Lecture 2Lecture 2

Valuation and the Valuation and the

Cost of CapitalCost of Capital

ValuationValuation Last time we argued that Last time we argued that

information about state-contingent information about state-contingent cash flows and how to price them cash flows and how to price them was crucial for valuation, and was crucial for valuation, and therefore, both for management therefore, both for management and market opinions about what and market opinions about what the firm should do and how to the firm should do and how to value what the firm is doing.value what the firm is doing.

Now we’ll be more precise about Now we’ll be more precise about how information is used in how information is used in valuation.valuation.

Weighted Average Cost of Weighted Average Cost of Capital (WACC) Model of Capital (WACC) Model of

ValuationValuation Framework defines “free cash flows” as Framework defines “free cash flows” as

focal point of valuationfocal point of valuation Discounting forecasted free cash flows Discounting forecasted free cash flows

requires one to take account of asset requires one to take account of asset risk (unlevered beta) as well as effect of risk (unlevered beta) as well as effect of debtdebt

This framework allows us to measure This framework allows us to measure the firm’s cost of capital, and to the firm’s cost of capital, and to evaluate projects.evaluate projects.

Also allows estimation of divisional cost Also allows estimation of divisional cost of capital.of capital.

WACCWACC Equity holders require rate of Equity holders require rate of

return Rreturn RLL

They contribute Equity/V = 1 – L They contribute Equity/V = 1 – L proportion of the firm (or division proportion of the firm (or division or project)or project)

Debt holders require rate of return Debt holders require rate of return RRDD

They contribute D/V = L They contribute D/V = L proportion of the value of the firm proportion of the value of the firm (or division or project)(or division or project)

WACC WACC

WACC is used by the market WACC is used by the market to discount expected Free to discount expected Free Cash Flows in order to arrive Cash Flows in order to arrive at value of the firm (or at value of the firm (or division or project). Because division or project). Because it measures the cost of it measures the cost of capital it is also used to capital it is also used to evaluate prospective projects.evaluate prospective projects.

WACCWACC Debt is tax-favored relative to Debt is tax-favored relative to

equity, so that in order to equity, so that in order to provide holders of debt a return provide holders of debt a return of Rof RDD the firm must earn R the firm must earn RDD(1-t)(1-t)

Formula for WACC:Formula for WACC:

WACC = RWACC = RDD(1-t)L + (1-L)R(1-t)L + (1-L)RLL

Deriving WACCDeriving WACCBy definition:By definition:

VVtt = {E[FCF = {E[FCFt+1t+1] + E[V] + E[Vt+1t+1]}/(1+WACC)]}/(1+WACC)

By using iteration, we can express By using iteration, we can express value in terms of WACC and value in terms of WACC and expected free cash flows. expected free cash flows.

Alternatively, we can write:Alternatively, we can write:

1+ WACC = {E[FCF1+ WACC = {E[FCFt+1t+1] + E[V] + E[Vt+1t+1]} / V]} / Vtt

Defining Free Cash FlowsDefining Free Cash Flows

FCF = Gross after-tax cash flow – FCF = Gross after-tax cash flow – Gross investmentGross investment

Gross after-tax cash flow = Net Gross after-tax cash flow = Net operating profit less adjusted operating profit less adjusted taxes attributable to EBITA taxes attributable to EBITA (which is approximately equal to (which is approximately equal to EBITA(1-t)) + Dep.EBITA(1-t)) + Dep.

Gross after-tax cash flow = Gross after-tax cash flow = EBITA(1-t) + Dep.EBITA(1-t) + Dep.

Defining FCF (Cont’d)Defining FCF (Cont’d)NOPLAT = Net operating profit less NOPLAT = Net operating profit less

adjusted taxesadjusted taxes

NOPLAT = Gross after-tax cash flow NOPLAT = Gross after-tax cash flow less Depreciationless Depreciation

NOPLAT = EBITA(1-t)NOPLAT = EBITA(1-t)

Gross investment = NINV + Gross investment = NINV + Depreciat.Depreciat.

FCF = NOPLAT – NINV FCF = NOPLAT – NINV

where NINV is net where NINV is net investmentinvestment

TaxesTaxes Note that EBITA(1-t) does not Note that EBITA(1-t) does not

take interest on debt tax shield take interest on debt tax shield into account. That is taken into into account. That is taken into account later.account later.

EBITA(1-t) is an approximation, EBITA(1-t) is an approximation, since tax consequences of since tax consequences of income is a complicated concept income is a complicated concept in practice. In particular, NOPLAT in practice. In particular, NOPLAT does not include non-operating does not include non-operating income or subtract taxes on non-income or subtract taxes on non-operating income.operating income.

Thinking about Free Cash Thinking about Free Cash FlowFlow

Assume no non-operating assets and Assume no non-operating assets and no goodwill amortizationno goodwill amortization

Where does FCF go?Where does FCF go?

FCF = Net income – NINV – principal FCF = Net income – NINV – principal payment + after-tax interest + payment + after-tax interest + principal paymentprincipal payment

FCF = {NI – NINV – PP} + {ATI + PP}FCF = {NI – NINV – PP} + {ATI + PP}

The first part is the part of free cash The first part is the part of free cash flow the firm keeps or pays as flow the firm keeps or pays as dividendsdividends

The second part is the part of free cash The second part is the part of free cash flow that goes to debtholdersflow that goes to debtholders

Taking New Financing into Taking New Financing into AccountAccount

FCF = {NI – NINV – PP} + {ATI + PP} FCF = {NI – NINV – PP} + {ATI + PP}

V = Value of old equity + Value of V = Value of old equity + Value of new equity + Value of old debt + new equity + Value of old debt + Value of new debtValue of new debt

FCF + V = {NI – NINV – PP + New FCF + V = {NI – NINV – PP + New debt + New Equity Issues +debt + New Equity Issues +

Value of old equity} +Value of old equity} +

{ATI + PP + value of old {ATI + PP + value of old debt after payment of PP}debt after payment of PP}

InterpretationInterpretation

This is the same as saying that This is the same as saying that FCF is the only leakage of FCF is the only leakage of value from the firm (other than value from the firm (other than taxes) and that is received by taxes) and that is received by those that have equity or debt those that have equity or debt claims on the firm.claims on the firm.

DefinitionsDefinitionsRRDD = Expected market return on debt = Expected market return on debt

RRDD ={E[interest]+ E[PP]+ E[capital ={E[interest]+ E[PP]+ E[capital gain]}/Dgain]}/D

RRLL = Expected market return on equity = Expected market return on equity

RRLL = {E[Dividend] + E[capital = {E[Dividend] + E[capital gain]}/(V-D)gain]}/(V-D)

Recall thatRecall that

1 + WACC = {E[FCF1 + WACC = {E[FCFt+1t+1] + E[V] + E[Vt+1t+1]} / V]} / Vtt

Almost there…Almost there…Assume no expected new debt or Assume no expected new debt or

equityequityRetained earnings add to equity valueRetained earnings add to equity valueE [FCF + V] = {E[Dividend] + E [FCF + V] = {E[Dividend] + E[Future value of current equity]} E[Future value of current equity]}

+ + {E[(1-t)Interest] + E[PP] + {E[(1-t)Interest] + E[PP] + E[Value of old debt]}E[Value of old debt]}

E[FCF+V] = (1+RE[FCF+V] = (1+RLL)(V-D) + R)(V-D) + RDD(1-(1-t)D+Dt)D+D

QED!QED!

E [FCFE [FCFt+1t+1+V+Vt+1t+1]/V]/Vtt = R = RLt Lt [(V-D)/V][(V-D)/V]tt + +

[(V-D)/V][(V-D)/V]t t + R+ RDtDt(1-t)[D/V](1-t)[D/V]tt + + [D/V][D/V]tt

Thus, if you are in a steady state,Thus, if you are in a steady state,

WACC = RWACC = RDD(1-t)L + (1-L)R(1-t)L + (1-L)RLL

InterpretationInterpretation This says that market returns and This says that market returns and

market values today reflect market values today reflect expectations of FCFs in the future expectations of FCFs in the future (note that left hand expression (note that left hand expression can be solved iteratively based on can be solved iteratively based on future expectfuture expecteed cash flows)d cash flows)

Taxes are total effective marginal Taxes are total effective marginal corporate rate (federal, state, corporate rate (federal, state, local)local)

Steady state assumes constancy Steady state assumes constancy of expected returns on equity and of expected returns on equity and debt and constancy of leverage. debt and constancy of leverage. Is this reasonableIs this reasonable??

Interpretation (Cont’d)Interpretation (Cont’d) For constant leverage assumption to For constant leverage assumption to

be literally true firm would have to be literally true firm would have to adjust debt and/or equity adjust debt and/or equity continuously to keep the market continuously to keep the market values of the two in fixed values of the two in fixed proportion. That is not realistic.proportion. That is not realistic.

But, firm could be implicitly But, firm could be implicitly targeting both leverage and the targeting both leverage and the return on debt if, for example, the return on debt if, for example, the firm were trying to maintain a given firm were trying to maintain a given debt rating (BBB) and if firm had debt rating (BBB) and if firm had stable FCF risk.stable FCF risk.

Interpretation (Cont’d)Interpretation (Cont’d) Note that RNote that RDD is not promised return is not promised return

but expected return on debt (if debt but expected return on debt (if debt is risky, promised return is higher)is risky, promised return is higher)

RRDD is increasing function of leverage is increasing function of leverage and FCF systematic risk. If leverage and FCF systematic risk. If leverage and FCF systematic risk are stable, and FCF systematic risk are stable, then so is expected return on debt.then so is expected return on debt.

These are not good assumptions for These are not good assumptions for young, growing firms or for LBOs, young, growing firms or for LBOs, but not too bad otherwise.but not too bad otherwise.

Estimating REstimating RDD If debt is not priced, look at comparable If debt is not priced, look at comparable

firms’ spreads or ratings on public debts firms’ spreads or ratings on public debts (where comparable means comparable (where comparable means comparable FCF risks and leverage); if highly rated FCF risks and leverage); if highly rated don’t worry about ex ante vs. ex postdon’t worry about ex ante vs. ex post

Similarly, could use scoring models Similarly, could use scoring models (Zeta score) to estimate default risk (Zeta score) to estimate default risk premium, or KMV (Black-Scholes based) premium, or KMV (Black-Scholes based) approachapproach

Once you have yield, mark down one Once you have yield, mark down one category to get expected returncategory to get expected return

Could you construct a beta of Could you construct a beta of debt?debt?

In theory, yes; in practice, no. In theory, yes; in practice, no. Debt markets are not always Debt markets are not always trading enough, and price trading enough, and price variation is small relative to variation is small relative to transaction costs.transaction costs.

Estimating REstimating RLL CAPM is still the best show in town, CAPM is still the best show in town,

but the current state of the art is to but the current state of the art is to use multiple factors (APM), allow use multiple factors (APM), allow coefficients to vary over time, and to coefficients to vary over time, and to “shrink” estimates to take account of “shrink” estimates to take account of biases that result from small sample biases that result from small sample size in estimating expected returns.size in estimating expected returns.

Recall that CAPM is not very useful in Recall that CAPM is not very useful in some cases (EM investments, where some cases (EM investments, where alternative approaches are better)alternative approaches are better)

Arbitrage Pricing ModelArbitrage Pricing Model CAPM does not take account of CAPM does not take account of

missing markets for many stocks, missing markets for many stocks, or of human capital.or of human capital.

Additional factors (for which Additional factors (for which separate betas are estimated) separate betas are estimated) include industrial production, include industrial production, short-term interest rate, yield short-term interest rate, yield curve, Baa-Aaa spread, which curve, Baa-Aaa spread, which make a big difference to make a big difference to estimates of composite betaestimates of composite beta..

CAPM vs. APM Estimates of CAPM vs. APM Estimates of RRLL

IndustryIndustry CAPMCAPM APMAPM DifferencDifferencee

S&LsS&Ls 15.815.8 19.619.6 -3.8-3.8

Big Big banksbanks

15.915.9 16.916.9 -1.0-1.0

P&C P&C Insur.Insur.

14.614.6 13.713.7 0.90.9

OilOil 14.414.4 19.119.1 -4.7-4.7

APM DetailsAPM Details

RRLL = R = Rff + [E(F + [E(F11 – R – Rff )] beta )] beta11 + +

[E(F[E(F22 – R – Rff )] beta )] beta22 + +

[E(F[E(F33 – R – Rff )] beta )] beta33 + … + …

[E(F[E(Fkk – R – Rff )] beta )] betakk

where E(F) measures expected return of where E(F) measures expected return of each factor and betas measure each factor and betas measure sensitivity of stock return of company to sensitivity of stock return of company to each factor.each factor.

Why use CAPM or APM at Why use CAPM or APM at all?all?

Does better at forecasting returns Does better at forecasting returns than simple average of historic than simple average of historic returns.returns.

Part of the reason for that is that Part of the reason for that is that average returns of all portfolios are average returns of all portfolios are measured with much more error measured with much more error than the covariance matrix of than the covariance matrix of returnsreturns

ExperimentExperiment Using a utility function and riskless Using a utility function and riskless

rate estimate, construct two rate estimate, construct two versions of efficient portfolios, one versions of efficient portfolios, one based on historical averages of based on historical averages of mean returns, the other estimating mean returns, the other estimating expected return using APM.expected return using APM.

Look at ex post performance of the Look at ex post performance of the two portfolios (M1, V1) vs. (M2, V2) two portfolios (M1, V1) vs. (M2, V2) evaluated using same utility evaluated using same utility function. (M2, V2) dominatesfunction. (M2, V2) dominates

Practical Tips for Estimating RPractical Tips for Estimating RLL

For U.S. publicly traded firms, For U.S. publicly traded firms, estimates often differ (different estimates often differ (different methods, periods, market methods, periods, market benchmarks). benchmarks).

Look for central tendenciesLook for central tendencies Do within-industry comparisons Do within-industry comparisons

(since systematic operating risk (since systematic operating risk should be similar for similar firms)should be similar for similar firms)

Use “shrinkage” to deal with Use “shrinkage” to deal with sampling bias [(0.6 x estimate) + sampling bias [(0.6 x estimate) + (0.4 x 1)] (0.4 x 1)]

Within-Industry ComparisonsWithin-Industry Comparisons For non-public firms, or when For non-public firms, or when

checking robustness of estimates checking robustness of estimates for publicly traded firms, it can be for publicly traded firms, it can be very useful to do within-industry very useful to do within-industry comparisonscomparisons

But these comparisons must take But these comparisons must take into account differences in into account differences in leverage. How does one control for leverage. How does one control for leverage? How does one “lever” or leverage? How does one “lever” or “unlever” an estimated beta?“unlever” an estimated beta?

Emerging MarketsEmerging Markets

Assumptions necessary for CAPM are not even Assumptions necessary for CAPM are not even close to true (distributional problems, close to true (distributional problems, institutional risks)institutional risks)

Best approach is to use sovereign spreads Best approach is to use sovereign spreads plus national stock volatility markup as plus national stock volatility markup as starting point for equity premium, and to starting point for equity premium, and to compute individual stock spreads over the compute individual stock spreads over the sovereign spread based on a firm-level sovereign spread based on a firm-level adjustment factor (relative volatility of that adjustment factor (relative volatility of that stock compared to others in the country is the stock compared to others in the country is the one typically used). one typically used).

There is little theoretical or empirical basis for There is little theoretical or empirical basis for any of this. Welcome to sausage making!any of this. Welcome to sausage making!

Levering or Unlevering BetasLevering or Unlevering Betas Two approaches are used, and Two approaches are used, and

they differ in their assumptions they differ in their assumptions about how the capital structure of about how the capital structure of the firm evolves over time.the firm evolves over time.

One approach assumes constant One approach assumes constant D; the other approach assumes D; the other approach assumes constant L. Which one you use constant L. Which one you use depends on which assumption is depends on which assumption is more realistic in the particular more realistic in the particular case (one can also use a case (one can also use a combination of the two).combination of the two).

Constant D ApproachConstant D Approach The comparable levered and unlevered The comparable levered and unlevered

firms are related in the following way, firms are related in the following way, under the assumption of constant D, under the assumption of constant D, and constant expected return on debt:and constant expected return on debt:

VVL L = V= VU U + tD+ tDwhere tax shield per period is worth where tax shield per period is worth

tRtRDDD, and is discounted as a perpetuity D, and is discounted as a perpetuity at the rate of Rat the rate of RDD

Note Graham’s evidence of underuse of Note Graham’s evidence of underuse of tax shield (firms could increase value of tax shield (firms could increase value of stock by 15.7% on average by raising stock by 15.7% on average by raising debt to the “kink” he defines with debt to the “kink” he defines with virtually no risk of causing distress)virtually no risk of causing distress)

Constant D Approach Constant D Approach (Cont’d)(Cont’d)

Using WACC formula, one can Using WACC formula, one can show that, measured in terms of show that, measured in terms of returns, returns,

RRL L – R– RD D = [1 +(1-t)D/(V-D)](R= [1 +(1-t)D/(V-D)](RU U – R– RDD))

Measured in terms of betaMeasured in terms of beta

bbL L – b– bD D = [1 +(1-t)D/(V-D)](b= [1 +(1-t)D/(V-D)](bU U – b– bDD))

If the riskiness of debt is small, If the riskiness of debt is small, this becomesthis becomes

bbL L = [1 +(1-t)D/(V-D)]b= [1 +(1-t)D/(V-D)]bUU

Constant L ApproachConstant L Approach This is not mathematically This is not mathematically

consistent, since WACC assumes consistent, since WACC assumes constant L, not constant D. constant L, not constant D. Constant L is better assumption Constant L is better assumption anyway. anyway.

When you take this into account, When you take this into account, the correct formulae become:the correct formulae become:

RRL L – R– RD D = [1 + D/(V-D)](R= [1 + D/(V-D)](RU U – R– RDD))

bbL L – b– bD D = [1 + D/(V-D)](b= [1 + D/(V-D)](bU U – b– bDD))

bbL L = [1 + D/(V-D)]b= [1 + D/(V-D)]bUU

(See proof below)(See proof below)

Risk Free Rate MeasureRisk Free Rate Measure No ideal measureNo ideal measure Long-term bond without effect of Long-term bond without effect of

inflation risk premium but with inflation risk premium but with expected inflation included expected inflation included would be ideal, but this does not would be ideal, but this does not existexist

A rough proxy is 10-year A rough proxy is 10-year Treasury less 1%Treasury less 1%

Equity Risk PremiumEquity Risk Premium This contributes more uncertainty to This contributes more uncertainty to

cost of capital than does estimate of cost of capital than does estimate of beta!beta!

Some economists see it as 2%, Some economists see it as 2%, others use a number as high as 8%others use a number as high as 8%

Even after 150 years of stock prices, Even after 150 years of stock prices, we really don’t know what the mean we really don’t know what the mean is, and to make matters worse, we is, and to make matters worse, we have a sense that it should change have a sense that it should change over time (theory)over time (theory)

Equity Premium EstimatesEquity Premium Estimates Short-sample problems with computing U.S. Short-sample problems with computing U.S.

equity premium from average experienced equity premium from average experienced returns (Fama and French 2002, Dimson et returns (Fama and French 2002, Dimson et al. 2003). This is even more true for al. 2003). This is even more true for emerging market countriesemerging market countries, and there are , and there are related concerns:related concerns: Distributions of returns not normalDistributions of returns not normal Survivorship biases (“submerging” firms, Survivorship biases (“submerging” firms,

markets)markets) Equity premium changes are unpredictable: Equity premium changes are unpredictable:

At any point in time, your best guess of the At any point in time, your best guess of the future is the long-term retrospective mean future is the long-term retrospective mean (Goval and Welch 2004)(Goval and Welch 2004)

Equity Premium Estimates Equity Premium Estimates (Cont’d)(Cont’d)

Dimson et al 2003, “Forward-Looking” Arith Mean, 1900-Dimson et al 2003, “Forward-Looking” Arith Mean, 1900-20022002

AUSAUS 7.67.6

ITAITA 5.65.6

CANCAN 5.55.5

DENDEN 2.72.7

FRAFRA 5.65.6

GERGER 5.15.1

JAPJAP 8.48.4

NETHNETH 5.95.9

SAFRSAFR 6.86.8

UKUK 5.15.1

USUS 6.46.4

Equity Premium Estimates Equity Premium Estimates (Cont’d)(Cont’d)

Dealing with the conundrum of time:Dealing with the conundrum of time: Clearly, equity premium has fallen over Clearly, equity premium has fallen over

time, and in theory should have (tech. time, and in theory should have (tech. change, reduced risk, rising P/E ratios), but change, reduced risk, rising P/E ratios), but when you carve up time you also get less when you carve up time you also get less accuracyaccuracy

Sensible forward-looking procedureSensible forward-looking procedure Begin with bond yield risk premium Begin with bond yield risk premium

(forward looking, and senior to equity in (forward looking, and senior to equity in firms that issue them)firms that issue them)

Use historical averages of equity premium, Use historical averages of equity premium, adjusted for current level of bond risk adjusted for current level of bond risk premiuim relative to its historical average premiuim relative to its historical average

Divisional WACCDivisional WACC Find comparable stand-alone Find comparable stand-alone

firms, in terms of FCF risk and firms, in terms of FCF risk and compute their unlevered costs of compute their unlevered costs of equity, average them.equity, average them.

Determine appropriate leverage Determine appropriate leverage and effective marginal tax rate, and effective marginal tax rate, and compute WACC from above and compute WACC from above formula (assuming constant L)formula (assuming constant L)

Does GAAP Matter?Does GAAP Matter? Earnings, per se, should not matter, since Earnings, per se, should not matter, since

sophisticated investors, who should set sophisticated investors, who should set prices, are forecasting cash flows.prices, are forecasting cash flows.

But earnings is the signal that is released But earnings is the signal that is released (and is correlated with FCF), so earnings (and is correlated with FCF), so earnings news should, and does, matter (and firms news should, and does, matter (and firms care a lot about “managing earnings” care a lot about “managing earnings” because of its signalling.” But evidence because of its signalling.” But evidence suggests earnings matter to firms’ suggests earnings matter to firms’ managers, managers, per seper se (Graham et al. 2004). (Graham et al. 2004).

GAAP rules, per se, should not matter; but GAAP rules, per se, should not matter; but there is lots of evidence that firms care a there is lots of evidence that firms care a great deal about GAAP rules that can be great deal about GAAP rules that can be unwound by anyone using firms’ accounts.unwound by anyone using firms’ accounts. FAS 123 (Calomiris 2005)FAS 123 (Calomiris 2005) FAS 133 (Pollock 2005)FAS 133 (Pollock 2005)

Graham et al. 2004Graham et al. 2004 Survey of 401 Financial Executives: What drives Survey of 401 Financial Executives: What drives

decisions about earnings reporting and decisions about earnings reporting and disclosure? disclosure?

Earnings viewed as key for outsiders (even Earnings viewed as key for outsiders (even more important than cash flows), and managers more important than cash flows), and managers are willing to sacrifice value to meet short-term are willing to sacrifice value to meet short-term earnings target (surprisingly, there is less earnings target (surprisingly, there is less concern about targets related to debt concern about targets related to debt covenants, employee bonuses).covenants, employee bonuses). 55% of managers would avoid a very positive NPV 55% of managers would avoid a very positive NPV

project to meet this quarter’s consensus earnings project to meet this quarter’s consensus earnings forecast.forecast.

Smooth earnings are seen as crucial for marketSmooth earnings are seen as crucial for market Voluntary disclosure to Voluntary disclosure to reducereduce perceived risk is perceived risk is

sometimes done, but also avoided to avoid setting sometimes done, but also avoided to avoid setting precedents for future disclosure.precedents for future disclosure.

Not accounting fraud, but neither is this Not accounting fraud, but neither is this strategy long-term value maximizing.strategy long-term value maximizing.

Pollock 2005Pollock 2005 FAS 133 creates differences in treatment FAS 133 creates differences in treatment

depending on whether one qualifies for depending on whether one qualifies for “hedge accounting” and this creates up “hedge accounting” and this creates up front differences in earnings and the risk front differences in earnings and the risk of accounting restatements related to of accounting restatements related to future behavior, or retrospective future behavior, or retrospective judgments about failure to qualifyjudgments about failure to qualify

It shouldn’t matter at all, since people can It shouldn’t matter at all, since people can do the math either way, but perception is do the math either way, but perception is that market is confused by either set of that market is confused by either set of rules. rules.

Restatements based on hedge accounting Restatements based on hedge accounting status changes have negative effectsstatus changes have negative effects

Calomiris 2005Calomiris 2005 ESO expensing should not matter much, since ESO expensing should not matter much, since

it can be reported (and added back) as a it can be reported (and added back) as a separate line (except insofar as earnings are separate line (except insofar as earnings are triggers for contracts).triggers for contracts).

CEOs of Silicon Valley are up in arms, and see CEOs of Silicon Valley are up in arms, and see this as having big effects on their ability to this as having big effects on their ability to maintain stock price and have access to maintain stock price and have access to funding.funding.

Substantively, ESO “expense” doesn’t look Substantively, ESO “expense” doesn’t look like an expense (high ESO “expense” => like an expense (high ESO “expense” => higher P/E, controlling for other factors), and higher P/E, controlling for other factors), and logically it is not an expense or an opportunity logically it is not an expense or an opportunity cost of the firm, although it should be viewed cost of the firm, although it should be viewed as a as a gross costgross cost in managerial accounting. in managerial accounting.

FCF vs. EPS ConclusionFCF vs. EPS Conclusion

We know how to value firms We know how to value firms assuming that only FCF is what assuming that only FCF is what matters in numerator, but in matters in numerator, but in practice, valuation seems not only to practice, valuation seems not only to depend on FCF, or at least market depend on FCF, or at least market participants that control firm participants that control firm decisions believe that it does not decisions believe that it does not only depend on FCF.only depend on FCF.

Proof of Constant L FormulaeProof of Constant L FormulaeRecall that FCF = Dividend + Retained Recall that FCF = Dividend + Retained

earnings + PP + (1-t)DRearnings + PP + (1-t)DRDD

Retained earnings are eventually paid out as Retained earnings are eventually paid out as dividends, so we can rewrite this as:dividends, so we can rewrite this as:

FCF + tDRFCF + tDRDD = Today’s dividend + future = Today’s dividend + future dividends resulting from retained earnings dividends resulting from retained earnings today + Rtoday + RDDDD

The value of the firm is the present value of The value of the firm is the present value of these cash flows for all periods, which is a these cash flows for all periods, which is a set of dividend and interest paymentsset of dividend and interest payments

Retained earnings are reinvested Retained earnings are reinvested We can divide the above into an FCF We can divide the above into an FCF

component paid as dividends and component paid as dividends and discounted at Rdiscounted at RUU a tDR a tDRDD component, component, discounted at Rdiscounted at RD D (use of tax shield is (use of tax shield is roughly as risky as repayment of debt)roughly as risky as repayment of debt)

Proof (Cont’d)Proof (Cont’d)VVLt Lt = E[FCF= E[FCFt+1 t+1 ] / (1+R] / (1+RUU) + tR) + tRDDDDtt /(1+ R /(1+ RDD) +) +

present value of expected Vpresent value of expected VLt+1Lt+1

Note that DNote that Dtt = LV = LVtt , so , soVVLt Lt = E[FCF= E[FCFt+1 t+1 ] / (1+R] / (1+RUU)(1- tLR)(1- tLRDD)/(1+ R)/(1+ RDD) +) +

present value of expected Vpresent value of expected VLt+1 Lt+1 divided bydivided by (1- tLR(1- tLRDD)/(1+ R)/(1+ RDD))

Successive substitution gives the result that present Successive substitution gives the result that present value is all future expected FCFs discounted by value is all future expected FCFs discounted by (1+R(1+RUU)(1- tLR)(1- tLRDD)/(1+ R)/(1+ RDD) )

We also know that present value is the value of We also know that present value is the value of expected future free cash flows discounted by WACC. expected future free cash flows discounted by WACC. Therefore,Therefore,

1+WACC = (1+R1+WACC = (1+RUU)(1- tLR)(1- tLRDD)/(1+ R)/(1+ RDD) ) WACC = RWACC = RUU – tLR – tLRDD(1+R(1+RUU)/(1+R)/(1+RDD))Recall that WACC = RRecall that WACC = RDD(1-t)L + (1-L)R(1-t)L + (1-L)RLL

Thus, RThus, RUU – tLR – tLRDD(1+R(1+RUU)/(1+R)/(1+RDD) = R) = RDD(1-t)L + (1-L)R(1-t)L + (1-L)RLL

(1+R(1+RUU)/(1+R)/(1+RDD) is approx one, so this reduces to:) is approx one, so this reduces to:RRUU =LR =LRDD+ (1-L)R+ (1-L)RLL