Valuing Common Stocks

Fundamentals of Corporate Finance Chapter 7 BMM

Finansiell ekonomi LiU2012

Keep in mind

• Present value concepts can be applied to the valuation of common stocks

• the relationship between stock price, earnings per share EPS and growth rate g

• learn the process of estimating the cost of equity

Learning objectives

1. Market Values, Book Values, and Liquidation Values

2. How to value Common Stocks3. Simplifying the Dividend Discount Model (the

discounted cash flow model)4. Growth Stocks and Income Stocks5. There Are No Free Lunches on Wall Street

Concepts and definitionsPrimary Market - Market for the sale of new securities

by corporations.

Secondary Market - Market in which previously issued securities are traded among investors.

Common Stock - Ownership shares in a publicly held corporation.

Some conceptsBook Value: Net worth of the firm according to the balance

sheet.Dividend: Periodic cash distribution from the firm to the

shareholders.P/E Ratio: Price per share divided by earnings per share.Earnings per share: EPS = Earnings/ number of sharesROE: return on equity= Earnings /Book value of equityNote, earnings =net income= årsresultat= vinst

Going concern value • The difference between a firm’s actual market

value and its’ liquidation value is the so called “going concern value.”

Market value-Liquidation Value = Going concern value

Liquidation Value Net proceeds that could be realized by selling

the firm’s assets and paying off its creditors.

Valuation of common stocksSingle period investment case• The (present) value of a common stock equals

the present value of dividends expected during the period plus the present value of the expected end-of-period price.

r

PDivP

1

Price 110

The present value of future cash flows from a stock is also called the Intrinsic value of the stock.

The DCF model: discounted cash flow method (Dividend Discount Model)

dividends) future dPV(expectePV(stock)

The value of any stock is the present value of its future cash flows. Dividends represent the future cash flows of the firm.

How Common Stocks Are Valued

Expected Return rThe percentage yield that an investor forecasts from a

specific investment over a set period of time.

Expected Return

rDiv P P

P1 1 0

0

Valuing Common Stocks

For a stock with no growth, and assuming the stock will exist indefinitely, we can value the stock as a PERPETUITY.

1 10

Div EPSPerpetuity P

r r

No growth means all earnings are paid to shareholders.

How Common Stocks Are Valued

Example: If Blue Sky is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00?

15.0100

1001105Return Expected

How Common Stocks Are ValuedThe price of any share of stock can be

thought of as the present value of the futures cash flows. For a stock the future cash flows are dividends and the ultimate sales price of the stock.

r

PDivP

1

Price 110

Present value of one period return

How Common Stocks Are Valued

Example - continued: Blue Sky price can be thought of as follows.

10015.1

1105Price 0

P

Valuing Common Stocks

Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).

PDiv

r g01

Given any combination of variables in the equation, you can solve for the unknown variable.

What is the value of the stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return. (note: suppose that Blue Sky invested 40% back to the company, the dividend becomes 5*60%=3.)

00.75$08.012.0

00.3$10

gr

DivP

Example: valuing stocks

Estimating the Cost of Equity Capital

Dividend Growth Rate can also be derived from applying the return on equity to the percentage of earnings plowed back into operations.

g = return on equity X plowback ratio

Valuing Common Stocks

Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

PDiv

r

Div

r

Div P

rH H

H01

12

21 1 1

( ) ( )

...( )

H - Time horizon for your investment.

How Common Stocks Are ValuedFormula

PDiv

r

Div

r

Div P

rH H

H01

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( ) ( )

...( )

HH

H

tt

t

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How Common Stocks Are Valued

ExampleBlue Sky is forecasted to pay a $5.00 dividend at the end of year one and a $5.50 dividend at the end of year two. At the end of the second year the stock will be sold for $121. If the discount rate is 15%, what is the price of the stock?

00.100$

)15.01(

12150.5

)15.01(

00.521

PV

PV

How Common Stocks Are Valued

ExampleCurrent forecasts are for Blue Sky to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

How Common Stocks Are ValuedExample

Current forecasts are for Blue Sky to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

00.75$

)12.01(

48.9450.3

)12.01(

24.3

)12.01(

00.3321

PV

PV

How Common Stocks Are Valued

Estimating the Cost of Equity CapitalExample – A stock was selling for $42.45 per

share at the start of 2012. Dividend payments for the next year were expected to be $1.68 a share. What is the dividend yield?

04.045.42

68.1Yield Dividend

Estimating the Cost of Equity Capital

Example - continued - Northwest Natural Gas stock was selling for $42.45 per share at the start of 2009. Dividend payments for the next year were expected to be $1.68 a share. What is the expected return, assuming a growth rate of 6.1%?

101.0

061.045.42

68.1

r

r

Estimating the Cost of Equity Capital

Required Return Measurements

0

1

P

Div YieldDividend

gP

Divr

gr

DivP

0

1

10 Restated

Estimating the Cost of Equity Capital

• Valuing Non-Constant Growth

HH

HH

r

P

r

Div

r

Div

r

DivPV

)1()1(...

)1()1( 22

11

gr

DivP H

H 1

The H period has a share value PH

it is evaluated as a growing perpetuity

Estimating the Cost of Equity Capital

Example – Phoenix produces dividends in three consecutive years of 0, 0.31, and 0.65, respectively. The dividend in year four is estimated to be .67 and should grow in perpetuity at 4%. Given a discount rate of 10%, what is the price of the stock?

13.9

)04.010.0(

67.0

)1.01(

1

)1.01(

65.0

)1.01(

31.0

)1.01(

03321

PV

Note here the discount factor is

1/(1+0,1)3

Stock Price and Earnings Per Share

• If a firm chooses to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.

Payout Ratio: Fraction of earnings paid out as dividends

Plowback Ratio: Fraction of earnings retained by the firm

The payout ratio= 1-Plowback ratio

Stock Price and Earnings Per ShareExample

Our company forecasts to pay a $8.33 dividend next year, which represents 100% of its earnings. This will provide investors with a 15% expected return. Instead, we decide to retain 40% of the earnings at the firm’s current return on equity of 25%. What is the value of the stock before and after the earnings distribution decision?

Example• Pay a $8.33 dividend next year, which represents 100% of its

earnings. a 15% expected return. • plowback 40% of the earnings at the firm’s current return

on equity of 25%. the value of the stock with and without growth:

56.55$15.0

33.80 P

No Growth With Growth

00.100$10.015.0

00.5

10.040.025.0

0

P

g

With growth of the equity, the price of the share worth more than before! 100-55,56=44,44

Stock Price and Earnings Per Share

Example - continuedIf the company did not plowback some earnings, the stock price would remain at $55.56. With the plowback, the price rose to $100.00.

The difference between these two numbers is called the Present Value of Growth Opportunities (PVGO).

44.44$56.5500.100 PVGORemain critical! The growth rate of dividend 10% would amount to huge payment after 10 year! Especially when it is close to the discount rate. (r-g should be larger than 0). The stock price will explode!

Stock Price and Earnings Per Share

Present Value of Growth Opportunities (PVGO): Net present value of a firm’s future investments.

Sustainable Growth Rate is the steady rate at which a firm can grow:

g = plowback ratio X return on equity.

1 1div divPVGO

r g r

Valuing a BusinessValuing a Business or Project

The value of a business or Project is usually computed as the discounted value of FCF out to a valuation horizon (H).

The valuation horizon is sometimes called the terminal value.

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 22

11

Valuing a BusinessValuing a Business or Project

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 22

11

PV (free cash flows) PV (horizon value)

Sustainable growth

• Long-term growth rate in dividends is a function of Plowback ratio and return on equity.

• Growth rate of equity=g• ROE= Earning/equity= (1+g)Earnings/(1+g)equityThe second year will have (1+g) Earnings to

distribute to shareholders. Keep the payout ratio constant, we will have an dividend growth (1+g).

No Free LunchesTechnical Analysts

Investors who attempt to identify undervalued stocks by searching for patterns in past stock prices.

Forecast stock prices based on the watching the fluctuations in historical prices (thus “wiggle watchers”)

No Free Lunches

Scatter Plot of NYSE Composite Index over two successive weeks.

Where’s the pattern?

Random Walk Theory

• Security prices change randomly, with no predictable trends or patterns.

• Statistically speaking, the movement of stock prices is random (skewed positive over the long term).

Random Walk Theory

$103.00

$100.00

$106.09

$100.43

$97.50

$100.43

$95.06

Coin Toss Game

Heads

Heads

Heads

Tails

Tails

Tails

Random Walk TheoryS&P 500 Five Year Trend?

or5 yrs of the Coin Toss Game?

80

130

180

Month

Lev

el

Random Walk TheoryS&P 500 Five Year Trend?

or5 yrs of the Coin Toss Game?

80

130

180

230

Month

Lev

el

Random Walk Theory

Last Month

This Month

Next Month

1,300

1,200

1,100

Market Index

Cycles disappear

once identified

Another ToolFundamental Analysts

Investors who attempt to find mispriced securities by analyzing fundamental information, such as accounting data and business prospects.

Research the value of stocks using NPV and other measurements of cash flow

Efficient Market Theory

Efficient Market - Market in which prices reflect all available information.

• Weak Form Efficiency– Market prices reflect all historical information

• Semi-Strong Form Efficiency– Market prices reflect all publicly available information

• Strong Form Efficiency– Market prices reflect all information, both public and

private

Efficient Market Theory

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24

2934

39

Days Relative to annoncement date

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lati

ve A

bn

orm

al R

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rn

(%)

Announcement Date

Market AnomaliesExisting Anomalies•The Earnings Announcement Puzzle•The New-Issue Puzzle

Old Anomalies•The Small Firm Effect•The January Effect•The PE Effect•The Neglected Firm Effect•The Value Line Effect

Behavioral Finance

• Attitudes towards risk• Beliefs about probabilities

Thank you! Problems? yinghong.chen@liu.se