
33、rojected2012Projected2013Projected2014Growth rate (g)27%27%13%TotalPer ShareEarnings after tax$80$0.952$1.2090$1.5355$1.7351Plus: Depreciation expense230.2740.34800.4419$0.4994Less: Capital expenditures380.4520.57400.7290$0.8238Less: Increase in net working capital410.4880.61980.7871$0.8894Equals: F
34、CFE240.2860.36320.4613$0.5213Terminal value$52.1300*Total cash flows to equity$0.3632$52.5913Discounted value$0.3186 $40.4673Current value per share$40.7859*Projected 2013 terminal value = (Projected 2014 FCFE)/(r - g)Projected 2013 Total cash flows to equity = Projected 2013 FCFE + Projected 2013 t
35、erminal valueDiscounted values obtained using k= 14%Current value per share=Sum of discounted projected 2012 and 2013 total FCFEc.i. The DDM uses a strict definition of cash flows to equity, i.e. the expected dividends on the common stock. In fact, taken to its extreme, the DDM cannot be used to est
36、imate the value of a stock that pays no dividends. The FCFE model expands the definition of cash flows to include the balance of residual cash flows after all financial obligations and investment needs have been met. Thus the FCFE model explicitly recognizes the firms investment and financing polici
37、es as well as its dividend policy. In instances of a change of corporate control, and therefore the possibility of changing dividend policy, the FCFE model provides a better estimate of value. The DDM is biased toward finding low P/E ratio stocks with high dividend yields to be undervalued and conve
38、rsely, high P/E ratio stocks with low dividend yields to be overvalued. It is considered a conservative model in that it tends to identify fewer undervalued firms as market prices rise relative to fundamentals. The DDM does not allow for the potential tax disadvantage of high dividends relative to t
39、he capital gains achievable from retention of earnings.ii. Both two-stage valuation models allow for two distinct phases of growth, an initial finite period where the growth rate is abnormal, followed by a stable growth period that is expected to last indefinitely. These two-stage models share the s
40、ame limitations with respect to the growth assumptions. First, there is the difficulty of defining the duration of the extraordinary growth period. For example, a longer period of high growth will lead to a higher valuation, and there is the temptation to assume an unrealistically long period of ext
41、raordinary growth. Second, the assumption of a sudden shift from high growth to lower, stable growth is unrealistic. The transformation is more likely to occur gradually, over a period of time. Given that the assumed total horizon does not shift (i.e., is infinite), the timing of the shift from high
42、 to stable growth is a critical determinant of the valuation estimate. Third, because the value is quite sensitive to the steady-state growth assumption, over- or underestimating this rate can lead to large errors in value. The two models share other limitations as well, notably difficulties in accu
43、rately forecasting required rates of return, in dealing with the distortions that result from substantial and/or volatile debt ratios, and in accurately valuing assets that do not generate any cash flows.4.a.The formula for calculating a price earnings ratio (P/E) for a stable growth firm is the div
44、idend payout ratio divided by the difference between the required rate of return and the growth rate of dividends. If the P/E is calculated based on trailing earnings (year 0), the payout ratio is increased by the growth rate. If the P/E is calculated based on next years earnings (year 1), the numer
45、ator is the payout ratio.P/E on trailing earnings:P/E = payout ratio (1 + g)/(k - g) = 0.30 1.13/(0.14 - 0.13) = 33.9P/E on next years earnings: P/E = payout ratio/(k - g) = 0.30/(0.14 - 0.13) = 30.0b.The P/E ratio is a decreasing function of riskiness; as risk increases, the P/E ratio decreases. In
46、creases in the riskiness of Sundanci stock would be expected to lower the P/E ratio.The P/E ratio is an increasing function of the growth rate of the firm; the higher the expected growth, the higher the P/E ratio. Sundanci would command a higher P/E if analysts increase the expected growth rate.The P/E ratio is a decreasing function of the market risk premium. An increased market risk premium increases the required rate of return, lowering the price of a stock relative to its earn