Issues in Business Valuation

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Issues in Business

Valuation

Cost of capital

FAS internal training7 September, 2005





What is cost of capital

� Cost of capital is the compensation expected by variousproviders of capital for the opportunity cost of investingtheir funds in one particular business instead of other(s)with equal risk.

� Cost of capital must:± Comprise a weighted average of the cost of all sources of capital± Post tax costs± Nominal rates of return± Adjusted for systematic risk borne by each provider ± Market value weights

± Subject to change with change in inflation, systematic risk andcapital structure

� Weighted average cost of capital (WACC) is the discountrate to convert expected FCF to all the capital providersinto present value.



WACC� WACC=Kb(1-t)(B/V) + Kp(P/V) + Ks(S/V)Kb : cost of debt

B: Market value of debt

V: Market value of enterprise

Kp: After tax cost of preferred stock

Ks: opportunity cost of equity capital

P: Market value of preferred stock

S: Market value of equity

� Other possible entries include:± Leases (operating and capital)± Subsidized debt

± Convertible or callable debt/preferred stock± Minority interest± Warrants and executive stock options± Income bonds, commodity index bonds, extendable, puttable or

retractable bonds



Some simplifying assumptions

� No distinction of callable and non callable debt� Non interest bearing liabilities are not included

such as accounts payable, though there is

implied financing cost which if separated fromoperating cost will complicate the process� It is theoretically correct to use different WACC

for each projection year, however we usually

use one WACC for the entire forecast period asat one point of time a company¶s capitalstructure will not reflect capital structure of thecompany for the rest of its life.



Calculation of WACCOpportunity cost

of non equity

capital

Opportunity cost

of non equity

capital

Developing market

value weights

Developing market

value weights

Opportunity

cost of equity

capital

Opportunity

cost of equity

capital

Circularity issue ± As we need to know market value weightsto determineWACC - which needs cost of equity. And cost of equity cannot be calculated without knowingWACC, as it iscalculated by discounting FCF with WACC.Existing or target capital structure

Capital structure of comparable companies in the industry



Estimating the existing capital structure

� Market value of listed capital structure� Problem arises when some of them are not listed

± Calculate the present value of stream of financingpayments using YTM of equivalent issue as discount

rate� Complex calculations in other/hybrid securities:

± Debt type financing ± fixed or variable/leases

± Equity linked

± Minority interests



Some other securities

� Option features: Option pricing� Swaps: if associated with a specific outstanding

instrument, we estimate the value of the µsyntheticsecurity¶

� Leases: No differentiation of capital and operatingleases, however operating leases may be kept out of valuation analysis - if insignificant

� Warrants and ESOP: Using option pricing

� Convertible securities: Using option pricing� Minority interest: is the claim of outside shareholders insubsidiary companies ± Using DCF or market multiples




of non equity

capital

Opportunity cost

of non equity

capital

Developing market

value weights

Developing market

value weights

Opportunity

cost of equity

capital

Opportunity

cost of equity

capital

Straight Investment grade debt ± Fixed and variable rateBelow investment grade debt ± Junk bondsSubsidized debt ± Tax free debtForeign currency denominated debtLeasesStraight preferred stock




of non equity

capital

Opportunity cost

of non equity

capital

Developing market

value weights

Developing market

value weights

Opportunity

cost of equity

capital

Opportunity

cost of equity

capital

Average beta for entire market portfolio is 1Unusual to find beta higher than 2 and that lower than 0.3Cost of equity increases linearly as a function of the measuredundiversifiable risk beta

CAPM

Cost of equity = Rf + beta [E(Rm) ± Rf]

Beta

Expected return

Rf

Rm

SMLMarket portfolio rate

1



Q -Why risk free rate of return?A -In finance, expected return on risky investment is always measured

relative to the risk free rate ± with the risk creating an expected riskpremium that is added on to the return on risk free asset.

Q ± What is risk free asset?

No variance in return -Actual return should always be equal toexpected return No reinvestment risk ± Duration matching strategy No default risk ± Government or proxy if Govt does not borrow OR

through using interest rate parity on forward currency contracts

Risk free rate of return

Forward rateHC,FC = Spot rate (1+interest rateHC)/(1+ interest rateFC)

Expected return Returns

Probability = 1



Risk free rate of return� Rf is return on security/portfolio

which has no default risk andcompletely uncorrelated with returns on anything else in theeconomy.

� Theoretically Rf will be return on azero beta, minimum varianceequity portfolio. However due tonon availability of data for same itcannot be constructed.

Alternatives for Rf:

T ±bills (short term GoIsecurities)10 Year T ± bonds (10

Year GoI bonds)30 Year T- bonds (Longterm GoI bonds)

10 Year GoI securities rate is generally recommended as its

duration is closer to the cash flows of the company being valuedMore appropriate compared to long term rate (30 years) as its priceis less sensitive to unexpected changes in inflation and lower liquiditypremium built into it.

M ost widely used



� Risk free rate should be used of the currency in which cash flows of the firm are estimated.

Issue for discussion

Change in interest rate

Level of inflation

Cash flows

reflectPurchasing power parityIf we assume

Discount rate

With equal impact onIf the differences in interest ratesacross the two currencies does notadequately reflect the difference ininflation, the values obtainedusing different currencies will bedifference OTHERWISE NOT

Low

High

Over valuation



� A forward looking rate based on past data� Market risk premium measures what investor on an average

demand as extra return for investing in this portfolio relative to therisk free asset

� Risk for the purpose of risk premium should be measured from the

perspective of the marginal investor given that the marginal investor is well diversified.� Therefore the risk that an investment adds to a diversified portfolio

should be measured and compensated� Only the undiversifiable ± market component of risk should be

rewarded.

� Company specific risk aspect is handled separately by beta.� Practical implication is that the market risk premium data is availablein the market without reference to which rf used. Hence for thepurpose of the analysis, consistency should be maintained for thetwo rates.

� Historical arithmetic average to be downward adjusted by 1.50-2.00% towards survivorship bias

Market risk premium



� Different methodologies used for estimatingmarket risk premium:

Time period used ¥ Since inception¥ 50/20/10 years¥ Standard error

Choice of risk free security Arithmetic vs geometric averages

± Moving average� For emerging markets with limited history, we

should not use market risk premiums (local),and should rather go through country risk

premium route using matured market riskpremium and adding the risk of the countryunder study ± This topic has already beendiscussed by Punita and Hormazd

Market risk premium

No statistically significant changes in the risk premium between 1926 to 1995.

Time period use SE

5 years 8.94%

10 years 6.32%

25 years 4.00%

50 years 2.83%

Longer vs. latest



Issues

Arithmetic average or Geometric average

�Arithmetic average is the best estimate of futureexpected returns as all possible paths are given equalweightage�Arithmetic average considers all the data pointsindependent�Arithmetic average is always higher than geometric

average

Greater the interval for taking average ± Lower thearithmetic average. Hence concluded that true marketpremium lies between arithmetic and geometricaverages

Issues in market risk premium



Issues in market risk premium

Issues

Either historical data or Exante estimates

�Ex ante estimates are based oncurrent value of share marketrelative to projections of earnings or cash flows.�E(Rm)=D/S+g approach may beused for Ex ante estimates. Further future cash flows may be estimated

for the purpose.�Many investment banks havestarted publishing estimates of themarket risk premium using ex anteapproach.�These ex ante approach basedpremium is generally lower than

historical based.

Issues

Survivorship bias

�Survival imparts a bias to ex postreturns�Empirical evidence ± US marketannual return exceeded medianreturn on a set of 11 countries with continuous histories dating to 1920sby 1.9% in real terms or 1.4% in

nominal terms.�However it is not necessary that theout-performance will be continuedfor next decade. Hence a downwardadjustment.



� Betas measure the risk added on to a diversifiedportfolio rather than total risk ± therefore aninvestment may be high risk individually but may below risk in terms of market risk

� Betas measure th

e relative risk, and th

us arestandardised around 1� Beta measures the risk added on by the investment

being analysed to a portfolio� However in practice, beta is calculated relative to

stock market index rather than portfolio

ISSUES-Just equity portfolio or to include other asset classes-Diversified domestically or internationally

Beta



� Choice of market indices:± Equity/+ debt± BSE/NSE

� Time period: No standards ±Theoretically 2 to 10 years ±Practically 3 to 5 years

Longer periods should be used for firms with stable business mix and leverage ratios. Shorter periods for

ones who have recently restructured, been acquired,divested business or changed their financial leverage etc.

Index used beta

Dow 30 0.99

S&P 500 1.13

NYSE composite 1.14

Wilshire 5000 1.05

MS Capital Index 1.06

Beta

Time period used Beta

estimated

3 years 1.04

5 years 1.13

7 years 1.09

10 years 1.18



� Choice of return

interval:

± Daily

± Weekly

± M onthly

± Quarterly

± Annually

Daily and weekly interval are likely to have

significant bias due to non trading problem

and illiquid stocks and speculation

Most preferred

BetaReturn interval

used

Beta

estimated

Daily 1.33

Weekly 1.38

Monthly 1.13

Quarterly 0.44

Annual 0.77



Beta

� Betas should be extracted from more than onesource

� Also should be compared with industry beta

� If beta from two sources vary by more than 0.2or it is more than 0.3 from the industry average,consider using industry average

�Wh

en using industry average, unlever th

e betaand relever it using the company¶s capitalstructure

BL = Bu ((1+(1-t)(D/E))



� Practitioners further adjust beta towards

one. Rationale is that over time there is a

tendency on the part of betas of all

companies to move towards one on

account of increase in size over time, their

becoming more diversified and have more

assets in place producing cash flows.

Beta ± in practise



� M odified regression betas:± Based on fundamental factors ± Income statement and balance

sheet

± Eg High payout ± low beta

± High variability of earnings and covariability ± High betaBeta*=0.7997 + 2.28 sd + 0.21 D/E -0.000005 m cap

* Rosenberg and M arathe

Alternatives to regression betas



� Relative risk measures± Relative volatility = (Std dev./Average std dev across all assets)

± Accounting betas - use accounting earnings than traded prices

� Biased up for safer firms and biased down for risky firms

� Influenced by non operating factors� At max, quarterly figures are available hence less data points




� Bottom up betas± Determined by three variables

� Type of business

� Degree of operating leverage

� Degree of financial leverage� Bottom up betas ± steps

± Identify the business/es that make up the firm/asset/project

± Estimate the unlevered beta for the units ± adjusted for changein operating leverage

± Take a weighted average of the adjusted unlevered betas± Calculate the leverage for the firm

± Estimate the levered beta


BL = Bu ((1+(1-t)(D/E))



Limitations of CAPM

The model makes unrealistic assumptionsThe parameters of the model cannot be estimated precisely� - Definition of a market index� - Firm may have changed during the 'estimation' period'

The model does not work well� - If the model is right, there should be

±a linear relationship between returns and betas± the only variable that should explain returns is betas

� - Th

e reality is th

at± the relationship between betas and returns is weak± Other variables (size, price/book value) seem toexplain differences in returns better.



Others measures for CoCCAPM -No transaction costs

-The diversified portfolio includes all tradedinvestments, held in proportion to their marketvalue

Betas measuredagainst marketportfolio

APM Investments with the same exposure to market

riskh

ave to trade at th

e same price ± Noarbitrage

Betas measured

against multiple(unspecified) marketrisk factors

Multi factor model

No arbitrage assumption Betas measuredagainst multiplespecified macroeconomic factors

Proxymodel

Over very long periods, high returns oninvestments must be compensation for higher market risk

Proxies for marketrisk, include marketcapitalisation andP/BV ratios



Extract of research papersResearch paper by Roelof Salomons and Henk Grootveld on

³The Equity Risk Premium ± Emerging versus Developed Markets´

Developed countriesCanadaFrance

GermanyItalyJapanUKUS

Emerging countriesChinaIndia

IndonesiaKoreaMalaysiaPakistanPhilippinesTaiwanThailandArgentina

ChileColumbiaPeruVenezuelaMexicoBrazil

United States1889-1978 ± Equity Risk Premium = 6.00% pa1802-1990 - Equity risk premium = 5.3% pa1988 ± 2001 ± Equity risk premium = 3.7% paMSCI

1988 ± 2001 ± Equity risk premium = 1.8% pa

G7 countries1988 ± 2001 ± Equity risk premium = 3.6% paIFC index of emerging markets

1985 ± 2001 ± Equity risk premium = 12.7% pa

*All the above averages are based on equal weightage to countries



Extract of research papersJames Dow paper on Cost of Capital

Country Risk premium

France 4.5%

Germany 4.8%

Japan 4.3%

UK 6.1%

US 4.5%

International comparison

Section on beta: ³If it has Greek letters, don¶t do it.´

TODAY WE WILL DISREGARD THIS ADVICE AND DO ß



Extract of research papersJavier Estrada paper on ³Systematic risk in Emerging Markets ± The D CAPM

This paper is a critic to CAPM especially in the Emerging markets. SinceCAPM measures risk by beta ± which follows from an equilibrium in which investors display mean-variance behavior. Risk here is measured by thevariance of returns.The semivariance of returns is considered more plausible measure of riskand can be used to generate an alternative behavior (mean-semivariancebehavior) ± called DOWNSIDE beta and an alternative pricing model (D-CAPM)





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Issues in Business Valuation

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