Capitulo 6 2 Parcial

©2012, The McGraw-Hill Companies

Chapter 07

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.To install these, click on the Office button then "Excel Options," "Add-Ins" and select"Go." Check "Analysis ToolPak" and "Solver Add-In," then click "OK."

Inputs are in BlueAnswers are in Red

Quiz1. 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 Amazon’s 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.


Quiz 2

Favored 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 $ 2.40 Dividend yield 8.00%

Solution:

Stock Price = $30.00


Quiz 3

Preferred Products has issued preferred stock with an $8 annual dividend that will be paid in perpetuity.

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 of return of the stock?

Annual dividend $ 8.00 Discount rate 12%

Solution:

a. Stock Price = $ 66.67

b. Stock Price after 1 year = $ 66.67

c. Stock Price $ 66.67 Dividend yield = 12.00%Capital gains yield = 0.00 Expected rate of return = 12.00%


Quiz 4

Waterworks 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 company’s stock?

Dividend yield 8.00%Constant growth rate 5.00%

Solution:

Expected rate of return = 13.00%

5.

Quiz 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.

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 stock’s present value is the same for investors with different time

horizons.

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?

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 stock’s present value is the same for investors with different time


Quiz 6

Steady 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 of return on the stock?

b. If the expected rate of return on the stock is 16.5%, what is the stock price?

Dividend per share $ 3.00 Constant growth rate 4.00%Current selling price (a) $30.00 Expected rate of return (b) 16.50%

Solution:

a. Expected rate of return = 14.00%

b. Stock price = $24.00


Quiz 7

BMM 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 $ 2.00 per quarterDividend yield 4.80%

Solution:

Annual dividend = $ 8.00 note: 4 times quarterly dividend for a whole year.Stock price = $166.67 dividend yield= dividend payment/stock price=

Stock price=8/0,048166.6667


note: 4 times quarterly dividend for a whole year.dividend yield= dividend payment/stock price=


Practice Problem 11

Integrated 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 $ 1.00 Constant growth rate 4.00%Discount rate (b) 12.00%

Solution:

a. Expected dividend:= $ 1.0400 = $ 1.0816 = $ 1.1249

b. $ 1.0400 Stock price = $ 13.00

c. $ 1.1249 Expected stock price = $14.6237

d. Year 1 Year 2 Year 3DIV $ 1.04 $ 1.08 $ 1.12 Selling price $ 14.62 Total cash flow $ 1.04 $ 1.08 $ 15.75 PV of cash flow $ 0.93 $ 0.86 $ 11.21 Sum of PV $ 13.00

Sum of PV = $13.00, the same as the answer to part (b).

DIV1

DIV2

DIV3

DIV1

DIV3


Integrated Potato Chips paid a $1 per share dividend yesterday. You expect the dividend to grow


Practice Problem 12

A 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 $ 40.00 Next dividend per share $ 4.00

15.00%

Reinvested earnings 40.00%

Solution:

g = 6.00%Discount Rate = 16.00%

Rate of return on reinvested funds


Practice Problem 13

Gentleman 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 $ 3.00 Constant growth rate 5.00%Discount rate (a) 15.00%Discount rate (b) 12.00%

Solution:

a. = $31.50

b. = $45.00

The lower discount rate makes the present value of future dividends higher.

Stock price (P0)

Stock price (P0)


Practice Problem 14

Arts 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 be the expected growth rate of the company’s dividends?

Annual dividend per share $ 5.00 Stock price $50.00 Expected rate of return 14.00%

Solution:

Expected growth rate = 4.00%


Practice Problem 15

Eastern 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 $ 1.64 Stock price $27.00 Growth rate of dividends (a) 3.00%Required rate of return (b) 10.00%Sustainable growth rate 5.00%Plowback ratio 0.40

Solution:

a. = 9.26%

b. = 3.74%

c. Return on equity = 12.50%

Expected rate of return (r)

Expected growth rate (g)


Practice Problem 16

You believe that the Non-stick Gum Factory will pay a dividend of $2 on its common stock next 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 to pay for the stock?

Dividend next year $ 2.00 Constant growth rate 6.00%Required rate of return 12.00%

Solution:

= $33.33 Stock price (P0)


Practice Problem 17

Horse and Buggy Inc. is in a declining industry. Sales, earnings, and dividends are all shrinking at a rate of 10% per year.

a.

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 the fact that the industry is declining mean that the stock is a bad buy?

Shrinking rate 10.00%Required rate of return 15.00%Dividend in 1st year $ 3.00

Solution:

a. = $12.00

b. = $10.80

c. = $12.00

= $10.80


d. “Bad companies” may be declining, but if the stock price already reflects this fact, the investor can still earn a fair rate of return.

If r = 15% and DIV 1 = $3, what is the value of a share?

Stock price (P0)

Stock price (P1)

Stock price (P0)

Stock price (P1)


Practice Problem 18

Metatrend’s 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 $ 6.00 Discount rate 15.00%Rate of return on reinvested earnings 15.00%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 = $ 6.00

= $40.00

(ii) Reinvest 40% of earnings:Growth Rate = 6.00%Dividend = $ 3.60

= $40.00

(iii) Reinvest 60% of earnings:Growth Rate = 9.00%Dividend = $ 2.40

= $40.00

b. (i) Reinvest 0% of earnings:Stock price with 15% rate of return = $40.00

= $40.00 PVGO = $ -

(ii) Reinvest 40% of earnings:Stock price with 15% rate of return = $40.00

= $51.43 PVGO = $11.43

(iii) Reinvest 60% of earnings:Stock price with 15% rate of return = $40.00

= $80.00 PVGO = $40.00

Stock price (P0)

Stock price (P0)

Stock price (P0)

Stock price (P0)

Stock price (P0)

Stock price (P0)


Practice Problem 19

You expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 in each of the next 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:Year 1 $ 1.00 Year 2 $ 1.25 Year 3 $ 1.50

Discount rate 10.00%Stock price after 3 years $20.00

Solution:

a. = $18.10

b. $18.10 Dividend yield = 5.52%

Stock price (P0)

Stock price (P0)


Practice Problem 20

Here are data on two stocks, both of which have discount rates of 15%:

Stock A Stock BReturn on equity 15.00% 10.00%Earnings per share $ 2.00 $ 1.50 Dividends per share $ 1.00 $ 1.00 Discount Rates 15.00% 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 A Stock Ba. Payout ratio 0.50 0.67

b. Growth rate (g) 7.50% 3.33%

c. Stock price $ 13.33 $ 8.57


Practice Problem 21

Web Cites Research projects a rate of return of 20% on new projects. Management plans to 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 return 20.00%Plow back ratio 30.00%Earnings per share $ 3.00 Rate of return on stocks 12.00%

Solution:

a. Sustainable growth rate = 6.00%

b. Sustainable growth rate = 6.00%Stock price = $ 35.00

c. No-growth value = $ 25.00 Sustainable growth rate = 6.00%Stock price = $ 35.00 PVGO = $ 10.00

d. Sustainable growth rate = 6.00%Stock price = $ 35.00 P/E ratio = 11.667

e. If all earnings were paid as dividends:Price = $ 25.00 P/E ratio 8.333

f. High P/E ratios reflect expectations of high PVGO.

=


Practice Problem 22

Fincorp 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 firm’s growth opportunities?

Dividend per share $ 2.40 Expected growth rate 4.00%Discount rate 12.00%Earnings per share (b) $ 3.10

Solution:

a. Stock price = $30.00

b. Stock price = $30.00 No-growth value = $25.83 PVGO = $ 4.17


Practice Problem 23

No-Growth Industries pays out all of its earnings as dividends. It will pay its next $4 per share dividend 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 $ 4.00 Discount rate 12.00%Discount rate (b) 10.00%

Solution:

a. = $33.33 Price-earnings ratio = $ 8.33

b. = $40.00 Price-earnings ratio = $10.00

Stock price (P0)

Stock price (P0)


Practice Problem 24

Stormy Weather has no attractive investment opportunities. Its return on equity equals the discount rate, 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 of

a. 0.00 b. 0.40 c. 0.80

Return on equity 10.00%Discount rate 10.00%Expected earnings per share $ 4.00

Solution:

a. Stock price = $40.00 P/E ratio = 10.00 Growth rate of dividends = 0.00%

b. Stock price = $40.00 P/E ratio = 10.00 Growth rate of dividends = 4.00%

c. Stock price = $40.00 P/E ratio = 10.00 Growth rate of dividends = 8.00%


Practice Problem 25

Trend-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-Line’s earnings per share will be $8, what part of Trend-Line’s value is due to assetsin place, and what part to growth opportunities?

Constant growth rate 6.00%Dividend per share $ 5.00 Expected rate of return (a) 10.00%Earnings per share (b) $ 8.00

Solution:

a. = $125.00

b. $ 80.00

PVGO = $ 45.00

Stock price (P0)

Value of assets in place

=


Practice Problem 26

Construct a market-value balance sheet for FedEx, using the information in Table 7.1 and stock prices reported in Sections 7.1 and 7.2. Assume that market and book values are equal for current assets, current liabilities, and debt and other long-term liabilities. How much extra value shows up on the asset side of the balance sheet?

Table 7.1

SIMPLIFIED BALANCE SHEET FOR FEDEX, MAY 31, 2010(Millions of dollars)

Current assets $ 7,284.00 Current liabilities $ 4,645.00

$ 17,618.00 $ 6,446.00

Shareholders’ equity $13,811.00 $ 24,902.00 Total liabilities and equity $24,902.00

Shares of stock outstanding: 314.00 million

Table 7.2

Stock Price

FedEx $ 83.75 $ 43.98 1.90 Johnson & Johnson 58.29 19.19 3.00 Campbell Soup 36.97 3.23 11.40 PepsiCo 64.89 12.39 5.20 Walmart 51.20 17.49 2.90 Dow Chemical 25.59 14.22 1.80 Amazon 132.49 13.07 10.10 McDonald’s 74.54 12.34 6.00 American Electric Power 36.11 27.70 1.30 GE 15.01 10.66 1.40

Solution:

SIMPLIFIED MARKET VALUE BALANCE SHEET FOR FEDEXMay 31, 2010

(Millions of dollars)

Current assets $ 7,284.00 Current liabilities $ 4,645.00

$ 17,618.00 $ 6,446.00

Growth opportunities $ 12,486.50 Shareholders’ equity $26,297.50 $ 37,388.50 Total liabilities and equity $37,388.50

Plant, equipment and other long-term assets

Debt and other long-term liabilities

Book Value per

share

Market-to-Book-Value

Ratio

Plant, equipment and other long-term assets

Debt and other long-term liabilities


Construct a market-value balance sheet for FedEx, using the information in Table 7.1 and stock

current assets, current liabilities, and debt and other long-term liabilities. How much extra value


Practice Problem 27

Castles 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 the stock.

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 expected rate of return on the stock.

Rate of return 20.00%Plowback ratio 0.30 Earnings this year $ 4.00 Expected rate of return 12.00%Plowback ratio (b) 0.20 Plowback ratio (c) 0.00

Solution:

a. = 6.00%

= $ 46.67 P/E ratio = $11.667

b. = 4.00%

= $ 40.00 P/E ratio = $ 10.00

c. = 0.00%

= $ 33.33 Earnings-price ratio (E/P) = 12.00%

Growth rate (g)

Stock price (P0)

Growth rate (g)

Stock price (P0)

Growth rate (g)

Stock price (P0)


Practice Problem 28

Grandiose 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 rate 20.00% gDiscount rate 10.00% rEnd-of-year dividend $ 2.00 div.

Solution:

a. $ 2.00

= $1.818

$ 2.40

= $1.983

$ 2.88

= $2.164

b. This could not continue indefinitely. If it did, the stock would be worth an infinite amount.

DIV 1

PV of DIV 1

DIV 2

PV of DIV 2

DIV 3

PV of DIV 3


Practice Problem 29

Start-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 be reinvested in the firm.

a. What will be Start-Up’s 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 $200.00 millionReturn on equity 24.00%Rate of return 15.00%Plowback ratio 50.00%Rate on equity (b) 10.00%

Solution:

a. Earnings = $ 48.00 millionDividends = $ 24.00 million

= 12.00%Market value = $800.00 millionMarket-to-book ratio = 4

b. Earnings = $ 20.00 millionDividends = $ 10.00 million

= 5.00%Market value = $100.00 millionMarket-to-book ratio = 1/2

Growth rate (g)

Growth rate (g)


Practice Problem 30

Planned Obsolescence has a product that will be in vogue for 3 years, at which point the firm

$ 2.00 $ 2.50 $18.00

Discount Rate 12.00%

Solution:

= $16.59

will 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

DIV 2

DIV 3

Stock price (P0)


Practice Problem 31

Tattletale 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 rate 20.00%Last dividend paid $ 2.00 Discount rate 15.00%Steady growth rate (b) 4.00%

Solution:

a. = $ 2.40

b. = $ 2.40 = $ 2.88 = $ 3.456 = $32.675 = $28.021

DIV 1

DIV 1

DIV 2

DIV 3

Stock price (P3)

Stock price (P0)


Practice Problem 32

Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate 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 rate 20.00%Last dividend paid $ 2.00 Discount rate 15.00%Steady growth rate (b) 4.00%

Solution:

a. = $ 2.40 = $ 2.88 = $ 3.456

= $ 32.675 div4 /(r-g) steady growth= $ 28.021 PV0 discount= $ 29.825 PV0= (Div. +P1)/(1+r)

Capital gain = $ 1.804 P1=(1+r)*P0-Div. eller kalkylera diskonterad kassaflöde från period 2 och 3 plus horizon värde 29.825

b. Expected rate of return = 15.00% (dividend+capital gain)/stock price

DIV 1

DIV 2

DIV 3

Stock price (P3)Stock price (P0)Stock price (P1)

Div1 Div2


kassaflöde

eller kalkylera diskonterad kassaflöde från period 2 och 3 plus horizon värde

PHDiv2 Div3


Challenge Problem 40

Computer 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 company’s reinvested funds?

Reinvests 60.00% of earningsStock sells for $50.00 Next dividend $ 2.50 per shareDiscount rate 15.00%

Solution:

Return on equity = 16.67%



A 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 $ 2.00 Year 2 $ 4.00

Growth rate 5.00%Expected rate of return 12.00%

Solution:

a. = $ 60.00 = $52.806

b. = $57.143

c. = $52.806 = $57.143

12.00%

Stock price (P2)Stock price (P0)

Stock price (P1)

Stock price (P0)Stock price (P1)Dividend yield plus capital appreciation = r

=



Phoenix 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 firm’s investors expect to earn a return of 14% onthis stock, what must be its price?

Dividend per share $ 1.00 Expected dividends increase $ 1.00 Dividend in third year $ 3.00 Long-term growth rate 6.00%Expected return 14.00%

Solution:

= $39.75 = $31.27

Stock price (P3)

Stock price (P0)



Compost Science, Inc. (CSI), is in the business of converting Boston’s sewage sludge intofertilizer. The business is not in itself very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is 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 an investor 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. CSI’s plant willtherefore be expanded gradually over 5 years. This means that CSI will have to reinvest 80% of its earnings for 5 years. Starting in year 6, however, it will again be able to pay out 60% of earnings. What will be CSI’s stock price once this announcement is made and its consequences for CSI are known?

Return on investment 10.00%Expected dividend $ 4.00 Reinvestment 40.00% of earningsGrowth rate 4.00%Stock price (a) $100.00 Expansion plan (c) 5.00 yearsReinvestment (c) 80.00% of earningsPayout ratio 60.00% of earnings

Solution:

a. Expected rate of return = 8.00%

b. Expected rate of return 8.00%Earnings = $6.6667 No-growth value = $ 83.33 PVGO = $ 16.67

c. Years1 2 3 4 5 6

Earnings $ 6.67 $ 7.20 $ 7.78 $ 8.40 $ 9.07 $ 9.80 Plowback 0.80 0.80 0.80 0.80 0.80 0.40DIV $ 1.33 $ 1.44 $ 1.56 $ 1.68 $ 1.81 $ 5.88 g 0.08 0.08 0.08 0.08 0.08 0.04

Expected rate of return 8.00%Stock price (P6) $152.81

$106.17 Stock price (P0)



Better Mousetraps has come out with an improved product, and the world is beating a path to its 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 sustainable

a.

b. What is the expected stock price 4 years from now? The discount rate is 10%.

c. What is the stock price today?

d.

e.

f. What is the expected rate of return to an investor who buys the stock now and sells it in 1 year?

Projected growth 20.00%Time $ 4.00 yearsSustainable growth rate 5.00%

$ 1.00 per shareDiscount rate (b) 10.00%

Solution:

a. = $ 1.20

= $ 1.44

= $ 1.728

= $ 2.0736

b. = $ 2.0736

= $ 43.5456

c. = $ 1.20

= $ 1.44

= $ 1.728

= $ 2.0736

= $ 43.5456

= $ 34.738

d. $34.73779 Dividend yield = 3.45%

e. = $ 37.012

f. $ 34.738

$ 37.012

growth rate will fall to 5%. The most recent annual dividend was DIV0 = 1 per share.

What are the expected values of DIV1 , DIV2 , DIV3 , and DIV4 ?

Find the dividend yield, DIV1 / P0 .

What will next year’s stock price, P1, be?

Annual dividend (DIV 0)

DIV1

DIV2

DIV3

DIV4

DIV4

Stock price (P4)

DIV1

DIV2

DIV3

DIV4

Stock price (P4)

Stock price (P0)

Stock price (P0)

Stock price (P1)

Stock price (P0)

Stock price (P1)



Better Mousetraps has come out with an improved product, and the world is beating a path to its door. As a result, the firm projects growth of 20% per year for 4 years. By then, other firms will have copycat technology, competition will drive down profit margins, and the sustainable growth

a. Compute the value of Better Mousetraps for assumed sustainable growth rates of 6% through 9%, 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 growth 20.00%Time $ 4.00 yearsSustainable growth rate 5.00%

$ 1.00 per shareDiscount Rate (b) 10.00%Sustainable growth range 6.00% - 0.50%

Solution:

a.,b.

= $ 1.20 = $ 1.44 = $ 1.728 = $ 2.0736

= $ 54.95 = $ 42.53

5.00% 34.74 6.00% 42.53 22.42%6.50% 48.09 13.08%7.00% 55.51 15.43%7.50% 65.90 18.71%8.00% 81.48 23.64%8.50% 107.44 31.87%9.00% 159.37 48.33%

c. The percentage change in the value of the firm increases at a faster rate with each 1%

changes in g as the sustainable growth rate approaches the discount rate. The dividend growth model is less reliable as the sustainable growth rate approaches the discount rate.

rate will fall to 5%. The most recent annual dividend was DIV0 = 1 per share.

Annual dividend (DIV0)

DIV1

DIV2

DIV3

DIV4

Stock price (P4)Stock price (P0)

Sustainable Growth Rates

Intrinsic Value (PV)

% Change in PV

increase in the assumed final growth rate, g. The intrinsic value is more sensitive to

Capitulo 6 2 Parcial

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