11

88

Stock ValuationStock Valuation

22

Key Concepts and SkillsKey Concepts and Skills

Understand how stock prices depend on future Understand how stock prices depend on future dividends and dividend growthdividends and dividend growth

Be able to compute stock prices using the Be able to compute stock prices using the dividend growth modeldividend growth model

Understand how corporate directors are electedUnderstand how corporate directors are elected Understand how stock markets workUnderstand how stock markets work Understand how stock prices are quotedUnderstand how stock prices are quoted

33

Chapter OutlineChapter Outline

Common Stock ValuationCommon Stock Valuation Some Features of Common and Preferred Some Features of Common and Preferred

StocksStocks The Stock MarketsThe Stock Markets

44

Cash Flows for StockholdersCash Flows for Stockholders If you buy a share of stock, you can If you buy a share of stock, you can

receive cash in two waysreceive cash in two ways The company pays dividendsThe company pays dividends You sell your shares, either to another You sell your shares, either to another

investor in the market or back to the investor in the market or back to the companycompany

As with bonds, the price of the stock is As with bonds, the price of the stock is the present value of these expected cash the present value of these expected cash flows flows

55

One-Period ExampleOne-Period Example Suppose you are thinking of purchasing the Suppose you are thinking of purchasing the

stock of Moore Oil, Inc. and you expect it to stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. that you can sell the stock for $14 at that time. If you require a return of 20% on investments If you require a return of 20% on investments of this risk, what is the maximum you would be of this risk, what is the maximum you would be willing to pay?willing to pay? Compute the PV of the expected cash flowsCompute the PV of the expected cash flows Price = (14 + 2) / (1.2) = $13.33Price = (14 + 2) / (1.2) = $13.33 Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33

66

Two-Period ExampleTwo-Period Example Now what if you decide to hold the stock Now what if you decide to hold the stock

for two years? In addition to the dividend for two years? In addition to the dividend in one year, you expect a dividend of in one year, you expect a dividend of $2.10 in two years and a stock price of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how $14.70 at the end of year 2. Now how much would you be willing to pay?much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)22 = =

13.3313.33

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Three-Period ExampleThree-Period Example Finally, what if you decide to hold the stock for Finally, what if you decide to hold the stock for

three years? In addition to the dividends at the three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now stock price is expected to be $15.435. Now how much would you be willing to pay?how much would you be willing to pay? PV = 2 / 1.2 + 2.10 / (1.2)PV = 2 / 1.2 + 2.10 / (1.2)22 + (2.205 + 15.435) / + (2.205 + 15.435) /

(1.2)(1.2)33 = 13.33 = 13.33

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Developing The ModelDeveloping The Model

You could continue to push back the year You could continue to push back the year in which you will sell the stockin which you will sell the stock

You would find that the price of the stock You would find that the price of the stock is really just the is really just the present value of present value of allall expected future dividendsexpected future dividends

So, how can we estimate all future So, how can we estimate all future dividend payments?dividend payments?

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Estimating Dividends: Special Estimating Dividends: Special CasesCases

Constant dividendConstant dividend The firm will pay a constant dividend foreverThe firm will pay a constant dividend forever This is like preferred stockThis is like preferred stock The price is computed using the perpetuity formulaThe price is computed using the perpetuity formula

Constant dividend growthConstant dividend growth The firm will increase the dividend by a constant The firm will increase the dividend by a constant percentpercent

every periodevery period Supernormal growthSupernormal growth

Dividend growth is not consistent initially, but settles Dividend growth is not consistent initially, but settles down to constant growth eventuallydown to constant growth eventually

1010

Zero GrowthZero Growth

If dividends are expected at regular intervals forever, If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of then this is a perpetuity and the present value of expected future dividends can be found using the expected future dividends can be found using the perpetuity formulaperpetuity formula

PP00 = D / R = D / R

Suppose stock is expected to pay a $0.50 dividend every Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly quarter and the required return is 10% with quarterly compounding. What is the price?compounding. What is the price?

PP00 = .50 / (.1 / 4) = $20 = .50 / (.1 / 4) = $20

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Dividend Growth ModelDividend Growth Model Dividends are expected to grow at a constant Dividends are expected to grow at a constant

percent per period.percent per period. PP00 = D = D11 /(1+R) + D /(1+R) + D22 /(1+R) /(1+R)22 + D + D33 /(1+R) /(1+R)33 + … + …

PP00 = D = D00(1+g)/(1+R) + D(1+g)/(1+R) + D00(1+g)(1+g)22/(1+R)/(1+R)22 + +

DD00(1+g)(1+g)33/(1+R)/(1+R)33 + … + …

With a little algebra and some series work, this With a little algebra and some series work, this reduces to:reduces to:

g-R

D

g-R

g)1(DP 10

0

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DGM – Example 1DGM – Example 1

Suppose Big D, Inc. just paid a dividend of $.50. Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on year. If the market requires a return of 15% on assets of this risk, how much should the stock assets of this risk, how much should the stock be selling for?be selling for?

PP00 = .50(1+.02) / (.15 - .02) = $3.92 = .50(1+.02) / (.15 - .02) = $3.92

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DGM – Example 2DGM – Example 2

Suppose TB Pirates, Inc. is expected to Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the pay a $2 dividend in one year. If the dividend is expected to grow at 5% per dividend is expected to grow at 5% per year and the required return is 20%, what year and the required return is 20%, what is the price?is the price? PP00 = 2 / (.2 - .05) = $13.33 = 2 / (.2 - .05) = $13.33 Why isn’t the $2 in the numerator multiplied by Why isn’t the $2 in the numerator multiplied by

(1.05) in this example?(1.05) in this example?

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Stock Price Sensitivity to Stock Price Sensitivity to Dividend Growth, gDividend Growth, g

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Stoc

k P

rice

D1 = $2; R = 20%

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Stock Price Sensitivity to Stock Price Sensitivity to Required Return, RRequired Return, R

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25 0.3

Growth Rate

Stoc

k P

rice

D1 = $2; g = 5%

1616

Example 8.3 Gordon Growth Example 8.3 Gordon Growth Company - ICompany - I

Gordon Growth Company is expected to pay a Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are dividend of $4 next period and dividends are expected to grow at 6% per year. The required expected to grow at 6% per year. The required return is 16%.return is 16%.

What is the current price?What is the current price? PP00 = 4 / (.16 - .06) = $40 = 4 / (.16 - .06) = $40 Remember that we already have the dividend Remember that we already have the dividend

expected next year, so we don’t multiply the dividend expected next year, so we don’t multiply the dividend by 1+gby 1+g

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Example 8.3 – Gordon Growth Example 8.3 – Gordon Growth Company - IICompany - II

What is the price expected to be in year 4?What is the price expected to be in year 4? PP44 = D = D44(1 + g) / (R – g) = D(1 + g) / (R – g) = D55 / (R – g) / (R – g) PP44 = 4(1+.06) = 4(1+.06)44 / (.16 - .06) = 50.50 / (.16 - .06) = 50.50

What is the implied return given the change in price What is the implied return given the change in price during the four year period?during the four year period?

50.50 = 40(1+return)50.50 = 40(1+return)44; return = 6%; return = 6% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6%PV = -40; FV = 50.50; N = 4; CPT I/Y = 6%

The price grows at the same rate as the dividendsThe price grows at the same rate as the dividends

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Nonconstant Growth Problem Nonconstant Growth Problem StatementStatement

Suppose a firm is expected to increase Suppose a firm is expected to increase dividends by 20% in one year and by 15% in dividends by 20% in one year and by 15% in two years. After that dividends will increase at two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is dividend was $1 and the required return is 20%, what is the price of the stock?20%, what is the price of the stock?

Remember that we have to find the PV of Remember that we have to find the PV of allall expected future dividends.expected future dividends.

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Nonconstant Growth – Example Nonconstant Growth – Example SolutionSolution

Compute the dividends until growth levels offCompute the dividends until growth levels off DD11 = 1(1.2) = $1.20 = 1(1.2) = $1.20 DD22 = 1.20(1.15) = $1.38 = 1.20(1.15) = $1.38 DD33 = 1.38(1.05) = $1.449 = 1.38(1.05) = $1.449

Find the expected future priceFind the expected future price PP22 = D = D33 / (R – g) = 1.449 / (.2 - .05) = 9.66 / (R – g) = 1.449 / (.2 - .05) = 9.66

Find the present value of the expected future cash Find the present value of the expected future cash flowsflows

PP00 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2) = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)22 = 8.67 = 8.67

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Quick Quiz – Part IQuick Quiz – Part I What is the value of a stock that is What is the value of a stock that is

expected to pay a constant dividend of $2 expected to pay a constant dividend of $2 per year if the required return is 15%?per year if the required return is 15%?

What if the company starts increasing What if the company starts increasing dividends by 3% per year, beginning with dividends by 3% per year, beginning with the next dividend? The required return the next dividend? The required return stays at 15%.stays at 15%.

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Using the DGM to Find RUsing the DGM to Find R

Start with the DGM:Start with the DGM:

gP

D g

P

g)1(D R

Rfor solve and rearrange

g-R

D

g - R

g)1(DP

0

1

0

0

100

2222

Finding the Required Return - Finding the Required Return - ExampleExample

Suppose a firm’s stock is selling for $10.50. Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the expected to grow at 5% per year. What is the required return?required return? R = [1(1.05)/10.50] + .05 = 15%R = [1(1.05)/10.50] + .05 = 15%

What is the dividend yield?What is the dividend yield? 1(1.05) / 10.50 = 10%1(1.05) / 10.50 = 10%

What is the capital gains yield?What is the capital gains yield? g =5%g =5%

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Table 8.1 - Summary of Stock Table 8.1 - Summary of Stock ValuationValuation

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Features of Common StockFeatures of Common Stock Voting RightsVoting Rights Proxy votingProxy voting Classes of stockClasses of stock Other RightsOther Rights

Share proportionally in declared dividendsShare proportionally in declared dividends Share proportionally in remaining assets during Share proportionally in remaining assets during

liquidationliquidation Preemptive right – first shot at new stock issue to Preemptive right – first shot at new stock issue to

maintain proportional ownership if desiredmaintain proportional ownership if desired

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Dividend CharacteristicsDividend Characteristics Dividends are not a liability of the firm until a dividend Dividends are not a liability of the firm until a dividend

has been declared by the Boardhas been declared by the Board Consequently, a firm cannot go bankrupt for not Consequently, a firm cannot go bankrupt for not

declaring dividendsdeclaring dividends Dividends and TaxesDividends and Taxes

Dividend payments are not considered a business Dividend payments are not considered a business expense; therefore, they are not tax deductibleexpense; therefore, they are not tax deductible

The taxation of dividends received by individuals The taxation of dividends received by individuals depends on the holding perioddepends on the holding period

Dividends received by corporations have a minimum Dividends received by corporations have a minimum 70% exclusion from taxable income70% exclusion from taxable income

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Features of Preferred StockFeatures of Preferred Stock DividendsDividends

Stated dividend that must be paid before dividends Stated dividend that must be paid before dividends can be paid to common stockholderscan be paid to common stockholders

Dividends are not a liability of the firm and preferred Dividends are not a liability of the firm and preferred dividends can be deferred indefinitelydividends can be deferred indefinitely

Most preferred dividends are cumulative – any Most preferred dividends are cumulative – any missed preferred dividends have to be paid before missed preferred dividends have to be paid before common dividends can be paidcommon dividends can be paid

Preferred stock generally does not carry voting Preferred stock generally does not carry voting rightsrights

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Stock MarketStock Market Dealers vs. BrokersDealers vs. Brokers New York Stock Exchange (NYSE)New York Stock Exchange (NYSE)

Largest stock market in the worldLargest stock market in the world MembersMembers

• Own seats on the exchangeOwn seats on the exchange• Commission brokersCommission brokers• SpecialistsSpecialists• Floor brokersFloor brokers• Floor tradersFloor traders

OperationsOperations Floor activityFloor activity

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NASDAQNASDAQ Not a physical exchange – computer-based quotation Not a physical exchange – computer-based quotation

systemsystem Multiple market makersMultiple market makers Electronic Communications NetworksElectronic Communications Networks Three levels of informationThree levels of information

Level 1 – median quotes, registered representativesLevel 1 – median quotes, registered representatives Level 2 – view quotes, brokers & dealersLevel 2 – view quotes, brokers & dealers Level 3 – view and update quotes, dealers onlyLevel 3 – view and update quotes, dealers only

Large portion of technology stocksLarge portion of technology stocks

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Work the Web ExampleWork the Web Example

Electronic Communications Networks provide Electronic Communications Networks provide trading in NASDAQ securitiestrading in NASDAQ securities

INET allows the public to view the “order book” INET allows the public to view the “order book” in real timein real time

Click on the web surfer and visit The Island!Click on the web surfer and visit The Island!

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Reading Stock QuotesReading Stock Quotes

Sample QuoteSample Quote55.93 44.40 38.60 HarleyDav .84f 1.50 16 24726 54.25 1.18 55.93 44.40 38.60 HarleyDav .84f 1.50 16 24726 54.25 1.18

What information is provided in the stock What information is provided in the stock quote?quote?

Click on the web surfer to go to Bloomberg Click on the web surfer to go to Bloomberg for current stock quotes.for current stock quotes.

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Quick Quiz – Part IIQuick Quiz – Part II

You observe a stock price of $18.75. You expect You observe a stock price of $18.75. You expect a dividend growth rate of 5% and the most a dividend growth rate of 5% and the most recent dividend was $1.50. What is the required recent dividend was $1.50. What is the required return?return?

What are some of the major characteristics of What are some of the major characteristics of common stock?common stock?

What are some of the major characteristics of What are some of the major characteristics of preferred stock?preferred stock?

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End of ChapterEnd of Chapter

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Comprehensive ProblemComprehensive Problem XYZ stock currently sells for $50 per XYZ stock currently sells for $50 per

share. The next expected annual share. The next expected annual dividend is $2, and the growth rate is 6%. dividend is $2, and the growth rate is 6%. What is the expected rate of return on What is the expected rate of return on this stock?this stock?

If the required rate of return on this stock If the required rate of return on this stock were 12%, what would the stock price be, were 12%, what would the stock price be, and what would the dividend yield be?and what would the dividend yield be?