Issues in Business Valuation Cost of capital FAS internal training 7 September, 2005
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Issues in Business
Valuation
Cost of capital
FAS internal training7 September, 2005
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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.
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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
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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.
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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
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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
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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
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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
Straight Investment grade debt ± Fixed and variable rateBelow investment grade debt ± Junk bondsSubsidized debt ± Tax free debtForeign currency denominated debtLeasesStraight preferred stock
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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
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
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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
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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
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� 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
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� 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
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� 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
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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
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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.
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� 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
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� 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
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� 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
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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))
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� 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
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� 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
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� 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
Alternatives to regression betas
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� 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
Alternatives to regression betas
BL = Bu ((1+(1-t)(D/E))
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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.
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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
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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
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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
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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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