Valuations - Damodaran

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Valuation: Lecture Note Packet 1

Intrinsic Valuation

Aswath Damodaran

Updated: January 2013

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The essence of intrinsic value

In intrinsic valuation, you value an asset based upon itsintrinsic characteristics.

For cash flow generating assets, the intrinsic value willbe a function of the magnitude of the expected cashflows on the asset over its lifetime and the uncertaintyabout receiving those cash flows.

Discounted cash flow valuation is a tool for estimatingintrinsic value, where the expected value of an asset is

written as the present value of the expected cash flowson the asset, with either the cash flows or the discountrate adjusted to reflect the risk.

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The two faces of discounted cash flow valuation

The value of a risky asset can be estimated by discounting theexpected cash flows on the asset over its life at a risk-adjusteddiscount rate:

where the asset has a n-year life, E(CFt) is the expected cash flow in period tand r is a discount rate that reflects the risk of the cash flows.

Alternatively, we can replace the expected cash flows with theguaranteed cash flows we would have accepted as an alternative(certainty equivalents) and discount these at the riskfree rate:

where CE(CFt) is the certainty equivalent of E(CFt) and rf is the riskfree rate.

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Risk Adjusted Value: Two Basic Propositions

If the value of an asset is the risk-adjusted present value of the cash flows:

The IT proposition: If IT does not affect the expected cash flows or the riskiness ofthe cash flows, IT cannot affect value.

The FOREVER LOSERproposition: For an asset to have value, the expected cashflows have to be positive some time over the life of the asset.

The ITS OKAYproposition: Assets that generate cash flows early in their life willbe worth more than assets that generate cash flows later; the latter may howeverhave greater growth and higher cash flows to compensate

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DCF Choices: Equity Valuation versus Firm

Valuation

Assets Liabilities

Assets in Place Debt

Equity

Fixed Claim on cash flows

Little or No role in managementFixed MaturityTax Deductible

Residual Claim on cash flowsSignificant Role in management

Perpetual Lives

Growth Assets

Existing Investments

Generate cashflows todayIncludes long lived (fixed) and

short-lived(workingcapital) assets

Expected Value that will becreated by future investments

Equity valuation: Value just the

equity claim in the business

Firm Valuation: Value the entire business

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Equity Valuation

Assets Liabilities


Equity

Discount rate reflects only thecost of raising equity financing

Growth Assets

Figure 5.5: Equity Valuation

Cash flows considered arecashflows from assets,after debt payments andafter making reinvestmentsneeded for future growth

Present value is value of just the equity claims on the firm

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Firm Valuation

Assets Liabilities


Equity

Discount rate reflects the costof raising both debt and equityfinancing, in proportion to theiruse

Growth Assets

Figure 5.6: Firm Valuation

Cash flows considered arecashflows from assets,prior to any debt paymentsbut after firm hasreinvested to create growthassets

Present value is value of the entire firm, and reflects the value ofall claims on the firm.

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Firm Value and Equity Value

To get from firm value to equity value, which of the followingwould you need to do?

a. Subtract out the value of long term debt

b. Subtract out the value of all debt

c.

Subtract the value of any debt that was included in the cost ofcapital calculation

d. Subtract out the value of all liabilities in the firm

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

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

b. lesser than the value you would have got in an equity valuationc. equal to the value you would have got in an equity valuation

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Cash Flows and Discount Rates

Assume that you are analyzing a company with the followingcashflows for the next five years.

Year CF to Equity Interest Exp (1-tax rate) CF to Firm

1 $ 50 $ 40 $ 90

2 $ 60 $ 40 $ 1003 $ 68 $ 40 $ 108

4 $ 76.2 $ 40 $ 116.2

5 $ 83.49 $ 40 $ 123.49

Terminal Value $ 1603.0 $ 2363.008

Assume also that the cost of equity is 13.625% and the firm canborrow long term at 10%. (The tax rate for the firm is 50%.)

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

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Equity versus Firm Valuation

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

Cost of Equity = 13.625%

Value 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

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

= $ 1873 - $ 800 = $1073

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First Principle of Valuation

Discounting Consistency Principle: Never mix and

match cash flows and discount rates.

Mismatching cash flows to discount rates is deadly.

Discounting cashflows after debt cash flows (equity cashflows) at the weighted average cost of capital will lead to

an upwardly biased estimate of the value of equity

Discounting pre-debt cashflows (cash flows to the firm) at

the cost of equity will yield a downward biased estimate ofthe value of the firm.

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The Effects of Mismatching Cash Flows and

Discount Rates

Error 1: Discount CF to Equity at Cost of Capital to get equityvalue PV 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 value PV 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 tosubtract out debt, and get too high a value for equity Value of Equity = $ 1613

Value of Equity is overstated by $ 540

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Discounted Cash Flow Valuation: The Steps

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 thecash 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 being valued,generally by estimating an expected growth rate in earnings.

Estimate when the firm will reach stable growthand what

characteristics (risk & cash flow) it will have when it does. Choose the right DCF model for this asset and value it.

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Generic DCF Valuation Model

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Same ingredients, different approaches

Input Dividend Discount

Model

FCFE (Potential

dividend) discount

model

FCFF (firm)

valuation model

Cash flow Dividend Potential dividends

= FCFE = Cash flows

after taxes,reinvestment needs

and debt cash

flows

FCFF = Cash flows

before debt

payments but afterreinvestment needs

and taxes.

Expected growth In equity income

and dividends

In equity income

and FCFE

In operating

income and FCFF

Discount rate Cost of equity Cost of equity Cost of capital

Steady state When dividends

grow at constant

rate forever

When FCFE grow at

constant rate

forever

When FCFF grow at

constant rate

forever

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Start easy: The Dividend Discount Model

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Moving on up: The potential dividendsor

FCFE model

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To valuing the entire business: The FCFF model

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DISCOUNTED CASH FLOWVALUATION: THE INPUTS

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Estimating Inputs: Discount Rates

While discount rates obviously matter in DCF valuation, theydont matter as much as most analysts think they do.

At an intuitive level, the discount rate used should beconsistent with both the riskiness and the type of cashflowbeing discounted. Equity versus Firm: If the cash flows being discounted are cash flows to

equity, the appropriate discount rate is a cost of equity. If the cashflows are cash flows to the firm, the appropriate discount rate is thecost of capital.

Currency: The currency in which the cash flows are estimated shouldalso be the currency in which the discount rate is estimated.

Nominal versus Real: If the cash flows being discounted are nominalcash flows (i.e., reflect expected inflation), the discount rate should benominal

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Risk in the DCF Model

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Not all risk is created equal

Estimation versus Economic uncertainty Estimation uncertainty reflects the possibility that you could have the wrong

modelor estimated inputs incorrectly within this model.

Economic uncertainty comes the fact that markets and economies can change overtime and that even the best models will fail to capture these unexpected changes.

Micro uncertainty versus Macro uncertainty Micro uncertainty refers to uncertainty about the potential market for a firms

products, the competition it will face and the quality of its management team.

Macro uncertainty reflects the reality that your firms fortunes can be affected bychanges in the macro economic environment.

Discrete versus continuous uncertainty Discrete risk: Risks that lie dormant for periods but show up at points in time.

(Examples: A drug working its way through the FDA pipeline may fail at some stageof the approval process or a company in Venezuela may be nationalized)

Continuous risk: Risks changes in interest rates or economic growth occurcontinuously and affect value as they happen.

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Risk and Cost of Equity: The role of the marginal

investor

While the notion that the cost of equity should be higher for riskierinvestments and lower for safer investments is intuitive, what riskshould be built into the cost of equity is the question.

While risk is usually defined in terms of the variance of actualreturns around an expected return, risk and return models in

finance assume that the risk that should be rewarded (and thusbuilt into the discount rate) in valuation should be the riskperceived by the marginal investor in the investment

Most risk and return models in finance also assume that themarginal investor is well diversified, and that the only risk that heor she perceives in an investment is risk that cannot be diversified

away (i.e, market or non-diversifiable risk). In effect, it is primarilyeconomic, macro, continuous risk that should be incorporated intothe cost of equity.

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The Cost of Equity: Competing Market Risk

Models

Model Expected Return Inputs Needed

CAPM E(R) = Rf + (Rm- Rf) Riskfree Rate

Beta relative to market portfolio

Market Risk Premium

APM E(R) = Rf + j (Rj- Rf) Riskfree Rate; # of Factors;Betas relative to each factor

Factor risk premiums

Multi E(R) = Rf + j (Rj- Rf) Riskfree Rate; Macro factors

factor Betas relative to macro factors

Macro economic risk premiums

Proxy E(R) = a + bj Yj Proxies

Regression coefficients

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The CAPM: Cost of Equity

Consider the standard approach to estimating cost

of equity:

Cost of Equity = Riskfree Rate + Equity Beta * (Equity Risk

Premium) In practice,

Government security rates are used as risk free rates

Historical risk premiums are used for the risk premium

Betas are estimated by regressing stock returns againstmarket returns

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I. A Riskfree Rate

On a riskfree asset, the actual return is equal to theexpected return. Therefore, there is no variance aroundthe expected return.

For an investment to be riskfree, then, it has to have

No default risk No reinvestment risk

1. Time horizon matters: Thus, the riskfree rates invaluation will depend upon when the cash flow isexpected to occur and will vary across time.

2. Not all government securities are riskfree: Somegovernments face default risk and the rates on bondsissued by them will not be riskfree.

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Test 1: A riskfree rate in US dollars!

In valuation, we estimate cash flows forever (or at

least for very long time periods). The right risk free

rate to use in valuing a company in US dollars would

bea. A three-month Treasury bill rate (0.1%)

b. A ten-year Treasury bond rate (2%)

c. A thirty-year Treasury bond rate (3%)

d. A TIPs (inflation-indexed treasury) rate (1%)

e. None of the above

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Test 2: A Riskfree Rate in Euros

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Test 3: A Riskfree Rate in Indian Rupees

The Indian government had 10-year Rupee bondsoutstanding, with a yield to maturity of about 8.5% onJanuary 1, 2012.

In January 2012, the Indian government had a local currency

sovereign rating of Baa3. The typical default spread (over adefault free rate) for Baa3 rated country bonds in early 2012was 2%. The riskfree rate in Indian Rupees is

a. The yield to maturity on the 10-year bond (8.5%)

b. The yield to maturity on the 10-year bond + Default spread (10.5%)

c. The yield to maturity on the 10-year bondDefault spread (6.5%)

d. None of the above

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Sovereign Default Spread: Three paths to the

same destination

Sovereign dollar or euro denominated bonds: Find sovereign bondsdenominated in US dollars, issued by emerging markets. Thedifference between the interest rate on the bond and the UStreasury bond rate should be the default spread. For instance, inJanuary 2012, the US dollar denominated 10-year bond issued bythe Brazilian government (with a Baa2 rating) had an interest rateof 3.5%, resulting in a default spread of 1.6% over the US treasuryrate of 1.9% at the same point in time. (On the same day, the ten-year Brazilian BR denominated bond had an interest rate of 12%)

CDS spreads: Obtain the default spreads for sovereigns in the CDSmarket. In January 2012, the CDS spread for Brazil in that market

was 1.43%. Average spread: For countries which dont issue dollar

denominated bonds or have a CDS spread, you have to use theaverage spread for other countries in the same rating class.

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Approach 1: Default spread from Government

BondsJanuary 2013

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Approach 2: CDS Spreads

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Approach 3: Typical Default Spreads: January

2013

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Getting to a risk free rate in a currency: Example

The Brazilian government bond rate in nominal reais inJanuary 2013 was 9.18%. To get to a riskfree rate in nominalreais, we can use one of three approaches. Approach 1: Government Bond spread

The 2020 Brazil bond, denominated in US dollars, has a spread of

0.74% over the US treasury bond rate. Riskfree rate in $R = 9.18% - 0.74% = 8.44%

Approach 2: The CDS Spread

The CDS spread for Brazil on January 1, 2013 was 1.42%.

Riskfree rate in $R = 9.18% - 1.42% = 7.76%

Approach 3: The Rating based spread Brazil has a Baa2 local currency rating from Moodys. The default

spread for that rating is 1.75%

Riskfree rate in $R = 9.18% - 1.75% = 7.43%

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No default free entity: Choices with riskfree

rates.

Estimate a range for the riskfree rate in local terms: Approach 1: Subtract default spread from local government bond rate:

Government bond rate in local currency terms - Default spread forGovernment in local currency

Approach 2: Use forward rates and the riskless rate in an index currency(say Euros or dollars) to estimate the riskless rate in the local currency.

Do the analysis in real terms (rather than nominal terms) using areal riskfree rate, which can be obtained in one of two ways from an inflation-indexed government bond, if one exists

set equal, approximately, to the long term real growth rate of the economyin which the valuation is being done.

Do the analysis in a currency where you can get a riskfree rate, sayUS dollars or Euros.

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Why do risk free rates vary across currencies?

January 2013 Risk free rates

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One more test on riskfree rates

In January 2013, the 10-year treasury bond rate in theUnited States was 1.76%, a historic low. Assume that youwere valuing a company in US dollars then, but werewary about the riskfree rate being too low. Which of the

following should you do?a. Replace the current 10-year bond rate with a more reasonable

normalized riskfree rate (the average 10-year bond rate overthe last 30 years has been about 4%)

b. Use the current 10-year bond rate as your riskfree rate but

make sure that your other assumptions (about growth andinflation) are consistent with the riskfree rate

c. Something else

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II. Equity Risk Premiums

The ubiquitous historical risk premium

The historical premium is the premium that stocks have historically

earned over riskless securities.

While the users of historical risk premiums act as if it is a fact (rather than

an estimate), it is sensitive to

How far back you go in history Whether you use T.bill rates or T.Bond rates

Whether you use geometric or arithmetic averages.

For instance, looking at the US:Arithmetic Average Geometric Average

Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds1928-2012 7.65% 5.88% 5.74% 4.20%

2.20% 2.33%

1962-2012 5.93% 3.91% 4.60% 2.93%

2.38% 2.66%

2002-2012 7.06% 3.08% 5.38% 1.71%

5.82% 8.11%

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The perils of trusting the past.

Noisy estimates: Even with long time periods of history,the risk premium that you derive will have substantialstandard error. For instance, if you go back to 1928(about 80 years of history) and you assume a standarddeviation of 20% in annual stock returns, you arrive at a

standard error of greater than 2%:Standard Error in Premium = 20%/80 = 2.26%

Survivorship Bias: Using historical data from the U.S.equity markets over the twentieth century does create a

sampling bias. After all, the US economy and equitymarkets were among the most successful of the globaleconomies that you could have invested in early in thecentury.

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Risk Premium for a Mature Market? Broadening

the sample

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Th i l t f ti ti dditi l


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The simplest way of estimating an additional

country risk premium: The country default spread

Default spread for country: In this approach, the countryequity risk premium is set equal to the default spread for thecountry, estimated in one of three ways: The default spread on a dollar denominated bond issued by the

country. Brazils 10 year $ denominated bond at the start of 2013 was

trading at an interest rate of 2.60%, a default spread of 0.84% over theUS treasury bond rate of 1.76%.

The ten year CDS spread for Brazil of 1.42%

Brazils sovereign local currency rating is Baa2. The default spread for aBaa2 rated sovereign is about 1.75%.

This default spread is added on to the mature market

premium to arrive at the total equity risk premium for Brazil,assuming a mature market premium of 5.80%. Country Risk Premium for Brazil = 1.75%

Total ERP for Brazil = 5.80% + 1.75% = 7.55%

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A ld d h i i h ddi i l


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A melded approach to estimating the additional

country risk premium

Country ratings measure default risk. While default risk premiumsand equity risk premiums are highly correlated, one would expectequity spreads to be higher than debt spreads.

Another is to multiply the bond default spread by the relativevolatility of stock and bond prices in that market. Using this

approach for Brazil in January 2013, you would get: Country Equity risk premium = Default spread on country bond* Country

Equity/ Country Bond Standard Deviation in Bovespa (Equity) = 21%

Standard Deviation in Brazil government bond = 14%

Default spread on C-Bond = 1.75%

Brazil Country Risk Premium = 1.75% (21%/14%) = 2.63% Brazil Total ERP = Mature Market Premium + CRP = 5.80% + 2.63% = 8.43%

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Country Risk PremiumsAndorra 1.95% 7.70%Austria 0.00% 5.75%

Belgium 1 20% 6 95%

Albania 6.75% 12.50%

Armenia 4 73% 10 48%


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Country Risk Premiums

July 2013

Black #: Total ERP

Red #: Country risk premium

AVG: GDP weighted average

Angola 5.40% 11.15%

Benin 8.25% 14.00%

Botswana 1.65% 7.40%

Burkina Faso 8.25% 14.00%

Cameroon 8.25% 14.00%

Cape Verde 6.75% 12.50%

Egypt 12.00% 17.75%Gabon 5.40% 11.15%

Ghana 6.75% 12.50%

Kenya 6.75% 12.50%

Morocco 4.13% 9.88%

Mozambique 6.75% 12.50%

Namibia 3.38% 9.13%

Nigeria 5.40% 11.15%

Rwanda 8.25% 14.00%

Senegal 6.75% 12.50%

South Africa 2.55% 8.30%

Tunisia 4.73% 10.48%Zambia 6.75% 12.50%

Africa 5.90% 11.65%

Belgium 1.20% 6.95%

Cyprus 16.50% 22.25%

Denmark 0.00% 5.75%

Finland 0.00% 5.75%

France 0.45% 6.20%

Germany 0.00% 5.75%

Greece 10.13% 15.88%

Iceland 3.38% 9.13%

Ireland 4.13% 9.88%

Isle of Man 0.00% 5.75%

Italy 3.00% 8.75%

Liechtenstein 0.00% 5.75%

Luxembourg 0.00% 5.75%

Malta 1.95% 7.70%

Netherlands 0.00% 5.75%

Norway 0.00% 5.75%

Portugal 5.40% 11.15%

Spain 3.38% 9.13%

Sweden 0.00% 5.75%

Switzerland 0.00% 5.75%Turkey 3.38% 9.13%

UK 0.45% 6.20%

W. Europe 1,.22% 6.97%

Argentina 10.13% 15.88%

Belize 14.25% 20.00%

Bolivia 5.40% 11.15%

Brazil 3.00% 8.75%

Chile 1.20% 6.95%

Colombia 3.38% 9.13%

Costa Rica 3.38% 9.13%

Ecuador 12.00% 17.75%

El Salvador 5.40% 11.15%

Guatemala 4.13% 9.88%Honduras 8.25% 14.00%

Mexico 2.55% 8.30%

Nicaragua 10.13% 15.88%

Panama 3.00% 8.75%

Paraguay 5.40% 11.15%

Peru 3.00% 8.75%

Suriname 5.40% 11.15%

Uruguay 3.38% 9.13%

Venezuela 6.75% 12.50%

Latin America 3.94% 9.69%

Canada 0.00% 5.75%

United States 0.00% 5.75%

North America 0.00% 5.75%

Armenia 4.73% 10.48%

Azerbaijan 3.38% 9.13%

Belarus 10.13% 15.88%

Bosnia 10.13% 15.88%

Bulgaria 3.00% 8.75%

Croatia 4.13% 9.88%

Czech Republic 1.43% 7.18%

Estonia 1.43% 7.18%

Georgia 5.40% 11.15%

Hungary 4.13% 9.88%

Kazakhstan 3.00% 8.75%

Latvia 3.00% 8.75%

Lithuania 2.55% 8.30%

Macedonia 5.40% 11.15%

Moldova 10.13% 15.88%

Montenegro 5.40% 11.15%

Poland 1.65% 7.40%

Romania 3.38% 9.13%

Russia 2.55% 8.30%

Serbia 5.40% 11.15%

Slovakia 1.65% 7.40%

Slovenia 4.13% 9.88%

Uganda 6.75% 12.50%

Ukraine 10.13% 15.88%

E. Europe/Russia 3.13% 8.88%

Bahrain 2.55% 8.30%

Israel 1.43% 7.18%

Jordan 6.75% 12.50%

Kuwait 0.90% 6.65%

Lebanon 6.75% 12.50%

Oman 1.43% 7.18%

Qatar 0.90% 6.65%

Saudi Arabia 1.20% 6.95%

UAE 0.90% 6.65%

Middle East 1.38% 7.13%

Australia 0.00% 5.75%

Cook Islands 6.75% 12.50%

New Zealand 0.00% 5.75%

Australia & NZ 0.00% 5.75%

Bangladesh 5.40% 11.15%

Cambodia 8.25% 14.00%

China 1.20% 6.95%

Fiji 6.75% 12.50%

Hong Kong 0.45% 6.20%

India 3.38% 9.13%

Indonesia 3.38% 9.13%

Japan 1.20% 6.95%

Korea 1.20% 6.95%

Macao 1.20% 6.95%

Malaysia 1.95% 7.70%

Mauritius 2.55% 8.30%

Mongolia 6.75% 12.50%

Pakistan 12.00% 17.75%

Papua NG 6.75% 12.50%

Philippines 4.13% 9.88%

Singapore 0.00% 5.75%

Sri Lanka 6.75% 12.50%

Taiwan 1.20% 6.95%

Thailand 2.55% 8.30%

Vietnam 8.25% 14.00%

Asia 1.77% 7.52%

F C t E it Ri k P i t


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From Country Equity Risk Premiums to

Corporate Equity Risk premiums

Approach 1: Assume that every company in the country is equallyexposed to country risk. In this case, E(Return) = Riskfree Rate + CRP + Beta (Mature ERP)

Implicitly, this is what you are assuming when you use the local Governmentsdollar borrowing rate as your riskfree rate.

Approach 2: Assume that a companys exposure to country risk is similar

to its exposure to other market risk. E(Return) = Riskfree Rate + Beta (Mature ERP+ CRP)

Approach 3: Treat country risk as a separate risk factor and allow firms tohave different exposures to country risk (perhaps based upon theproportion of their revenues come from non-domestic sales) E(Return)=Riskfree Rate+ (Mature ERP) + (CRP)

Mature ERP = Mature market Equity Risk Premium

CRP = Additional country risk premium

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A h 1 & 2 E ti ti t i k


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Approaches 1 & 2: Estimating country risk

premium exposure

Location based CRP: The standard approach in valuation is toattach a country risk premium to a company based upon itscountry of incorporation. Thus, if you are an Indian company,you are assumed to be exposed to the Indian country riskpremium. A developed market company is assumed to beunexposed to emerging market risk.

Operation-based CRP: There is a more reasonable modifiedversion. The country risk premium for a company can becomputed as a weighted average of the country risk

premiums of the countries that it does business in, with theweights based upon revenues or operating income. If acompany is exposed to risk in dozens of countries, you cantake a weighted average of the risk premiums by region.

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O ti b d CRP Si l M lti l


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Operation based CRP: Single versus Multiple

Emerging Markets

Single emerging market: Embraer, in 2004, reported that it derived 3% of

its revenues in Brazil and the balance from mature markets. The mature

market ERP in 2004 was 5% and Brazils CRP was 7.89%.

Multiple emerging markets: Ambev, the Brazilian-based beverage

company, reported revenues from the following countries during 2011.

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Extending to a multinational: Regional breakdown


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Extending to a multinational: Regional breakdown

Coca Colas revenue breakdown and ERP in 2012

Things to watch out for

1. Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia

2. Obscure aggregations including Eurasia and Oceania

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Two problems with these approaches..

Focus just on revenues: To the extent that revenues arethe only variable that you consider, when weighting riskexposure across markets, you may be missing otherexposures to country risk. For instance, an emergingmarket company that gets the bulk of its revenues

outside the country (in a developed market) may stillhave all of its production facilities in the emergingmarket.

Exposure not adjusted or based upon beta: To the extentthat the country risk premium is multiplied by a beta, weare assuming that beta in addition to measuringexposure to all other macro economic risk also measuresexposure to country risk.

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Approach 3: Estimate a lambda for country risk

Source of revenues: Other things remaining equal, acompany should be more exposed to risk in a country ifit generates more of its revenues from that country.

Manufacturing facilities: Other things remaining equal, afirm that has all of its production facilities in a riskycountryshould be more exposed to country risk thanone which has production facilities spread over multiplecountries. The problem will be accented for companiesthat cannot move their production facilities (mining andpetroleum companies, for instance).

Use of risk management products: Companies can useboth options/futures markets and insurance to hedgesome or a significant portion of country risk.

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Estimating Lambdas: The Revenue Approach

The easiest and most accessible data is on revenues. Most companies break theirrevenues down by region.

= % of revenues domesticallyfirm/ % of revenues domestically average firm Consider, for instance, Embraer and Embratel, both of which are incorporated and

traded in Brazil. Embraer gets 3% of its revenues from Brazil whereas Embratelgets almost all of its revenues in Brazil. The average Brazilian company gets about

77% of its revenues in Brazil: LambdaEmbraer = 3%/ 77% = .04

LambdaEmbratel = 100%/77% = 1.30

Note that if the proportion of revenues of the average company gets in themarket is assumed to be 100%, this approach collapses into the first one.,

There are two implications

A company

s risk exposure is determined by where it does business and not by where it islocated

Firms might be able to actively manage their country risk exposure

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A richer lambda estimate: Use stock returns and country


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A richer lambda estimate: Use stock returns and country

bond returns: Estimating a lambdafor Embraer in 2004

Embraer versus C Bond: 2000-2003

Return on C-Bond

20100-10-20-30

ReturnonEmbraer

40

20

0

-20

-40

-60

Embratel versus C Bond: 2000-2003

Return on C-Bond

20100-10-20-30

ReturnonEmbratel

100

80

60

40

20

0

-20

-40

-60

-80

ReturnEmbraer= 0.0195 + 0.2681ReturnC BondReturnEmbratel= -0.0308 + 2.0030ReturnC Bond

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Estimating a US Dollar Cost of Equity for


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Estimating a US Dollar Cost of Equity for

Embraer - September 2004

Assume that the beta for Embraer is 1.07, and that the US $ riskfree rateused is 4%. Also assume that the risk premium for the US is 5% and thecountry risk premium for Brazil is 7.89%. Finally, assume that Embraergets 3% of its revenues in Brazil & the rest in the US.

There are five estimates of $ cost of equity for Embraer: Approach 1: Constant exposure to CRP, Location CRP

E(Return) = 4% + 1.07 (5%) + 7.89% = 17.24%

Approach 2: Constant exposure to CRP, Operation CRP

E(Return) = 4% + 1.07 (5%) + (0.03*7.89% +0.97*0%)= 9.59%

Approach 3: Beta exposure to CRP, Location CRP

E(Return) = 4% + 1.07 (5% + 7.89%)= 17.79%

Approach 4: Beta exposure to CRP, Operation CRP

E(Return) = 4% + 1.07 (5% +( 0.03*7.89%+0.97*0%)) = 9.60%

Approach 5: Lambda exposure to CRP

E(Return) = 4% + 1.07 (5%) + 0.27(7.89%) = 11.48%%

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Valuing Emerging Market Companies with


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Valuing Emerging Market Companies with

significant exposure in developed markets

The conventional practice in investment banking is to add the countryequity risk premium on to the cost of equity for every emerging marketcompany, notwithstanding its exposure to emerging market risk. Thus, in2004, Embraer would have been valued with a cost of equity of 17-18%even though it gets only 3% of its revenues in Brazil. As an investor, whichof the following consequences do you see from this approach?

a. Emerging market companies with substantial exposure in developedmarkets will be significantly over valued by equity research analysts.

b. Emerging market companies with substantial exposure in developedmarkets will be significantly under valued by equity research analysts.

Can you construct an investment strategy to take advantage of themisvaluation? What would need to happen for you to make money of this

strategy?

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Implied Equity Premiums

Lets start with a general proposition. If you know the pricepaid for an asset and have estimates of the expected cashflows on the asset, you can estimate the IRR of these cashflows. If you paid the price, this is what you have priced theasset to earn (as an expected return).

If you assume that stocks are correctly priced in the aggregateand you can estimate the expected cashflows from buyingstocks, you can estimate the expected rate of return on stocksby finding that discount rate that makes the present valueequal to the price paid. Subtracting out the riskfree rate

should yield an implied equity risk premium. This implied equity premium is a forward looking number and

can be updated as often as you want (every minute of everyday, if you are so inclined).

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Implied Equity Premiums: January 2008

We can use the information in stock prices to back out how risk averse the market is and how much of a riskpremium it is demanding.

If you pay the current level of the index, you can expect to make a return of 8.39% on stocks (which is obtained bysolving for r in the following equation)

Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 8.39% - 4.02% = 4.37%

1468.36 =61.98

(1+ r)+

65.08

(1+ r)2+

68.33

(1+ r)3+

71.75

(1+ r)4+

75.34

(1+ r)5+

75.35(1.0402)

(r .0402)(1+ r)5

January 1, 2008S&P 500 is at 1468.364.02% of 1468.36 = 59.03

Between 2001 and 2007dividends and stock

buybacks averaged 4.02%of the index each year.

Analysts expect earnings to grow 5% a year for the next 5 years. Wewill assume that dividends & buybacks will keep pace..Last years cashflow (59.03) growing at 5% a year

After year 5, we will assume thatearnings on the index will grow at4.02%, the same rate as the entireeconomy (= riskfree rate).

61.98 65.08 68.33 71.75 75.34

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Implied Risk Premium Dynamics

Assume that the index jumps 10% on January 2 and that nothing elsechanges. What will happen to the implied equity risk premium?

a. Implied equity risk premium will increase

b. Implied equity risk premium will decrease

Assume that the earnings jump 10% on January 2 and that nothing else

changes. What will happen to the implied equity risk premium?a. Implied equity risk premium will increase


Assume that the riskfree rate increases to 5% on January 2 and thatnothing else changes. What will happen to the implied equity riskpremium?

a. Implied equity risk premium will increase


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A year that made a difference The implied


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A year that made a difference.. The implied

premium in January 2009

Year Market value of index Dividends Buybacks Cash to equity Dividend yield Buyback yield Total yield2001 1148.09 15.74 14.34 30.08 1.37% 1.25% 2.62%

2002 879.82 15.96 13.87 29.83 1.81% 1.58% 3.39%

2003 1111.91 17.88 13.70 31.58 1.61% 1.23% 2.84%

2004 1211.92 19.01 21.59 40.60 1.57% 1.78% 3.35%

2005 1248.29 22.34 38.82 61.17 1.79% 3.11% 4.90%

2006 1418.30 25.04 48.12 73.16 1.77% 3.39% 5.16%2007 1468.36 28.14 67.22 95.36 1.92% 4.58% 6.49%

2008 903.25 28.47 40.25 68.72 3.15% 4.61% 7.77%

Normalized 903.25 28.47 24.11 52.584 3.15% 2.67% 5.82%

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The Anatomy of a Crisis: Implied ERP from


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The Anatomy of a Crisis: Implied ERP from

September 12, 2008 to January 1, 2009

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An Updated Equity Risk Premium:

On January 1, 2013, the S&P 500 was at 1426.19, essentially unchangedfor the year. And it was a year of macro shockspolitical upheaval in the

Middle East and sovereign debt problems in Europe. The treasury bond

rate dropped below 2% and buybacks/dividends surged.

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Implied Premiums in the US: 1960-2012

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Implied Premium versus Risk Free Rate

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Equity Risk Premiums and Bond Default Spreads

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Equity Risk Premiums and Cap Rates (Real


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Equity Risk Premiums and Cap Rates (Real

Estate)

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Why implied premiums matter?

In many investment banks, it is common practice (especiallyin corporate finance departments) to use historical riskpremiums (and arithmetic averages at that) as risk premiumsto compute cost of equity. If all analysts in the departmentused the geometric average premium for 1928-2012 of 4.2%

to value stocks in January 2013, given the implied premium of5.78%, what were they likely to find?

a. The values they obtain will be too low (most stocks will lookovervalued)

b. The values they obtain will be too high (most stocks will look

under valued)c. There should be no systematic bias as long as they use the

same premium to value all stocks.

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Which equity risk premium should you use?

If you assume this Premium to use

Premiums revert back to historical norms

and your time period yields these norms

Historical risk premium

Market is correct in the aggregate or that

your valuation should be market neutral

Current implied equity risk premium

Marker makes mistakes even in the

aggregate but is correct over time

Average implied equity risk premium over

time.

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And the approach can be extended to emerging markets


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pp g g

Implied premium for the Sensex (September 2007)

Inputs for the computation Sensex on 9/5/07 = 15446

Dividend yield on index = 3.05%

Expected growth rate - next 5 years = 14%

Growth rate beyond year 5 = 6.76% (set equal to riskfree rate)

Solving for the expected return:

Expected return on stocks = 11.18% Implied equity risk premium for India = 11.18% - 6.76% =

4.42%

15446 =537.06

(1+ r)+

612.25

(1+ r)2+

697.86

(1+ r)3+

795.67

(1+ r)4+

907.07

(1+ r)5+

907.07(1.0676)

(r .0676)(1+ r)5

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Can country risk premiums change? Brazil CRP


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Can country risk premiums change? Brazil CRP

& Total ERP from 2000 to 2012

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Implied Equity Risk Premium comparison:


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Implied Equity Risk Premium comparison:

January 2008 versus January 2009

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Country ERP (1/1/08) ERP (1/1/09)

United States 4.37% 6.43%

UK 4.20% 6.51%

Germany 4.22% 6.49%Japan 3.91% 6.25%

India 4.88% 9.21%

China 3.98% 7.86%Brazil 5.45% 9.06%


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Th CAPM B t


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The CAPM Beta

The standard procedure for estimating betas is to regressstock returns (Rj) against market returns (Rm) -Rj = a + b Rm

where a is the intercept and b is the slope of the regression.

The slope of the regression corresponds to the beta ofthe stock, and measures the riskiness of the stock.

This beta has three problems:It has high standard error

It reflects the firms business mix over the period of the

regression, not the current mixIt reflects the firms average financial leverage over the periodrather than the current leverage.

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B t E ti ti Th N i P bl


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Beta Estimation: The Noise Problem

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B t E ti ti Th I d Eff t


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Beta Estimation: The Index Effect

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Stock-priced based solutions to the Regression


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p g

Beta Problem

Modify the regression beta by changing the index used to estimate the beta

adjusting the regression beta estimate, by bringing in informationabout the fundamentals of the company

Estimate the beta for the firm using

the standard deviation in stock prices instead of a regression againstan index

Relative risk = Standard deviation in stock prices for investment/Average standard deviation across all stocks

Estimate the beta for the firm from the bottom up without

employing the regression technique. This will require understanding the business mix of the firm

estimating the financial leverage of the firm

Imputed or implied beta (cost of equity) for the sector.

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Alt ti f l ti i k f it


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Alternative measures of relative risk for equity

Accounting risk measures: To the extent that you dont trust market-priced based measures of risk, you could compute relative risk measuresbased on Accounting earnings volatility: Compute an accounting beta or relative volatility

Balance sheet ratios: You could compute a risk score based upon accounting ratioslike debt ratios or cash holdings (akin to default risk scores like the Z score)

Proxies: In a simpler version of proxy models, you can categorize firmsinto risk classes based upon size, sectors or other characteristics.

Qualitative Risk Models: In these models, risk assessments are based atleast partially on qualitative factors (quality of management).

Debt based measures: You can estimate a cost of equity, based upon anobservable costs of debt for the company. Cost of equity = Cost of debt * Scaling factor

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D t i t f B t & R l ti Ri k


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Determinants of Betas & Relative Risk

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In a perfect world we would estimate the beta


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p

of a firm by doing the following

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Adjusting for operating leverage


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Adjusting for operating leverage

Within any business, firms with lower fixed costs (as apercentage of total costs) should have lower unleveredbetas. If you can compute fixed and variable costs foreach firm in a sector, you can break down the unleveredbeta into business and operating leverage components. Unlevered beta = Pure business beta * (1 + (Fixed costs/ Variable

costs))

The biggest problem with doing this is informational. It isdifficult to get information on fixed and variable costs forindividual firms.

In practice, we tend to assume that the operatingleverage of firms within a business are similar and usethe same unlevered beta for every firm.

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Adjusting for financial leverage


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Adjusting for financial leverage

Conventional approach: If we assume that debt carriesno market risk (has a beta of zero), the beta of equityalone can be written as a function of the unlevered betaand the debt-equity ratio

L= u(1+ ((1-t)D/E))

In some versions, the tax effect is ignored and there is no (1-t) inthe equation.

Debt Adjusted Approach: If beta carries market risk andyou can estimate the beta of debt, you can estimate thelevered beta as follows:

L= u(1+ ((1-t)D/E)) - debt(1-t) (D/E)

While the latter is more realistic, estimating betas for debt can bedifficult to do.

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Bottom up Betas


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Bottom-up Betas

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Why bottom up betas?


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Why bottom-up betas?

The standard error in a bottom-up beta will be significantlylower than the standard error in a single regression beta.Roughly speaking, the standard error of a bottom-up betaestimate can be written as follows:

Std error of bottom-up beta =

The bottom-up beta can be adjusted to reflect changes in thefirms business mix and financial leverage. Regression betasreflect the past.

You can estimate bottom-up betas even when you do nothave historical stock prices. This is the case with initial publicofferings, private businesses or divisions of companies.

Average Std Error across Betas

Number of firms in sample

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Bottom-up Beta: Firm in Multiple Businesses


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SAP in 2004

Approach 1: Based on business mix

SAP is in three business: software, consulting and training. We will

aggregate the consulting and training businesses

Business Revenues EV/Sales Value Weights Beta

Software $ 5.3 3.25 17.23 80% 1.30

Consulting $ 2.2 2.00 4.40 20% 1.05

SAP $ 7.5 21.63 1.25

Approach 2: Customer Base

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Embraers Bottom up Beta


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Embraer s Bottom-up Beta

Business Unlevered Beta D/E Ratio Levered betaAerospace 0.95 18.95% 1.07

Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (D/E Ratio)

= 0.95 ( 1 + (1-.34) (.1895)) = 1.07

Can an unlevered beta estimated using U.S. and Europeanaerospace companies be used to estimate the beta for a Brazilianaerospace company?

a. Yes

b. NoWhat concerns would you have in making this assumption?

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Gross Debt versus Net Debt Approaches


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Gross Debt versus Net Debt Approaches

Analysts in Europe and Latin America often take the difference betweendebt and cash (net debt) when computing debt ratios and arrive at verydifferent values.

For Embraer, using the gross debt ratio Gross D/E Ratio for Embraer = 1953/11,042 = 18.95%

Levered Beta using Gross Debt ratio = 1.07

Using the net debt ratio, we get Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity

= (1953-2320)/ 11,042 = -3.32%

Levered Beta using Net Debt Ratio = 0.95 (1 + (1-.34) (-.0332)) = 0.93

The cost of Equity using net debt levered beta for Embraer will be much

lower than with the gross debt approach. The cost of capital for Embraerwill even out since the debt ratio used in the cost of capital equation willnow be a net debt ratio rather than a gross debt ratio.

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The Cost of Equity: A Recap


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The Cost of Equity: A Recap

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88

Estimating the Cost of Debt


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Estimating the Cost of Debt

The cost of debt is the rate at which you can borrow atcurrently, It will reflect not only your default risk but also thelevel of interest rates in the market.

The two most widely used approaches to estimating cost ofdebt are:

Looking up the yield to maturity on a straight bond outstanding fromthe firm. The limitation of this approach is that very few firms havelong term straight bonds that are liquid and widely traded

Looking up the rating for the firm and estimating a default spreadbased upon the rating. While this approach is more robust, differentbonds from the same firm can have different ratings. You have to use a

median rating for the firm When in trouble (either because you have no ratings or

multiple ratings for a firm), estimate a synthetic rating foryour firm and the cost of debt based upon that rating.

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Estimating Synthetic Ratings


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Estimating Synthetic Ratings

The rating for a firm can be estimated using the financialcharacteristics of the firm. In its simplest form, the rating

can be estimated from the interest coverage ratio

Interest Coverage Ratio = EBIT / Interest Expenses

For Embraers interest coverage ratio, we used the

interest expenses from 2003 and the average EBIT from

2001 to 2003. (The aircraft business was badly affected

by 9/11 and its aftermath. In 2002 and 2003, Embraer

reported significant drops in operating income)

Interest Coverage Ratio = 462.1 /129.70 = 3.56

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Interest Coverage Ratios, Ratings and Default


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Spreads: 2003 & 2004

If Interest Coverage Ratio is Estimated Bond Rating Default Spread(2003) Default Spread(2004)> 8.50 (>12.50) AAA 0.75% 0.35%

6.50 - 8.50 (9.5-12.5) AA 1.00% 0.50%

5.50 - 6.50 (7.5-9.5) A+ 1.50% 0.70%

4.25 - 5.50 (6-7.5) A 1.80% 0.85%

3.00 - 4.25 (4.5-6) A 2.00% 1.00%

2.50 - 3.00 (4-4.5) BBB 2.25% 1.50%

2.25- 2.50 (3.5-4) BB+ 2.75% 2.00%

2.00 - 2.25 ((3-3.5) BB 3.50% 2.50%

1.75 - 2.00 (2.5-3) B+ 4.75% 3.25%

1.50 - 1.75 (2-2.5) B 6.50% 4.00%

1.25 - 1.50 (1.5-2) B 8.00% 6.00%

0.80 - 1.25 (1.25-1.5) CCC 10.00% 8.00%

0.65 - 0.80 (0.8-1.25) CC 11.50% 10.00%

0.20 - 0.65 (0.5-0.8) C 12.70% 12.00%

< 0.20 (


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Cost of Debt computations

Companies in countries with low bond ratings and high default riskmight bear the burden of country default risk, especially if they aresmaller or have all of their revenues within the country.

Larger companies that derive a significant portion of their revenuesin global markets may be less exposed to country default risk. Inother words, they may be able to borrow at a rate lower than the

government. The synthetic rating for Embraer is A-. Using the 2004 default

spread of 1.00%, we estimate a cost of debt of 9.29% (using ariskfree rate of 4.29% and adding in two thirds of the countrydefault spread of 6.01%):

Cost of debt= Riskfree rate + 2/3(Brazil country default spread) + Company defaultspread =4.29% + 4.00%+ 1.00% = 9.29%

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Synthetic Ratings: Some Caveats


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Synthetic Ratings: Some Caveats

The relationship between interest coverage ratios andratings, developed using US companies, tends to travelwell, as long as we are analyzing large manufacturingfirms in markets with interest rates close to the US

interest rate They are more problematic when looking at smaller

companies in markets with higher interest rates than theUS. One way to adjust for this difference is modify theinterest coverage ratio table to reflect interest rate

differences (For instances, if interest rates in anemerging market are twice as high as rates in the US,halve the interest coverage ratio.

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93

Default Spreads: The effect of the crisis of


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2008.. And the aftermath

Default spread over treasury

Rating 1-Jan-08 12-Sep-08 12-Nov-08 1-Jan-09 1-Jan-10 1-Jan-11

Aaa/AAA 0.99% 1.40% 2.15% 2.00% 0.50% 0.55%

Aa1/AA+ 1.15% 1.45% 2.30% 2.25% 0.55% 0.60%

Aa2/AA 1.25% 1.50% 2.55% 2.50% 0.65% 0.65%

Aa3/AA- 1.30% 1.65% 2.80% 2.75% 0.70% 0.75%

A1/A+ 1.35% 1.85% 3.25% 3.25% 0.85% 0.85%

A2/A 1.42% 1.95% 3.50% 3.50% 0.90% 0.90%A3/A- 1.48% 2.15% 3.75% 3.75% 1.05% 1.00%

Baa1/BBB+ 1.73% 2.65% 4.50% 5.25% 1.65% 1.40%

Baa2/BBB 2.02% 2.90% 5.00% 5.75% 1.80% 1.60%

Baa3/BBB- 2.60% 3.20% 5.75% 7.25% 2.25% 2.05%

Ba1/BB+ 3.20% 4.45% 7.00% 9.50% 3.50% 2.90%

Ba2/BB 3.65% 5.15% 8.00% 10.50% 3.85% 3.25%

Ba3/BB- 4.00% 5.30% 9.00% 11.00% 4.00% 3.50%

B1/B+ 4.55% 5.85% 9.50% 11.50% 4.25% 3.75%

B2/B 5.65% 6.10% 10.50% 12.50% 5.25% 5.00%

B3/B- 6.45% 9.40% 13.50% 15.50% 5.50% 6.00%

Caa/CCC+ 7.15% 9.80% 14.00% 16.50% 7.75% 7.75%

ERP 4.37% 4.52% 6.30% 6.43% 4.36% 5.20%

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Updated Default Spreads - January 2013


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Updated Default Spreads January 2013

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Rating 1 year 5 year 10 year 30 yearAaa/AAA 0.04% 0.16% 0.41% 0.65%

Aa1/AA+ 0.07% 0.35% 0.57% 0.84%

Aa2/AA 0.09% 0.53% 0.73% 1.03%

Aa3/AA- 0.12% 0.58% 0.78% 1.09%

A1/A+ 0.15% 0.62% 0.82% 1.15%

A2/A 0.36% 0.77% 0.95% 1.23%

A3/A- 0.41% 1.04% 1.31% 1.74%

Baa1/BBB+ 0.63% 1.28% 1.55% 1.99%

Baa2/BBB 0.81% 1.53% 1.84% 2.33%

Baa3/BBB- 1.29% 1.98% 2.28% 2.74%

Ba1/BB+ 2.07% 2.78% 3.12% 3.56%

Ba2/BB 2.85% 3.58% 3.97% 4.39%

Ba3/BB- 3.63% 4.38% 4.81% 5.21%

B1/B+ 4.41% 5.18% 5.65% 6.03%

B2/B 5.19% 5.98% 6.49% 6.85%

B3/B- 5.97% 6.78% 7.34% 7.68%

Caa/CCC+ 6.75% 7.57% 8.18% 8.50%

Subsidized Debt: What should we do?


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Subsidized Debt: What should we do?

Assume that the Brazilian government lends money toEmbraer at a subsidized interest rate (say 6% in dollar

terms). In computing the cost of capital to value

Embraer, should be we use the cost of debt based upon

default risk or the subisidized cost of debt?a. The subsidized cost of debt (6%). That is what the

company is paying.

b. The fair cost of debt (9.25%). That is what the company

should require its projects to cover.

c. A number in the middle.

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Weights for the Cost of Capital Computation


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Weights for the Cost of Capital Computation

In computing the cost of capital for a publicly tradedfirm, the general rule for computing weights for debt

and equity is that you use market value weights (and

not book value weights). Why?

a. Because the market is usually right

b. Because market values are easy to obtain

c. Because book values of debt and equity are meaningless

d. None of the above

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Estimating Cost of Capital: Embraer in 2004


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Estimating Cost of Capital: Embraer in 2004

Equity Cost of Equity = 4.29% + 1.07 (4%) + 0.27 (7.89%) = 10.70%

Market Value of Equity =11,042 million BR ($ 3,781 million)

Debt Cost of debt = 4.29% + 4.00% +1.00%= 9.29%

Market Value of Debt = 2,083 million BR ($713 million)

Cost of Capital

Cost of Capital = 10.70 % (.84) + 9.29% (1- .34) (0.16)) = 9.97% The book value of equity at Embraer is 3,350 million BR.

The book value of debt at Embraer is 1,953 million BR; Interestexpense is 222 mil BR; Average maturity of debt = 4 years

Estimated market value of debt = 222 million (PV of annuity, 4 years,9.29%) + $1,953 million/1.09294= 2,083 million BR

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If you had to do it.Converting a Dollar Cost of

l l l f l


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Capital to a Nominal Real Cost of Capital

Approach 1: Use a BR riskfree rate in all of the calculationsabove. For instance, if the BR riskfree rate was 12%, the costof capital would be computed as follows: Cost of Equity = 12% + 1.07(4%) + 27 (7. %) = 18.41%

Cost of Debt = 12% + 1% = 13%

(This assumes the riskfree rate has no country risk premiumembedded in it.)

Approach 2: Use the differential inflation rate to estimate thecost of capital. For instance, if the inflation rate in BR is 8%and the inflation rate in the U.S. is 2%

Cost of capital=

= 1.0997 (1.08/1.02)-1 = 0.1644 or 16.44%

(1+Cost of Capital$) 1+ InflationBR

1+ Inflation$

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Dealing with Hybrids and Preferred Stock


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Dealing with Hybrids and Preferred Stock

When dealing with hybrids (convertible bonds, forinstance), break the security down into debt and equityand allocate the amounts accordingly. Thus, if a firm has$ 125 million in convertible debt outstanding, break the$125 million into straight debt and conversion optioncomponents. The conversion option is equity.

When dealing with preferred stock, it is better to keep itas a separate component. The cost of preferred stock isthe preferred dividend yield. (As a rule of thumb, if the

preferred stock is less than 5% of the outstanding marketvalue of the firm, lumping it in with debt will make nosignificant impact on your valuation).

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Decomposing a convertible bond


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Decomposing a convertible bond

Assume that the firm that you are analyzing has $125million in face value of convertible debt with a stated

interest rate of 4%, a 10 year maturity and a market

value of $140 million. If the firm has a bond rating of A

and the interest rate on A-rated straight bond is 8%, youcan break down the value of the convertible bond into

straight debt and equity portions.

Straight debt = (4% of $125 million) (PV of annuity, 10 years, 8%)

+ 125 million/1.0810 = $91.45 million Equity portion = $140 million - $91.45 million = $48.55 million

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Recapping the Cost of Capital


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Recapping the Cost of Capital

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II. ESTIMATING CASH FLOWS

Cash is king

Steps in Cash Flow Estimation


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Steps in Cash Flow Estimation

Estimate the current earnings of the firm If looking at cash flows to equity, look at earnings after interest

expenses - i.e. net income

If looking at cash flows to the firm, look at operating earnings aftertaxes

Consider how much the firm invested to create future growth If the investment is not expensed, it will be categorized as capital

expenditures. To the extent that depreciation provides a cash flow, itwill cover some of these expenditures.

Increasing working capital needs are also investments for future

growth

If looking at cash flows to equity, consider the cash flows fromnet debt issues (debt issued - debt repaid)

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Measuring Cash Flows


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g

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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Measuring Cash Flow to the Firm


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g

EBIT ( 1 - tax rate)

- (Capital Expenditures - Depreciation)

- Change in Working Capital

= Cash flow to the firm Where are the tax savings from interest payments in

this cash flow?

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From Reported to Actual Earnings


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p g

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I. Update Earnings


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p g

When valuing companies, we often depend upon financialstatements for inputs on earnings and assets. Annual reports areoften outdated and can be updated by using- Trailing 12-month data, constructed from quarterly earnings reports.

Informal and unofficial news reports, if quarterly reports are unavailable.

Updating makes the most difference for smaller and more volatilefirms, as well as for firms that have undergone significantrestructuring.

Time saver: To get a trailing 12-month number, all you need is one10K and one 10Q (example third quarter). Use the Year to datenumbers from the 10Q:

Trailing 12-month Revenue = Revenues (in last 10K) - Revenues from first 3quarters of last year + Revenues from first 3 quarters of this year.

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II. Correcting Accounting Earnings


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g g g

Make sure that there are no financial expenses mixed in withoperating expenses Financial expense: Any commitment that is tax deductible that you have to

meet no matter what your operating results: Failure to meet it leads toloss of control of the business.

Example: Operating Leases: While accounting convention treats operating

leases as operating expenses, they are really financial expenses and needto be reclassified as such. This has no effect on equity earnings but doeschange the operating earnings

Make sure that there are no capital expenses mixed in with theoperating expenses Capital expense: Any expense that is expected to generate benefits over

multiple periods. R & D Adjustment: Since R&D is a capital expenditure (rather than an

operating expense), the operating income has to be adjusted to reflect itstreatment.

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The Magnitude of Operating Leases


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g p g

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Dealing with Operating Lease Expenses


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g p g p

Operating Lease Expenses are treated as operating expensesin computing operating income. In reality, operating leaseexpenses should be treated as financing expenses, with thefollowing adjustments to earnings and capital:

Debt Value of Operating Leases = Present value of Operating

Lease Commitments at the pre-tax cost of debt When you convert operating leases into debt, you also create

an asset to counter it of exactly the same value.

Adjusted Operating Earnings Adjusted Operating Earnings = Operating Earnings + Operating Lease

Expenses - Depreciation on Leased AssetAs an approximation, this works:

Adjusted Operating Earnings = Operating Earnings + Pre-tax cost ofDebt * PV of Operating Leases.

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The Collateral Effects of Treating Operating

Leases as Debt


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Leases as Debt

C o n v en t i o na l Ac c o u n ti n g O p e r at i n g L e a s es Tr e a t ed a s D e b t

Income Statement

E B IT & L e as e s = 1 , 9 90

- Op L ea ses = 9 78

E BI T = 1 ,0 12

I n c o m e S t a t e me n t

E BI T& L ea se s = 1 ,9 9 0

- D e pr ec n : O L = 6 2 8

EBIT = 1,362

I n te r es t e x p en s e w i ll r i s e t o r e fl e ct t h e

c o n ve r s i on o f o p e ra t i n g l ea s e s a s d e b t . Ne t

i n c o me s h o u l d n o t c h an g e .

B a l an c e S h ee t O ff b al an ce s he et ( No t s ho wn a s d eb t o r a s a n

a s s e t ). On l y t h e c o n v en t i o na l d e b t o f $1, 970

m i l l i on s h o w s u p o n b a l a n c e s h ee t

Balance SheetAsset Liability

O L A s se t 4 3 9 7 O L D eb t 4 3 97

T o ta l d eb t = 4 3 9 7 + 1 9 70 = $ 6 ,3 6 7 mi l l io n

C o st o f c a pi t al = 8 . 20 % (7 3 5 0/ 9 32 0 ) + 4 %

( 1970/9320) = 7. 31%

C o s t o f eq u i t y f o r Th e G ap = 8. 20%A f t e r- t a x c o s t o f d eb t = 4%

M a r k et va l u e o f e q u i ty = 7350

C o st o f c a pi t al = 8 . 20 % (7 3 50 / 13 7 1 7) + 4 %

( 6 36 7 /1 3 7 17 ) = 6 . 25 %

Return on capital = 1012 (1-.35)/(3130+1970)

= 1 2. 90 %

R e t ur n o n c a p i t al = 1362 ( 1- . 35) / ( 3130+ 6367)

= 9 .3 0%

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The Magnitude of R&D Expenses


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R&D Expenses: Operating or Capital Expenses


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Accounting standards require us to consider R&D as anoperating expense even though it is designed to

generate future growth. It is more logical to treat it as

capital expenditures.

To capitalize R&D, Specify an amortizable life for R&D (2 - 10 years)

Collect past R&D expenses for as long as the amortizable life

Sum up the unamortized R&D over the period. (Thus, if the

amortizable life is 5 years, the research asset can be obtained byadding up 1/5th of the R&D expense from five years ago, 2/5th

of the R&D expense from four years ago...:

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The Effect of Capitalizing R&D at SAP


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Convent ional Account ing R&D treated as capital expenditureIncome Statement

E BI T& R &D = 3 04 5- R & D = 1 0 20

E B IT = 2 0 25

EBIT (1-t) = 1285 m

Income Statement

E B I T & R & D = 3 0 4 5- A mo rt : R &D = 9 03

E BI T = 2 14 2 ( In cr ea se o f 1 17 m )

E BI T ( 1- t) = 1 35 9 m

I gn or ed t ax b en ef it = ( 10 20 -9 03 )( . 36 54 ) = 4 3A d ju s te d E BI T ( 1 -t ) = 1 3 59 + 43 = 1 4 02 m

( I n c r e as e o f 1 1 7 m i l li o n )N e t I n c om e w i ll a l so i n cr e as e b y 1 1 7 m i ll i on

Balance Sheet

O f f b a la n ce s h ee t a s se t . B o ok v a lu e o f e q ui ty at

3 , 7 6 8 m i l li o n E u ro s i s u n d e r st a t e d b e c a u seb i g g es t a ss e t i s of f t h e b o o ks .

B a l an c e S h e et

A s s e t L i a b il i t y

R & D A s se t 2 9 14 B o ok E q ui t y + 29 1 4T o t a l B o o k E q u i ty = 3 76 8 + 2 91 4 = 6 7 8 2 m i l

Capital ExpendituresC o n ve n t i on a l n e t c a p e x of 2 m i l li o n

Euros

Capital ExpendituresN et Ca p e x = 2+ 1 020 90 3 = 1 19 mil

C a sh F lo w s

E B IT ( 1 -t ) = 1 2 85

- N et Ca p Ex = 2

FCFF = 1283

Cash Flows

E BI T ( 1- t) = 14 02

- N et C ap E x = 1 19

F CF F = 1 28 3 m

Return on ca pital = 1285/(3768+530) Return on capital = 1402/( 6782+530)

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III. One-Time and Non-recurring Charges


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Assume that you are valuing a firm that is reporting aloss of $ 500 million, due to a one-time charge of $ 1billion. What is the earnings you would use in yourvaluation?

a. A loss of $ 500 million

b. A profit of $ 500 million

Would your answer be any different if the firm hadreported one-time losses like these once every fiveyears?

a. Yes

b. No

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IV. Accounting Malfeasance.


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Though all firms may be governed by the same accountingstandards, the fidelity that they show to these standards can vary.More aggressive firms will show higher earnings than moreconservative firms.

While you will not be able to catch outright fraud, you should lookfor warning signals in financial statements and correct for them: Income from unspecified sources - holdings in other businesses that are

not revealed or from special purpose entities.

Income from asset sales or financial transactions (for a non-financial firm)

Sudden changes in standard expense items - a big drop in S,G &A or R&Dexpenses as a percent of revenues, for instance.

Frequent accounting restatements

Accrual earnings that run ahead of cash earnings consistently

Big differences between tax income and reported income

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V. Dealing with Negative or Abnormally Low

Earnings


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Earnings

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What tax rate?


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The tax rate that you should use in computing the after-tax operating income should be

a. The effective tax rate in the financial statements (taxespaid/Taxable income)

b. The tax rate based upon taxes paid and EBIT (taxes paid/EBIT)

c. The marginal tax rate for the country in which the companyoperates

d. The weighted average marginal tax rate across the countries inwhich the company operates

e. None of the abovef. Any of the above, as long as you compute your after-tax cost of

debt using the same tax rate

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The Right Tax Rate to Use


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The choice really is between the effective and the marginaltax rate. In doing projections, it is far safer to use themarginal tax rate since the effective tax rate is really areflection of the difference between the accounting and thetax books.

By using the marginal tax rate, we tend to understate theafter-tax operating income in the earlier years, but the after-tax tax operating income is more accurate in later years

If you choose to use the effective tax rate, adjust the tax rate

towards the marginal tax rate over time. While an argument can be made for using a weighted average

marginal tax rate, it is safest to use the marginal tax rate of the country

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A Tax Rate for a Money Losing Firm


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Assume that you are trying to estimate the after-taxoperating income for a firm with $ 1 billion in netoperating losses carried forward. This firm is expected tohave operating income of $ 500 million each year for thenext 3 years, and the marginal tax rate on income for all

firms that make money is 40%. Estimate the after-taxoperating income each year for the next 3 years.

Year 1 Year 2 Year 3

EBIT 500 500 500

TaxesEBIT (1-t)

Tax rate

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Net Capital Expenditures


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Net capital expenditures represent the differencebetween capital expenditures and depreciation.Depreciation is a cash inflow that pays for some or alot (or sometimes all of) the capital expenditures.

In general, the net capital expenditures will be afunction of how fast a firm is growing or expecting togrow. High growth firms will have much higher netcapital expenditures than low growth firms.

Assumptions about net capital expenditures cantherefore never be made independently ofassumptions about growth in the future.

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Capital expenditures should include


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Research and development expenses, once they have beenre-categorized as capital expenses. The adjusted net cap exwill be Adjusted Net Capital Expenditures = Net Capital Expenditures +

Current years R&D expenses - Amortization of Research Asset

Acquisitions of other firms, since these are like capitalexpenditures. The adjusted net cap ex will be Adjusted Net Cap Ex = Net Capital Expenditures + Acquisitions of other

firms - Amortization of such acquisitions

Two caveats:1. Most firms do not do acquisitions every year. Hence, a normalized

measure of acquisitions (looking at an average over time) should beused

2. The best place to find acquisitions is in the statement of cash flows,usually categorized under other investment activities

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Ciscos Acquisitions: 1999


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Acquired Method of Acquisition Price PaidGeoTel Pooling $1,344

Fibex Pooling $318

Sentient Pooling $103

American Internet Purchase $58

Summa Four Purchase $129

Clarity Wireless Purchase $153

Selsius Systems Purchase $134

PipeLinks Purchase $118

Amteva Tech Purchase $159

$2,516

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Ciscos Net Capital Expenditures in 1999


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Cap Expenditures (from statement of CF) = $ 584 mil- Depreciation (from statement of CF) = $ 486 mil

Net Cap Ex (from statement of CF) = $ 98 mil

+ R & D expense = $ 1,594 mil- Amortization of R&D = $ 485 mil

+ Acquisitions = $ 2,516 mil

Adjusted Net Capital Expenditures = $3,723 mil

(Amortization was included in the depreciation number)

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Working Capital Investments


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In accounting terms, the working capital is the differencebetween current assets (inventory, cash and accountsreceivable) and current liabilities (accounts payables, shortterm debt and debt due within the next year)

A cleaner definition of working capital from a cash flow

perspective is the difference between non-cash currentassets (inventory and accounts receivable) and non-debtcurrent liabilities (accounts payable)

Any investment in this measure of working capital ties upcash. Therefore, any increases (decreases) in working capitalwill reduce (increase) cash flows in that period.

When forecasting future growth, it is important to forecastthe effects of such growth on working capital needs, andbuilding these effects into the cash flows.

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Working Capital: General Propositions


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Changes in non-cash working capital from year toyear tend to be volatile. A far better estimate of non-cash working capital needs, looking forward, can beestimated by looking at non-cash working capital as

a proportion of revenues Some firms have negative non-cash working capital.

Assuming that this will continue into the future willgenerate positive cash flows for the firm. While this

is indeed feasible for a period of time, it is notforever. Thus, it is better that non-cash workingcapital needs be set to zero, when it is negative.

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Volatile Working Capital?


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Amazon Cisco MotorolaRevenues $ 1,640 $12,154 $30,931

Non-cash WC -$419 -$404 $2547

% of Revenues -25.53% -3.32% 8.23%

Change from last year $ (309) ($700) ($829)

Average: last 3 years -15.16% -3.16% 8.91%Average: industry 8.71% -2.71% 7.04%

WC as % of Revenue 3.00% 0.00% 8.23%

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Dividends and Cash Flows to Equity


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In the strictest sense, the only cash flow that an investorwill receive from an equity investment in a publiclytraded firm is the dividend that will be paid on the stock.

Actual dividends, however, are set by the managers ofthe firm and may be much lower than the potential

dividends (that could have been paid out) managers are conservative and try to smooth out dividends

managers like to hold on to cash to meet unforeseen futurecontingencies and investment opportunities

When actual dividends are less than potential dividends,

using a model that focuses only on dividends will understate the true value of the equity in a firm.

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Measuring Potential Dividends


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Some analysts assume that the earnings of a firm represent itspotential dividends. This cannot be true for several reasons: Earnings are not cash flows, since there are both non-cash revenues and

expenses in the earnings calculation

Even if earnings were cash flows, a firm that paid its earnings out asdividends would not be investing in new assets and thus could not grow

Valuation models, where earnings are discounted back to the present, willover estimate the value of the equity in the firm

The potential dividends of a firm are the cash flows left over afterthe firm has made any investmentsit needs to make to createfuture growth and net debt repayments (debt repayments - newdebt issues) The common categorization of capital expenditures into discretionary and

non-discretionary loses its basis when there is future growth built into thevaluation.

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Estimating Cash Flows: FCFE


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Cash flows to Equity for a Levered FirmNet Income

- (Capital Expenditures - Depreciation)

- Changes in non-cash Working Capital

- (Principal Repayments - New Debt Issues)

= Free Cash flow to Equity

I have ignored preferred dividends. If preferred stock

exist, preferred dividends will also need to be nettedout

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Estimating FCFE when Leverage is Stable


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Net Income- (1- ) (Capital Expenditures - Deprec

Valuations - Damodaran

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