SKEMA BUSINESS SCHOOL

Corporate Investment Banking Job Interview Training

Lecture 3 – DCF & Multiples
marco.ghitti@skema.edu
Plan for the Day
Last time
• Introducing the Main Restatement of Financial Statements
• Getting to know Ratio & Common Size Analysis
• Overview on Consolidation Procedures

Today
• Main questions for today:
— Analysing different Cash Flow Measures for Valuation
— Focusing on DCF Valuation Models
— Getting to know the Principles of Relative Valuation
— Focusing on Multiples

For the Next Time

• Review the material covered in class (Damodaran, Ch. 4, 7-8, 10-15, 17-20)
Agenda
1. Cash Flow Measures

2. Cost of Equity

3. Cost of Capital

4. Growth

5. DCF Models

6. Multiples
1. Cash Flow Measures: Free Cash Flows
1. Free Cash flows to Equity (FCFE) – Equity Side Valuation
+ Net Income – Adjusted
+/- Non Cash Expenditure (other than D&A) / Non Cash Revenues
- Net Capex = (Capital Expenditures – D&A)
- Changes in non-cash Working Capital
- (Principal Debt Repayments - New Debt Issues)
= Free Cash Flows to Equity
2. Free Cash flows from Operations (FCFO) – Asset Side Valuation
+ FCFE
+ Interest Expense (1 – Tax Rate)
+ (Principal Debt Repayments - New Debt Issues)
= Free Cash Flows from Operations (FCFO)
____________________________________________________________________
+ Operating Income (EBIT) – Adjusted
+/- Non Cash Expenditure (other than D&A) / Non Cash Revenues
- Taxes on EBIT
- Reinvestment Needs (Net Capital Expenditures and Working Capital)
= Free Cash Flows from Operations (FCFO)
[Ignoring preferred dividends. If preferred stock exist, preferred dividends will also need to be netted out]
2. Cost of Equity: Models
• All models of risk and return in finance are built around:
− a rate that investors can make on riskless investments; and the
− risk premium(s) investors charge to invest in the average-risk investment.

!"#& % ' #( ) *!" #$ + #( %

Capital Asset
Pricing Model • Only one source of market risk, captured
in market portfolio, whose expected
return is !"#$ %
• Beta expresses the exposure to such risk
0

Multifactor !"#& % ' #( ) , *- !".#- + #(/%

Models -12
• Multiple “i” sources of risks, whose
expected return is !"#- %
• Betas express the exposure to such risks
2. Cost of Equity: Determinants
• Government issues (no default risk) Data Provider
Risk-free • Zero coupon (no reinvestment risk) • Bloomberg
(Rf) • Duration matching with cash flows • Factset
• Currency/inflation consistency • Eikon

Data Provider

• Forward looking (implied ERP) • Bloomberg

Risk premium • Factset
(ERP) • Consistency with Rf
• Historic ERP • Damodaran
• Fernandez

• Bottom-up approach Data Provider

• Broad mkt index (MSCI) • Bloomberg
β levered • Factset
• Long vs short time period
(βl)
• Return frequency • Eikon
• Datastream
β4 ' β5 · 1 ) 1 + 89 · : ⁄;
2. Cost of Equity: Risk-free (Principles)
• On a risk-free asset, the actual return is equal to the expected return.
Therefore, there is no variance around the expected return.
• For an investment to be risk-free, then, it has to have:
− no default risk;
− no re-investment risk.

1. Time horizon:
− the risk-free rates in valuation will depend upon when the cash flow is expected to
occur and will vary across time;
− practical solutions, if the term-structure is well-behaved, involve “duration
matching”.
2. Not all government securities are risk-free:
− some governments face default risk and the rates on bonds issued by them will not be
risk-free. This is true also if they borrow in a currency other than their own.
3. Consistency principle:
− nominal cash-flows require nominal risk-free rates;
− currency of the cash-flows must be the currency of the risk-free rate.
2. Cost of Equity: Risk-free (Real vs Nominal)
• Under conditions of high and unstable inflation, valuation is often
done in real terms.
• For consistency, cash flows are estimated using real growth rates and
without allowing for growth coming from price inflation.
• How to estimate real expected rate of return?

1. “Subtracting” inflation rate (standard approach):

− Rf real ≈ Rf nominal – expected inflation (i) → holds only for low “i”.
− Rf real ≈ {[(1 + Rf nominal) / (1 + i)] -1 }
2. Use inflation indexed Treasuries (TIPs):
− TIPs offer a guaranteed real return → only for US (low and stable “i”).
3. No financial markets frictions (Capitals can flow freely):
− no differences in real Rf across countries → use TIPs for all countries.
4. Financial markets frictions:
− expected long term real Rf should equal Expected long term growth (“g”).
2. Cost of Equity: Risk-free (Country Differences)

Source: A. Damodaran
2. Cost of Equity: Risk-free (Default Spread)
1. Local Currency Government Bond
1. Default spread approach:
• Rf Local Currency (LC) = Government Bond rate – Default Spread
• Default spread are taken from rating USD credit spread (see next)
• For countries which do not issue USD bonds, use the average spread for other
countries in the same rating class.
2. Insurance (Credit Default Spread – CDS) approach:
• Rf Local Currency (LC) = Government Bond rate – CDS
2. Build-up approach
• If there is no traded government bond in local foreign currency
• Build up Rf = Expected inflation + Expected l/t real growth rate
3. Derivatives Markets (no frictions in capital markets)
• Use Covered-Interest Parity (CIP) to back out Rf in Local Currency (LC)
.-./0&' /
• =>? !?" ?!$% &', )*+ ' *,>$ ?!$% &', )*+
.-./0)*+ /

4. Risk-free Rate Conversion (frictions in capital markets)

• Use Uncovered-Interest Parity to back out Rf LC
.-.12,%3$%" 4506!$7>5)* /
• - ) /0)* ' .- ) /0&' /
.-.12,%3$%" 4506!$7>5&' /
2. Cost of Equity: ERP (Principles)
• The Equity Risk Premium: the premium a well diversified marginal
investor requires to hold the market portfolio rather than a risk-free
asset.
• The Historical Equity Risk Premium: the premium that stocks have
historically earned over riskless securities over long time periods.
− Implicit assumption: history can forecast the future.
• The Implied Equity Risk Premium: the forward looking premium that
is implicitly priced in the current stock market level, given expected
aggregate cash flows and risk-free rates.
− Implicit assumption: the market, overall and on average, is correctly priced.

There is no consensus amongst academics and practitioners about the

correct measure of the equity risk premium (Fernandez et al., 2017).
2. Cost of Equity: ERP (Principles)
• Historical ERP for US
Arithmetic Average Geometric Average
ERP vs T-bill ERP vs T-Bond ERP vs T-Bills ERP vs T-Bond
1928 – 2017 8.09% 6.38% 6.26% 4.77%
Std error 2.10% 2.24%
1968 – 2017 6.58% 4.24% 5.28% 3.29%
Std error 2.39% 2.70%
2008 – 2017 9.85% 5.98% 8.01% 4.56%
Std error 6.12% 8.70%

• Implied ERP (January 2008 and January 2009)

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%
2. Cost of Equity: ERP (Country Risk Premium)
1. Assume that every company in the country is equally exposed to country risk:
#&,89: ' #; ) * ;<=89 ) ><=?,89:
1 ) B@A
#&,@A ' .1 ) #&,89: / · +1
1 ) B89:
− Implicitly, this is what you are assuming when you use the local Government’ s dollar
borrowing rate as your risk-free rate.
2. Assume that a company’ s exposure to country risk is similar to its exposure to
other market risk:
#&,89: ' #; ) * ;<=89 ) ><=?,89:
1 ) B@A
#&,@A ' .1 ) #&,89: / · +1
1 ) B89:
− Implicit assumption: country risk is a portion of market risk.
3. Treat country risk as a separate risk factor and allow firms to have different
exposures to country risk:
#&,89: ' #; ) * ;<=89 ) C.><=?,89: /
1 ) B@A
#&,@A ' .1 ) #&,89: / · +1
1 ) B89:
− Implicit assumption: multifactor model.
2. Cost of Equity: ERP (Country Risk Premium)
There are 3 ways to compute CRP. These are shown below.

• CRP is equal to the default spread of the bond issued by the country.
#&,89: ' #; ) * ;<=89 ) :D(EFG8 HI#DEJ

• CRP is based upon the market volatility relative to U.S. stock market.
H8ELJE#J :DMBE8BNL?
;<=? ' ;<=89 ⋅
H8ELJELJ :DMBE8BNL89
><=? ' ;<=? + ;<=89

• CRP is computed by multiplying the bond default spread by the

relative volatility of stock and bond prices in that market.
><=? ' >NFL8#O :D(EFG8 HI#DEJ ⋅ σQR5-ST,? ⁄σUV0WX,?
2. Cost of Equity: Beta (Principles)
• The standard procedure for estimating betas is to regress stock returns (Ri)
against market returns (Rm):
<- ' E ) * <Y
>NM <- , <$ [-,$
*' ' \
ZE# <$ [$
—“a” is the intercept and β is the slope of the regression, which corresponds to the β of
the stock, and measures the riskiness of the stock, relative to the risk of the market.
• “Reconciling” CAPM and the regression, the Jensen’s “alpha”:
!"#- % ' #( ) *! #$ + #( ' #( 1 + * ) *! #$
— compare “a” from the regression (ex-post) with “rf(1-β) “ (ex-ante):
a > rf(1-β) stock did better than expected, over a certain period
a = rf(1-β) stock did as expected, over a certain period
a < rf(1-β) stock did worse than expected, over a certain period

• Blume’s adjustment (e.g. Bloomberg): *]W^ ' *_]` 2/3 ) 1.00 1/3 .
• This approach presents the following shortcomings:
• high standard errors;
• firm’s business mix and leverage over the regression period, not the current ones;
• not available for private firms / not reliable for illiquid markets.
2. Cost of Equity: Beta (Problems)
The major problems we have seen can be summarized as follows:
1. Historical returns:
The use of a longer time period allows for a greater number of observations in the
regression. Longer time periods, though, might be biased due to structural changes in the
firm/industry risk profile. This is the main reason to support the use of a shorter period
of historical records in the range between 2 and 5 years.
2. Return type:
Both stock returns and market returns should be calculated considering both the capital
gains and the dividends received during the period under consideration.
Some sources calculate stock and market index returns only based on price changes
without considering dividends.
3. Frequency (Return Interval):
Using daily returns increases the number of observations in the regression. Nevertheless,
such an approach exposes the estimation process to a significant bias in beta estimates
caused by the lack of liquidity of certain stocks.
4. The market index:
Due to the emergence of internationally diversified investors who allocate their assets in
different markets, it is becoming increasingly common to calculate β with respect to
international indices, (e.g. Morgan Stanley Capital Index).
2. Cost of Equity: Beta (Solutions)
1. Modify the regression beta by:
— changing the index used to estimate the beta;
— changing the frequency of returns;
— changing the length of the observation period;
— reducing the biases (see Dimson, 1979; Schles and Williams (1977)).

2. Estimate the beta for the firm from the bottom-up (preferable
approach). This will require (more on this later):
— understanding the type of business / businesses the firm is in;
— understanding the business mix of the firm;
— estimating the financial leverage of the firm.

j k
f g ' f ! ⋅ h! ) f i ⋅ hi ' f ! ⋅ ) fi ⋅ ⟷ fg ' ∑571- f7 ⋅ h7
j.k j.k
2. Cost of Equity: Beta (Bottom-up Approach)
Beta of Equity (Levered β)

Financial Leverage:
Beta of Firm Other things remaining equal, the greater
(Unlevered β) the proportion of capital that a firm raises
from debt, the higher its equity beta will
be.

Nature of product or service offered Operating Leverage

by company: (Fixed Costs as % of total costs):
Other things remaining equal, the Other things remaining equal, the
more discretionary the product or greater the proportion of the costs that
service, the higher the beta. are fixed, the higher the beta of the
company. Implications
1. Highly levered firms
should have higher
Implications Implications betas than firms with
less debt.
1. Cyclical companies should have higher 1. Firms with high infrastructure needs
betas than noncyclical companies. and rigid cost structures should have 2. Equity β (Levered β)
2. Luxury goods firms should have higher higher betas than firms with flexible = Unlevered β ·
betas than basic goods. cost structures. (adjustment)
3. High priced goods/service firms should 2. Smaller firms should have higher
have higher betas than low prices betas than larger firms.
goods/services firms. 3. Young firms should have higher
4. Growth firms should have higher betas. betas than more mature firms.
2. Cost of Equity: Beta (Bottom-up Approach)

Adjust the business β Use the financial

for the operating leverage of the firm to
Start with the β of the
leverage of the firm to estimate the levered
business the firm is in
arrive to the unlevered (equity) β for the firm
β for the firm (Hamada’s equation)

:
β4&n&o&W ' β504&n&o&W · 1 ) 1 + 89 ·
;
3. Cost of Capital: Models
Tax Rate Market Value
1. Debt
Marginal Tax Rate
2. Equity
reflecting tax benefits
3. Hybrid Securities
of Debt

: ; H
pq>> ' #W .1 + 89 / ) #& ) #X
: ) ; ) H Text : ) ; ) H :);)H

Cost of Debt (rd) Cost of Equity (re) Cost of Hybrid Securities (rs)

Based of: Please, refer to previous slides Has to reflect expected

- current cost of borrowing payments and current
- synthetic rating market values of any hybrid
securities
3. Cost of Capital: Determinants
• Risk-free consistency Data Provider
• Default spread: Bloomberg
Cost of debt •
(Rd) − CDS spread • Factset
− Rating • Eikon
− ICR

Data Provider
• Nominal vs marginal • Bloomberg
Tax rate • Marginal and effective • Factset
(Tc) tax rate should be close in
• Damodaran
the long term
• KPMG

• Always use market value Data Provider

(Book value if no listed • Bloomberg
Weights securities) • Factset
(D/E) • Target leverage • Eikon
• Consider all claims • Brokers
(hybrid securities)
4. Growth: Fundamental Approaches (equity side)
• The Fundamentals’ approach estimates Growth as an endogenous variable
rather than an exogenous one.
1. EPS Growth:
r ' /%$%5$7>5 /!$7> i · /%$s?5 >5 1ts7$u /v1
xyz {xy.z|}/
• Growth in Net Income (NI), wS ' (1);
xy.z|}/
xyz|}
• <~;S{2 ' ↔ ÉÑS{2 ' ÖZS{\ · <~;S{2 (2); BV = book value of Equity.
ŸÄÅ|Ç
• Assuming no Equity injections:
• ÉÑS ' ÖZS{2 · <~;S ' ÖZS{\ ) <D8EBLDJ ;E#LBLwÜS{2 · <~;S .3/
• Assuming constant ROE (<~;S ' <~;S{2 ) and substituting (2) and (3) into (1):
<D8EBLDJ ;E#LBLwÜS{2
wS ' · <~; ' <D8DL8BNL #E8BN · <~; ' á · <~; .5/
ÉÑS{2
All figures should be adjusted consistently with the adjustments made to Cash Flows
(R&D, Operating Leases, …)
Implicit assumptions:
- constant ROE over time;
- no equity issuance is allowed, therefore NI Growth = EPS’ Growth;
- no other comprehensive income (OCI) in the book value of equity.
4. Growth: Fundamental Approaches (equity side)
• The Fundamentals’ approach estimates Growth as an endogenous variable
rather than an exogenous one.
2. Net Income (NI) Growth:
r ' i · /v1
• same derivation as approach 1, but the retention ratio (b);
• ;âFB8O #DBLMDÜ8DJS ' .>EIDäS + :&qS / ) Δp>S )
+ ÉDç :Dá8 BÜÜFDJS + :Dá8 <DIEBJS
QR5-ST o&-0n&XS&Wz
• Equity Reinvestment Rate: áS '
xyz
• Expected Growth Rate: wS.2 ' áS · <~;
All figures should be adjusted consistently with the adjustments made to Cash Flows
(R&D, Operating Leases, …).
Implicit assumptions:
- constant ROE over time;
- Equity issuance is allowed;
- Expected growth in net income may be different from expected growth in EPS due
to equity issuance;
- no other comprehensive income (OCI) in the book value of equity.
4. Growth: Fundamental Approaches (asset side)
• We can apply the Fundamentals’ approach to estimate Growth of
Operating Income.
3. Stable Return on Capital (ROC) scenario:
r ' i · /v'
• b = reinvestment rate;
A]é&èz {:&êz .ë íAz
• Reinvestment Rate '
QUyìz 2{Sî
QUyì 2{Sî
• Return on Capital (ROC) =
.Uï QR5-ST.Uï V; :&ñS {A]Xó/
All figures should be adjusted consistently with the adjustments made to Cash Flows
(R&D, Operating Leases, …).
Implicit assumptions:
- constant ROC and EBIT margins over time;
- “b” from recent financial statements is forward looking;
- accounting ROC is a good measure of required returns on assets (it is better to
check with industry average);
- no Other Comprehensive Income in the Book Value of Equity.
4. Growth: Fundamental Approaches (recap)
• Fundamental equation for growth:
− Dividend approach: w ' <D8DL8BNL <E8BN á · <~; ) ò%<~;
− FCFE approach: w ' ;âFB8O <DBLMDÜ8YDL8 <E8D · <~; ) ò%<~;
− FCFF approach: w ' <DBLMDÜ8YDL8 <E8D · <~> ) ò%<~>
• In stable growth, firms cannot count on efficiency delivering growth,
because they reached stable level and thus they have to reinvest to deliver the
growth rate that you have forecast (i.e. ò%<~; and ò%<~C goes to zero/:
− Dividend approach: w ' <D8DL8BNL <E8BN á · <~;
− FCFE approach: w ' ;âFB8O <DBLMDÜ8YDL8 <E8D · <~;
− FCFF approach: w ' <DBLMDÜ8YDL8 <E8D · <~>
• Reinvestment rate in stable Growth is a function of stable Growth rate and
what the firm will earn as a return on capital in perpetuity:
− Dividend approach: <D8DL8BNL <E8BN ' w/<~;
− FCFE approach: ;âFB8O <DBLMDÜ8YDL8 <E8D ' w/<~;
− FCFF approach: <DBLMDÜ8YDL8 <E8D ' w/<~>

Need to estimate both “g” and ROE/ROC: assumptions’ consistency is the key
5. DCF Valuation: DDM Models
Key concept: Equity value = PV of expected dividends on it

S1£
! :=HS
;âFB8O ZEGFD ' ,
1 ) ¢& S
S12
where:
− E(DPS) = Expected DPS;
− ke = Cost of Equity (required return on equity).
• When an investor buys a stock, s/he expects to get two types of CF:
(i) dividends during the period the stock is held;
(ii) price at the end of the holding period (i.e. capital gain). Price itself can be
seen as a function of future DPS in perpetuity.
• The most used DDM models are the:
− Gordon Growth Model;
− Two Stages Model.
5. DCF Valuation: DDM Models
• The Gordon model can be used to value a firm that is in “steady
state” with dividends growing at a rate that can be sustained forever:
! :=HS.2
;âFB8O MEGFDS '
.¢& + w/
where:
− E(DPS) = Expected DPS;
− ke = Cost of equity (required return on equity);
− g = Stable growth rate.
• Stable growth rate:
+ w ' 1 + =EONF8 #E8BN · <~;;
+ Growth of DPS should be equal to growth of earnings.
• Limitations:
+ it is extremely sensitive to assumptions about “g”.
• Firms Model Works Best for:
+ firms growing at a rate ≤ the nominal growth rate in the economy;
+ firms with well-established and constant dividend pay-out policies.
5. DCF Valuation: FCFE Models
• With a FCFE model we discount potential dividends rather than
actual dividends (as done with the traditional DDM). Thus:
− the FCFE models are “simple” variants on the DDM, with one significant change:
FCFE replace dividends.
• By replacing dividends with FCFE we implicitly assume that the FCFE will
be paid out to stockholders. There are two consequences.
1. Cash.
No future cash build-up since the available cash after debt payments and
reinvestment needs is assumed to be paid out to stockholders each period.
2. Growth.
Expected growth in FCFE will include growth in income from operating assets and
not growth in income from increases in marketable securities.

• Many firms pay out less to stockholders (in dividends and buybacks), than
they have available in FCFE:
a) Desire for stability/ Signaling prerogatives;
b) Future investment needs;
c) Tax optimization.
5. DCF Valuation: FCFE Models
• This model is designed to value firms that are growing at a stable growth rate
and are hence in “steady state”:
! §>§;S.2
;âFB8O MEGFDS '
¢D + w
where:
− E(FCFE) = Expected FCFE;
− ke = Cost of equity (required return on equity);
− g = Stable growth rate.
• Stable growth rate:
− w ' ;âFB8O <DBLMDÜ8YDL8 #E8D · ÉNL•Eܶ <~;;
− stable growth rate consistent with the nominal growth rate in the Economy/Industry.
• Limitations:
− it is extremely sensitive to assumptions about “g”;
− if we estimate “g” looking at the industry average, the valuation can be skewed.
• Firms model works best for:
− better model to use than the DDM for stable firms that pay out dividends that are
unsustainably high or are significantly lower than the FCFE.
5. DCF Valuation: FCFE Models
DDM FCFE Model
Implicit Only dividends are paid. The FCFE is paid out to stockholders.
assumption Remaining portions of earnings The remaining earnings are invested only
are invested back into the firm, in operating assets.
some in operating assets and some
in cash and marketable securities.
Expected Measures growth in income from Measures growth only in income from
growth both operating and cash assets. In operating assets. In terms of fundamentals,
terms of fundamentals, it is the it is the product of the equity reinvestment
product of the retention ratio and rate and the noncash ROE.
ROE.

• FCFE models and DDM can lead to the same value, when:
- dividends = FCFE (trivial case);
- FCFE > dividends, but the excess cash over dividends (FCFE -dividends) is
invested in projects with zero NPV
5. DCF Valuation: FCFF Models
• This model, unlike the DDM and FCFE model, values the firm
(Enterprise Value) rather than its sole equity.
− the value of equity, however, can be extracted from the value of the firm by
subtracting the market value of outstanding (net) debt.
• The advantage of using the firm approach (asset side) is that:
− CF relating to debt do not have to be considered explicitly since the FCFO is
a pre debt CF; whereas,
− they have to be taken into account in estimating FCFE.

• In cases where the leverage is expected to change significantly over

time, this is a significant time saver, since:
− estimating (i) new debt issues and (ii) debt repayments when leverage is
changing can become increasingly cumbersome;
− however, the firm valuation approach does require information about (i)
debt ratios and (ii) interest rates to estimate the WACC.
5. DCF Valuation: FCFF Models
• A firm with FCFF growing at a stable growth rate (steady-state) can be
valued using the following equation(1):
§>§§1
;Z '
pq>> + w
where:
− FCFF = Expected FCFF;
− WACC = Weighted average cost of capital;
− g = Stable growth rate.
• Stable growth rate:
− w ' <DBLMDÜ8YDL8 #E8D · <~>;
− stable growth rate consistent with the nominal growth rate in the Economy/Industry.
• Limitations:
− it is extremely sensitive to assumptions about “g” and CAPEX relative to D&A;
− sensitivity is accentuated when using WACC (which is lower than ke);
− WACC should also be reflective of a Stable Growth firm (β, D/E).
• Firms model works best for:
− firms that either have very high or very low leverage or are changing their leverage.
(1) For a two step model use the same equation for the FCFE model, substituting FCFE with FCFF and Ke with WACC.
5. DCF Valuation: Two-stage Models
• The DDM, FCFE and FCFF Models can be adapted to reflect two or more
different stages of growth rather than directly assuming a steady state.
• DDM (Two-stage):
S10 S10
! :=HS ! =0 ! :=HS ! :=H0.2
;âFB8O MEGFD ' , S) 0 ', S) 0
S12 1 ) ¢&,óß 1 ) ¢&,óß S12 1 ) ¢&,óß ¢&,XS + w0 1 ) ¢&,óß
• FCFE (Two-stage):
S10 0
! §>§;S ) ®Z ! §>§;S ! §>§;0.2
;âFB8O MEGFD ' , ', S) 0
1 ) ¢&,óß 8 1 ) ¢&,óß L
1 ) ¢&,óß ¢&,XS + w0 1 ) ¢&,óß
S12 S12
• FCFF (Two-stage):
S10 0
! §>§§S ) ®Z ! §>§§S ! §>§§0.2
;Z ' , ', S) 0
1 ) pE••óß 8 1 ) pE••óß L
1 ) pE••óß pE••XS + w0 1 ) pE••óß
S12 S12

where:
− ke = Cost of equity (hg = high growth; st = stable growth);
− Wacc = Weighted average cost of capital (hg = high growth; st = stable growth);
− g = Growth rate (gn = stable growth rate).
5. DCF Valuation: APV Models
• The APV approach estimates the value of the firm in three steps:
1. Value of unlevered firm:
ZEGFD N( FLGDMD#DJ (B#Y ' ; §>§~1 ⁄ ©F + w0
or
='=v$ ='=v5¨- ⁄ ™s,Í$ {r5
Value of unlevered firm = ∑$15
$1- $ ) 5
-. ™s,´r -.™s,´r

- ρu = Unlevered ke (“hg” – high growth; “st”: stable growth).

2. Expected tax benefit (TB) from borrowing:
– D is low and fixed: =Z ®Ö ' 89 · ¢W · : ⁄¢W ' 89 :
– D is “high” and/or D/E predetermined:
5
! $3 · Ð" · +$ $3 · Ð" · +5.-
gÆ Øk ' , )
- ) ™s $ - ) ™s 5 · .™s + r5 /
$1-
3. Estimating expected bankruptcy costs (BC) and net effect:
gÆ k' ' ±!k'
- ̟a = Probability of default;
- BC = Present value of the bankruptcy cost.
Æ!6s% >0 6%Ò%?%" 07?Ó ' )56%Ò%?%" Æ!6s% ) gÆ Øk + gÆ.k'/
5. DCF Valuation: APV Models
• The advantage of the APV approach are the following:
− it (i) separates the effects of debt into different components and (ii) allows the analyst
to use different discount rates for each component;
− we don’t assume that the debt ratio stays unchanged forever, which is an implicit
assumption in the cost of capital approach;
− we have the flexibility to keep the dollar value of debt fixed and to calculate the
benefits and costs of the fixed dollar debt.
• There are difficulties, though, that we ought to take into account:
− it is difficult to estimate the probabilities of default and cost of bankruptcy;
− many analyses ignore the expected bankruptcy costs, leading them to the conclusion
that firm value increases as firms borrow money. Not surprisingly, this would yield to
the conclusion that the optimal debt ratio for a firm is 100% debt.
• Generally speaking:
− with the same assumptions, the APV and the cost of capital conclusions give very
similar answers. However, the APV approach is more practical when firms are
evaluating a “stable” dollar amount of debt, while the cost of capital approach is
easier when firms are analysing debt proportions (D/E).
6. Relative Valuation: Underlying Principles
• The value of an asset is compared to the values of
comparable assets.
Principles • Assets need to be actively traded on well function markets.
• You can use either stock market multiples or transaction
multiples.

• To value firms on a relative basis, prices have to be

standardized.
Uniformity • Covert prices into multiples of earnings (P/E), book values
(P/BV), EBITDA (EV/EBITDA), etc..
• Keep consistency between numerator and denominator.

• To value firms on a relative basis, it is crucial to identify

comparable firms (peers).
• Assess similarities based on:
Peers
− growth potential and activity;
− riskiness of business (and country);
− cash flow generation.
6. Relative Valuation: Underlying Principles
• How to define the right peer group:

• Comparables will be identified on the basis of the main activity

Activity • In case of diversification, portfolios can be vertically integrated or
geographically

• The markets may be growing at a different pace, and the multiples

Country may differ from country wise
• Some accounting issues may occur

• 2 to 3 years Growth will be a strong support to higher multiples

Growth • PEG is nevertheless not a good indicator, introducing usually much
dispersion in the multiples

• Risk associated with the cyclicality, operating leverage, financial

Risk debt, geographic and political unrest
• The higher the risks, the lower the multiples
6. Relative Valuation: Underlying Principles
Market Value of Equity Market Value for the Firm Market Value of Operating
Assets of Firm
Firm Value = Mkt Value of Equity
+ Mkt Value of Debt Enterprise Value (EV) = Mkt
Value of Equity + Mkt Value of
Debt - Cash

ÉFYD#E8N# ' p¶E8 ONF E#D IEOBLw (N# 8¶D EÜÜD8

¥FG8BIGD '
:DLNYBLE8N# ' p¶E8 ONF E#D wD88BLw BL #D8F#L

Revenues: Earnings: Cash flow: Book Value:

a) Accounting revenues; a) To Equity investors: a) To Equity: a) Equity:
b) Drivers: − net income; − net income + − BV of equity.
− customers; − earnings per share depreciation; a) Firm:
− subscribers; (EPS). − FCFE. − BV of equity + BV of
− units; a) To Firm: a) To Firm: debt.
− …. − operating income − FCFO. c) Invested capital:
(EBIT). − BV of equity + BV of
− EBIT + DA (EBITDA) debt – Cash.
6. Relative Valuation: Valuation Perspective

Source: Massari et al.

6. Relative Valuation: Different Multiples
• Multiples can refer to values taken from two market context:
1. the stock market (stock market multiples);
2. the market for corporate control (deal multiples).
• These two types of multiples usually lead to the estimation of
different values. In normal situation:
− stock multiples express stand-alone values.
• These multiples cannot provide sufficient information to estimate the market
price attached to the entire firm.
− deal multiples refer to expected market prices.
• These multiples cannot provide reliable stand-alone values.
• Analysts usually try to overcome the problem of expected market
prices by adjusting:
− the valuation estimate obtained through stock market multiples with the so-
called acquisition premium.
6. Valuation Process: Key Steps
• There are four basic steps to using multiples wisely and for detecting
misuse in the hands of others:
1. define the multiple → definitional test
The first step is to ensure that the multiple is defined consistently and that it is
measured uniformly across the firms being compared.
2. describe the multiple → descriptional test
The second step is to be aware of the cross–sectional distribution of the
multiple, not only across firms in the sector being analyzed but also across the
entire market;
3. analyze the multiple → analytical test
The third step is to analyze the multiple and understand not only what
fundamentals determine it but also how changes in these fundamentals
translate into changes in the multiple.
4. apply the multiple → application test
The final step is finding the right firms to use for comparison and controlling
for differences that may persist across these firms.
6. Valuation Process: Key Steps
• In more details, the valuation process is the following:

Source: BNP Paribas

6. Equity side Multiples: P/E
• P/E multiple is the most widely used (and misused) of all multiples.
=
' ¥E#¢D8 MEGFD ID# ܶE#D⁄;E#LBLwÜ ID# ܶE#D
;
• There are a number of variants on the basic P/E based on:
1. Price:
− it is usually the current price (though some analysts like to use average
price over the last 6 months or year to smooth volatility).
2. Earnings per share:
− time variants: (i) EPS in most recent financial year (current), (ii) EPS in
most recent four quarters (trailing), (iii) EPS expected in next fiscal year or
next four quarters (both called forward), or (iv) EPS in some future year;
− share outstanding variants: (i) primary EPS, (ii) diluted EPS or (iii)
partially diluted EPS;
− composition variants: before or after extraordinary items;
− accounting variants: measured using different accounting rules (operating
leases, R&D, etc.).
6. Equity side Multiples: P/E
• The current P/E ratio for a stable growth firm can be derived from the
stable growth DDM:
=µ =EONF8 #E8BN 1 ) w0
' >F##DL8 =; '
;=Hµ ¢& + w0
• If the P/E ratio is stated in terms of expected earnings in the next time
period (EPS1), we can derive the forward P/E ratio:
=µ =EONF8 #E8BN
' §N#çE#J =; '
;=H2 ¢& + w0

• We can state the payout ratio as a function of the (i) expected growth
rate and (ii) return on equity (ROE):
=EONF8 #E8BN ' 1 + w0 ⁄<~;0
• Substituting back into the aforementioned equation, we get:
=µ 1 + w0 ⁄<~;0
' §N#çE#J =; '
;=H2 ¢& + w0
6. Equity side Multiples: P/BV
• The Price-to-Book Value (P/BV) ratio is computed by dividing the
market price per share by the current BV of equity per share:
= =#B•D ID# ܶE#D
'
ÖZ ÖNN¢ MEGFD N( DâFB8O ID# ܶE#D
• While the multiple is fundamentally consistent there is a potential for
inconsistency:
1. shares outstanding. If there are multiple classes of shares outstanding, the price per
share can be different for different classes of shares and it is not clear how the book
equity should be apportioned among shares;
2. preferred stocks. You should not include the portion of the equity that is attributable
to preferred stocks in computing the BV of equity, since the market value of equity
refers only to common equity.
• Some of the problems can be alleviated by computing the P/BV ratio
using the total market value of equity and BV of equity:
= ¥E#¢D8 MEGFD N( DâFB8O
'
ÖZ ÖNN¢ MEGFD N( DâFB8O
6. Equity side Multiples: P/BV
• The determinants of the P/BV ratio can be derived from a DCF model:
− the value of equity in a stable growth DDM can be written as:
:=H2
=µ '
¢& + w0
• Substituting for DPS1 = EPS1 · (Payout ratio), the value of the equity
can be written as:
;=H2 · =EONF8 #E8BN
=µ '
¢& + w0
• Defining the ROE = EPS1 / BV of Equity0, the value of equity can be
written as:
ÖZµ · <~; · =EONF8 #E8BN
=µ '
¢& + w0
• Rewriting in terms of the P/BV ratio:
=µ <~; · =EONF8 #E8BN
'
ÖZµ ¢& + w0
6. Asset side Multiples: EV/EBITDA
• The EV/EBITDA multiple relates:
1. the total market value of the firm net of cash (EV); to the
2. earnings before interest, taxes, D&A (EBITDA) of the firm:
;Z ¥E#¢D8 MEGFD N( DâFB8O ) ¥E#¢D8 MEGFD N( JDá8 + >Eܶ
'
;ÖÑ®:q ;ÖÑ®:q
• Since the interest income from the cash is not counted as part of the
EBITDA:
− not netting out the cash will result in an over-statement of the EV/EBITDA
multiple.
• The EV/EBITDA multiple is particularly useful for firms in sectors
that require:
− large investments in infrastructure; with
− long gestation periods.
Telecom companies or companies involved in airport or toll road construction
would be good examples.
6. Asset side Multiples: EV/EBITDA
• The determinants of the EV/EBITDA multiple can be extracted using
a simple FCFO valuation model:
§>§~2
ZEGFD N( (B#Y ' ;Z '
pq>> + w
• We can write the FCFO in terms of the EBITDA:
§>§~ ' ;ÖÑ® 1 + 8 + >q=;Ö + :q ) ∆p>
' ;ÖÑ®:q + :q 1 + 8 + >q=;Ö + :q ) ∆p>
' ;ÖÑ®:q 1 + 8 + :q 1 + 8 + <DBLMDÜ8YDL8
• Substituting back into the first equation, we get:
;ÖÑ®:q2 1 + 8 + :q2 1 + 8 + <DBLMDÜ8YDL82
;Z '
pq>> + w
• Dividing both sides by the EBITDA and removing the subscripts
yields the following:
:q <DBLMDÜ8YDL8
;Z 1 + 8 + 1 + 8 +
' ;ÖÑ®:q ;ÖÑ®:q
;ÖÑ®:q pq>> + w