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Risk Analysis in InvestmentValuation: an Introduction

Emanuele [email protected]


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Discounted Cash Flow


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Discounted Cash Flows

n Investment must be characterized in terms of Timing

n Qualitative Analysis: j=1mn What are the types of cash flows that investors have rights to

receive

n Quantitative Analysis (Forecast): xitn Estimation of the cash flow value

t


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Decision Criteria

n Net Present Value (NPV) :

n Where T is the valuation horizon, t is the CF timing, m isthe number of equity cash flow types

n Internal Rate of Return (IRR)

1

1( )1

mt

jTj

tt e

x

Vk

=

=

=+


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55

The Decision Making Process

Yes/N

oValuationCriteria

Decision SupportModel

Inputs

SensitivityAnalysis

Assumptions

Clemen (1997,

Ch.1)


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66

Sensitivity Analysis Uses

n Model Output:

n Model Correctness

n Stress Test

n Equilibrium stability and changes (Samuelson

Comparative Statics)

n Parameter Importance

)X,...,X,f(XY n11=


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77

Sensitivity Analysis

CorrectnessTest

ImportanceMeasures

RiskAnalysis

UncertaintyAnalysis


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88

Importance Measures

Is it possible to quantify the relevance of each factor in themodel?

What assumption influences the outcome of the

decision the most?

Is it possible to quantify the relevance of groups ofassumptions?

Sensitivity Analysis methods have been developed withthe purpose of answering those questions


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99

Uncertainty Analysis

Is it possible to quantify the degree of confidence of thedecision maker in the model results?

What uncertain factor influences uncertainty the most?

Where should one focus to reduce uncertainty in theModel results?

Global Sensitivity Analysis methods have beendeveloped to answer these questions


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1010

Risk Analysis Insights

How is risk distributed among factors

What assumption to monitor in order to reduce risk?

Sensitivity analysis results share a risk analysis interpretation


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1111

Risk Analysis Insights

How is risk distributed among factors

What assumption to monitor in order to reduce risk?

Sensitivity analysis results share a risk analysis interpretation


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1212

The Differential Importance Measure

n Let f(x) be a function differentiable at x0. Provided thatf(x0) is not orthogonal to dx, then the importance of xsat x0 is defined as [Borgonovo and Peccati (2004),(2006)]:

n Ds(x0,dx) is the fraction of the differential of f(x0) that isassociated with parameter xs.

=

==n

1j

j

1

j

s

1

s

x

s1

s

dx)x(f

dx)x(f

df

fd)dx,x(D 1


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DIM Main Properties

n H1: Uniform Changes n H2: Proportional Changes

=

=n

1j

1

j

1

s1

s

)x(f

)x(f)x(D1

j,idxdx ij = )ji(j,idx

dx

i

j=

=

=

n

1j

1

j

1

j

1

s

1

s1

s

x)x(f

x)x(f)x(D1

)dx,x(D)dx,x(D

1m

1js

1

s,...,s,s jm11

==

3) DIM accounts for the way parameters are varied

1) Additivity:

2) Sum: 1)dx,x(D)dx,x(D1

n

1j

s

1

S j==

=


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1414

Application to the financialanalysis of a Project FinanceInfrastructure Project

A Parking Lot


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Large Projects Valuation: Criteria

n Sponsors Side:

n or

n Lenders Side

n or

( )= +

=N

ii

e

e

i

k

CFNPV

1 1

jj

j

jPI

FCFDSCR

+=


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Identification of Key Drivers

n Complex Non-linear models (Van Groenendaal (1998),

Kleijnen and Van Groenendaal (1997), (2002)).n Absence of analytical expression:

n Sensitivity Analysis (SA) plays a crucial role in unveilingModel dependence on the parameters

n SA essential in fully exploiting model information

n Sensitivity Analysis method should be:n Quantitative and Model freen Enable to evidence effect of multiple factors (interactions)n Avoid top-down or a priori parameter selection, since one

runs the risk of excluding relevant parameters

n High Number of parameters leads ton Computational issues (i.e. high computational cost [Kleijnenand Van Groenendaal (2002)] )

n Issue in communication of the results when high number ofparameters


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Parameter Importance in Investment Evaluation

n Investment criterion is a function of the exogenous variables(factors) that influence the project economnics [Borgonovo andPeccati (2006)]:

n These factors become input parameters (X) for the model

n Parameter Influence is given by:

Since in a financial model parameters have different dimensions.

=

=n

j

jj

ss

s

xxv

xxvxD

1

11

11

1

)(

)()(1

)(xvV =


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Project Contractual Structure

Operation&

Mantenance Contract

Merchant Sale

EngineeringProcurementConstruction

Contract

SPC

InsuranceContracts

ShareholderAgreement

LoanAgreement Pr

ice

Marke

t

Risk


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Cash Flows Estimation

RevenuesNet of Turnover Tax

LESS Operating Expenses

EBITDA

LESS Long-term loans interest

Subdebt Interests

Interest Income

EBTDA

LESS Depreciation

EBT

LESS Taxes

Net Profit

LESS Dividends

Equals Retained Earnings

Legal Reserve

Income Statement

Revenues Netof TurnoverTax

LESS OperatingExpenses

LESS Taxes

Operating Cash Flows

Plus Trapped cash Previous year

Cash Before Capex

LESS Capital Expenditures

Plus Equity Injections

Plus Subdebt Injection

Plus Principal Injections

Cash Flows Available for interest payment

Less Debt Interests

Cash Flows Available for principal payment

LESS Principal Repayment

equals Cash FlowsAvailable forSDinterest

LESS ShareholderInterests

Equals CashFlows AvailableforSDPrincipal

LESS Shareholder PrincipalLESS IOE

equals Cash flow available for dividends

Dividends

Equals Trapped cash

Cash Flow Statement

Balance

Sheet

Assets

Current Assets

Cash

Inventory

RiceivableLong Term Assets

Total Assets

Liabilities

Current Debt

Equity

Retained Earnings

Legal Reserve

Shareholder Debt

Debt

Total Liabilities

n Project economic life projection

n High level of accuracy for multi-million deals


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2020

ModelStructure

InputsAuxiliaryCalculatio

ns

Finstat

s

Results


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Methodological Approach

n Number of parameters: 428

n Input Categories Defined by Financial Model:n Revenuesn Construction Costsn Fiscaln

Financialn Macroeconomicn Opex

n Valuation Criteria: NPV and

n Grouping on three levels

n Level 3: individual inputs (428)n Level 2: 17 groupsn Level 1: 6 groups

n Statistical Comparison through Savage Score corr. Coeff.


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Equity NPV,Sponsors side


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Parameter ranking (Level 3)


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NPV: Level 1

1.00

.00

.00

.00

1.

11

.11

.11

Opex Constr.

Costs

Infl Rev Ass Fisc. Financing

NPV: factors grouped into main categories1


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NPV: Level 2, 17 categories

%1

%11

%11

%11

%11

%11

%11

Opex Parcheggi Autom Amm GiOcc Perc. Occ. mesiOccupaz Ass.Fiscali k

NPV: Importanza gruppi di ipotesi (Livello )1


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Summary on NPV results

1. Revenue parameters are the most importantones

1. ke plays a significant role

1. Leverage is not among 20 most relevantinputs.

1. 60 Parameters were non-influential: modelcorroboration


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2727

Debt Service Coverage Ratio:Lenders side


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2828

DSCR: Level 3


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DSCR: Level 1

.111

.000

.000

.000

.000

.111

.111

.111

.111

Opex Constr.

Costs


DSCR: Level


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DSCR: Level 3

%1

%11

%11

%11

%11

%11

%11

O pe x A ule P arc h. V ia b. V . A uto m. Infl. A m m. Ta riffe G iO cc N ro t P e rc .

Occ.

PostiD iStmesiOc c Pos tMotAs s.Fisc.Ass.Fin/k k

DSCR Level


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3131

Observations

1. Revenue assumptions are the most important ones

1. The cost of debt plays a relevant role (simmetric ke)

1. Leverage is significant (8th)

1. Equity relevant parameters (ke and retention ratio are noninfluential)

1. Income taxes influence NPV but little DSCR


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3232

Cross Comparison


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3333

Individual Parameter Ranking

Rank

NPV Parameter

Rank

DSCR Parameter

1 Nr. Of parking slots from year on1 1 Nr. Of parking slots from year on1

1 Daily occupation days from year on1 1 Daily occupation days from year on1

1 Tariff for first two hours 1 Tariff for first two hours

1 Rotation number for the first hours1 1 Rotation number for the first hours1

1 Percentage of Occupation of the First hours1 1 Percentage of occupation for the first two hours after 1 year

1 ke 1 kd

1 Tariff after the first two hours 1 Rooms construction costs

1 Rotation number after the first hours1 1 Leverage

1 VAT on Revenues 1 Tariff after first hours1

00 kd 1 Rotation number after first two hours

11 Night Tariff 1 Percentage of Occupation after two hours from year on1 1

Rotation Number 11 VAT on Revenues

Percentage of nightly occupation 11 Night Tariff

00 Rooms construction costs 11 Number of Night Rotation

111 Geological Inspection Cost 11 Percentage of Night Occupation after year1 111 Days payables for electricity connection costs 111 Cost for workplace set up


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Ranking Analysis

X


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Level 3

n Financial Structuring

1

.00

.00

.00

.00

1

.11

.11

.11

Opex Constr.

Costs


NPV vs DSCR: Parameter Group Importance

NPV

DSCR


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3636

NPV vs DSCR, Level 2

%1

%11

%11

%11

%11

%11

%11

OPEX

ROOMS

PARKING

GREEN

AUTOM

INFLATION

AMORTIZ

TARIFF

DAYS

ROTATIONS

PERC.OCC

NrofPLACES

OCC

TIME

Slotsforbikes

FISCAL

FINANCIAL k

NPV vs DSCR importance of categories11

NPV

DSCR


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Conclusions (1)

n Sensitivity Analysis plays a key role to deepen theunderstanding of the investment financial performance,since an analytical expression of the valuation criterion isnot available.

n Large complex modelsn

High Number of Parameters Computational Costsn Analysis Communication Results Synthesis1

n Methodologyn Use of the differential importance measures enables to

solve the above issues thanks to the additivity property

n Numerical Computation: Algorithm based on Cauchyssequence convergence criterionn Statistical Comparison for Ranking: Savage Score

Correlations and Rank Correlations


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Conclusions (2)

n Financial Model with 428 parameters

n Synthesis of the results grouping parameters inthe corresponding categories

n Results have enabled us to:

n Identify key drivers for sponsors (NPV) and forlenders (DSCR) wihtout a-priori screening

n Individual parameter ranking needs not to bethe same

n Cost of Equity/Debtn Leverage

n different attention in negotiation


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3939

Uncertainty and Risk


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Hertz (1964)

n Of all the decisions that business executives must make, noneis more challenging andhas received more attention - thanchoosing among alternative capital investment opportunities.What makes this kind of decision so demanding, of course, isnot the problem of projecting return on investment under any

given set of assumptions. The difficulty is in the assumptionsand in their impact. Each assumption involves its own degree -often a high degree - of uncertainty; and, taken together, thesecombined uncertainties can multiply into a total uncertainty ofcritical proportions. This is where the element of risk enters,

and it is in the evaluation of risk that the executive has beenable to get little help from currently available tools andtechniques.


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Cash Flows are uncertain

n Cash flows depend on exogenous variableswhich are not known at the moment theinvestment is evaluated.

n The valuation criterion then becomes a random

variable


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A direct quote from an early classic

n It should be recognized that, as defined, P isactually a random variable rather than aconstant.

n Hillier (1963), MS.


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An ExampleFrom Van Horne (1967), Capital Budgeting Decisions Involving Risky Investments,Management Science


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How do we value this investment?

n Expected present value:

n One needs to discount, instead of pointestimates, the expected values of the cash flows

n The equation is obtained by the additivity of theexpectation operator.

1

1

[ ]

[ ]

( )1

mt

jTj

tt e

E x

E V

k

=

=

=

+


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Solution

n See excel spreadsheet model


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Software for Uncertainty Analysis

n @Riskn Monte Carlo

n Latin Hypercube Sampling

n Best Fitn Distribution Fitting

n Crystal Ball

n SIMLAB

n Global SA

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