投资学10版习题答案CH18

1、CHAPTER 18: EQUITY VALUATION MODELSPROBLEM SETS1. Theoretically, dividend discount models can be used to value the stock of rapidly growing companies that do not currently pay divide nds; in this see nario, we would be valuing expected divide nds in the relatively more distant future. However, as a

2、practical matter, such estimates of payments to be made in the more distant future are notoriously inaccurate, ren deri ng divide nd discount models problematic for valuation of such companies; free cash flow models are more likely to be appropriate. At the other extreme, one would be more likely to

3、 choose a dividend discount model to value a mature firm paying a relatively stable dividend.2 It is most important to use multistage divide nd discount models when valuing companies with temporarily high growth rates. These companies tend to be companies in the early phases of their life cycles, wh

4、en they have numerous opportunities for reinvestment, resulti ng in relatively rapid growth and relatively low divide nds (or, in many cases, no dividends at all). As these firms mature, attractive investment opportunities are less numerous so that growth rates slow.p。PVGO $41$0.560.093. The in tri

5、nsic value of a share of stock is the in dividualinvestor1 s assessment of the true worth of thestock. The marketcapitalizatio n rate is the market con sen sus for the required rateof retur n for the stock .If the intrin sic value of the stock isequal to its price, then the market capitalization rat

6、e is equalto the expected rate of return. On the other hand, if thein dividual inv estor believes the stock is un derpricedintrinsic value > price), then that investor' s expected rate ofreturn is greater tha n the market capitalizatio n rate.4. First estimate the amount of each of the n ext

7、two divide nds andthe terminal value. The current value is the sum of the present value ofthese cash flows, disco un ted at %k $A§20A °.05 The PVGO is $: The required return is 9%. The Gordon DDM uses the divide nd for period ( go,9%t +1) which would be .$35 士匚(k0.05)k$lA0.050.088%$35Di0.1

8、6gg 0.12,or 12% $508.a.b Po ®$18.18k g 0.160.05The price falls in response to the more pessimisticdivide nd forecast. The forecast forcurre nt year earnings,however, is unchanged. Therefore, the P/E ratio falls. The lower P/E ratio is evidenee of the diminished optimism concerning the firm'

9、s growth prospects.9. a. g = ROEb= 16%=8%D = $2(1- b) = $2(1 - = $1Po Dl 也-kg 0.12 0.08$25.00b. Pa = Po(1 + g)3 = $25 3 = $10. a. k rtE(rm) rt6%1.25 (14%6%)16%$10.601$1.0636%Di Eo(1 g) (1 b) $3(1.06)Di $1.06Fo 1kg 0.16 0.06b. Leading Po/ Ei = $ =Trailing Po Eo = $ =c. PVGO p0 I $1 o .60 醫 $9275The l

10、ow P/E ratios and n egative PVGO are due to a poor ROE(9%) that is less than the market capitalization rate (16%).9% = 3%, and Di to:d. Now, you revise b to 1/3, g to 1/3Ed (1 + g) (2/3)$3(2/3) = $Thus:Vo in creases because the firm pays out more earnings in stead of reinvesting a poor ROE. This inf

11、ormation is not yet known to the rest of the market.11. a.PoDikg$80.10 0.05$160$12$120b. The divide nd payout ratio is 8/12 = 2/3, so the plowback ratio is b = 1/3. The implied value of ROE on future inv estme nts is found by solvi ng:g = b ROE with g = 5% and b = 1/3 ROE = 15%c. Assu ming ROE = k,

12、price is equal to:Pok0.10-$120)Therefore, the market is pay ing $40 per share ($160 for growth opport un ities.12. a. k = D/P-+ g$2 = $1 g = b ROE =Therefore: k = ($1/$10) + = , or 20%b. Si nee k = ROE, the NPV of future in vestme nt opport un ities iszero:PVGO P。旦 $10$100ke. Si nee k = ROE, the sto

13、ck price would be un affected byeutt ing the divide nd and inv est ing the additi onal earnings.-8%) = %13. a. k = rt + B E(m ) - rj = 8% + (15%g = b ROE =20% = 12%b.Vo dZW1 12kg 0.1640.12$101.82Pi = Vi = Vo(1E(r)+ g) = $1 DiP P)Pn=S$4.48$ 门 104$100$1000.1852,or 18.52%14.Time:0EtDt%The year 6 earnin

14、gs estimate is based on growth rate of17.a. v5Dekg主Q $180.820.150.09Vo$180.82(1k) 51-155$89.90b.The price should rise by 15% per year un til year 6: becausethere is no divide nd, the en tire retur n must be in capital gains.c. The payout ratio would have no effect on intrin sic value because ROE = k

15、.15. a. The solutio n is show n in the Excel spreadsheet below:In putsYearDivide nd)iv growtherm valuenv estorbeta0.952010.780.78mkt prem0.082010.850.85rf0.0220140.930.93k equity0.0960/.20151.001.00plowback0.75/20161.090.0861.09roe0.092011.180.0841.18term gwth0.068/r1.280.0821.282011.380.0801.38/r1.

16、490.0781.492021.600.0761.60Value line /2021.720.0751.72forecasts of2021.850.0731.85annual divide nds/P20241.980.0711.98/2022.120.0692.12/I 20262.260.0672.26Tran siti onal periodX20272.410.067J0.3392.75with slowiig divide nd/growth31.21=PV of CBeginning of contE17*(1+F17)/(B5 F17)1growth periodNPV(B5

17、,H2:H17)b., c. Using the Excel spreadsheet, we find that the intrinsicvalues are $ and $5 respectively.16. The soluti ons derived from Spreadsheet are as follows:In tri nsicIn tri nsicIn tri nsicIn tri nsicValue:Value:Value perValue perFCFFFCFEShare: FCFFShare: FCFEa.100,00075,128b.109,42281,795c.89

18、,69366,014Time:Dt$g%a. The divide nd to be paid at the end of year 3 is the firstin stallme nt of a divide nd stream that will in creaseindefinitely at the constant growth rate of 5%. Therefore, we can use the con sta nt growth model as of the end of year 2 in order to calculate intrin sic value by

19、add ing the prese nt value of the first two divide nds plus the prese nt value of the price of the stock at the end of year 2.The expected price 2 years from now is:P2 = D/( k - g) = $- = $The PV of this expected price is $ = $The PV of expected divide nds in years 1 and 2 is$1.25$1.5625 水2$2.131.20

20、 1.20Thus the curre nt price should be: $ + $ = $b. Expected divide nd yield = Di/ Po = $ = , or %c. The expected price one year from now is the PV at that time ofP2and D2:Pl = ( D2 + F2)/ =($ + $/=$The implied capital gain is(Pi - Po)/ R = ($-$/$ = = %The sum of the implied capital gains yield and

21、the expected divide nd yield is equal to the market capitalizatio n rate. This is consistent with the DDM.18.Time:014b = (100% plowbackDivide nds = 0 for the n ext four years, so ratio).ADs $10368$69.12k 0.15(Sinee k=ROE, knowing the plowback rate is unnecessary)Vo P" 4$39.52(1 k) 1.15b. Price

22、should in crease at a rate of 15% over the n ext year,so that the HPR will equal k.19. Before-tax cash flow from operatio ns$2,100,000Depreciati on210,000Taxable In come1,890,000Taxes ( 35%)661,500After-tax uni everaged in come1,228,500After-tax cash flow from operati1,438,500(After-tax uni everaged

23、 in come + depreciati on)New in vestme nt (20% of cash flow from operati ons)420,000Free cash flow(After-tax cash flow from operati ons -new investment)$1,018,500The value of the firm debt plus equity) is:Ci$1,018,500Vo 时5$14,550,000kg 0.120.05Since the value of the debt is $4 million, the value of

24、theequity is $10,550,000.20. a. g = ROE b = 20%=10%DikgDo(1 g) $0.50 1.10kg 0.15 0.10b. Time EPSDivide n Comme ntg = 10%, plowback =匚PS has grow n by 10% based on lastyear' s earnings plowback and ROE;this year1 s earnings plowback rationow falls to and payout ratio =EPS grows by (15%) = 6% andp

25、ayout ratio =c-At time 2:6$07696 水s$8.551 0.15kg006At time 0:i/ “ cc $0.726$8.551 水小乂 $°552$7.4931.15(1-15)P°= $11 and Pi = P°(1 + g) = $(Because the market is un aware of the cha nged competitive situation, it believes the stock price should grow at 10% per year.)P2 = $ after the mar

26、ket becomes aware of the changed competitive situati on.P3 = $= $ (The new growth rate is 6%.)Year($12.10 $11) $0.55$110.150,or 15.0%Return0.233,or 23.3%($8.551$12.10)$0.726$12.1035&节卿0.150,or 15.0%$8.551Moral: In normal periods when there is no special information, the stock return = k = 15%. W

27、hen special in formatio n arrives, all the abno rmal retur n accrues in that period , as one would expect in an efficie nt market.CFA PROBLEMS1 a.This director is con fused .In the con text ofcon sta nt growth rthftlel., Po = Di/ k - g), it is true that price is higher whendivide nds are higher hold

28、 ing everyth ing else in clud ing divide nd growth con sta nt . But everyth ing else will not be con sta nt. If the firm in creases the divide nd payout 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 in crease in divide

29、nd payout will reduce thesusta in able growth rate as less funds are reinv ested in the firm. The susta in able growth rate.ROE plowback) will fall as plowback ratio falls.(ii) The in creased divide nd payout rate will reduce the growth rate of book value for the same reason less funds are reinv est

30、ed in the firm.Eo = $Db = $EiEo =$=$DEi=$=$E2E°2 =$2 = $=d2E2=$=$E3Eo2=$ 2 = $DsE3=$=$3. a. Free cash flow to equity (FCFE) is defi ned as the cash flow rema ining after meet ing all finan cial obligati ons (in clud ing debt payme nt) and after coveri ng capital expe nditure and working capital

31、 needs. The FCFE is a measure of how much the firm can afford to pay out as divide nds but, i n a give n year, may be more or less tha n the amount actually paid out.Sun dan ci's FCFE for the year 2008 is computed as follows:FCFE = Earnings + Depreciati onCapital expe ndituresIn crease in NWC=$8

32、0 millio n + $23 million millio n $38 millio n $41 millio n = $24FCFE per share =匹氏$2" million $o.286# of shares outsta nding 84 millio n sharesAt this payout ratio, Sundan ci's FCFE per share equals divide nds per share.b. The FCFE model requires forecasts of FCFE for the high growth years

33、 (2012 and2013) 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 comp onents of FCFE are expected to grow at the same rate, the values can be obtained by project ing the FCFE at th

34、e com mon rate. (Alternatively, the comp onents of FCFE can be projected and aggregated for each year.)This table shows the process for estimat ing the curre nt per share value:FCFE Base Assumpti onsShares outsta nding: 84 millio n,k =14%Projecte dActualProjectedProjected2014201120122013Growth rate

35、(g)27%27%13%TotalPer ShareEarnings after tax$80$ $Plus: Depreciati on expe nse23$Less: Capital expe nditures38$Less: In crease in net work ing41$capitalEquals: FCFE24$Terminal value$*Total cash flows to equity$?Disco un ted value$?$?Curre nt value per share * Projected 2013 termi nal value =(Project

36、ed 2014 FCFE)/($§ rg)Projected 2013 Total cash flows to equity =Projected 2013 FCFE + Projected 2013 termi nal value § Current value per share=Sum of discounted projected 2012 and 2013 total FCFEDisco un ted values obta ined using k= 14%c. i. The DDM uses a strict definition of cash flows

37、to equity, . the expected dividends on the common stock .In fact, take n to its extreme, the DDM cannot be used to estimate the value of a stock that pays no divide nds. The FCFE model expands the defi nition of cash flows to in elude the bala nee of residual cash flows after all financial obligati

38、ons and in vestment n eeds have been met. Thus the FCFE model explicitly recognizes the firm*sinvestment and financing policies as well as its dividend policy. In instances of a change of corporate control, and therefore the possibility of cha nging divide nd policy, the FCFE model provides a better

39、 estimate of value. The DDM is biased toward findi ng low P/E ratio stocks with high divide nd yields to be undervalued and conversely, 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 marke

40、t prices rise relative to fundamentals The DDM does not allow for the potential tax disadva ntage of high divide nds relative to the 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 gro

41、wth rate is abnormal, followed by a stable growth period that is expected to last indefinitely. These twostage models share the same limitations with respect to the growth assumptions. First, there is the difficulty of defining the duration of the extraordinary growth period. For example, a Ion ger

42、period of high growth will lead to a higher valuation, and there is the temptation to assume an unrealistically long period of extraordinary 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,

43、over a period of time Given that the assumed total horizon does not shiftis in finite), the timing of the shift from high 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

44、this rate can lead to large errors in value. The two models share other limitations as well, notably difficulties in accurately 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

45、 generate any cash flows.4. a. The formula for calculating a price earnings ratio (P/E) for a stable growth firm is the dividend payout ratio divided by the d iff ere nee betwee n the required rate of return and the growth rate of dividends. If the P/E is calculated based on trailing earnings (year

46、0), the payout ratio is in creased by the growth rate. If the P/E is calculated based on next year's earnings (year 1), the numerator is the payout ratio.P/E on trailing earnings:P/E = payout ratio(1 +g)/( k g) = /P/E on n ext year's earnin gs:P/E = payout ratio/( k g)=b. The P/E ratio is a

47、decreas ing function of risk in ess; as risk in creases, the P/E ratio decreases .In creases in the risk in ess 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.

48、 Sundanci would comma nd a higher P/E if an alysts in crease the expected growth rate.The P/E ratio is a decreasing function of the market risk premiam. An in creased market risk premium in creases the required rate of return, loweri ng the price of a stock relative to its earnin gs. A higher market

49、 risk premium would be expected to lower Sun dan ci's P/E ratio.5. a. The susta in able growth rate is equal to:Plowback ratio x Return on equity = b x ROENet in come - (Divide nds per share Shares outsta nding)where bNet in comeROE = Net in come/Beg inning of year equityIn 2010:b = 208- x 100)/

50、208 =ROE = 208/1380 =Sustai nable growth rate = x = %In 2013:b = 275x 100)/275 =ROE = 275/1836 =Susta in able growth rate =b. i. The in creased rete nti on ratio in creased the susta in able growth rate.Rete nti on ratio =Net in come (Divide nd per share Shares outsta ndi ng)Net in comeRetention rat

51、io increased from in 2010 to in 2013.This in crease in the rete nti on ratio directly in creased the susta in able growth rate because the rete ntio n ratio is one of the two factors determ ining the susta in able growth rate.ii. The decrease in leverage reduced the susta in able growth rate.Finan c

52、ial leverage = (Total assets/Beg inning of year equity)Finan cial leverage decreased from (3230/1380) at the beg inning of 2010 to at the beg inning of 2013 (3856/1836)This decrease in leverage directly decreased ROE (and thus the susta in able growth rate) because finan cial leverage is one of the

53、factors determ ining ROE (and ROE is one of the two factors determ ining the susta in able growth rate).6. a.The formula for the Gordon model is/ Do(1 g)Vokgwhere:D = Divide nd paid at time of valuati ong = Annual growth rate of divide ndsk = Required rate of return for equityIn the above formula,Po

54、, the market price of the com monstock, substitutes forVo and g becomes the divide nd growthrate implied by the market:P°=Dox(1 +g)/( k - g)Substitut ing, we have:=x (1 +g)/ - g) g = %b. Use of the Gordon growth model would be in appropriate to value Dyn amic s com mon stock, for the followi ng

55、 reas ons: i. The Gordon growth model assumes a set of relati on ships about the growth rate for divide nds, earnin gs, and stock values. Specifically, the model assumes that divide nds, earnings, and stock values will grow at the same constant rate.In valui ng Dyn amic ' s com mon stock, the Gordon growth model is in appropriate because man ageme ntf s divide nd policy has