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ValuationValuationCurriculum designed for use with the Iowa Electronic Markets

by

Roger IgnatiusThomas A. Rietz

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Valuation: Lecture OutlineValuation: Lecture Outline

Principles of Valuation Discounted Dividend Models

Constant Dividend Model Constant Growth Model

Discounted Cash flow Model Market Multiple Models

P/E versus Past and Peers P/S versus Past and Peers P/CF versus Past and Peers

Summary

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Principles of ValuationPrinciples of Valuation

Book Value Depreciated value of assets minus outstanding

liabilities Liquidation Value

Amount that would be raised if all assets were sold independently

Market Value (P) Value according to market price of outstanding

stock Intrinsic Value (V)

NPV of future cash flows (discounted at investors’ required rate of return)

Intrinsic Valuation ProcedureIntrinsic Valuation Procedure

Asset Characteristics• Size of Future Cash flows• Time of Future Cash flows• Risk of Future Cash flows

Investor Characteristics• Assessment of Cash

flow Riskiness• Risk Preferences

Investors’ Required Rate of Return (k)

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Where Does the Discount Where Does the Discount Rate (k) Come From?Rate (k) Come From? CAPM: k = rf + xRP Beta () is estimated using historical data

and is available from many sources The risk free rate (rf) is the current

Treasury rate Typically the 3-mo rate, but other are

sometimes used The risk premium (RP) is a historical

average relative to the rf used

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Example: Estimating k for Example: Estimating k for Wal-Mart (WMT) on 4/27/01Wal-Mart (WMT) on 4/27/01 Inputs

Three month Treasury rate: 3.75% Historical average RP (1926-1996):

8.74% Beta for Dell (from MoneyCentral): 0.9

Computing k: CAPM: k = 0.0375 + 0.9x0.0874 =

11.62%

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6%

8%

10%

12%

14%

16%

18%

20%

22%

24%

26%

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Change in Input

Re

qu

ire

d R

etu

rn (

k)

fro

m C

AP

M Change in Risk FreeRate

Change in RiskPremium

Change in Beta(Scale ShowsChange / 10)

Sensitivity to CAPM InputsSensitivity to CAPM Inputs

Initial values:

Rf = 3.75%RP = 8.47%Beta = 1.5

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Discounted Dividend ModelsDiscounted Dividend Models

Dividends will be Forecast directly Assumed to be constant Assumed to grow at a constant rate or Some combination of the above

Stock pricing relationship:

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Constant Dividend (Zero Constant Dividend (Zero Growth Model) ModelGrowth Model) Model

If Dt is constant, then it is an ordinary perpetuity:

Stock pricing relationship:

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Example: Wal-Mart (4/27/01)Example: Wal-Mart (4/27/01)

The price of Wal-Mart was actually $52.83 Can you explain the difference?

41.2$1162.0

28.0$0

WMTP

The current (annual) dividend is: $0.28 According to the constant dividend (zero

growth) model:

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$0

$1

$2

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$6

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$8

$9

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Change in Dividend(Scale showsChange / 10)

Change in DiscountRate

Sensitivity to Constant Sensitivity to Constant Dividend Model InputsDividend Model Inputs

Initial values:

D0 = $0.50k = 12%

Why do a firm’s dividends Why do a firm’s dividends grow?grow? Because earnings grow. Why? Because of reinvested funds

Used to expand or to undertake new projects Used in positive NPV projects

Leads to Earnings growth Investments growth and Dividend growth

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Constant Growth ModelConstant Growth Model

If Dt grows at a constant rate, g, then it is a growth perpetuity:

gk

gD

gk

D

k

DP

tt

)1(

)1(01

1

10

Stock pricing relationship:

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How do You Estimate Growth How do You Estimate Growth (g)?(g)?

NOTE: Must have g<k in the long run!0

0

0

0

0

0

0

1

1

)1(

PD

PDk

ggP

gDg

P

Dk

Historical average Average analyst forecast Sustainable growth

g = (1-Payout Ratio)xROE Required return versus dividend yield:

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Estimating g for Wal-Mart Estimating g for Wal-Mart (4/27/01)(4/27/01)

What should it be? 1st 3 are too high b/c long run must have g<k Guess: 11%?

%03.11

83.52$28.0$1

83.52$28.0$1162.0

g

5 year historical average: 19.72% Average 5-year analyst forecast: 14.4% Sustainable growth

g = (1-0.17)x0.22 = 18.26% Required return versus dividend yield:

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Example: Wal-Mart (4/27/01)Example: Wal-Mart (4/27/01)

The price of Wal-Mart was actually $52.83 Notes:

Must have g<k in long run As gk, the price increases without bound

13.50$11.01162.0

11.128.0$0

P

Current (annual) dividend is: $0.28 If we use estimated growth of 11%:

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Change in Dividend(Scale showsChange / 10)

Change in DiscountRate

Growth Rate

Sensitivity to Constant Growth Sensitivity to Constant Growth Model InputsModel Inputs

Initial values:

D0 = $0.50k = 12%g = 6%

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Summary of Dividend Summary of Dividend Discount ModelsDiscount Models Represents the value of dividends

received by shareholders Requires

A discount rate (k) Dividends (D) Steady or zero growth (g, with g<k)

Trouble valuing Companies with D=0 Fast growing companies with g>k

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Discounted Cash Flow ModelDiscounted Cash Flow Model Shareholders receive or “own”:

1. Dividends2. Re-invested earnings The effects of re-invested earnings are

captured in dividend growth if a firm pays dividends and growth can be estimated

An alternative valuation comes from valuing cash flows available to stockholders directly

Useful for companies that pay no dividends

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What Constitutes Cash flows?What Constitutes Cash flows?

There is some debate over exactly what constitutes cash flows

The GAAP cash flow statement: CF = NI + depreciation – preferred

stock dividends This should represent CFs that are

either1. Paid out in common stock dividends or

2. Re-invested

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What Discount Rate Should What Discount Rate Should be used?be used? It depends on the definition of CFs

If CFs are defined as those available to all investors, WACC should be used

If CFs are defined as those available to common stockholders, k from CAPM should be used

We will use the latter

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Example: Estimating k for K-Example: Estimating k for K-Mart (K) on 4/27/01Mart (K) on 4/27/01 Inputs

Three month Treasury rate: 3.75% Historical average RP (1926-1996):

8.74% Beta for K-Mart (from MoneyCentral): 1

Computing k: CAPM: k = 0.0375 + 1x0.0874 = 12.49%

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How do You Estimate Growth How do You Estimate Growth (g)?(g)? CFs will also grow Use methods similar to dividend growth, but

Analysts forecasts are typically unavailable For many companies, dividend yield cannot be

used b/c there is no dividend Often, earnings or sales growth are used

Expenses and re-investment need to be relatively constant percentages of sales

NOTE: Must have g<k in the long run!

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Estimating g for K-Mart Estimating g for K-Mart (4/27/01)(4/27/01)

5 year sales growth: 2.35% Analysts’ 5 year earnings forecast: 10.3% Suppose, you believe K-Mart will not grow at all!

Dec-00 Dec-99 Dec-98 Dec-97 Dec-96

Net Income $ (244.00) $ 403.00 $ 518.00 $ 249.00 $ (220.00)Dep & Amort $1,460.00 $2,070.00 $1,762.00 $1,555.00 $1,427.00 Pref Div -$ -$ -$ -$ -$ Cashflow 1,216.00$ 2,473.00$ 2,280.00$ 1,804.00$ 1,207.00$ Growth -50.83% 8.46% 26.39% 49.46%Avg Growth: 8.37%

From the historical income statement:

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Example: K-Mart (4/27/01)Example: K-Mart (4/27/01)

The price of K-Mart was actually $9.82 What must the market be expecting for K-Mart’s growth

in the future?

01.20$00.01249.0

00.150.2$0

P

According to the last statements: CF = $1,216 million Shares = 486.5 million

CF/Share = $2.50 If we use estimated growth of 0.0%:

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Change in Cashflow(Scale showsChange / 10)

Change in DiscountRate

Growth Rate

Sensitivity to Constant Growth Sensitivity to Constant Growth Cash flow Model InputsCash flow Model Inputs

Initial values:

CF0 = $0.50k = 12%g = 6%

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Summary of Discounted Cash Summary of Discounted Cash flow Modelsflow Models Represents the value of cash flows available

to shareholders Requires

A discount rate (k) A reasonable measure of cash flows

o IMPORTANT: How much depreciation MUST be replaced ? Model assumes zero.

Steady or zero growth (g, with g<k) Trouble valuing

Companies with CF<0 Fast growing companies with g>k Companies with necessary replacement of

depreciated assets

Market MultiplesMarket Multiples

Valuations are derived by:1. Forecasting earnings, sales or cash

flows

2. Applying the company’s historical P/E, P/S or P/CF to forecast

3. Applying industry average P/E, P/S or P/CF to current inputs

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Why do P/E Ratios Make Why do P/E Ratios Make Sense?Sense?

A company with a payout less than 1 will grow and be valued at:

rE

P

r

E

r

DP

1110

1

0

1

1

1 1

E

PVGO

rE

PPVGO

r

EP

A company with a payout ratio of 1 will not grow and be valued at:

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Logic of Market Multiple Logic of Market Multiple ModelsModels Sales, earnings and cash flow drive profits,

growth and value P/S, P/E & P/CF ratios show the relationship

between price and these value drivers Firms within an industry have similar sales,

profit and cash flow patterns and similar required returns

Therefore, a reasonable value for a firm is its sales, earnings or cash flows times the respective industry ratio

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P/E Ratio ValuationP/E Ratio Valuation

If company “j” is “valued at industry ratios” relative to earnings:

j

jjj

E

PEP

0

011

i

i

Industry

jj

E

PAvgEP

0

000

If company “j” is “valued at historical ratios” relative to earnings:

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Example: Wal-Mart (4/27/01)Example: Wal-Mart (4/27/01)

Valued at historical P/E ratio: Analysts forecast next year’s earnings for WMT

at $1.58 WMT’s recent P/E was 37.7 Then: P = $1.58x37.7 = $59.57

Valued at industry average P/E ratio: This year, earnings for WMT were $1.40 The industry average P/E was 36.0 Then: P = $1.40x36.0 = $50.40

The price of Wal-Mart was actually $52.83

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Change in Earnings

Change BenchmarkP/E Ratio (Scaleshows Change / 10)

Sensitivity to P/E Multiple Sensitivity to P/E Multiple Model InputsModel Inputs

Initial values:

E1 = $1.50P/E = 35

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P/S Ratio ValuationP/S Ratio Valuation

Using current sales, a company “j” is “valued at industry ratios” relative to sales:

j

jjj

S

PSP

0

011

i

i

Industry

jj

S

PAvgSP

0

000

For companies w/o earnings, P/S is sometimes used

If you have a sales forecast, company “j” is “valued at historical ratios” relative to sales:

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Example: Amazon (4/27/01)Example: Amazon (4/27/01)

For the year ending 12/00 Sales = 2,762 million (income statement) Shares = 357.1 million (balance sheet)

Sales/Share = 2762/357.1 = 7.73 Industry average P/S = 3.46 So, using industry P/S Amazon should be

priced at: 3.46x7.73 = $26.76 The price of Amazon was actually $15.27

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Change in Sales

Change BenchmarkP/S Ratio (Scaleshows Change / 10)

Sensitivity to P/S Multiple Sensitivity to P/S Multiple Model InputsModel Inputs

Initial values:

S1 = $3.00P/S = 15

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P/CF Ratio ValuationP/CF Ratio Valuation

• Using current cash flow, company “j” is “valued at industry ratios” relative to cash flows:

j

jjj

CF

PCFP

0

011

i

i

Industry

jj

CF

PAvgCFP

0

000

• For companies w/o dividends, P/CF is sometimes used

• If you have a cash flow forecast, company “j” is “valued at historical ratios” relative to cash flows:

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Example: K-Mart (4/27/01)Example: K-Mart (4/27/01)

For the year ending 12/00 CF = 1,216 million (discussed previously) Shares = 486.5 million (balance sheet)

CF/Share = 1216/486.51 = 2.50 Industry average P/CF = 21.3 Using industry P/CF K-Mart should be

priced at: 21.3x2.50 = $53.24 The price of K-Mart was actually $9.82 Is K-Mart undervalued or in serious

trouble?

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$0

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Change in Cashflow

Change BenchmarkP/CF Ratio (Scaleshows Change / 10)

Sensitivity to P/CF Multiple Sensitivity to P/CF Multiple Model InputsModel Inputs

Initial values:CF = $1.00P/S = 30

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Summary of Market Multiples Summary of Market Multiples ModelsModels Valuations using historical and industry

ratios Provide useful benchmarks Useful when dividends and cash flows cannot

be discounted directly Can be compared to current ratios as a

measure of market sentiment Weaknesses

Misleading for firms that are changing rapidly or do not resemble the industry

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SummarySummary

• Discounted Dividend w/ dividends and

constant expected (possibly zero) growth in dividends

• Discounted Cash flow w/o dividends and

constant expected (possibly zero) growth in cash flows

• P/E, P/S and P/CF ratios Comparison with past

or industry

• Why several methods? Each has strengths

and weaknesses Different methods

useful in different situations

Each gives a different “take” on the value of the company’s stock

Provides a range of valuations instead of point estimates