Equity Valuation

Equity Valuation ❂

Basic Types of Models • Balance sheet models • Dividend discount models • EPS (cashflow) discount models

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Modeling Framework • Deterministicdynamics • Stochastic dynamics

Fair Value vs Market Price ❂

Fair Value • Self assigned Value • Variety of models are used for estimation

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Market Price • Consensus value assessment by all market participants

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Trading Signal • FV > MP: Buy • FV < MP: Sell or Short Sell • FV = MP: Hold or Fairly Priced

Dividend Discount Models ❂

∞

Dt Vo = ∑ t t =1 (1 + k ) V0 = Value of Stock Dt = Dividend k = required return

No Growth Model ❂

D Vo = k

Where the stock has earnings and dividends that are expected to remain constant foreever.

Example: Preferred Stock

No Growth Model: Example ❂

D Vo = k E1 = D1 = $5.00 k = .15 Then, V0 = $5.00 / .15 = $33.33

Constant Growth Model ❂

Do (1 + g ) Vo = k−g

g = constant perpetual growth rate

Constant Growth Model: Example ❂

Do (1 + g ) Vo = k−g E1 = $5.00 b = 40% k = 15%

D1 = $3.00

(1-b) = 60% g = 8%

(b: EPS retention ratio)

V0 = 3.00 / (.15 - .08) = $42.86

Estimating Dividend Growth Rates ❂

g = ROE × b

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g = growth rate in dividends

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ROE = Return on Equity for the firm

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b = EPS retention rate (1- dividend payout ratio)

Partitioning Value: Growth and No Growth Components ❂

E1 Vo = +PVGO k Do (1 +g ) E1 PVGO = − ( k −g ) k

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PVGO = Present Value of Growth Opportunities

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E1 = Earnings Per Share for period 1

Partitioning Value: Example ROE = 20%

b = 40%

E1 = $5.00

D1 = $3.00

g = .20 x .40 = .08

or 8%

k = 15%

Partitioning Value: Example ❂

3 Vo = = $42.86 (.15−.08) 5 NGVo = = $33.33 .15 PVGO = $42.86 − $33.33 = $9.52 • Vo = value with growth • NGVo = no growth component value • PVGO = Present Value of Growth Opportunities

Multi-Period Dividend-Discount Model ❂

D D + V = (1+ k ) (1+ k ) 1

0

2

1

2

+P D ... + (1+ k ) N

PN = expected sales price of stock at time N N = number of years the stock is to be held

N N

Practical Difficulties with DDM ❂

Some firms do not pay dividends

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Can you forecast future dividends?

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Can you predict the terminal liquidation value Pn ?

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What about the discount rate k? (perhaps, the CAPM? The APT?)

Multi-Period Earnings-Discount Model ❂

(1 − b) E N + P N (1 − b) E1 (1 − b) E 2 + ... + V0= 1 2 N (1 + k ) (1 + k ) (1 + k )

PN = expected sales price of stock at time N N = number of years the stock is to be held

Practical Concerns with EDM ❂

EPS forecasts are available from I/B/E/S, First Call, Zacks, ….

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Dividend payout ratio (1-b) can be estimated, either based on cash dividend or dividend-in-kind

❂ But, what about Pn

and k?

P/E Ratios P0 d = E k − g

d: dividend payout ratio k: cost-of-capital (or, risk-adjusted discount rate) g: EPS growth rate

P/E Example k = 12.5% g = 9% Thus,

d = 40%

P/E = (1 - .60) / (.125 - .09) = 11.4

If E = $2.73, we have P = 11.4 X 2.73 =$31.14

Problems with P/E Ratios ❂

What is E ? • E = trailing 12-month EPS? • E = 12-month-forward EPS?

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What is g ? • g = average historical EPS growth? • g = expected next-yr EPS growth? • g = long-run EPS growth?