Post on 02-Jan-2021
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 comparables approach
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
The equity cost analysis in neoclassical perspective
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
The equity cost analysis in neoclassical perspective
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
The Capital Asset Pricing Model (CAPM)
Portfolio Risk
Diversificationprocess
Maxdiversification
Number of stocks
Systematicrisk
Specificrisk
Maxdiversification
The Capital Asset Pricing Model (CAPM)
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
The Capital Asset Pricing Model (CAPM)
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
The Capital Asset Pricing Model (CAPM)
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 Capital Asset Pricing Model (CAPM)
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
The Capital Asset Pricing Model (CAPM)
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 Capital Asset Pricing Model (CAPM)
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).
The Capital Asset Pricing Model (CAPM)
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
The Capital Asset Pricing Model (CAPM)
6.2-B6.2-Ajkejke
jj
Rischio
specifico
mRmR
Reward ofspecific risk
Market model
The Capital Asset Pricing Model (CAPM)
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 Capital Asset Pricing Model (CAPM)
• 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.
The comparables approach
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
The comparables approach
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 comparables approach
• 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)
The bottom up approach: general framework
The bottom up approach: general framework
Sector'sVolatility
Strategicinvestments
IntrinsicBusiness risk
UnleveredRisk
OperatingLeverage
FixedInvestments
FixedCostsLevered
Risk
FinancialLeverage
LeveredRisk
= IntrinsicBusiness Risk
X OperatingLeverage
FinancialLeverage
X
Unlevered Risk
Intrinsic business risk
Specific risk according to bottom up approach
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)
Specific risk according to bottom up approach
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)
Specific risk according to bottom up approach
I~ROROIσ2n
1iiiu
p
n
1iii ROII~RO;
NIEBITROI p
DOL = 1su = IBR
DOL > 1su > IBR
n
1iii ROII~RO;
NIEBITROI p
Dall’approccio top down all’approccio bottom up (5/7)
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
Dall’approccio top down all’approccio bottom up (6/7)
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
Specific risk according to bottom up approach
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
Specific risk according to bottom up approach
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
Specific risk according to bottom up approach
;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
Specific risk according to bottom up approach
I~ROL~DOV~RE
IBRσ 2u
Specific risk according to bottom up approach
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 depends on the following ratios:
j
jj
j
jj NI
FCμ;
NICM
θ
Specific risk according to bottom up approach
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
Bottom up analysis of unlevered risk: dynamic approach
Specific risk according to bottom up approach
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).
Bottom up analysis of unlevered risk: dynamic approach
Specific risk according to bottom up approach
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
Specific risk according to bottom up approach
Assumptions
• Each industrial sector absorbs a share of market volatility
• Each firm absorbs a share of sector volatility
The reworking of CAPM according to bottom up approach
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
The reworking of CAPM according to bottom up approach
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
The reworking of CAPM according to bottom up approach
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 reworking of CAPM according to bottom up approach
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 reworking of CAPM according to bottom up approach
The correction factor (f):dynamic approach
The reworking of CAPM according to bottom up 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
The reworking of CAPM according to bottom up approach
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 reworking of CAPM according to the Total Beta Model
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
The reworking of CAPM according to the Total Beta Model
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