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Chapter 13

Equity Valuation

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Good Company= Good stock?

Good Company Bad Company

Cheap stock Buy Avoid

Expensive stock Avoid Sell

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Fundamental Stock Analysis: Models of Equity Valuation

• Outline– Balance sheet appoach– Dividend Discount Models

• Constant dividend growth model• Non-constant dividend growth model

– Price/Earning Ratio models– Free Cash Flow(FCF) models

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Intrinsic Value and Market Price• Intrinsic Value

– The present value of all future cash flows– The true intrinsic value is not observable – Variety of models are used for estimation

• Market Price– Consensus value of current market participants

(buyers and sellers)– Price of last stock market transaction

• Trading Signal– IV > MP(discount, on sale) Buy– IV < MP(too expensive) Sell or Short Sell– IV = MP(fair) Hold

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Intrinsic Value and Market Price

• In the long-run, market price should converge to intrinsic value

• Remember: value(intrinsic) is what you get, price(market) is what you pay. Pay less, get more!

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Balance Sheet Valuation• A share of stock represents a slice of the

ownership( F assets are claims on real assets)– Claims of Equity (on balance sheet)

• Book Value: net worth of a company as reported on balance sheet

• However, BV and MV could be significantly different– BV represents past, while MV represents future– Stocks are also Claims of future Earnings and

Dividends.

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Balance Sheet Valuation

• BV is still relevant in stock valuation• Is BV a floor of stock price?

– BV(Equity)=Asset-Liability– When MV is much lower than BV, the whole

company can be sold at a higher price than MV– However, Asset can be overvalued (Goodwill). Net

tangible assets might be more useful.– Examples: BBI

• Should I be concerned if MV/BV is too high?– Rich evaluation invites competition– Competition and Tobin’s Q (MV/replacement cost)

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Book value and stock price: reality check

• Most stocks are sold at a price higher than book value

• Researches show that, on average and over long term, lower Price/Book stock has higher return – Higher Risk of low P/B stock– Investors chasing glamour stock(high P/B)

stock

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Dividend Discount Models:General Model

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

• V0 = Value of Stock• Dt = Dividend• k = required return

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No Growth Model

k

DVo

• Stocks that have earnings and dividends that are expected to remain constant

• Preferred Stock

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No Growth Model: Example

E1 = D1 = $5.00

k = .15

V0 = $5.00 / .15 = $33.33

VD

ko

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Constant growth stock

• A stock whose dividends are expected to grow forever at a constant rate, g.

D1 = D0 (1+g)1

D2 = D0 (1+g)2

Dt = D0 (1+g)t

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Constant Growth Model

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

• g = constant perpetual growth rate

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What happens if g > ks?

• If g > ks, the constant growth formula leads to a negative stock price, which does not make sense.

• The constant growth model can only be used if:– ks > g

– g is expected to be constant forever

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What is the stock’s market value?

• K=13%

• D0 = $2 and g is a constant 6%,

• Using the constant growth model:

$30.29

0.07

$2.12

0.06 - 0.13

$2.12

g - k

D P

s

10

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What would the expected price today be, if g = -5%?, if g=0?

• When g=-5% D1=1.9, P=1.9/(13%+5%)=10.56• When g=0, The dividend stream would be a

perpetuity.

2.00 2.002.00

0 1 2 3ks = 13% ...

$15.38 0.13

$2.00

k

PMT P

^

0

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Supernormal growth:What if g = 30% for 3 years before achieving long-run growth of 6%?

• Can no longer use just the constant growth model to find stock value.

• However, the growth does become constant after 3 years.

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Valuing common stock with nonconstant growth

rs = 13%

g = 30% g = 30% g = 30% g = 6%

P 0.06

$66.543

4.658

0.13

2.301

2.647

3.045

46.114

54.107 = P0

^

0 1 2 3 4

D0 = 2.00 2.600 3.380 4.394

...

4.658

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Nonconstant growth:What if g = 0% for 3 years before long-run growth of 6%?

ks = 13%

g = 0% g = 0% g = 0% g = 6%

0.06 $30.29P3

2.12

0.13

1.77

1.57

1.39

20.99

25.72 = P0

^

0 1 2 3 4

D0 = 2.00 2.00 2.00 2.00

...

2.12

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Practical problem with dividend model• How to estimate g

– Using historical average– When ROE and dividend payout ratio are

constant:– Dividend growth rate=Return on Equity*plowback ratio

– g=ROE* b

– Derive the relationship

» Dividend will grow the same rate as Earning (constant dividend payout ratio)

» Earning will grow at the same rate as Equity (constant ROE)

» Equity will grow at ROE*b

• How to estimate k

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Practical problem with dividend model

• Dividend model is forward looking. Inputs are future dividends, which are not observable

• Historical dividends and dividend growth rate are not an accurate estimates of future dividend growth rate

• Many companies are not paying dividends

• For those who pay, dividend growth rate can change dramatically overtime

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Price Earnings Ratios• What is P/E

– P/E=current stock price/annual earning per share– It measures how much investors are willing to pay

for $1 of current earnings– If earning is constant, P/E measures the number

of years for investor to breakeven– Earning yield, (E/P, the reverse/reciprocal of P/E)

measures your current return on investment– From 1920-1990, P/E average is about 15

• Uses– Relative valuation– Extensive Use in industry

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The simple P/E approach

• Current(trailing) PE approach:– Find E– Assign a reasonable P/E ratio– P=E*assigned P/E

• Forward PE approach– Find forward E– Assign a reasonable forward P/E ratio– Price target in the future=forward

E*assigned forward P/E

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P/E=?

• P/E Ratios are a function of two factors– Required Rates of Return (k)– Expected growth in Dividends

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Pitfalls in Using PE Ratios

• Investors make fatal mistakes when:– PE with abnormal once-only Es.– PE with skewed E due to GAAP (AAPL

subscription treatment of iPhone revenue)– Inflated PE: When earning is close to 0 – Negative PE

• Solution– Normalized PE– Forward PE (option vs. facts)

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Free Cash Flow (FCF):

• Def: Cash available to the firm (or equity holder) net of capital expenditures.

• Idea: FCF is the cash shareholder (investor) can withdraw from the company without affecting its normal operation and expansion

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FCF: Calculating

• FCFE=NI+Dep-Capital Expenditure-Increase in NWC

• Practically: Cash Flow from Operating Activity-Capital expenditure

• MV=PV of all Future FCF