Valuation in 30 minutes presentation

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Valuation in 30 minutes, giveor take a few…

Aswath Damodaran

www.damodaran.com

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Assets Liabilities

Debt

Equity

Fixed Claim on cash flowsLittle or No role in managementFixed MaturityTax Deductible

Residual Claim on cash flowsSignificant Role in management

Assets in Place

Growth Assets

Existing InvestmentsGenerate cashflows todayIncludes long lived (fixed) and

short-lived(workingcapital) assets

Expected Value that will becreated by future investments

Perpetual Lives

Equity valuation: Value just theequity claim in the business

DCF Choices: Equity Valuation versus FirmValuation

Firm Valuation: Value the entire business

Growth created by making newinvestments; function of amount and

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More generally… The value of any business is afunction of..

Efficiency GrowthGrowth generated byusing existing assetsbetter

Stable growth firm,with no or verylimited excess returns

Expected Growth during high growth period

Length of the high growth periodSince value creating growth requires excess returns,this is a function of- Magnitude of competitive advantages- Sustainability of competitive advantages

Cost of capital to apply to discounting cashflowsDetermined by- Operating risk of the company- Default risk of the company- Mix of debt and equity used in financing

Are you investing optimally for Determinants of Firm Valuefuture growth?

Growth from new investmentsHow well do you manage yourexisting investments/assets?

quality of investments

Cashflows from existing assets

Is there scope for moreefficient utilization of exstingassets?

Cashflows before debt payments,but after taxes and reinvestment tomaintain exising assets

Are you building on yourcompetitive advantages?

Are you using the rightamount and kind ofdebt for your firm?

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Estimating cash flows to a business

Cash flows can be measured to

All claimholders in the firm

EBIT (1- tax rate)- ( Capital Expenditures - Depreciation)- Change in non-cash working capital= Free Cash Flow to Firm (FCFF)

Just Equity Investors

Net Income- (Capital Expenditures - Depreciation)- Change in non-cash Working Capital- (Principal Repaid - New Debt Issues)- Preferred Dividend

Dividends+ Stock Buybacks

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Cost of Equity = Riskfree Rate+ Beta X (Risk Premium)

Has to be default free, inthe same currency as cashflows, and defined in sameterms (real or nominal) asthecash flows

Historical Premium1. Mature Equity Market Premium:Average premium earned bystocks over T.Bonds in U.S.2. Country risk premium =Country Default Spread* (σEquity/σCountry bond)

Implied PremiumBased on how equity ispriced todayand a simple valuationmodel

or

Cost of Capital = Cost of Equity (Equity/(Debt + Equity)) + Cost of Borrowing (1-t) (Debt/(Debt + Equity))

Cost of borrowing should be based upon(1) synthetic or actual bond rating(2) default spreadCost of Borrowing = Riskfree rate + Default spread

Marginal tax rate, reflectingtax benefits of debt

Weights should be market value weightsCost of equitybased upon bottom-upbeta

Cost of Capital: Weighted rate of return demanded by all investors

And discount rates…

Cost of Equity: Rate of Return demanded by equity investors

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Where does growth come from?

To grow, a company has to reinvest. How much it will have to reinvestdepends in large part on how fast it wants to grow and what type ofreturn it expects to earn on the reinvestment.

–  Reinvestment rate = Growth Rate/ Return on Capital

Expected Growth

Retention Ratio=1 - Dividends/NetIncome

Net Income

Return on EquityNet Income/Book Value ofEquity

X

Operating Income

ReinvestmentRate =(Net CapEx + Chg inWC/EBIT(1-t)

Return on Capital =EBIT(1-t)/Book Value ofCapital

X

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All good things come to an end… stablegrowth and beyond.."

No matter how great a company’s products and management are, twoforces operate to drag the company’s growth rate down towards thegrowth rate of the economy. The first is scale. As companies grow,they get larger, and as they get larger, it becomes more difficult togrow. The second is competition.

Both forces also operate to pull down the return on capital for acompany towards its cost of capital. Mature companies earn muchlower returns on capital, relative to their cost of capital.

From a mechanical standpoint, this effectively allows us to stopestimating cash flows at some point and estimate a terminal value, byassuming that cash flows will grow at a constant rate forever beyondthat point. The “mature” company that we visualize should have amature company’s cost of capital and a mature company’s return oncapital.

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Closing Thoughts on Valuation

Valuation is simple. We choose to make it complex.

The biggest enemies of good valuations are biases and preconceptionsthat you bring into the valuations.

You cannot value equity precisely. Be ready to be wrong and do nottake it personally.

Making a model bigger will not necessarily make it better.

Aswath Damodaran 6

Assets Liabilities

Debt

Equity



Assets in Place

Growth Assets




Perpetual Lives


DCF Choices: Equity Valuation versus Firm Valuation


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Assets Liabilities

Debt

Equity



Assets in Place

Growth Assets




Perpetual Lives


DCF Choices: Equity Valuation versus FirmValuation


Growth created by making newinvestments; function of amount and

3

More generally… The value of any business is afunction of..

Efficiency GrowthGrowth generated byusing existing assetsbetter

Stable growth firm,with no or verylimited excess returns

Expected Growth during high growth period

Length of the high growth periodSince value creating growth requires excess returns,this is a function of- Magnitude of competitive advantages- Sustainability of competitive advantages

Cost of capital to apply to discounting cashflowsDetermined by- Operating risk of the company- Default risk of the company- Mix of debt and equity used in financing

Are you investing optimally for Determinants of Firm Valuefuture growth?

Growth from new investmentsHow well do you manage yourexisting investments/assets?

quality of investments

Cashflows from existing assets

Is there scope for moreefficient utilization of exstingassets?

Cashflows before debt payments,but after taxes and reinvestment tomaintain exising assets

Are you building on yourcompetitive advantages?

Are you using the rightamount and kind ofdebt for your firm?

CFn

Aswath Damodaran 7

Cash flowsFirm: Pre-debt cashflowEquity: After debtcash flows

Firm: Growth inOperating EarningsEquity: Growth inNet Income/EPS

CF1 CF2 CF3 CF4 CF5

Forever

Firm is in stable growth:Grows at constant rateforever

Terminal Value

.........ValueFirm: Value of Firm

Equity: Value of Equity

Valuation with Infinite Life

DISCOUNTED CASHFLOW VALUATION

Expected Growth

Length of Period of High Growth

Discount RateFirm:Cost of Capital

Equity: Cost of Equity

FCFFn

Aswath Damodaran 8

Cashflow to FirmEBIT (1-t)- (Cap Ex - Depr)- Change in WC= FCFF

Expected GrowthReinvestment Rate* Return on Capital

FCFF1 FCFF2 FCFF3 FCFF4 FCFF5


Terminal Value= FCFF n+1/(r-gn)

.........

Cost of Equity Cost of Debt(Riskfree Rate+ Default Spread) (1-t)

WeightsBased on Market Value

Forever

Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))

Value of Operating Assets+ Cash & Non-op Assets= Value of Firm- Value of Debt= Value of Equity

Riskfree Rate :- No default risk- No reinvestment risk- In same currency andin same terms (real ornominal as cash flows

+Beta- Measures market risk X

Risk Premium- Premium for averagerisk investment

Type ofBusiness

OperatingLeverage

FinancialLeverage

Base EquityPremium

Country RiskPremium


Expected Growth

Aswath Damodaran 9

Terminal Value10= 7300/(.0808-.04) = 179,099

Cost of Equity11.70%

Cost of Debt(4.78%+..85%)(1-.35)= 3.66%

WeightsE = 90% D = 10%

Cost of Capital (WACC) = 11.7% (0.90) + 3.66% (0.10) = 10.90%

Op. Assets 94214+ Cash:- Debt=Equity-Options

12838272

87226479

Value/Share $ 74.33

Riskfree Rate:Riskfree rate = 4.78%

+Beta1.73 X

Risk Premium4%

Unlevered Beta forSectors: 1.59

Amgen: Status QuoReinvestment Rate60%

in EBIT (1-t).60*.16=.0969.6%

Return on Capital16%

Stable Growthg = 4%; Beta = 1.10;Debt Ratio= 20%; Tax rate=35%Cost of capital = 8.08%ROC= 10.00%;Reinvestment Rate=4/10=40%

Term Yr1689812167

48677300

Amgen was tradingat $63.65/share

First 5 yearsGrowth decreasesgradually to 4%

Debt ratio increases to 20%Beta decreases to 1.10

On May 11,2007,

D/E=11.06%

Year 1 2 3 4 5 6 7 8 9 10EBITEBIT (1-t)- Reinvestment= FCFF

$9,221$6,639$3,983$2,656

$11,195$7,276$4,366$2,911

$7,975$7,975$4,785$3,190

$8,741 $9,580 $10,392 $11,157 $11,853 $12,460 $12,958$8,741 $9,580 $10,392 $11,157 $11,853 $12,460 $12,958$5,244 $5,748 $5,820 $5,802 $5,690 $5,482 $5,183$3,496 $3,832 $4,573 $5,355 $6,164 $6,978 $7,775

Cap Ex = Acc Cap Ex(1218) +Acquisitions (3975) + R&D (2216)

Current Cashflow to FirmEBIT(1-t)= :7336(1-.28)= 6058- Nt CpX= 6443- Chg WC 37= FCFF - 423Reinvestment Rate = 6480/6058

=106.98%Return on capital = 18.26%

Expected Growth

Aswath Damodaran 10

Terminal Value10= 1717/(.0662-.0341) = 53546

Cost of Equity8.77%

Cost of Debt(3.41%+..35%)(1-.3654)= 2.39%

WeightsE = 98.6% D = 1.4%

Cost of Capital (WACC) = 8.77% (0.986) + 2.39% (0.014) = 8.68%

Op. Assets 31,615+ Cash: 3,018- Debt 558- Pension Lian 305- Minor. Int. 55=Equity 34,656-Options 180Value/Share106.12

Riskfree Rate:Euro riskfree rate = 3.41%

+Beta1.26 X

Risk Premium4%

Unlevered Beta forSectors: 1.25

SAP: Status QuoReinvestment Rate57.42%

in EBIT (1-t).5742*.1993=.114411.44%

Return on Capital19.93%

Stable Growthg = 3.41%; Beta = 1.00;Debt Ratio= 20%Cost of capital = 6.62%ROC= 6.62%; Tax rate=35%Reinvestment Rate=51.54%

Term Yr5451354318261717

Avg Reinvestmentrate = 36.94%

Current Cashflow to FirmEBIT(1-t) : 1414- Nt CpX 831- Chg WC - 19= FCFF 602Reinvestment Rate = 812/1414

=57.42%

SAP was trading at122 Euros/share

First 5 yearsGrowth decreasesgradually to 3.41%

Debt ratio increases to 20%Beta decreases to 1.00

On May 5, 2005,

YearEBITEBIT(1-t)- Reinvestm= FCFF

12,4831,576905671

22,7671,7561,008748

33,0831,9571,124833

43,4362,1811,252929

53,8292,4301,3951,035

64,2062,6691,5011,168

74,5522,8891,5911,298

84,8543,0801,6601,420

95,0973,2351,7051,530

105,2713,3451,7241,621

D/E=1.6%

+ Lambda0.10 X

Country RiskPremium2.50%

Aswath Damodaran 1

Discounted Cash Flow Valuation:Basics

Aswath Damodaran

∑

Aswath Damodaran 2

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

Value = t

t =n CF t

t = 1(1+r)

Aswath Damodaran 3

Equity Valuation versus Firm Valuation

n

n

Value just the equity stake in the business

Value the entire business, which includes, besides equity, the otherclaimholders in the firm

CF to Equityt

∑ (1+ k )t

Aswath Damodaran 4

I.Equity Valuation

n The value of equity is obtained by discounting expected cashflows to equity,i.e., the residual cashflows after meeting all expenses, tax obligations andinterest and principal payments, at the cost of equity, i.e., the rate of returnrequired by equity investors in the firm.

n

where,

CF to Equityt= Expected Cashflow to Equity in period t

ke = Cost of Equity

The dividend discount model is a specialized case of equity valuation, and thevalue of a stock is the present value of expected future dividends.

Value of Equity =t=n

t=1 e

CF to Firm t

∑ = t 1(1+WACC)t

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II. Firm Valuation

n The value of the firm is obtained by discounting expected cashflows tothe firm, i.e., the residual cashflows after meeting all operatingexpenses and taxes, but prior to debt payments, at the weightedaverage cost of capital, which is the cost of the different componentsof financing used by the firm, weighted by their market valueproportions.

where,

CF to Firmt = Expected Cashflow to Firm in period tWACC = Weighted Average Cost of Capital

Aswath Damodaran

Value of Firm =t=n

Aswath Damodaran 6

Firm Value and Equity Value

n

o

o

o

o

n

o

o

o

To get from firm value to equity value, which of the following wouldyou need to do?

Subtract out the value of long term debt

Subtract out the value of all debt

Subtract the value of all non-equity claims in the firm, that areincluded in the cost of capital calculation

Subtract out the value of all non-equity claims in the firm

Doing so, will give you a value for the equity which is

greater than the value you would have got in an equity valuation

lesser than the value you would have got in an equity valuation

equal to the value you would have got in an equity valuation

Aswath Damodaran 7

Cash Flows and Discount Rates

n Assume that you are analyzing a company with the following cashflows forthe next five years.

Int Exp (1-t)

$ 40

$ 40

$ 40

$ 40

$ 40

Year

1

2

3

4

5

Terminal Value

CF to Equity

$ 50

$ 60

$ 68

$ 76.2

$ 83.49

$ 1603.0

CF to Firm

$ 90

$ 100

$ 108

$ 116.2

$ 123.49

$ 2363.008n

n

Assume also that the cost of equity is 13.625% and the firm can borrow longterm at 10%. (The tax rate for the firm is 50%.)

The current market value of equity is $1,073 and the value of debt outstandingis $800.

Aswath Damodaran 8

Equity versus Firm Valuation

Method 1: Discount CF to Equity at Cost of Equity to get value of equity

n

n

Cost of Equity = 13.625%

PV of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 +76.2/1.136254 + (83.49+1603)/1.136255 = $1073

Method 2: Discount CF to Firm at Cost of Capital to get value of firm

Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%

WACC = 13.625% (1073/1873) + 5% (800/1873) = 9.94%

PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 +(123.49+2363)/1.09945 = $1873

n PV of Equity = PV of Firm - Market Value of Debt

= $ 1873 - $ 800 = $1073

Aswath Damodaran 9

First Principle of Valuation

n

n

Never mix and match cash flows and discount rates.

The key error to avoid is mismatching cashflows and discount rates,since discounting cashflows to equity at the weighted average cost ofcapital will lead to an upwardly biased estimate of the value of equity,while discounting cashflows to the firm at the cost of equity will yielda downward biased estimate of the value of the firm.

Aswath Damodaran 10

The Effects of Mismatching Cash Flows andDiscount Rates

Error 1: Discount CF to Equity at Cost of Capital to get equity valuePV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 +

(83.49+1603)/1.09945 = $1248

Value of equity is overstated by $175.

Error 2: Discount CF to Firm at Cost of Equity to get firm valuePV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 + 116.2/1.136254 +

(123.49+2363)/1.136255 = $1613

PV of Equity = $1612.86 - $800 = $813

Value of Equity is understated by $ 260.

Error 3: Discount CF to Firm at Cost of Equity, forget to subtract out debt, andget too high a value for equity

Value of Equity = $ 1613

Value of Equity is overstated by $ 540

Aswath Damodaran 11

Discounted Cash Flow Valuation: The Steps

n

n

n

n

n

Estimate the discount rate or rates to use in the valuation• Discount rate can be either a cost of equity (if doing equity valuation) or a

cost of capital (if valuing the firm)• Discount rate can be in nominal terms or real terms, depending upon

whether the cash flows are nominal or real• Discount rate can vary across time.

Estimate the current earnings and cash flows on the asset, to eitherequity investors (CF to Equity) or to all claimholders (CF to Firm)Estimate the future earnings and cash flows on the firm beingvalued, generally by estimating an expected growth rate in earnings.Estimate when the firm will reach “stable growth” and whatcharacteristics (risk & cash flow) it will have when it does.Choose the right DCF model for this asset and value it.

Aswath Damodaran 12

Cash flowsFirm: Pre-debt cashflowEquity: After debtcash flows

Firm: Growth inOperating EarningsEquity: Growth inNet Income/EPS

CF1 CF2 CF3 CF4 CF5

Forever


Terminal Value

CFn.........Value

Firm: Value of Firm

Equity: Value of Equity

Generic DCF Valuation Model


Expected Growth

Length of Period of High Growth

Discount RateFirm:Cost of Capital

Equity: Cost of Equity

Aswath Damodaran 13

DividendsNet Income* Payout Ratio= Dividends

Return on Equity

Dividend1 Dividend2 Dividend3 Dividend4

Forever


Terminal Value= Dividend n+1/(ke-gn)Dividend5 Dividendn.........

Discount at Cost of Equity

Cost of Equity

Value of Equity




Type ofBusiness

OperatingLeverage

FinancialLeverage

Base EquityPremium

Country RiskPremium

EQUITY VALUATION WITH DIVIDENDS

Expected GrowthRetention Ratio *

Aswath Damodaran 14

Cashflow to EquityNet Income- (Cap Ex - Depr) (1- DR)- Change in WC (!-DR)= FCFE

Expected GrowthRetention Ratio *Return on Equity

FCFE1 FCFE2 FCFE3 FCFE4

Forever


Terminal Value= FCFE n+1/(ke-gn)

FCFE5 FCFEn.........

Financing WeightsDebt Ratio = DR

Discount at Cost of Equity

Cost of Equity

Value of Equity




Type ofBusiness

OperatingLeverage

FinancialLeverage

Base EquityPremium

Country RiskPremium

EQUITY VALUATION WITH FCFE

Aswath Damodaran 15

Cashflow to FirmEBIT (1-t)- (Cap Ex - Depr)- Change in WC= FCFF

FCFF1 FCFF2 FCFF3 FCFF4 FCFF5


Terminal Value= FCFFn+1/(r-gn)

FCFFn.........

Cost of Equity Cost of Debt(Riskfree Rate+ Default Spread) (1-t)

WeightsBased on Market Value

Forever

Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))

Value of Operating Assets+ Cash & Non-op Assets= Value of Firm- Value of Debt= Value of Equity




Type ofBusiness

OperatingLeverage

FinancialLeverage

Base EquityPremium

Country RiskPremium

VALUING A FIRM

Expected GrowthReinvestment Rate* Return on Capital

Valuation in 30 minutes presentation

Economy & Finance

managementfixed

manage yourexisting

verylimited

growth inoperating

growth innet

high growth

unlevered

cash flowssignificant