50850909 valuation models

8/3/2019 50850909 Valuation Models

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Aswath Damodaran 1

Valuation Models

Aswath Damodaran


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Misconceptions about Valuation

Myth 1: A valuation is an objective search for true value

Truth 1.1: All valuations are biased. The only questions are how much

and in which direction.

Truth 1.2: The direction and magnitude of the bias in your valuation is

directly proportional to who pays you and how much you are paid.

Myth 2.: A good valuation provides a precise estimate of value

Truth 2.1: There are no precise valuations

Truth 2.2: The payoff to valuation is greatest when valuation is least

precise.

Myth 3: . The more quantitative a model, the better the valuation

Truth 3.1: Ones understanding of a valuation model is inversely

proportional to the number of inputs required for the model.

Truth 3.2: Simpler valuation models do much better than complex ones.


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Approaches to Valuation

Valuation Models

Asset BasedValuation

Discounted Ca shflowModels

Relat ive Valuation Contingent ClaimModels

LiquidationValue

ReplacementCost

Equity ValuationModels

Firm ValuationModels

Cost of capitalapproach

APVapproach

Excess ReturnModels

Stable

Two-stage

Three-stageor n- stage

Current

Normalized

Equity

Firm

Earnings BookValue

Revenues Sec tor specific

Sector

Market

Option todelay

Option toexpand

Option t oliquidate

Patent UndevelopedReserves

Youngfirms

Undevelopedland

Equity introubledfirm

Dividends

Free Cashflowto Firm


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Basis for all valuation approaches

The use of valuation models in investment decisions (i.e., in decisions

on which assets are under valued and which are over valued) are based

upon

a perception that markets are inefficient and make mistakes in assessing

value

an assumption about how and when these inefficiencies will get corrected

In an efficient market, the market price is the best estimate of value.

The purpose of any valuation model is then the justification of this

value.


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Discounted Cash Flow Valuation

What is it: In discounted cash flow valuation, the value of an asset is

the present value of the expected cash flows on the asset.

Philosophical Basis: Every asset has an intrinsic value that can be

estimated, based upon its characteristics in terms of cash flows, growth

and risk.

Information Needed: To use discounted cash flow valuation, you

need

to estimate the life of the asset

to estimate the cash flows during the life of the asset

to estimate the discount rate to apply to these cash flows to get present

value

Market Inefficiency: Markets are assumed to make mistakes in

pricing assets across time, and are assumed to correct themselves over

time, as new information comes out about assets.


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Discounted Cashflow Valuation: Basis forApproach

where CFt is the cash flow in period t, r is the discount rate appropriategiven the riskiness of the cash flow and t is the life of the asset.

Proposition 1: For an asset to have value, the expected cash flowshave to be positive some time over the life of the asset.

Proposition 2: Assets that generate cash flows early in their life will

be worth more than assets that generate cash flows later; the lattermay however have greater growth and higher cash flows tocompensate.

Value =CF

t

(1+r)t

t =1

t = n


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Generic DCF Valuation Model

Cash flowsFirm: Pre-debt cash

flowEquity: After debtcash flows

Expected GrowthFirm: Growth inOperating EarningsEquity: Growth inNet Income/EPS

CF1 CF2 CF3 CF4 CF5

Forever

Firm is in stable growth:Grows at constant rateforever

Terminal Value

CFn.........

Discount RateFirm:Cost of Capital

Equity: Cost of Equity

ValueFirm: Value of Firm

Equity: Value of Equity

DISCOUNTED CASHFLOW VALUATION

Length of Period of High Growth



DividendsEPS = 1.54 Eur * Payout Ratio 58.44%

DPS = 0.90 Eur

Expecte d Growth41.56% *16% = 6.65%

0.96 Eur 1.02 Eur 1.09 Eur 1.16 Eur 1.24 Eur

Forever

g =4%: ROE = 8.95%(=Cost of equity)Beta = 1.00Payout = (1- 4/8.95) = .553

Terminal Value= EPS6*Payout/(r-g)

= (2.21*.553)/(.0895-.04) = 24.69

.........

Cost of Equity4.95% + 0.95 (4%) = 8.75%

Discount atCost of Equity

Value of Equity pershare = 20.48 Eur

Risk free Rate:Long term bond r ate inEuros4.95% +

Beta0.95 X

Risk Premium4%

Average beta for European banks =0.95 Mature Market

4%Country Risk0%

VALUING ABN AMRO

RetentionRatio =41.56%

ROE = 16%

DPS

EPS 1.64 Eur 1.75 Eur 1.87 Eur 1.99 Eur 2.12 Eur



In this model the basic assumption is that dividends will grow at the same

rate into an indefinite future.

P0 = D(1+g)2 + D(1+g)2 + D(1+g)3 +..+D(1+g)N

1+r (1+r)2 (1+r )3 (1+r)n

When the period approaches to infinity eq takes form:

P0 = D1

r - g

CONSTANT GROWTH MODEL



Assumptions :

The firms dividend policy must be stable.

The firm will earn a stable return over there.

The analyst should predict 3 basic variables:

Next years dividend. Firms long term growth rate.

Required rate of return of the investor.



CONDITIONS FOR PURCHASE/SALE OFSTOCK

If

Theoretical value > Actual price = buy

Theoretical value < Actual price = sell



EXAMPLE

ABC Companys:

Expected dividend per share =

Rs 3.50 Growth rate of dividend=10%

Required rate of return= 15%

Market price = Rs 75

P0 = ?

P0 = D1

rg

D1 = 3.50

r = 0.15

g = 0.10

= 3.50

.05

= Rs 70

Thr< M.P, investor is advised not

to buy.


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TWO STAGE GROWTH MODEL

The growth stages are divided into two:

Period of extraordinary growth.

constant growth period of infinite nature.

The extra ordinary growth period will continue for some period followedby the constant growth rate.

Example: Information technology


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Present value of the stock or price=

present value of the dividend during the above normal growth period

present value of stock price at the end of the above normal growth period

P0 = ND0(1+gs)t + DN+1 X 1(1+rs)

t (rs - gn) (1+rs)N

DO = Dividend of the previous period

gs = Above normal growth rate

gn = Normal growth rate

rs = Required rate of return

N = Period of above normal-growth


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THE THREE-PHASE MODEL

Dividends are assumed to grow at a constant rate ga for a period of A years.After the phase A the growth rate of the dividend declines for A+1 yrsthrough out the phase B & the decline in the dividend rate would be linear.Afterwards there would be perpetual growth rate gn. Some times the gawould be less than gn & in the second phase there would be linear growthrate.

P0=AD0 (1+ga)t +BDt-1(1+gb) + DB(1+gn)

(1+r)t (1+r)t r-gn(1+r)B

D0 = Dividend of the previous period.

gs = Above normal growth rate.

gn = Normal growth rate

rs = Required rate of return

N = Period of above normal growth


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Choosing the right Discounted Cashflow Model

Can you estimate cash flows?

Yes No

Use dividenddiscount model

Is leverage stable orlikely to change overtime?

Stable

leverage

Unstable

leverage

Are the current earningspositive & normal?

Yes

Use currentearnings asbase

No

Is the causetemporary?

Yes No

Replace currentearnings withnormalizedearnings

Is the firmlikely tosurvive?

Yes No

Adjust

margins overtime to nursefirm to financialhealth

Does the firm

have a lot ofdebt?

YesNo

Value Equityas an optionto liquidate

Estimateliquidationvalue

What rate is the firm growingat currently?

< Growth rateof economy

Stable growthmodel

> Growth rate ofeconomy

Are the firms

competitiveadvantges timelimited?

Yes No

2-stagemodel

3-stage orn-stagemodel

FCFE FCFF


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An Example: Price Earnings Ratio: Definition

PE = Market Price per Share / Earnings per Share

There are a number of variants on the basic PE ratio in use. They are

based upon how the price and the earnings are defined.

Price: is usually the current priceis sometimes the average price for the year

EPS: earnings per share in most recent financial year

earnings per share in trailing 12 months (Trailing PE)

forecasted earnings per share next year (Forward PE)

forecasted earnings per share in future year


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Which approach should you use? Dependsupon the asset being valued..

Mature businessesSeparable & marketable assets

Growth businessesLinked and non-marketable asset

Liquidation &Replacement costvaluation

Other valuation models

Asset Marketability and Valuation Approaches

Cashflows currently orexpected in near future

Assets that will nevergenerate cashflows

Discounted cashflowor re lative valuationmodels

Relative valuation models

Cash Flows and Valuation Approaches

Cashflows if a contingencyoccurs

Option pricing models

Unique asset or businessLarge number of similarassets that are priced

Discounted cashflowor option pr icingmodels

Relative valuation models

Uniqueness of Asset and Valuation Approaches


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And the analyst doing the valuation.

Very short time horizonLong Time Horizon

Liquidation value Discounted Cashflow value

Investor Time Horizon and Valuation Approaches

Option pricingmodels

Relative valuation

Markets are correct onaverage but make mistakeson individual assets

Discounted Cashflow value

Views on market and Valuation Approaches

Option pricing models

Relative valuation

Markets make mistakes bucorrect them over time

Asset markets and financialmarkets may diverge

Liquidation value

50850909 valuation models

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