valuing stocks

Chapter 07Chapter 07Inputs are in BlueAnswers are in RedNOTE: Some functions used in these spreadsheets may require thatthe "Analysis ToolPak" or "Solver Add-In" be installed in Excel.To install these, click on the Office buttonthen "Excel Options," "Add-Ins" and select"Go." Check "Analysis ToolPak" and"Solver Add-In," then click "OK."

&C2012, The McGraw-Hill Companies

1Quiz1. Dividend discount model. Amazon.com has never paid a dividend, but in august 2010 the market value of its stock was $57billion. Does this invalidate the dividend discount model?Answer: No, this does not invalidate the dividend discount model. The dividend discount model allows for the fact that firms may not currently pay dividends. As the market matures, and Amazons growth opportunities moderate, investors may justifiably believe that Amazon will enjoy high future earnings and will then pay dividends. The stock price today can still reflect the present value of the expected per-share stream of dividends.

2Quiz 2Favored stock will pay a dividend this year of $2.40 per share. Its dividend yield is 8%. At what priceis the stock selling?Dividend per share$2.40Dividend yield8.00%Solution:Stock Price=$30.00


3Quiz 3Preferred Products has issued preferred stock with an $8 annual dividend that will be paid inperpetuity.a.If the discount rate is 12%, at what price should the preferred sell?b.At what price should the stock sell 1 year from now?c.What is the dividend yield, the capital gains yield, and the expected rate ofreturn of the stock?Annual dividend$8.00Discount rate12%Solution:a.Stock Price=$66.67b.Stock Price after 1 year=$66.67c.Stock Price$66.67Dividend yield=12.00%Capital gains yield=0.00Expected rate of return=12.00%


4Quiz 4Waterworks has a dividend yield of 8%. If its dividend is expected to grow at a constant rate of 5%,what must be the expected rate of return on the companys stock?Dividend yield8.00%Constant growth rate5.00%Solution:Expected rate of return=13.00%


5Quiz 5. How can we say that price equals to the present value of all future cash flows when many actual investors may be seeking capital gains and planing to hold their shares for only a year or two? Explain.5.The value of a share of common stock equals the present value of dividends received out to the investment horizon plus the present value of the forecast stock price at the horizon. But the stock price at the horizon date depends on expectations of dividends from that date forward. So, even if an investor plans to hold a stock for only a year or two, the price ultimately received from another investor depends on dividends to be paid after the date of purchase. Therefore, the stocks present value is the same for investors with different time horizons.

6Quiz 6Steady As She Goes, Inc., will pay a year-end dividend of $3 per share. Investors expect thedividend to grow at a rate of 4% indefinitely.a.If the stock currently sells for $30 per share, what is the expected rate ofreturn on the stock?b.If the expected rate of return on the stock is 16.5%, what is the stock price?Dividend per share$3.00Constant growth rate4.00%Current selling price (a)$30.00Expected rate of return (b)16.50%Solution:a.Expected rate of return=14.00%b.Stock price=$24.00


7Quiz 7BMM Industries pays a dividend of $2 per quarter. The dividend yield on its stock is reportedat 4.8%. What price is the stock selling at?Dividend$2.00per quarterDividend yield4.80%Solution:Annual dividend=$8.00note: 4 times quarterly dividend for a whole year.Stock price=$166.67dividend yield= dividend payment/stock price=Stock price=8/0,048166.6666666667


11Practice Problem 11Integrated Potato Chips paid a $1 per share dividend yesterday. You expect the dividend to growsteadily at a rate of 4% per year.a.What is the expected dividend in each of the next 3 years?b.If the discount rate for the stock is 12%, at what price will the stock sell?c.What is the expected stock price 3 years from now?d.If you buy the stock and plan to hold it for 3 years, what payments will you receive?What is the present value of those payments? Compare your answer to (b).Per share dividend$1.00Constant growth rate4.00%Discount rate (b)12.00%Solution:a.Expected dividend:DIV1=$1.0400DIV2=$1.0816DIV3=$1.1249b.DIV1$1.0400Stock price=$13.00c.DIV3$1.1249Expected stock price=$14.6237d.Year 1Year 2Year 3DIV$1.04$1.08$1.12Selling price$14.62Total cash flow$1.04$1.08$15.75PV of cash flow$0.93$0.86$11.21Sum of PV$13.00Sum of PV = $13.00, the same as the answer to part (b).


12Practice Problem 12A stock sells for $40. The next dividend will be $4 per share. If the rate of returnearned on reinvested funds is a constant 15% and the company reinvests 40%of earnings in the firm, what must be the discount rate?Stock price$40.00Next dividend per share$4.00Rate of return on reinvested funds15.00%Reinvested earnings40.00%Solution:g=6.00%Discount Rate=16.00%


13Practice Problem 13Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that thedividend will increase by 5% per year indefinitely.a.What price should the stock sell at? The discount rate is 15%.b.How would your answer change if the discount rate were only 12%? Why does the answerchange?Annual dividend per share$3.00Constant growth rate5.00%Discount rate (a)15.00%Discount rate (b)12.00%Solution:a.Stock price (P0)=$31.50b.Stock price (P0)=$45.00The lower discount rate makes the present value of future dividends higher.


14Practice Problem 14Arts and Crafts, Inc., will pay a dividend of $5 per share in 1 year. It sells at $50 a share,and firms in the same industry provide an expected rate of return of 14%. What must bethe expected growth rate of the companys dividends?Annual dividend per share$5.00Stock price$50.00Expected rate of return14.00%Solution:Expected growth rate=4.00%


15Practice Problem 15Eastern Electric currently pays a dividend of about $1.64 per share and sells for $27 a share.a.If investors believe the growth rate of dividends is 3% per year, what rate of return do theyexpect to earn on the stock?b.If investors required rate of return is 10%, what must be the growth rate they expect of thefirm?c.If the sustainable growth rate is 5% and the plowback ratio is .4, what must be the rate ofreturn earned by the firm on its new investments?Dividend per share$1.64Stock price$27.00Growth rate of dividends (a)3.00%Required rate of return (b)10.00%Sustainable growth rate5.00%Plowback ratio0.40Solution:a.Expected rate of return (r)=9.26%b.Expected growth rate (g)=3.74%c.Return on equity=12.50%


16Practice Problem 16You believe that the Non-stick Gum Factory will pay a dividend of $2 on its common stocknext year. Thereafter, you expect dividends to grow at a rate of 6% a year in perpetuity.If you require a return of 12% on your investment, how much should you be prepared topay for the stock?Dividend next year$2.00Constant growth rate6.00%Required rate of return12.00%Solution:Stock price (P0)=$33.33


17Practice Problem 17Horse and Buggy Inc. is in a declining industry. Sales, earnings, and dividendsare all shrinking at a rate of 10% per year.a.If r = 15% and DIV 1 = $3, what is the value of a share?b.What price do you forecast for the stock next year?c.What is the expected rate of return on the stock?d.Can you distinguish between bad stocks and bad companies? Does thefact that the industry is declining mean that the stock is a bad buy?Shrinking rate10.00%Required rate of return15.00%Dividend in 1st year$3.00Solution:a.Stock price (P0)=$12.00b.Stock price (P1)=$10.80c.Stock price (P0)=$12.00Stock price (P1)=$10.80Expected rate of return=15.00%d.Bad companies may be declining, but if the stock price alreadyreflects this fact, the investor can still earn a fair rate of return.


18Practice Problem 18Metatrends stock will generate earnings of $6 per share this year. The discount rate for the stockis 15%, and the rate of return on reinvested earnings also is 15%.a.Find both the growth rate of dividends and the price of the stock if the company reinvests thefollowing fraction of its earnings in the firm: (i) 0%; (ii) 40%; (iii) 60%b.Redo part (a) now assuming that the rate of return on reinvested earnings is 20%. What is thepresent value of growth opportunities for each reinvestment rate?Earnings$6.00Discount rate15.00%Rate of return on reinvested earnings15.00%Reinvestment: (a)(i)0.00%(ii)40.00%(iii)60.00%Rate of return on reinvestment (b)20.00%Solution:a.(i) Reinvest 0% of earnings:Growth Rate=0%Dividend=$6.00Stock price (P0)=$40.00(ii) Reinvest 40% of earnings:Growth Rate=6.00%Dividend=$3.60Stock price (P0)=$40.00(iii) Reinvest 60% of earnings:Growth Rate=9.00%Dividend=$2.40Stock price (P0)=$40.00b.(i) Reinvest 0% of earnings:Stock price with 15% rate of return=$40.00Stock price (P0)=$40.00PVGO=0.0(ii) Reinvest 40% of earnings:Stock price with 15% rate of return=$40.00Stock price (P0)=$51.43PVGO=$11.43(iii) Reinvest 60% of earnings:Stock price with 15% rate of return=$40.00Stock price (P0)=$80.00PVGO=$40.00


19Practice Problem 19You expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 in each of thenext 3 years. You believe the stock will sell for $20 at the end of the third year.a.What is the stock price if the discount rate for the stock is 10%?b.What is the dividend yield?Dividends:Year1$1.00Year2$1.25Year3$1.50Discount rate10.00%Stock price after 3 years$20.00Solution:a.Stock price (P0)=$18.10b.Stock price (P0)$18.10Dividend yield=5.52%


20Practice Problem 20Here are data on two stocks, both of which have discount rates of 15%:Stock AStock BReturn on equity15.00%10.00%Earnings per share$2.00$1.50Dividends per share$1.00$1.00Discount Rates15.00%15.00%a.What are the dividend payout ratios for each firm?b.What are the expected dividend growth rates for each firm?c.What is the proper stock price for each firm?Solution:Stock AStock Ba.Payout ratio0.500.67b.Growth rate (g)7.50%3.33%c.Stock price$13.33$8.57


21Practice Problem 21Web Cites Research projects a rate of return of 20% on new projects. Management plansto plow back 30% of all earnings into the firm. Earnings this year will be $3 per share, andinvestors expect a 12% rate of return on stocks facing the same risks as Web Cites.a.What is the sustainable growth rate?b.What is the stock price?c.What is the present value of growth opportunities?d.What is the P/E ratio?e.What would the price and P/E ratio be if the firm paid out all earnings as dividends?f.What do you conclude about the relationship between growth opportunities and P/E ratios?Projected Rate of return20.00%Plow back ratio30.00%Earnings per share$3.00Rate of return on stocks12.00%Solution:a.Sustainable growth rate=6.00%b.Sustainable growth rate=6.00%Stock price=$35.00c.No-growth value=$25.00Sustainable growth rate=6.00%Stock price=$35.00PVGO=$10.00d.Sustainable growth rate=6.00%Stock price=$35.00P/E ratio=11.667e.If all earnings were paid as dividends:Price=$25.00P/E ratio=8.333f.High P/E ratios reflect expectations of high PVGO.


22Practice Problem 22Fincorp will pay a year-end dividend of $2.40 per share, which is expected to grow at a 4%rate for the indefinite future. The discount rate is 12%.a.What is the stock selling for?b.If earnings are $3.10 a share, what is the implied value of the firms growth opportunities?Dividend per share$2.40Expected growth rate4.00%Discount rate12.00%Earnings per share (b)$3.10Solution:a.Stock price=$30.00b.Stock price=$30.00No-growth value=$25.83PVGO=$4.17


23Practice Problem 23No-Growth Industries pays out all of its earnings as dividends. It will pay its next $4 per sharedividend in a year. The discount rate is 12%.a.What is the price-earnings ratio of the company?b.What would the P/E ratio be if the discount rate were 10%?Dividend per share$4.00Discount rate12.00%Discount rate (b)10.00%Solution:a.Stock price (P0)=$33.33Price-earnings ratio=$8.33b.Stock price (P0)=$40.00Price-earnings ratio=$10.00


24Practice Problem 24Stormy Weather has no attractive investment opportunities. Its return on equity equals the discountrate, which is 10%. Its expected earnings this year are $4 per share. Find the stock price, P/E ratio,and growth rate of dividends for plowback ratios ofa.0.00b.0.40c.0.80Return on equity10.00%Discount rate10.00%Expected earnings per share$4.00Solution:a.Stock price=$40.00P/E ratio=10.00Growth rate of dividends=0.00%b.Stock price=$40.00P/E ratio=10.00Growth rate of dividends=4.00%c.Stock price=$40.00P/E ratio=10.00Growth rate of dividends=8.00%


25Practice Problem 25Trend-Line Inc. has been growing at a rate of 6% per year and is expected to continue to do soindefinitely. The next dividend is expected to be $5 per share.a.If the market expects a 10% rate of return on Trend-Line, at what price must it be selling?b.If Trend-Lines earnings per share will be $8, what part of Trend-Lines value is due to assetsin place, and what part to growth opportunities?Constant growth rate6.00%Dividend per share$5.00Expected rate of return (a)10.00%Earnings per share (b)$8.00Solution:a.Stock price (P0)=$125.00b.Value of assets in place=$80.00PVGO=$45.00


26Practice Problem 26Construct a market-value balance sheet for FedEx, using the information in Table 7.1 and stockprices reported in Sections 7.1 and 7.2. Assume that market and book values are equal forcurrent assets, current liabilities, and debt and other long-term liabilities. How much extra valueshows up on the asset side of the balance sheet?Table 7.1SIMPLIFIED BALANCE SHEET FOR FEDEX, MAY 31, 2010(Millions of dollars)Current assets$7,284.00Current liabilities$4,645.00Plant, equipment and other long-term assets$17,618.00Debt and other long-term liabilities$6,446.00Shareholders equity$13,811.00$24,902.00Total liabilities and equity$24,902.00Shares of stock outstanding:314.00millionTable 7.2Stock PriceBook Value per shareMarket-to-Book-Value RatioFedEx$83.75$43.981.90Johnson & Johnson58.2919.193.00Campbell Soup36.973.2311.40PepsiCo64.8912.395.20Walmart51.2017.492.90Dow Chemical25.5914.221.80Amazon132.4913.0710.10McDonalds74.5412.346.00American Electric Power36.1127.701.30GE15.0110.661.40Solution:SIMPLIFIED MARKET VALUE BALANCE SHEET FOR FEDEXMay 31, 2010(Millions of dollars)Current assets$7,284.00Current liabilities$4,645.00Plant, equipment and other long-term assets$17,618.00Debt and other long-term liabilities$6,446.00Growth opportunities$12,486.50Shareholders equity$26,297.50$37,388.50Total liabilities and equity$37,388.50


27Practice Problem 27Castles in the Sand generates a rate of return of 20% on its investments and maintains a plowbackratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on thestock.a.Find the price and P/E ratio of the firm.b.What happens to the P/E ratio if the plowback ratio is reduced to .20?c.Show that if plowback equals zero, the earnings-price ratio, E/P, falls to the expectedrate of return on the stock.Rate of return20.00%Plowback ratio0.30Earnings this year$4.00Expected rate of return12.00%Plowback ratio (b)0.20Plowback ratio (c)0.00Solution:a.Growth rate (g)=6.00%Stock price (P0)=$46.67P/E ratio=$11.667b.Growth rate (g)=4.00%Stock price (P0)=$40.00P/E ratio=$10.00c.Growth rate (g)=0.00%Stock price (P0)=$33.33Earnings-price ratio (E/P)=12.00%


28Practice Problem 28Grandiose Growth has a dividend growth rate of 20%. The discount rate is 10%. The end-of-yeardividend will be $2 per share.a.What is the present value of the dividend to be paid in year 1? Year 2? Year 3?b.Could anyone rationally expect this growth rate to continue indefinitely?Dividend growth rate20.00%gDiscount rate10.00%rEnd-of-year dividend$2.00div.Solution:a.DIV 1$2.00PV of DIV 1=$1.818DIV 2$2.40PV of DIV 2=$1.983DIV 3$2.88PV of DIV 3=$2.164b.This could not continue indefinitely. If it did, thestock would be worth an infinite amount.


29Practice Problem 29Start-Up Industries is a new firm that has raised $200 million by selling shares of stock.Management plans to earn a 24% rate of return on equity, which is more than the 15%rate of return available on comparable-risk investments. Half of all earnings will bereinvested in the firm.a.What will be Start-Ups ratio of market value to book value?b.How would that ratio change if the firm can earn only a 10% rate of return on itsinvestments?Amount raised$200.00millionReturn on equity24.00%Rate of return15.00%Plowback ratio50.00%Rate on equity (b)10.00%Solution:a.Earnings=$48.00millionDividends=$24.00millionGrowth rate (g)=12.00%Market value=$800.00millionMarket-to-book ratio=$4b.Earnings=$20.00millionDividends=$10.00millionGrowth rate (g)=5.00%Market value=$100.00millionMarket-to-book ratio=1/2


30Practice Problem 30Planned Obsolescence has a product that will be in vogue for 3 years, at which point the firmwill close up shop and liquidate the assets. As a result, forecast dividends are DIV 1 = $2,DIV 2 = $2.50, and DIV 3 = $18. What is the stock price if the discount rate is 12%?DIV 1$2.00DIV 2$2.50DIV 3$18.00Discount Rate12.00%Solution:Stock price (P0)=$16.59


31Practice Problem 31Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growthrate in earnings and dividends to continue for another 3 years.a.If the last dividend paid was $2, what will the next dividend be?b.If the discount rate is 15% and the steady growth rate after 3 years is 4%, what should thestock price be today?Growth rate20.00%Last dividend paid$2.00Discount rate15.00%Steady growth rate (b)4.00%Solution:a.DIV 1=$2.40b.DIV 1=$2.40DIV 2=$2.88DIV 3=$3.456Stock price (P3)=$32.675Stock price (P0)=$28.021


32Practice Problem 32Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growthrate in earnings and dividends to continue for another 3 years. The last dividend paid was $2The discount rate is 15% and the steady growth rate after 3 years is 4%a.What is your prediction for the stock price in 1 year?b.Show that the expected rate of return equals the discount rate.Growth rate20.00%Last dividend paid$2.00Discount rate15.00%Steady growth rate (b)4.00%Solution:a.DIV 1=$2.40PHDIV 2=$2.88DIV 3=$3.456Stock price (P3)=$32.675div4 /(r-g)steady growthkassafldeStock price (P0)=$28.021PV0discountStock price (P1)=$29.825PV0= (Div. +P1)/(1+r)Capital gain=$1.804P1=(1+r)*P0-Div.eller kalkylera diskonterad kassaflde frn period 2 och 3 plus horizon vrde29.825b.Expected rate of return=15.00%(dividend+capital gain)/stock price

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40Challenge Problem 40Computer Corp. reinvests 60% of its earnings in the firm. The stock sells for $50, and thenext dividend will be $2.50 per share. The discount rate is 15%. What is the rate of returnon the companys reinvested funds?Reinvests60.00%of earningsStock sells for$50.00Next dividend$2.50per shareDiscount rate15.00%Solution:Return on equity=16.67%


41Challenge Problem 41A company will pay a $2 per share dividend in 1 year. The dividend in 2 years will be$4 per share, and it is expected that dividends will grow at 5% per year thereafter.The expected rate of return on the stock is 12%.a.What is the current price of the stock?b.What is the expected price of the stock in a year?c.Show that the expected return, 12%, equals dividend yield plus capital appreciation.Dividend per share:Year 1$2.00Year 2$4.00Growth rate5.00%Expected rate of return12.00%Solution:a.Stock price (P2)=$60.00Stock price (P0)=$52.806b.Stock price (P1)=$57.143c.Stock price (P0)=$52.806Stock price (P1)=$57.143Dividend yield plus capital appreciation = r=12.00%


42Challenge Problem 42Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy.Today, it announced a $1 per share dividend to be paid a year from now, the first dividend sincethe crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the thirdyear (in which dividends are $3 per share) dividend growth is expected to settle down to a moremoderate long-term growth rate of 6%. If the firms investors expect to earn a return of 14% onthis stock, what must be its price?Dividend per share$1.00Expected dividends increase$1.00Dividend in third year$3.00Long-term growth rate6.00%Expected return14.00%Solution:Stock price (P3)=$39.75Stock price (P0)=$31.27


43Challenge Problem 43Compost Science, Inc. (CSI), is in the business of converting Bostons sewage sludge intofertilizer. The business is not in itself very profitable. However, to induce CSI to remain inbusiness, the Metropolitan District Commission (MDC) has agreed to pay whatever amountis necessary to yield CSI a 10% return on investment. At the end of the year, CSI is expectedto pay a $4 dividend. It has been reinvesting 40% of earnings and growing at 4% a year.a.Suppose CSI continues on this growth trend. What is the expected rate of return for aninvestor who purchases the stock at the market price of $100?b.What part of the $100 price is attributable to the present value of growth opportunities?c.Now the MDC announces a plan for CSI to also treat Cambridge sewage. CSIs plant willtherefore be expanded gradually over 5 years. This means that CSI will have to reinvest80% of its earnings for 5 years. Starting in year 6, however, it will again be able to payout 60% of earnings. What will be CSIs stock price once this announcement is madeand its consequences for CSI are known?Return on investment10.00%Expected dividend$4.00Reinvestment40.00%of earningsGrowth rate4.00%Stock price (a)$100.00Expansion plan (c)5.00yearsReinvestment (c)80.00%of earningsPayout ratio60.00%of earningsSolution:a.Expected rate of return=8.00%b.Expected rate of return8.00%Earnings=$6.6667No-growth value=$83.33PVGO=$16.67c.Years123456Earnings$6.67$7.20$7.78$8.40$9.07$9.80Plowback0.800.800.800.800.800.40DIV$1.33$1.44$1.56$1.68$1.81$5.88g0.080.080.080.080.080.04Expected rate of return8.00%Stock price (P6)$152.81Stock price (P0)$106.17


44Challenge Problem 44Better Mousetraps has come out with an improved product, and the world is beating a path toits door. As a result, the firm projects growth of 20% per year for 4 years. By then, other firmswill have copycat technology, competition will drive down profit margins, and the sustainablegrowth rate will fall to 5%. The most recent annual dividend was DIV0 = 1 per share.a.What are the expected values of DIV1 , DIV2 , DIV3 , and DIV4 ?b.What is the expected stock price 4 years from now? The discount rate is 10%.c.What is the stock price today?d.Find the dividend yield, DIV1 / P0 .e.What will next years stock price, P1, be?f.What is the expected rate of return to an investor who buys the stock now and sells it in1 year?Projected growth20.00%Time$4.00yearsSustainable growth rate5.00%Annual dividend (DIV 0)$1.00per shareDiscount rate (b)10.00%Solution:a.DIV1=$1.20DIV2=$1.44DIV3=$1.728DIV4=$2.0736b.DIV4=$2.0736Stock price (P4)=$43.5456c.DIV1=$1.20DIV2=$1.44DIV3=$1.728DIV4=$2.0736Stock price (P4)=$43.5456Stock price (P0)=$34.738d.Stock price (P0)$34.73779Dividend yield=3.45%e.Stock price (P1)=$37.012f.Stock price (P0)$34.738Stock price (P1)$37.012Expected rate of return=10.00%


45Challenge Problem 45Better Mousetraps has come out with an improved product, and the world is beating a path to itsdoor. As a result, the firm projects growth of 20% per year for 4 years. By then, other firms willhave copycat technology, competition will drive down profit margins, and the sustainable growthrate will fall to 5%. The most recent annual dividend was DIV0 = 1 per share.a.Compute the value of Better Mousetraps for assumed sustainable growth rates of 6% through9%, in increments of 5%.b.Compute the percentage change in the value of the firm for each 1-percentage-point increasein the assumed final growth rate, g.c.What happens to the sensitivity of intrinsic value to changes in g? What do you concludeabout the reliability of the dividend growth model when the assumed sustainable growth ratebegins to approach the discount rate?Projected growth20.00%Time$4.00yearsSustainable growth rate5.00%Annual dividend (DIV0)$1.00per shareDiscount Rate (b)10.00%Sustainable growth range6.00%-0.50%Solution:a.,b.DIV1=$1.20DIV2=$1.44DIV3=$1.728DIV4=$2.0736Stock price (P4)=$54.95Stock price (P0)=$42.53Sustainable Growth RatesIntrinsic Value (PV)% Change in PV5.00%34.746.00%42.5322.42%6.50%48.0913.08%7.00%55.5115.43%7.50%65.9018.71%8.00%81.4823.64%8.50%107.4431.87%9.00%159.3748.33%c.The percentage change in the value of the firm increases at a faster rate with each 1%increase in the assumed final growth rate, g. The intrinsic value is more sensitive tochanges in g as the sustainable growth rate approaches the discount rate. The dividendgrowth model is less reliable as the sustainable growth rate approaches the discount rate.


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