\A/ P-s 2083
POLICY RESEARCH WORKING PAPER 208 3
INFRISK Increased exposure to risk has
been an inevitable
consequence of recent
A Computer Simulation Approach economic, technological, and
to Risk Management in Infrastructure financial changes, the
Project Finance Transactions defining themes of the 1990s.
In the face of such
developments, the viability of
Mansoor Dailami long-term capital investments
Ilya Lipkovich -particularly in the core
!John Van Dyck
infrastructure sectors of
power, transport, and
telecommunications -
hinges critically on how the
risks associated with such
investments are evaluated
and managed.
The World Bank
Economic Development Institute
Regulatory Reform and Private Enterprise Division H
March 1999 Yil
P POLICY RESEARCH WORK1NG PAPER 2083
Summary findings
Few issues in moderni finance have inspired the interest to im:Irastructure project finance transactions that involve
of both practitioners and theoreticians more than risk the private sector. Developed in-house in the Economic
evaluation and managemnent. The basic principle Development Institute of the World Bank, INFRISK is a
governing risk management in an infrastructure prolect guide to practitioners in the field and a training tool for
finance deal is intuitive and well-articulated: allocate Faising awareness and improving expertise in the
project-specific risks to parties best able to bear them application of modern r isk management techniquies.
(taking into account each party's appetite for, and TNFRISK can analyze a project's exposure to a variety
aversion to, risk); control performance risk through of market, credit, and performance risks from the
incentives; and use market hedging irnstruments perspective of key contracting parties (project promoter,
(derivatives) for covering marketwide risks arising from creditor, and government). Their model is driven by the
fluctuations in, for instance, interest and exchange rates, concept of the project's economic viability.
among other things. Drawing on recent developments in the literature on
In practice, however, governments have been asked to project evaluatior under uncertainty, INFRISK generates
provide guarantees for various kinds of projects, often at probability distributions for key decisioni variables, such
no charge, because of preblems associated with rmarket as a project's net present value, internal rate of return, or
imperfections: capacity to serv ice its debt on time during the life of the
* Derivative markets (swaps, forwards) for currency project.
and interest-rate risk hedging either do not exist or are Computationaily, INFRISK works in conjunction with
inadequately developed in most developing countries. Microsof'-t Excel and supports both the construction and
- Limited contracting possibilities (because of the operation phiases of a capital investment project. For
problems with credibility or enforcement). a particular risk variable of interest (such as the revenue
Differing methods for risk measurement and stream, operations and maintenance costs, and
evaluation. construction costs, among others) the program first
Two factors distinguish the financing of infrastructure generates a stream of probability distributions for each
projects from corporate and traditional limited-recourse year of a project's life through a Monte Carlo simulation
project finance: 1) a high concentration of project risk technique. One of the key contributions made by
early in the project life cycle (pre-completion), and 2) a INFRISK .s to enable the use of a broader set of
risk profile that changes as the project comes to fruition, probability distributions (uniform, normal, beta, and
with a relatively stable cash flow subject to market and lognormal) in conducting Monte Carlo simulations
regulatory risk once the project is completed. rather than relying only on the commonly used normal
Dailami, Lipkovich, and Van Dyck introduce distribution. A user's guide provides instruction on the
INFRISK, a computer-based risk-management approach use of the package.
This paper - a product of the Regulatory Reform and Private Enterprise Division, Economic Development Institute -is
part of a larger effort in the institute to address the training needs of Bank client countries as well as support the Bank's owln
lending and advisory services in promoting infrastructture development and rnodernization in developing countries. Copies
of this paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Bill
Nedrow, room G2-072, telephone 202-473-1585, fax 202-334-8350, Internet address wnedrow Cowocldbank.org. Policy
Research Working Papers are also posted on the Web at http:i//www.worldbank.orgilhtml"dec"Publications!Workpapers/
home.html. The authors may be contacted at mdailamidfworldbank.org, ilipkovich@(§rworldbank.org, or
jvandyck@worldbank.org. March 1999. (33 pages)
The Plolicy Research Working Paper Series disseminates the findings of work in prog ress to encourage the exchange of ideas about
developrment issues. An objective of the series is to get the findings out quicUEl, eve7n1,f the presenstations are less than fully polished'. T'he
papers carrv the names of the authors and sho,ld be cited accordingly. Tie findings, interpretations, and conclusions expressed in this
paper are entirely those of the authoors. They do siot necessarily represent the 'ieur of the W"orld Bank, its Executive Directors, or the
cotntries they represent.
Produced by the Policy Research Dissc'anafion Center
A computer simulation approach to risk management in
infrastructure project finance transactions
Designed and developed by
Mansoor Dailami,
Ilya Lipkovich,
and
John Van Dyck
Regulatory Reform and Private Enterprise Division
Economic Development Institute of the World Bank
Managing Risk
Few issues in modem finance have inspired the interest of both practitioners and
theoreticians more than the subject of risk evaluation and management.' "The ability to
understand, measure, and weigh risk is," according to Peter Bernstein, "at the heart of
modem life.2" Virtually every investment and financing decision involving intertemporal
allocation of resources under uncertain conditions is associated with some risk, which is
in effect, either assumed in the expectation of a higher return, or is transferred to others
through hedging and/or contracting arrangements.
Yet, increased exposure to risk has been an inevitable consequence of recent
economic, technological, and financial changes, which have come to represent the
defining themes of the 1990s. These include the globalization of economic activity, the
mobility of capital flows across national boundaries, widespread privatization of public
sector enterprises, intensified competition, and high volatility in international financial
and currency markets. In the face of such paradigmatic developments, the viability of
long-term capital investments, particularly in the core infrastructure sectors of power,
transport and telecommunications, hinges critically on how risks associated with such
investments are evaluated and managed.
The basic principle governing risk management in an infrastructure project
finance deal is intuitive and well articulated:3 allocate project-specific risks to parties best
able to bear them (taking into account each party's appetite for and aversion to risk),
control performance risk through incentives, and use market hedging instruments
(derivatives) for covering market-wide risks arising from fluctuations in, for instance,
interest and exchange rates. In practice, however, difficulties arise due to market
imperfections, i.e., derivative markets (swaps, forwards) for currency and interest rate
risk hedging that are either non-existent or not sufficiently developed in most emerging
countries, limited contracting possibilities (due to enforceability and credibility
problems), and differing methodologies for risk measurement and evaluation. As a
result, governments have been asked to provide guarantees for various kinds to projects,
often at no charge.
Project Risk Evaluation
There are two important aspects of infrastructure project finance that distinguish it
from corporate and traditional limited recourse project finance: (a) a high concentration
of project risks in the early phase of project life cycle, i.e. the pre-completion phase; and
' Not surprisingly, risk management has grown in recent years into a mature discipline with a wealth of literature,
specialized skills, and sophisticated computer-basted systems that can be applied to investment project appraisal,
pension plans, portfolio asset allocation, credit derivatives, regulatory capital adequacy for the banking sector,
and derivative trading.
2 See Bernstein (1996).
3The argument for risk management in project finance is stronger than in corporate finance. In the case of corporate
finance, the argument for risk management or hedging rests on the notion that hedging adds value to the extent
that it helps ensure that a company has sufficient internal funds available to take advantage of attractive
investment opportunities. See Froot, Scharfstein, and Stein (1993). In a project finance deal, risk management
bears directly on the success or failure of the project.
(b) a risk profile that undergoes important changes as the project comes to fruition, with a
relatively stable stream of cash flows that is subject to market and regulatory risks once
the project is completed. Figure 1 below describes the main risks that arise in the
development and operational phases.
Figure 1: Project life cycle: main risks
* Construction Operation
Main Risks: Main Risks:
* Completion Risk * Performance Risk
* Cost Overrun Risk * Regulatory Risk
* Performance Risk * Environmental Risk
* Environmental Risk * Off-take Risk
(Power Projects)
* Market Risk
(Toll Roads)
Risk Management Through Contracts
Project finance transactions are typically governed by a nexus of long-term formal
contracts, written between the project promoter, the host country government, creditors,
input suppliers, contractors, operators, and service providers (in the case of power).
Three classes of contracts are important: concession agreements that stipulate a property
rights transfer from the government to the project company, performance contracts
between the project company and contractors and operators, and loan contracts between
creditors and the project company. Such contracts are designed to share risk and to
protect contracting parties against opportunistic "hold-up" behavior by others. In
practice, they address two important characteristics of infrastructure investments: (i) a
high degree of asset specificity; and (ii) large project-specific risks that cannot be
diversified in financial markets.
In such "relationship-specific" investments, i.e. constructing a power plant, road,
or bridge which cannot readily be removed and used elsewhere, investors are hesitant to
make investments without adequate contractual protection. Once the investment is sunk,
the incentive system and the bargaining power of contracting parties change vis-a-vis
each other.4 Anticipating such an outcome, project promoters often insist on
governments providing various kinds of guarantees to cover, for instance, the credit risk
of the power purchaser under an IPP arrangement, or a minimum level of revenue in a
toll road project.
4See Dailami and Klein (1999) for a further discussion of the contracting forms in infrastructure finance transactions
and for a review of the related literature.
2
INFRISK: A Tool for Risk Management
This study introduces INFRISK, a computer based risk management approach to
infrastructure project finance transactions that involve the private sector. Increasing the
participation of the private sector in the provision and financing of infrastructure services
is a common policy objective in countries around the world. As governments are turning
to private firms as owners, operators, and financiers of infrastructure, the traditional
financing structures and risk allocation strategies (once based on the sovereign's ability to
tax and borrow) are now giving way to a reliance on fee-based project financing where
risk management takes on a far greater importance.
INFRISK, developed in-house within the Economic Development Institute of the
World Bank, is intended as a guide to practitioners in the field and as a training tool for
raising awareness and expertise in the application of modern risk management
techniques. It is capable of analyzing a project's exposures to a variety of market, credit,
and performance risks from the perspective of key contracting parties in an infrastructure
transaction, i.e. the project promoter, creditor, and the government. An infrastructure
project is brought to financial closure, i.e. a transaction takes place, when these parties
strike a balance, reaching a common ground of interest and understanding.
Figure 2: Major Parties to an Infrastructure Project: Analytical Framework
i",
Securnty and Assurance
ofDbtRpaymnent
Term Debt Capita
It is useful to think of this common ground as the solution to a bargaining game
within which each party maximizes its objectives, subject to the constraints set by the
willingness of others to participate. Modeling such a sequential multi-party bargaining
game is difficult, as most game theoretic approaches rely heavily on the idea of "utility,"
which is difficult to apply operationally.5 The perspective that drives the INFRISK
"analytic" is the concept of the economic viability of a project (see Box 1).
5 While the objectives of the creditor and project promoter can be reasonably specified as the security of loaned funds
and the optimization of investment value, respectively, the government presents difficulties. Even a simplistic
fiscalist approach to governments' behavior requires the estimation of social welfare losses from discriminatory
taxation and the social cost-benefit calculus of the public finance alternative.
3
Box 1: Economic Wability of a Project
The economic viability of a project is an important concept in the process of project selection, and can
be analyzed at two levels. The first level takes into account the particular regulatory structure in place
for the project, including the determination of a tariff and the type of government support (guarantees,
fiscal incentives, and credit enhancement). Here, viability boils down to whether cash flows are
sufficient to service the project's debt on time, and to pay a fair return to its equity holders. At a
deeper level of analysis, however, economic viability also depends heavily on the consistency of the
tariff rate, the government's credibility in honoring a contracted rate level, and the project's cash flow
stream. Project viability therefore hinges on the government's tariff policy and support for the project,
since cash flows in monopolistic markets depend importantly on the tariff charged.
We analyze project viability from the perspective of creditors and equity holders in the project. From
the viewpoint of equity holders, we focus on the main project metrics such as IRR and NPV. A
project's IRR is a function of the tariff charged on the supply of infrastructure services, government
support, and the financing mix and terms; more specifically, we assume:
IRR = f(m,r,l,s, ir)
Where m is debt maturity, r is interest rate, I is a measure of the project's debt-equity ratio, ir is the
tariff charged, and s represents a vector of government support, i.e. tax incentives, depreciation
allowances, and guarantees provided to the project. In general IRR is an increasing function of m, 1, s
and ir, but a decreasing function of r.
From the creditor's perspective, we focus on the project's capacity to borrow. We define loan
payment capacity in terms of two main leverage ratios: i.e. interest coverage and debt service
coverage. From a lender's point of view, the key criteria are the probability that such coverages are
not less than some target levels, thus defining the following probabilities:
Prob[Interest coverage < aJ] = F1
Prob[Debt service coverage < a2] = 82
Where a, and a2 are leverage coverage ratios, and E1 and 62 are the respective confidence levels with
which the lender feels comfortable.
Earnings Before Interest and Taxes
Interest coverage = ______ _________
Interest Payment
Debt Service Coverage = Earnings Before Interest, Tax and Depreciation
Interest-+ Principal Repayment
I - Tax Rate
The government's willingness to participate is given by a social welfare function, W, defined as:
i Al - (1 + A)(t), if the investment is made
{0, if there is no investment }
where 0 < A < 1 is a measure of welfare-loss from distortionary taxation, I is the project's investment
size, and t is the present value of the net transfer of resources from the government to the private
sector.
4
Project evaluation under uncertainty
INFRISK draws on recent developments in the literature on project evaluation
under uncertainty6 to generate probability distributions for key decision variables, such as
a project's net present value (NPV), internal rate of return (IRR), or a project's capacity
to service its debt on time during the life of the project. Such distributions are then used
in assessing a project's economic viability, which is taken as the key criterion in project
selection. Thus, judgement on the economic viability of a project is not based solely on a
single "best estimate" of a project's metrics, i.e. net present value or debt service
capacity, but also on the possible ranges of such variables and the likelihood of their
occurrence within given ranges (see Box 1).
INFRISK is capable of handling several sources of uncertainty and risk bearing on
a project's economic viability. Such risks, for example, could be associated with the
revenue stream (tariff rate, demand forecast for electricity in a power project, or traffic
volume forecast in a toll road project), operations and maintenance costs, and
construction cost. The user has the option of choosing the key risk variable or variables
upon which to focus, depending on the specific features of the infrastructure project at
hand and the questions being addressed.
For a particular risk variable of interest, the program first generates a stream of
probability distributions for each year of a project's life through a Monte Carlo
simulation technique, the methodology for which is well known and is described in Box 2
and Annex 1. Typically, the relevant risk variable in a project, i.e. demand forecast,
costs, and tariffs can be quantified in terms of both single best-guess estimates as well as
a range of estimates over the life of a project or the early years in a project's life. Using
such information, a suitable probability distribution is assigned to each risk variable
within a specified range. Care must be taken to ensure that such a priori assigned
probability distributions are consistent with the economic/statistical time series
characteristics of relevant risk variables. For instance, exchange rates are known to obey
a log-normal distribution, while revenue from a toll-road project is likely to exhibit an
asymmetric probability distribution profile, such as a Beta distribution. INFRISK offers
the flexibility of incorporating four classes of probability distributions (uniformn, normal,
lognormal, and beta) which provide a broad menu of probabilistic representation of
relevant economic variables in an infrastructure project.
Specification of uncertainty through time may affect a project's cash flows and is
also an important issue in project valuation. The pattern according to which uncertainty
is resolved over time clearly varies from project to project, and requires careful
consideration. For most infrastructure projects, the nature of risk changes fundamentally
as the project reaches completion and is ready for operation. For this reason, INFRISK
explicitly recognizes the two main phases of project development and project operation.
To specify how risk evolves over time, we focus on the variance of a given risk variable.
6 The literature on project appraisal under uncertainty goes back to Hertz (1964, 1979) and work done at The World
Bank in the early 1 970s (Pouliquen, 1970, World Bank, 1970). Subsequent contributions include Hertz and
Thomas (1983), and most recently, the application of real option-theoretic models to project valuation. See also
Paddock, Siegel and Smith (1988); as well as Copeland and Keenan (1998).
5
As shown in Box 2, information on the evolution of variance can be obtained from the
time series' characteristics of the variable, or from the estimated range.7
Computationally, INFRISK works in conjunction with Microsoft Excel and
supports both the construction and the operation phases of a capital investment project.
The input to the simulation exercise includes data on projected revenues, operating costs,
and other risk variable inputs which are part of the standard forecasting and cash flow
analysis.
INFRISK Analytics
At the heart of INFRISK is a generic financial model, describing the year to year
uses and sources of funds in the context of the project's initial capitalization, its income-
expenditure flows, cash flows, as well as certain specific accounts established for
servicing of debt (debt service reserve), operations and maintenance, tax payments, and
general accounts (see Table 3 in the Annex). The drawdown of funds during the
construction period and the distribution of cash flows during the operation phase are
governed by a hierarchy of claims embedded in the contracts and loan covenants. If a
project, for instance, takes three years to be constructed and the distribution of total
capital expenditures is given by 25% (1st year), 50% (2nd year), and 25% (3rd year), it is
assumed that equity funds are also drawn according to the same pattern. INFRISK,
however, has the flexibility of incorporating a different pattern of capital expenditure
disbursement, as well as equity drawdown, depending on the particular project at hand.
Driving the financial model are project specific sub-models determining operating
revenues and costs, as functions of tariffs, capacity, output, and input prices and
quantities. In a power project, for instance, operating revenues could consist of payments
for electric generating capacity and energy, and associated steam (in a cogenerated plant),
as provided under the Power Purchase Agreement, and operating costs dependent on fuel
usage and prices as well as the operation and maintenance expenses.
Currently, INFRISK operates on an annual, year-by-year basis. Work, however, is
underway to introduce calendar time (day, month, year) as the basis for analysis in line
with the actual functioning of financial markets and contracts.
Box 2: Probabilistic-based simulation
Technically, the stochastic process { Y, I t1. T } can represent the possible realization of a risk variable,
Y, in an infrastructure project, over the project's lifetime, where T is the life of the project, i.e. concession
period. It is useful to represent the value of Y in year t ( Y, ) as the sum of its projected value, Au, and a
random variable, u,, as follows:
Y,- (1)
U= a, 1/2 £(2)
7 In much of the finance literature, risk is modeled to evolve monotonically with time, through the dominant application
of diffusion process of Brownian motion, where variance increases through time.
6
where { ct } is an independently distributed random sequence, with a mean of zero and unit variance, that
is, E ( s1) 0, var ( E,) = 1, E ( s, , 6, ) = 0, and t s.
From equations (1) and (2), it is easy to see that E ( Y,) = Au,, and var ( Y,) = a, as ( t = 1,...,T). Thus in
generating the probability distribution functions { F, (c) t 1,.. , T } for { Y, }, it is necessary to specify ,A,,
a, as well as the specific distribution fonn of e,.
In principle, ,u, can be estimated from infonnation contained in a project description. In the case that { Yt
t,.. .,T } represents a project's operating revenues, for instance, it is possible to write p, = ,u ( Xt, 6 )
where Xt is a vector of exogenous variables indicating relevant demand and technical factors and ,8 is a
corresponding vector of fixed parameters. In this case Au, can be interpreted as the projected or forecasted
operating revenues over a project's lifetime, which is generated from assumptions on the tariff structure,
demand forecast, and any indexation or escalation factor involved.
Computationally, the Monte Carlo simulation technique used in INFRISK is based on N randomly sampled
iterations ( N = 1000 ) for a risk variable { Yt I 1,. ., T }. The ilh iteration is given by:
Y,i= + +1 ,(3)
for each year in the life of the project. Thus, focusing on the first year of the project's operation, we have:
Yl' =j`+ fa ef (4)
One representation of (4) is the Martingale process, suggested by Hurley (1998), which is given by:
Y,= Y,, + u, (5)
u, =a 6,, (6)
letting a, = 62 y''. Then we have E ( Y,)= Y t= 1,...,T and
vrY (I - ' ),5, ,., 7
In most cases analysts have reliable information not only about the projected Au,, but also a range
range(Y,)= maxY, - min Y, } within which , can be assumed to lie. Using the information on the
projected range of a risk variable, it is possible to estimate a Thus, for the normal distribution, we
estimate the standard deviation in the first year as:
, range(Y,) (8)
d
where the constant d can be taken as 6, given that for the normal distribution most of the
data (approximately 99.7%) falls in the interval of 6 standard deviations around the mean.
For the uniform distribution, el - U(-0.5 range(YI), 0.5 range(Yi)), and
range(Y,) (9)
V12
For the transformed beta distribution, ul - range(YI)beta(a, b)+A, (A is the mean
preserving constant), A = YI - range(Y, )a I(a + b), and
a = range(Y) - 0.16(rangel) (10)
1 a+b+l) a+b
when a=2, b =5, for instance.
7
Model of an IPP - The Indiantown Cogeneration Project
To illustrate the application of INFRISK to a real-life project, we draw on the
Indiantown Cogeneration Project in this section. This project provides an excellent test
case due to the extensive amount of
detailed public information that is Indiantown Cogeneration Project
available on the project's financing mix, Characteristics of the project
regulatory environment, and projected * LIai- I.diantaon.Flolda, USA
operating results which are contained in . Capacidt 330 MW
the prospectus for the 1994 bond issues. . P., ,P-rhas Sa leof bothc p odly ndeneto
This information is readily obtainable AgreemeMT. FfondtPoer and Liyh p(1996.2025)
through the U.S. Securities and Exchange (2) catiiable mondhly enypayrgl
Comrnission and the project company. A . FinandngTenns: (I) SiO5nFi.tMoriageBon.ds,tentamnch.
detailed examination of the Indiantown (2) ih2iae Taex e 7mpt BondS in8 t5ao
project is also available from Finnerty
(1996).
The Indiantown Cogeneration Project is a coal-fired facility with an electric
generating capacity of 330 megawatts (MW) and a steam export capability of 175,000
pounds per hour. Construction of the facility, located in Martin County, Florida, began
on October 21, 1992 and was completed in 1996. Construction of the project was
financed with a $140 million equity contribution from the partners, $505 million in First
Mortgage Bonds (1994), and $125 million in tax-exempt bonds (1994) arranged through
the Martin County Industrial Development Authority.
The project company entered into a Indiantown Cogeneration Project
30-year Power Purchase Agreement (PPA)
with the Florida Power & Light Company pcmpnY:
(FPL), a utility under the regulatory
authority of the Florida Public Service
Commission. FPL's service area covers 35 P-o ePu.e.unAgrmt:
counties in Florida with a population of 6 FRndnPomedtUgog idie.tD C
million or approximately half the of .M.)
population of Florida. The PPA features a R -
two-tiered pricing arrangement consisting
of: (i) a fixed capacity charge covering
fixed operational costs, and other financial commitments; and (ii) a variable energy
charge covering costs of fuel and variable operations and maintenance expenses.
Additionally, the project company contracted to provide its cogenerated steam to the
Caulkins Indiantown Citrus Company for a period of 15 years.
The following section presents a simplified financial model of such an IPP. The
purpose is to highlight the implications for project viability of the credit risk of the utility
off-taker. The model focuses on features such as pricing and long-term contracting,
which are common in IPPs.8
8 See Dailami (1999) for a more detailed discussion.
8
The basic equations determining contracted revenues, expenses, and escalation
factors can be summarized as:
Basic equations:
Electric operating revenue:
Rt =8760[XM(;rc + zf )]+)eQt (1)
Electric output:
Qt dtM (2)
Operating costs:
Et = f(M)Pf +OMt (3)
Operating income:
It = Rt - Et (4)
Escalation factors:
Tf = )rf (1 + gl)t (6)
7ct = ,e (I + g2)t (7)
pf =Pf (1 + g)t1 (8)
t 1I g
where:
Rt = contracted electricity revenue in year t (million US$)
M installed capacity (MW)
A capacity payment multiplier
f = capacity rate ($/KWh)
Wf = fixed capacity rate for operational costs ($/KWh)
o-f = variable unit energy price ($/KWh)
OMt operations and maintenance expenses
Q energy produced (KWh x 103)
gi = rate of inflation in the GDP price deflator
g2 = projected rate of inflation in the fuel price
In discussing revenue risk, we first distinguish between a contracted level of
revenue Rt and the actual level of revenue At . The actual level of revenue will be a
random variable depending on the level of actual demand and whether the utility actually
pays as agreed.
9
To incorporate the credit risk of utility off-takers, we have:
Rt = min(Rt . Z ) (9)
where Zt is a random variable reflecting the capacity payment of the off-taker.
We assume that the payment capacity of the utility off-taker can be characterized
by a nornal probability distribution with a mean equal to its promised or contracted
payment to the IPP, i.e. R, and a standard deviation of 9'/o. Thus:
Z N(R,02R2 ) (10)
Note that 0 measures the degree of riskiness of the utility off-taker. The higher
the value of 9, the higher the riskiness or the lower the creditworthiness of the off-taker.
Figures 3, 4, and 5 show respectively, the simulated probability distributions for
the Indiantown Power project's net present value, dividend payment, and debt service
ratio in the year 2005.9
9 Alternatively, the payment capacity of power purchaser can be characterized by two distributions:
(i) a discrete distribution describing that the power purchaser is not able to serve its contractual
value R, on time and in full. Let this probability be P, in year t.
(ii) given that the power purchaser is in default, let the proportion of contracted value that can be
recovered in year t be denoted by a random variable y,, with support (Osy,sl ), and with the
conditional probability distribution #,(e), which can be assumed to obey a beta distribution. In this
case, R will be determined by the joint distribution ofp and y, i.e. R = g(p, y) with the expected
value given by E(R ) R (I - P ) + Pt Rt fo YoSt (y)dy. See Dailami (1999) for details on this
t t t
approach.
10
Figure 3: Probability Distribution of Net Present Value
Riskfactor: Total Revenue
Histogram of Monte Carlo Simulation, 1000 iterations
180 ---
160 1 Mean: 25.71
1- Median: 27.89
j ') 120 +Prob. <0: 19.7%
(D 100 -
80-l[ .:l|ll[
u 60~
40-+
20 -n0
Net present value of Indiantown Power Project
Figure 4: Probability Distribution of Dividend in Year 2005
Riskfactor: Total Revenue
Histogram of Monte Carlo Simulation, 1000 iterations
180-
180 - I Mean: 35.71
160 I
140 2 Median: 36.32
120 Probability < 0: 9.5%
a100 il|l
- 80
60
40-'-
20
Dividend, 2005
11
Figure 5: Probability Distribution of Debt Service in Year 2005
Riskfactor: Total Revenue
Histogram of Monte Carlo Simulation, 1000 iterations
180- Mean: 1.36
160 Median: 1.37
140 Probability < 1.25: 41.3%
L 120,
I 1 0 _ _ _ _ _ _ _ _
80-
i 160M
40-
20- L
Debt Service Coverage, 2005
Figure 6: Probability Distrbution of Interest Service in Year 2005
Risk factor: Total Revenue
* ~~Histogram of Monte Carlo Simulation, 1000 iterations
180
160- Mean: 2.07
140-~ Median: 2 08
'120~ Probability < 1.5 25.4%
0 80-
U- 60'
404
MC)o ,Dm t CD m O C'. CO Om L~UO NLfo
Interest Coverage, 2005
12
User Guide
Summary Version
i3
13
This user guide is divided into three main sections:
1. Inputting project data into INFRISK
II. Using the dialog boxes to specify desired setings for the simulation
III. Customizing and understanding the simulation output
1. Inputting Project Data into INFRISK
In INFRISK, the project data for the simulation is inputted both through an input
sheet and the INFRISK dialog boxes. The input sheet contains fundamental project data
for each year of the project. The data on this sheet is divided into two sections: one for
the construction period and one for the operational period.
The program offers a large degree of flexibility when the user is creating her own
input sheet. Different types of inputs can be placed anywhere within the appropriate
section (construction or operation) and in the order of the user's choice. However, the
two sections must be separated, and each of them starts with the heading line that labels
the subsequent columns with the year identifiers (i.e., 1992, 1993, etc.). For the
Construction Phase table, the heading line must contain YRCON in the second column
(as shown on the example sheet below). Correspondingly, for the Operation Phase table,
the heading line must contain YROPER in the second column. To identify the data, the
user must include the appropriate label (for example, "OR" for operating revenues) in the
second column as in the example below. The label in the first column is for descriptive
purposes only and may be customized as desired by the user. Annex 1 provides a
typology of flow and stock variables familiar to INFRISK.
Figure 7: INFRISK Input Sheet
FinancongCoslsdoringC ..n.t-o-o IK USD 0 .50.6 98.e88
C.pilaIConsW1lIoeCos- .CK USO 109.8825 105.6825 1096825 109 825
R.44e98el1.nges89rCKdeorandorn1Ru00uellons Cl2oKAng, USD 21.9355 219385 211340 21.93G5
DBA-t2 US0 0 12 B o
DBA-11 USD 0 113 0 3
Othe -.i841 -~edft8 COlK USO 49249 49.849 41.849
Eq8A8 ES 9US 109.88 30.32 0 0
End,gEEhR.t. El US9 1 I 1
DBA-1 USO 0 4.21 0.157 0
DBA.2 USD 0 8 4.39e 0
6BA.3 USO 0 8 4.8S 0
DBA.4 US 8 0 4.C5M 8
DBA-S US9 0 0 5.132- 0
DBA-6 USD 0 0 S.133. 0
DBA-7 USO 0 8 9828 0
OBA-S USO 0 0 4.998 0
MEAS LUSO 0 0 197.839 0
00A-10 l8o U 0 819.01 250.392
Ph.s. 298oPh~ 1wr .I3W7 7W 1JAW .ftw wt JW
Filed Cap.o Pp-n,t US9 118.412 123.575 124212 124.937 125.79 126.W31 12A40S ¶2Y337
V.i.b,R P.... USO 49.4041 61.844 63.834 888894 688572 84831 738974 70819
1MM8 18 38.419 189248 188.891 184284 191.442 201.38 228 18
s7R-d,-P aq#i3Av? OR US9 49.404 61.844 83.834 68884 66.575 64.931 73974 76.818
ORR.7g. US0 24.702 30.9.2 31.917 33.047 342875 32A255 35.587 36.4095
0US 14.503 1.485- 18.007 17.795 16.757 20.025 21.3=3 18.81
The program also permits the user to switch easily between different sets of
projections for a project. This is done on the main dialog (shown on the next page) by
selecting the name of the sheet containing the desired data in the combo box labeled
"input sheet."
14
11. Using the dialog boxes to specify desired settings for the simulation
The INFRISK Main Dialog
Once the main proj ect data are entered in the input sheet, the user can specify the
settings regulating the functioning of the INFRISK simulation. This is done through the
main dialog's key sections, which cover the following areas:
- Macroeconomic Parameters
- Construction Cost (Note: Information on construction costs can be viewed but
not changed in the dialog box. It can only be changed on the input sheet.)
* Risk Variables
* Debt Capital Info
* Equity Capital Info
Output Options
Clicking the mai button in any of these sections allows the user to modify the
simulation settings. For example, to set the tNxrISK simultionedit button in the
macroeconomic parameters section, which will open a dialog where the tax rate can be
changed.Thefnothngeoin pages give a more detailed breakdown of the capabilities of each
of the sections of the main dialog box.
15
Macroeconomic Parameters
IWsUT_-;AuTA%-xVt ParameteFs Ii
DlscU rate
4 Tax Rate
fW Asses Ufe fr DepwjaWn (yewrs)
Welfare-Loss Mease of t&K*Ion
In this dialog, the user can specify the main macroeconomic parameters that have direct
influence on a project's cash flows, such as the applicable discount rate, the corporate
income tax rate, allowable asset life for calculating depreciation for tax purposes, and a
measure of welfare-loss due to distortionary taxation (used in the INFRISK social welfare
function to calculate the government's willingness to participate in a project.)
Construction Cost
iw1tiflTirnio Into
Constmuctton Peawod
Total Cost (Lcu) 1438.73
Constuctkon Costs Aiocauton
1992 1993 1T 1996
1iO9,w8 1109.68a ji09, 11 F,
This dialog is for infornational purposes only and allows the user to view
information on the construction period, total construction cost, and the allocation
schedule of costs over the construction period. Changing this data can be done through
the specified input sheet via the variable labeled as CK.
16
Risk Variables
INFRISK is capable of handling several sources of uncertainty and risk that
influence a project's economic viability. Such risks, for example, could be associated
with revenue stream (tariff rate or traffic volume forecast in a toll road project),
operations and maintenance costs, and projected construction cost (in an IPP). The user
has the option of choosing the key "risk variable" upon which to focus, depending on the
specific features of the infrastructure project at hand.
For a particular risk variable, the program generates a number of probability
distributions for each year of the project's life (concession) using a Monte Carlo
simulation technique.
INFRISK can use one of four
5eVrs~t40:E d probability distributions
~Exch Rae . Reveues & Mantenance (uniform, normial, beta, and
Constructionte CostRts l '0 t Operations &Maintenance log-normal) as the error
Other Operating Expenses j generator. Uncertainty through
time is incorporated by
specifying how the parameter
(i.e. mean and variance)
changes over time (see Annex
for details).
Once a variable is selected for the Monte Carlo simulation, the Risk Variable
Options dialog opens, allowing the user to specify the desired options. The projection of
the data section of this dialog determines the source of data for the variable - it is either
stored in the input sheet specified in the main dialog, or can be generated according to the
user's specifications (by specifying lag, intercept, and slope). By manipulating these
1 7
three parameters, the user can specify a variety of models. For instance, the random walk
process for the logs of exchange rate can be easily specified by putting a unit coefficient
for the lagged value and zeros for all other. If the user does not know the values for some
parameters, he can check the estimated option, then INFRISK will use the data specified
at the data for estimation textbox to obtain its own estimate.
The Random Component section allows the user to specify the distribution
function, and other parameters associated with it. If the data are expected to possess a
stochastic term, the user can provide the parameters for the error term, namely its
distribution and the standard deviation. Several options can be used to specify the
standard deviations for the random process:
* User-defined standard deviation
* Estimated from the historical data (the location to historical data is specified
in the data for estimation text box) using their residuals from the trend or
deviations from a random walk model (first differences), when the projected
values are used as the mean.
* Estimated from the ranges provided by the user in the input sheet. The ranges
must be labeled following the format Range (for instance,
"ORRange").
In this section, the user can also specify the following:
* Distribution. Allows the user to select the probability distribution function for the
error term. Presently, INFRISK can handle four different error distributions:
Normal, Lognormal, Beta, and Uniform. The "Beta distribution" option allows
the user to model the errors around the trend using a right-skewed distribution
based upon a member from the beta family (as an example, see Box 4 for a formal
description of Beta distribution, its probability density function, and some
important parameters).
* Positioning. Specifies whether the selected distribution is positioned around,
above, or below the trend. Also the user can truncate all generated values above
or below the mean value of the given distribution.
* Correlated With option allows the user to impose a certain correlation between
pairs of random variables. For instance, in our example, the random component
of Revenues can be correlated with the random component of the Maintenance
costs (for a toll road project, it is safe to assume that toll road revenues are
positively correlated with maintenance costs). The value of the correlation
coefficient can be any number from -1 to 1 and is specified in the correlation
coefficient edit box.
18
Box4
The beta probability distribution function is given by the following expression:
fix, ca, B) = k(a,P)*x'-1(1-x)P-, 0< x <1, cr, ,B > 0,
Where the coefficient k(a,,) = F(a+c )/F(u)/F(l3) does not depend on x. It can be easily shown
that:
1t= E(X) = a/(o+P
a2= Var(X) = CCp/(a+p+,)/(a+2
m = Mode(X) = (a-1)/(ct+P-2)
Table I contains the values of some important parameters of beta distribution for the case of
oc=2, P=5
Table I
mode 0.2
2
p 5
________________ 0.286
Ci 0.160
Prob(x<4) 0.548
,Prob(x. For
instance, if the name of a given debt instrument is Loanl, the label will be
SAMLoanl.
* Disbursement Plan over Construction Period. Provides edit boxes that
allow the user to specify how the disbursement of the debt is distributed
over the construction period. This information is also stored in the input
sheet under the variables labeled as DBA. For instance, if the
name of a given debt instrument is Loan2, the label will be DBALoan2.
Box 5: Debt Parameters
INFRISK is capable of handling a wide menu of debt instruments, i.e. loans, bonds, and
LCs. This representation is sufficiently general to encompass the main characteristics
n the payment of both a loan and a bond issue. As an illustration, consider a debt with
the face value $D contracted at time 0, and to mature at time m, where m < T, when T is
the length of concession. Associated with this debt is a stream of contractual payments,
.e., amortization, interest, and commitment fees, depending on the nature of the debt
nstrument, and characteristics. Thus, for a given time (X),
DS(t) = AM(X) + R(-) + COM(r),
where DS = debt service payment, AM amortization, R = interest, and COM
commitment fees, and
D= EAM(r)
In the case of a bond with fixed coupons and bullet payments at the maturity dates we
have:
AM(r) = O, V T = 1, m - 1, and AM(m) = D, and R(r) = D x c,
where c is the fixed coupon rate. In the case of a loan, interest is paid on disbursed and
utstanding amounts, and the commitment is charged on the amount committed, but not
yet disbursed. Amortization is often agreed in advance, including grace periods. In a
loan with periodic equal payments, the payment is defined as follows:
PMT = L (I + i)-
L = Initial loan
PAMT = end of period payment (equal payments)
i = interest rate
N = number of end of period payments
The amortization part of the payment is as follows
AMTn = L I(1)
Equity Capital Info
The Equity Capital Info dialog is designed to permit the user to store and edit key
information concerning equity capital in a project. Such information relates to the
amount, currency, and disbursement plan over the construction phase of the project's
equity.
23
Ill. Customizing and understanding the simulation output
Output Options Dialog
E n1 Options
-Ca,u for EMono** W'I-Y
7CWend tyeir: -i est'or -
f Mhii 0 ~~~~- 1996 , 3 R 4 r c ''
?Ir'2g*eo < Jv f j fbay f-N.be b,wmW^ < . '
-et tco5erske <10 Ye01
F J.25 11996J akMcYtg
F v1* :E .-
{; '' Mhk' ] , ,.'Fl - -W -- , ,.-
o F#we - G-Se Chat Year.
~~~~~~~~~~~~~~~ Tid test run :
This dialog allows the customization of the two main types of output generated by
INFRISK: (i) the simulation analysis and (ii) the economic viability analysis.
The simulation analysis provides informnation on the estimated probability that a
given risk variable will be lower than a specified minimum level (denoted as "minimum"
in the dialog). These estimates are calculated for each year of the project's lifetime. The
user can also choose to generate charts showing the probability distribution estimates in a
selected year for each risk variable. Figure 9 shows a sample INFRISK output sheet;
examples of INFRISK's chart output can be found in Figures 3-6.
Figure 9: INFRISK Output Shee
hca 1un96g 1997 1993 1399 2000 2001 2802 2003 2004
Numbf - of iteralons I 100I
a
Expected Dividierds 8.002 9.542, 8.950 7.418 6.710 6.685 2.850. 3.337~ 2.375:
Eiqpeoto Cash Flow 118.362 120.151 119.357: 118.717 118.705 115.218 110.683 113.189 113.08
Probabit8foity.1dend below 0 0-178 0.108 0.2,27 0,264. 02312 0-200 0.433 0.3339 0.435
6Eted VaJueof Debt Servie Coverage 1.043 1.857 L.OW4 l.M2 1.0,03 1.006 0.949: 0.935 0.907
ProbabiNlt1 of Debt Service Coverage Below 1.25 0.073 0.32 0.917 0.931 2.948 0.347 0.97! 0.805 0.991
cvpavte.Va*of lnterest CoveTage 1.28i1 .337 1.341A, 1.314 1.334 1.333 1273 1.348 I.8
NJet Present Value of Cash Flow 321.5S9
I Internal rate of aRetur on the Expected DiVidends NIA
24
Charts of the simulation analysis can also be produced by checking the
appropriate box, if desired. Figure 10 gives an example of the chart output for the
distribution of the net present value of cash flow.
Figure 10: INFRISK Chart Output
-sent value:Frequencypmnuative %9 1 : T
24SR80 1 } .10%< Histogram
4%3 4%
266.38 9. 1.30%
275.52 2l 4.20%' 180 - 100%
288.87 42 8.41% ~ 160 0
297.12 as 17.32%2 140 - S0%
30.37 113M 2 08.3 - 7012
317.62 19 43.54% 100 %
27.87 163 59.86% i 80 X 4
338.12 184 76.2% X 0 3
348.37 94 85.89% 4020
3M8.62 24S.877 t.89% 0 i 0%
368.87 420 970% 0 9.0%
379.12 1 299.10% 5 ~ ~~
388.37 5 99.60%
399.62 2 89.80 11 e r § ~OI
409.87, 2 100.00% N et pre s ent valIue of NC F
More 0 00.00%
Sumnmary
Men 321.117.
Standard i 24.76
Median 321 .768
Min 245 .877
Mx 409.867
Count 1000_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
The economic viability analysis can be undertaken from the perspectives of the
parties involved in an infrastructure project: the project promoter (investor), the creditor,
and the host government. This analysis will show whether the probability of a given
variable meeting the specified criterion falls within the accepted confidence level. A
"pass" result indicates that the estimated probability generated by the Monte Carlo
simulation is below that specified by the user "confidence level." The viability analysis
provides the following options:
* From the investor's perspective:
(a) Probability of the internal rate of return being smaller than a specified level.
(b) Probability of the net present value being smaller than zero should be smaller
than the specified level.
(c) Probability of dividend being negative or smaller than the specified level.
* From the creditor's perspective:
(a) Probability of the interest coverage ratio being smaller than a specified level.
(b) Probability of the debt service ratio being smaller than a specified level.
* From the government's perspective:
(a) Probability of social benefits from the project being smaller than a specified
level.
25
The economic viability analysis report provides the user with information on each
particular constraint. The output explains why the project does not pass certain
requirements. Figure 11 shows an example of the viability output.
Figure 11: INFRISK Economic Viability Output
Test Name Test Result Maximum Year of
Probability of First
Being Below Failure
Acceptable Level
Dividend failed 0.978 1996
IRR test NA
NPV passed 0.000
Debt Service coverage ratio failed 1.000 1996
Interest coverage ratio failed 0.924 1996
Social Benefits not selected
Box 6: Computation of NPV and IRR in INFRISK
1. NPV. INFRISK calculates NPV in according to the following equation:
NPV=Ec(_1) ES, + LS, +BS, + NCFj
(1 + r)N =' (1 + r)i+c
Where c and o are the respective number of construction and operation periods, and
ES;,= Equity allocation during 14h construction period
ES, = Loan allocation during i construction period
BSj = Bond allocation during i construction period
NCFi = Net cash flow associated with the project in ii" operating period
NCF = TOR-TOE-TAX+DEP (see also ANNEX 1)
r = a specified annual discount rate
2. IRR. The IRR function is closely related to NPV. It is the rate that equates NPV to a value of
zero (from the point of view of the investor). However, the cash flow used for NPV and IRR in
INFRISK is not the same. For IRR we use the Equity on the negative side and the Dividend on the
positive side of the equation. The solution is found using the Excel built-in function which
employs an iterative method that clearly depends on starting values. Theoretically, there may be as
many solutions as the power of the respective polynomial; however, we solve for a local solution
close to the assumed discount rate. If no solution is returned by the Excel IRR function, we
indicate this situation by printing N/A in the corresponding cell.
26
Annex 1: Project Financial Accounts
Indiantown Cogeneration Project, selected years
A. Project Initial Capitalization (Construction Phase)
1993
Bonds (disbursed in year) BS 127.21
Equity (disbursed in year) ES 30.32
Letters of credit LCS 0.00
Loans LS 0.00
Construction Costs CK 109.68
Financing Costs during Construction IK 9.89
Other capital expenditures OK 49.85
Debt service reserve DRK 0.00
Total Capital Expenditures KS=CK+IK+DRK+OK 169.42
Ending Exch Rate Et 1.00
B. Income-Expenditure Table
1996
Operating Revenues OR 185.45
Investment Income INV 3.36
Total Operating Revenues TOR 188.81
Operation and Maintenance OME 11.55
Insurance and Administration INSA 0.00
Fees on Loans FEE 0.00
Other Expenses 14.59
Disposal Cost 48.49
Other Operating Expenses OEE 63.08
Total Operating Expenses TOE=OME+FEE+OEE+INSA 74.63
Interest Payment INTP 57.69
Tax Withheld WTX 0
Scheduled Amortization SAM 8.80
Depreciation* DEP 43.87
Income Before Taxes INBT 12.62
Tax TAX 3.78
C. Cash Flows Table
1996
Income Before Taxes INBT 12.62
Total Debt Service TDS 66.49
Equity Funds EF 140
Debt Funds DF 675
Capital Expenditure CKF=CK+OK 159.53
Loan Repayment LAM 0.00
Bond Repayment BAM 8.80
Credit Letter Repayment LCAM 0.00
Debt Repayment DAM=LAM+BAM+CAM 8.80
Tax TAX 3.78
Operating Cash Flow OCF=OR-OME-INSA 197.00
Net Cash Flow NCF=TOR-TOE- 177.26
TAX+DEP
Equity Cash Flows (Dividend) DIV=TOR-TOE-TDS 47.69
General Account GA 0.00
Debt Service Reserve Fund DSR 0.00
Maintenance Account MA 0
Exchange Rate Xt 1.00
*In general DEP can be a non linear function of CK, i(CK)
Note: INVf (G,A, r) where r= applicable interest rate
27
Annex 2: Details on generation of random variates for Monte-Carlo
Simulation
This section describes the computational methodology for generating the four
classes of probability distributions - uniform, normal, lognormal, and beta - that are used
in the Monte Carlo simulation adapted in INFRISK.
Uniform random variate
The uniform random variate u is generated using a built-in Excel function RAND.
This function returns a (0,1) variable. To transform it with an error term possessing a
required standard deviation, we first standardize u a by centering around the mean value
of 0.5 and dividing by its standard deviation of (1/12)0.5 such as
U* (u-0.5)
u -
71/12
Then we multiply u* by the desired standard deviation.
Normal random variate.
Following Maindonald (1984), we used the Marsaglia and Bray's polar method (a
variation of Box-Muller method).
Step 1. Generate uniformn (0,1) variates ul, u2. Transform them into uJ=2uI-l,
U2=2U2- 1, so that new uniform variables will be distributed in (-1,1)
Step2. Let w = u2 + u2, if w > I skip and select a new pair of uniform ul, u2 until
the restriction is satisfied.
Step 3 Set v ,then set z = ulv which will serve as a standard
normal (0,1) variate that is further transformed by multiplying by the
desirable standard deviation and adding the projected mean /trend.
Lognormal variate
The lognormal variate is obtained by first generating a normal variate and
applying the exponential transformation to new series y = exp(ln(Y) + zo) where z is a
standard normal variate. The user should bear in mind that when supplying a for the
lognormal distribution, he should convert it into a log scale himself
Beta random variate
The beta random variate with parameters a and P is generated by using the
following simple algorithm adopted from Maindonald.
Step 1 Generate uniform (0,1) variables ul, u2.
28
Step 2 Let v, = u/'a +24"
Step 3 if w=vl+v2 < 1 put x=vl/w. Otherwise, take new ul, u2. and go to Step
2.
INFRISK always assumes a = 2, fr=5 because the resulting distribution is skewed
to a reasonable degree, as was justified in some experiments. Thus, obtained beta variate
is standardized by subtracting its mean and dividing by its standard deviation (see Box 5).
The obtained standardized variate is further transformed by multiplying by the desirable
standard deviation and adding the projected mean /trend.
29
Annex 3: Preparing data on projected variables in the Input Sheet
To perform analysis on her own data, the user should provide a sheet with certain
variables for the construction and operation periods. We already mentioned that the
projected values for the simulated variables can be stored in the input sheet. Also there
are some other "non-risk" variables that can be stored in the input sheet.
It is important that the user follows the right format when entering the data in the
input sheet. The first column will normally have the name of the variable of interest
(optional), while the second column must contain the correct label of the variable, which
is not optional. The third column must contain the identified units (currency). The US
dollar should be specified as USD. The next columns are the data columns, which must
contain the numerical values for the corresponding variables The data are split into two
tables, one for the construction phase, the other for the operating phase. Each table must
have a heading line that contains the year identifiers in the corresponding columns as well
as table identifiers in the second column (see example in the Figure ). Those are YRCON
for the construction table, and YROPER for the operation table.
Sources of Uncertainty Labels
Revenues OR
Operations & Maintenance OME
Other Operating Expenses OEE
Investment Income INV
Ending Exch Rate* Xt
Interest Rate Ir
Construction Costs /Equity** CK/ES
* The exchange rate is a macroeconomic variable and the data should be provided for
both construction (if it is not omitted) and operation period. In the former case, the label
is Et, in the latter Xt. The exchange rate is always in terms of local currency/USD
* *if the source of uncertainty is associated with construction costs, it also automatically
makes equity random so as to balance sources and uses of the funds
The user can also store in the input sheet information on the ranges of all
simulated variables. The labels for these data should follow the format: RANGE; for instance, ORRange for the Revenues. This information will be used if
the user selects the Estimatedfrom Projected Ranges option for the error standard
deviation of the simulated variable.
The following variables are not considered sources of uncertainty and are
optional. If omitted in the input sheet they will be assumed to have a value of zero.
Non-random variables for the Labels
construction period
Debt Service Reserve DRK
Other capital Expenditures OK
Interest during construction IrC
Exchange rate durung construction Et
Financing Costs during IK
30
Construction
Non-random variables for the Labels
operation period
Insurance and Administration INSA
Deposits to Major Maintenance DMA
Accounts
Withheld tax payment WTP
Fees on Loans FEE
Non-random part of the revenues* NR
*This quantity will be added to the random part of the revenues in all subsequent
calculations and is useful when we need to model the stream of revenues as consisting of
two parts, one effected by random factors and the other fixed at certain level.
As was explained earlier, the user can also store in the input sheet information on
the amortization schedules for the loans. The labels for these data should follow the
format SAM; for instance, if the name of the loan is LOANI, then the
information on the amortization schedule should be stored in the row labeled as SAM
LOAN 1. This information will be utilized by INFRISK when the user specifies the
repayment plan as Defined Schedule in the Parameters of the Debt Instrument dialog.
31
Annex 4: Charts
Probability of Insufficient Debt
Coverage Under Different Scenarios
f 80% Interest Rate = 10.5%
o 70%
u
-1 60%
..50%
430%
b20%
10%
- revenues only- -revenues & maintenance, uncorrelated
Flow chart diagram of INFRISK
Information Probability
* Input Data distribution of
* Parameters main variables
Company Lender Government
IRR, NPV Debt Coverage Social benefits of
| l Ratios project net of subsidies
No No Yes1 N
L--4~~~~ ~ ~~ - ------
Transaction.
32
References
Bernstein, Peter L. 1996. Against the Gods: The Remarkable Story of Risk. New York:
John Wiley and Sons.
Copeland, T.E. and P.T. Keenan. 1988. "Making Options Real." The McKinsey
Quarterly, No. 3.
Dailami, Mansoor. 1999. "The Government as Guarantor in Infrastructure Finance."
World Bank Working Paper (unpublished).
Dailami, Mansoor and Michael Klein. 1999. "On Government Support and Contracts in
Infrastructure Finance in Emerging Markets." World Bank (unpublished).
Finnerty, John D. 1996. Project Financing: Asset-Based Financial Engineering. New
York: John Wiley & Sons.
Froot, K.A., D.S. Scharfstein, and J.C. Stein. 1993. "Risk Management: Coordinating
Corporate Investment and Financing Policies." The Journal of Finance, No. 5.
Hertz, David B. 1964. "Risk Analysis in Capital Investment." Harvard Business
Review, January-February 1964.
Hertz, David B. 1979. "Risk Analysis in Capital Investment." Harvard Business Review,
HBR Classic, September-October 1979, pp 169-182.
Hertz, David B., and H. Thomas. 1983. Risk Analysis and its Applications. New York:
John Wiley and Sons.
Hurley, W.J. 1998. "On the Use of Martingales in Monte Carlo Approaches to
Multiperiod Parameter Uncertainty in Capital Investment Risk Analysis." In The
Engineering Economist, Vol. 43, No. 2.
Maindonald, J.H. 1984. Statistical computation. New York: John Wiley and Sons.
Paddock, J. Siegel, D., and J. Smith. 1998. "Option Pricing: A New Approach to Mine
Valuation." CIMBulletin, 79.5.
Pouliquen, Louis Y. 1970. "Risk Analysis in Project Appraisal." Staff Occasional
Paper. Washington, DC: The World Bank.
The World Bank. 1970. "Techniques for Project Appraisal under Uncertainty." Staff
Occasional Paper No. 10. Washington, DC: The World Bank.
33
P cliy 7Raeu 8rch Working Paper Series
Contact
TiVte Aucthor Date for paper
WP32059 Financial In termediation and Growth: Ross Lavine February 1999 K. Labrie
Causality and Causes Norman Loayza 31001
Thorsten Beck
WPS2O60 The Macroeconomics o7 06ayad Daniel Kaufmann February 1999 D. Bouvet
Exchange-Rate Unification: Theory Stephen A. O'Connell 35818
And Evidence from Tanzania
WPS2061 A Framework for Regulating Hannie van Greuning February 1999 A. Thornton
Microfinance Institutiones JeaUs>1o Gailardo 80409
Sikki Randhawa
WPS2062 Does Financial Reforrm increase C(riana Bandiera February 1999 A. Yaptenco
or Redu e Savings? Gerard Caprio, Jr. 38526
Ps7