Prof. Antonio Renzi€¦ · Dall’approccio top down all’approccio bottom up (7/7) Motivations...

Venture evaluation (2) : the equity cost

Prof. Antonio Renzi

Entrepreneurship and new ventures finance

Agenda

The need to contextualize the equity cost analysis

The equity cost analysis in the neoclassical perspective

The equity cost analysis as a piece of actualization process

The Capital Asset Pricing Model (CAPM)

The comparables approach

2


The bottom up approach: general framework

The reworking of CAPM according to bottom up approach

Specific risk according to bottom up approach

The reworking of CAPM according to the Total Beta Model

The reworking of CAPM according to four correction factors

The need to contextualize the equity cost analysis

Key word: Contextualization

• Contextualization of the valuation object

• Contextualization the subjective perspective of the investor

In venture finance processes the valuation objects are new ventures

The actors involved in a venture finance process tend to have a longterm perspective.

Key word: Contextualization

• Contextualization of the valuation object

• Contextualization the subjective perspective of the investor

In venture finance processes the valuation objects are new ventures

The actors involved in a venture finance process tend to have a longterm perspective.

The equity cost analysis as a piece of actualization process

DCF and equity cost (kej)

τ)(1SD

Dk

SDS

kerateDiscountjj

jij

jj

jj

Asset side valuation

firm toflowscashFreeresultsExpected

τ)(1SD

Dk

SDS

kerateDiscountjj

jij

jj

jj

jkerateDiscount

Equity side valuation

equity toflowscashFreeresultsExpected

The equity cost analysis as a piece of an actualization process

APV and equity cost

Unleveredequity value

)(kecostequityUnleveredrateDiscount j(u)

flowscashfree UnlveredresultsExpected

Levered equity value

(+)Fiscal benefits

Failure risk(-)

Financial leverage

The equity cost analysis in neoclassical perspective

Market equilibrium hypothesis

The market equilibrium hypothesis is linked to the followingassumptions:

• Informational efficiency

• Economic rationality of investors

The market equilibrium hypothesis is linked to the followingassumptions:

• Informational efficiency

• Economic rationality of investors


Informational efficiency• Everyone has the availability of the best information about eachstock;• Therefore, among the different types of investors, there aren'tdifferences about the possibility to optimize investments decisions.

Economic rationality• Each investor aspires to maximize his (or her) economic utility• The economic utility is maximized when for a given level of risk theexpected return is maximum, or for a given level of expected returnthe risk is minimum.• Each investor has the knowledge to make a risk-return analysis• The personal emotions of investors don't act on their investmentdecisions

• Each investor aspires to maximize his (or her) economic utility• The economic utility is maximized when for a given level of risk theexpected return is maximum, or for a given level of expected returnthe risk is minimum.• Each investor has the knowledge to make a risk-return analysis• The personal emotions of investors don't act on their investmentdecisions


Informational efficiencyEconomic rationality

Homogeneityof expectations

Equilibrium hypothesis and market prices

Equilibrium: Demand of Stock = Supply of stocks

Market prices = Fair values (or intrinsic values)

No stock is overestimated or underestimated

The three fundamental theoretical steps

Markowitzs’sTheory

FOCUS

Financial portfolios’optimization

Tobin’sTheorem

Expected returnin equilibrium conditions

AUTHORS

Tobin’sTheorem

Expected returnin equilibrium conditions

Capital AssetPricing Model

(CAPM) ofSharp and

others

Expected return infunction of systematic

risk

Specific risk and systematic risk


Portfolio Risk

Diversificationprocess

Maxdiversification

Number of stocks

Systematicrisk

Specificrisk

Maxdiversification


Assumptions

• Market equilibrium;• Diversification as tool for optimizing financial portfolios• The investor operates just as a take-over and take-risk: He can’taffect the market prices.

Variables of CAPM:• Risk free rate (Rf);• Market return(Rm );•Beta (βj).

kej = f(Rf, Rm, βj)

Assumptions

• Market equilibrium;• Diversification as tool for optimizing financial portfolios• The investor operates just as a take-over and take-risk: He can’taffect the market prices.

Variables of CAPM:• Risk free rate (Rf);• Market return(Rm );•Beta (βj).

kej = f(Rf, Rm, βj)

jmj βRf)-R~(Rfke RfR~Rfke

βm

jj

2m

mj,j σ

σβ

CAPM Formula


σj,m = covariance j,m; σ2j = variance m

Covariance is a measure of how much two random variables change together.

The covariance j,m measures how j return changes for each change of theaverage return of market portfolio and vice versa.

Variance m measures the capital market volatility.

σj,m = systematic risk of j

σ2j = 100% of systematic risk

βj = systematic risk coefficient

Covariance is a measure of how much two random variables change together.

The covariance j,m measures how j return changes for each change of theaverage return of market portfolio and vice versa.

Variance m measures the capital market volatility.

σj,m = systematic risk of j

σ2j = 100% of systematic risk

βj = systematic risk coefficient

n

1i

2mim

n

1imimjji

2m

mj,j

)R~(R

)R~)(Rkeke(

σσ

βp

p

Covariance Formulas


Approach based on subjectiveprobabilities (according to theoriginal theory)

n

1i

2mim

n

1imimjji

2m

mj,j

)R(R

)R)(Rkeke(

σσ

β Approach based on historicaldata (according to the practiceof analysts)


The security market lineke

Rm

. .. . .

k

j

mn

o jβRf)-mR~(Rfke

ββ = 1

Risk premiumRf

. .k

The SML shows the expected return of single stocks as a function of systematicrisk. The “m” point indicates the expected return of market portfolio. An individualstock with β = 1 entails the same risk-return relationship of the market portfolio.

Sjτ)1(D

1ββ jj(u)j(L)

The effect of financial leverage on beta size


βj(u) = unlevered beta (business j)βj(L) = levered beta (business j)Dj = debt valueSj = equity valueDj / Sj = financial leverage

βj(u) = unlevered beta (business j)βj(L) = levered beta (business j)Dj = debt valueSj = equity valueDj / Sj = financial leverage

Sjτ)1(D

βββ

effectLeverage

jj(u)j(u)j(L)

SjD

τ111

ββ

Leverage

j

j(u)

j(L)

The CAPM assumes the possibility to measure systematic risk with adirect correlation between returns of individual stock and returns ofmarket portfolio. The market equilibrium hypothesis causeshomogeneous expectations.

From the application point of view, analysts use CAPM with strongcompromises, so that the model used in the real world is substantiallydifferent from its the original version


The CAPM assumes the possibility to measure systematic risk with adirect correlation between returns of individual stock and returns ofmarket portfolio. The market equilibrium hypothesis causeshomogeneous expectations.

From the application point of view, analysts use CAPM with strongcompromises, so that the model used in the real world is substantiallydifferent from its the original version

Analysts prefer to build linear regression based on historical data

According to the top-down approach, the historical performances of astock are estimated, period by period, as a percentage change of itsmarket value. Furthermore, the market portfolio is generallyapproximated to a sufficiently representative basket of securities(stock index).


Market modelAnalysts prefer to build linear regression based on historical data

According to the top-down approach, the historical performances of astock are estimated, period by period, as a percentage change of itsmarket value. Furthermore, the market portfolio is generallyapproximated to a sufficiently representative basket of securities(stock index).

β = Regression coefficientα = Regression interceptε = Standard error.

εRβαke mjj

6.2-B6.2-A

jj

Rischio

specifico

Market model


6.2-B6.2-Ajkejke

jj

Rischio

specifico

mRmR

Reward ofspecific risk

Market model


2,10,01350,0161β j

R-squared (R2) is a measure of how close thedata are to the fitted regression line. 1-R2 is ameasure of specific risk:

1-0,739 = 0,261

α

• The market model is not applicable in direct way in the case ofprivate firms: absence of data about past prices

• In the case of new businesses the valuation problem regardsespecially unlevered beta

• In the case of new business, the hypothesis of maximumdiversification is not realistic.

• The CAPM implicitly assumes the absence of liquidity risk of thesecurities; risk that, instead, is normally present in the case of start-up.

Applied problems of the CAPM in relation to new businesses


• The market model is not applicable in direct way in the case ofprivate firms: absence of data about past prices

• In the case of new businesses the valuation problem regardsespecially unlevered beta

• In the case of new business, the hypothesis of maximumdiversification is not realistic.

• The CAPM implicitly assumes the absence of liquidity risk of thesecurities; risk that, instead, is normally present in the case of start-up.

The easiest way to estimate the beta of a private firm is to use theunlevered beta of the sector which the enterprise belongs.


s(u)j(u) ββ:Hypothesis RfR~)t1(SD

1βRfke mj

js(u)j

NββN

1ii(u)j(s)

RfR~)t1(SD

1βRfke mj

js(u)j

βj(u) = Unlevered beta of the firm jβj(L) = Levered beta of the firm jβs(u) = Average unlevered beta of the

sector sDj = Debt of jSj = Equity of j

)t1(SD

1ββj

js(u)j(L)

Example of comparables approach: New business in the filed ofHealthcare Support Services


Source:Damodaran, http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html

• The equality βj(u) = βs(u) occurs when, for instance, a large privatecompany is similar (in terms of size and strategies) - to a certaincluster of public companies.

• However, such circumstances occur rather infrequently: in mostcases, unlisted companies differ markedly in terms of both structuraland strategic than those listed.

•The problem about a low comparability among companies listed andunlisted arises even more clearly in the case of start-ups.

• The comparable beta can be assumed as the starting point; the finalresult (βj(u)) should be estimated taking into account the characteristicsof the new business.

Ipotesi:


• The equality βj(u) = βs(u) occurs when, for instance, a large privatecompany is similar (in terms of size and strategies) - to a certaincluster of public companies.

• However, such circumstances occur rather infrequently: in mostcases, unlisted companies differ markedly in terms of both structuraland strategic than those listed.

•The problem about a low comparability among companies listed andunlisted arises even more clearly in the case of start-ups.

• The comparable beta can be assumed as the starting point; the finalresult (βj(u)) should be estimated taking into account the characteristicsof the new business.

According to the bottom-up approach, the risk (specific andsystematic) comes from the combination between firm characteristicsand the volatility degree of a certain core business.

Equity cost = f (firm specific factors, intrinsic business risk, capital market volatility)



Sector'sVolatility

Strategicinvestments

IntrinsicBusiness risk

UnleveredRisk

OperatingLeverage

FixedInvestments

FixedCostsLevered

Risk

FinancialLeverage

LeveredRisk

= IntrinsicBusiness Risk

X OperatingLeverage

FinancialLeverage

X

Unlevered Risk

Intrinsic business risk


Exogenous volatility

Price and demand volatilitycaused by macroeconomic

factors

Endogenous volatility

Price and demand volatilitycaused by strategic

decisions

Volatility inrevenues

V~REREVIBR2n

1iii

p

n

1iii REVV~RE p

Dall’approccio top down all’approccio bottom up (7/7)

Motivations bottom up approach• Analysis of the risk factors.

•Analysis about the effect of management decisions on risk (for instancehow a growth strategy affects the systematic risk)

• Evaluation of private firms

• Evaluation of market efficiency

• Analysis of the risk factors.

•Analysis about the effect of management decisions on risk (for instancehow a growth strategy affects the systematic risk)

• Evaluation of private firms

• Evaluation of market efficiency

Degree of operating leverage (DOL)


REVREV

EbitEbit

REVREV

EbitEbitDOL (t0)

(t0)(t0)(t0)

The value of DOL can be positive, null or negative. The use ofDOL in a risk return analysis requires a positive value:

The value of DOL can be positive, null or negative. The use ofDOL in a risk return analysis requires a positive value:

REVREV

EbitEbitDOL'

2(t0)

(t0)

DOL measures that part of intrinsic absorbed by aspecific business

Unlevered risk (su), degree of operating leverage (DOL),intrinsic business risk (IBR) and unlevered risk (su)


I~ROROIσ2n

1iiiu

p

n

1iii ROII~RO;

NIEBITROI p

DOL = 1su = IBR

DOL > 1su > IBR

n

1iii ROII~RO;

NIEBITROI p


Growing unlevered risk due to greater volatility in the competitive environment

Unlevered risk with a constant operating leverage

Decreasing unlevered risk due to lower volatility in the competitive environment

I~RO I~RO I~RO

su = 0,1 su = 0,2 su = 0,4


Unlevered risk with a constant IBRGrowing unlevered risk due to greater DOL

I~RO I~RO I~RO

DOL = 1 DOL = 2 DOL = 5

Decreasing unlevered risk due to lower DLO

DOL and fixed costs


Q(p)REVc);Q(pEbit0)FC0;c0;p(

If price per unit (p), cost per unit (c) are and fixed costs (FC)constants, the DOL depends on fixed costs:

(t0)

(t0)

(t0)(t0)(t0)

(t0)(t0)

(t0)

(t0)

(t0) EbitFC

1FCVCREV

VCREVΔQ(p)Q(p)

Ebitc)ΔQ(p

REVREV

EbitEbitDOL

EbitFC

1DOL'2

(t0)

(t0)

(t0)

(t0)

(t0)(t0)(t0)

(t0)(t0)

(t0)

(t0)

(t0) EbitFC

1FCVCREV

VCREVΔQ(p)Q(p)

Ebitc)ΔQ(p

REVREV

EbitEbitDOL

The increase endogenous risk depends on the increase in resources (+ FC) and / orloss of efficiency (- Ebit)

Bottom up analysis of unlevered risk: static approach

Constant values of price per unit, variable cost per unit, fixedcosts and net investments

ROIEBITCFO1

VIBRROIDOL'

VIBRσ 2

t0

2

t0

t0

t0

2t0

t0u


Bottom up analysis of unlevered risk: static approach

Constant values of price per unit, variable cost per unit, fixedcosts and net investments

Specific unlevered risk: static approach(Forecasting analysis)

Analysis phases :

;REV)V~(RERevenuesExpected

;ROI)I~(ROROIExpected

i

n

1ii

i

n

1ii

p

p


;REV)V~(RERevenuesExpected

;ROI)I~(ROROIExpected

i

n

1ii

i

n

1ii

p

p

T~EBIFC1)O~(DLDOLExpected

;t~Ebi)t~(EbiEbitExpectedn

1ii

p

I~ROL~DOV~RE

IBRσ 2u


I~ROL~DOV~RE

IBRσ 2u

Bottom up analysis of unlevered risk: dynamic approach

In the case of no constant value of price per unit, variablecost per unit, fixed costs and net investments, the unleveredrisk depend on the following ratios:

j

jj

j

jj NI

FCμ;

NICM

θ


j

jj

j

jj NI

FCμ;

NICM

θ

CM = Contribution margin (Revenues – Variable Costs)FC = Fixed costsNI = Net investments

j

j

j

jjjjj NI

CostsFixed-

NICostsVariableREV

μθROI



Independent variables

• Variance of θ (volatility of contribution margin). It affects in positiveway the unlevered risk (σu).

• Variance of µ (structural instability: volatility of the ratio FC/NI). Itaffects in positive way the unlevered risk (σu).

• Covariance θ ,µ. It affects in negative way the unlevered risk (σu).

• Variance of θ (volatility of contribution margin). It affects in positiveway the unlevered risk (σu).

• Variance of µ (structural instability: volatility of the ratio FC/NI). Itaffects in positive way the unlevered risk (σu).

• Covariance θ ,µ. It affects in negative way the unlevered risk (σu).



μθ,22μjσ2

θjσσ j(u)

Managerial interpretation ofsq,m

•sq,m>0 shows the managerial capability to compensate the growthin investment and fixed costs with the increase in contributionmargin. It decreases the unlevered risk linked to growth strategies.

•sq,m<0 amplifies the unlevered risk caused by growth strategies

Managerial interpretation ofsq,m

•sq,m>0 shows the managerial capability to compensate the growthin investment and fixed costs with the increase in contributionmargin. It decreases the unlevered risk linked to growth strategies.

•sq,m<0 amplifies the unlevered risk caused by growth strategies

Assumptions

• Each industrial sector absorbs a share of market volatility

• Each firm absorbs a share of sector volatility


Beta of sector x Correction Factor = Firm’s BetaBeta of sector x Correction Factor = Firm’s Beta

Static approach: Correction Factor = f(ROI, DOL)

Dynamic approach: Correction Factor = f(sq,sm,sq,m)

Correction Factor


Static approach: Correction factor comes from the relationshipbetween the firm DOL and the sector DOL.

Dynamic approach: Correction factor comes from the relationshipcomes from the drivers of firm risk in dynamic conditions (σθ, σµ,σθ ,µ) and the same variables referred to the sector.

Static approach: Correction factor comes from the relationshipbetween the firm DOL and the sector DOL.

Dynamic approach: Correction factor comes from the relationshipcomes from the drivers of firm risk in dynamic conditions (σθ, σµ,σθ ,µ) and the same variables referred to the sector.

The correction factor (f):static approach

j(s)

j(u)2

S

j

j

jjjj β

βI~ROI~RO

L~DOL~DO

γλ

Constant values of price per unit, variable cost per unit, fixed costsand net investments . In addition this formula assumes constant themarket quote of j


Constant values of price per unit, variable cost per unit, fixed costsand net investments . In addition this formula assumes constant themarket quote of j

S)τ1(D

1ββj

j

bj(u)β

js(u)bj(L)


The correction factor (f):static approach

ββ

σ2σσσ2σσ

ρρ

j(s)

j(u)

θsμs,2μs

2θs

θjμj,2μj

2θj

ms,

mj,j

The correction factor (f):dynamic approach


The correction factor (f):dynamic approach


Trade-off between growth and conservation

s(u)

μjθj,2μj

2θj

ms,

mj,jj

sinvestmentstrategicWith

j(G)

strategicisinvestment

strategicWithout

j σσ-

ρρ

γλ

Short-term effects


jj(G)

jj(G)

jj(G)

)

)

)

c

b

a The strategic growth decreases theunlevered beta

The strategic growth doesn’t affectthe unlevered beta

The strategic growth increases theunlevered beta

The issue of diversificationThe CAPM considers pure financial investors. Normally they pay alittle attention to strategic perspectives of firms. Therefore theyconsider the “diversification power” like the main way to optimize theirrisk-return relationship.

However, there are other types of investors who look at the risk-return relationship with a logic partially or totally different thetraditional financial logic. This happens when an operators hasinterest in a long-term perspective.

Typically the entrepreneur doesn’t diversify. He tends to invest hiscapital in one business.

The typical venture capitalist doesn’t exploit the overall diversificationbenefits. In fact he tends to combine the diversification benefits withspecialization benefits.


The issue of diversificationThe CAPM considers pure financial investors. Normally they pay alittle attention to strategic perspectives of firms. Therefore theyconsider the “diversification power” like the main way to optimize theirrisk-return relationship.

However, there are other types of investors who look at the risk-return relationship with a logic partially or totally different thetraditional financial logic. This happens when an operators hasinterest in a long-term perspective.

Typically the entrepreneur doesn’t diversify. He tends to invest hiscapital in one business.

The typical venture capitalist doesn’t exploit the overall diversificationbenefits. In fact he tends to combine the diversification benefits withspecialization benefits.

Total Beta (Tb)

σσσβ

ρβ

Tβmk,

mkj(L)

mk,

j(L)j


ρk,m = correlation coefficient between the portfolio of investor (k) and market portfolio (m)σk,m = covariance between the portfolio of investor and market portfolioσk = st. deviation of portfolio kσm = st. deviation of m

ρk,m = correlation coefficient between the portfolio of investor (k) and market portfolio (m)σk,m = covariance between the portfolio of investor and market portfolioσk = st. deviation of portfolio kσm = st. deviation of m

The reworking of CAPM according to four correction factors

π

ρ1

S)τ1(D

1βRfRmRfke)4(

j

jTβ

)3(

mk,

anlysisupBottom

bj(L)β

)2(

j

j

bj(u)β

)1(

js(u)j

factorCorrectionfactor

CorrectionfactorCorrection

factorCorrection

π

ρ1

S)τ1(D

1βRfRmRfke)4(

j

jTβ

)3(

mk,

anlysisupBottom

bj(L)β

)2(

j

j

bj(u)β

)1(

js(u)j

factorCorrectionfactor

CorrectionfactorCorrection

factorCorrection

πj measures the premium linked to the liquidity risk

Prof. Antonio Renzi€¦ · Dall’approccio top down all’approccio bottom up (7/7) Motivations...

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Transcript of Prof. Antonio Renzi€¦ · Dall’approccio top down all’approccio bottom up (7/7) Motivations...