JASPERS Staff Working Papers

Monte Carlo simulation of Cost-Benefit Analysis results

Francesco Angelini and Marko Kristl

January 2013

JASPERS Staff Working Papers are prepared by JASPERS experts with the aim of facilitating the discussions with counterparts in the context of their different assignments, mostly in terms of project scoping and applicable criteria and methodology. These papers normally originate as part of the assessment of a specific project, in which case the version published here is edited to be made non-project and non-country specific and therefore easily applicable to other projects in the sector. This particular paper presents a spreadsheet model developed by JASPERS that can be integrated in the Cost-Benefit Analysis prepared by the project promoters in order to perform a simplified probabilistic risk analysis on the key CBA results through a Monte Carlo simulation. Disclaimer and Copyright This report is provided in good faith, to be used at the risk of the reader. JASPERS does not warrant the accuracy or completeness of the information contained in this report nor does it assume any legal liability or responsibility, direct or indirect, for any damages or loss caused or alleged to be caused by or in connection with the use of or reliance on materials contained in this report. This report has not been formally discussed or approved by the European Commission. The comments expressed in this report do not necessarily state or reflect the views of the JASPERS partners (European Commission, EIB, EBRD and KfW). In particular, the views expressed herein cannot be taken to reflect the official opinion of the European Union. EIB retains copyright to this report on behalf of JASPERS. Permission to reproduce and distribute this report in whole or in part for non-commercial purposes and without fee is hereby granted provided that JASPERS is acknowledged.

Vienna, October 2012

Guidance Note Authors: F. Angelini, M. Kristl

Spreadsheet model for Monte Carlo simulations of CBA results - Instructions

Disclaimer: JASPERS assistance is provided in good faith and with reasonable care and due diligence (diligentia quam in suis), drawing on the experience and business practices of its partners, the EIB, the EBRD and KfW; however, the beneficiaries acknowledge that EIB in its role as JASPERS will not be responsible for any loss or damage resulting from any advice provided by JASPERS.

1. Background

The Funding Application for Major Projects requires information on Risk Assessment. The Commission’s Guide to Cost-Benefit Analysis (CBA) explains the different techniques to carry out a Risk Assessment (see § 2.6, Annex H and the case studies in § 4). One of the required steps is a probabilistic risk analysis. This entails the simulation of a probability distribution for the project CBA results (e.g. Net Present Value or Internal Rate of Return) starting from the specification of probability distributions that reflect the potential variability of the key project variables (e.g. investment cost, revenue).

In JASPERS experience, performing a probabilistic risk analysis has often proved challenging for project promoters. For cases where a detailed risk analysis is not carried out, JASPERS developed a spreadsheet model that can be integrated in the CBA prepared by the project promoters in order to perform a simplified probabilistic risk analysis on the key CBA results. The purpose of this Guidance Note is to provide instructions for the use of this risk analysis model.

2. Spreadsheet model for risk analysis

The JASPERS spreadsheet model enables the project promoter to run a “Monte Carlo” simulation of the CBA results only by making assumptions about the possible variability range (i.e. a minimum and a maximum value) of a given project variable. The model includes two sheets:

1. A sheet for the simulation of the probability distribution and related descriptive statistics of the project Economic Net Present Value (ENPV).

2. A similar sheet for the Financial Net Present Value (FNPV/K, i.e. an estimate of the after-EU-grant profitability). It is assumed here that the level of the requested EU grant is independent of the simulated changes in project variables (e.g. when an investment cost overrun is simulated the EU grant does not increase proportionally).

The variables that are modelled in the simulation are the Investment cost, Operating and Maintenance (O&M) costs and the project Benefits (for the ENPV) or Revenue (for the FNPV/K).

Each sheet contains two windows, one for inputting the risk analysis assumptions and one that presents the results of the Monte Carlo simulation, i.e. a histogram graph with the simulated probability distribution, a line graph plotting the cumulative distribution and a box with the descriptive statistics (e.g. mean, standard deviation).

It should be noted that the model employs a simplified method, where probability distributions are applied to aggregated elements of the NPV (e.g. benefits) and not to basic variables (e.g. demand volume, demand growth, various investment components, which may have very different risk profile, etc.). This simplification implicitly assumes that there is a linear and proportional relation between these basic variables and aggregated variables and that all project impacts (benefits) have the same variability. This may not always be the case. For this reason, whenever possible, JASPERS recommends that promoters develop a more detailed and project-specific risk analysis.

The repeated random sampling behind the Monte Carlo simulation is based on a “VBA macro” included in the spreadsheet. For this reason the “macros” should be enabled when opening the file.

3. Instructions for using the spreadsheet model

The assumptions for the Monte Carlo simulation are inputted in the following window.1

Once the assumptions are inputted, the probability distribution for the NPV and the associated statistics are generated by clicking on the “Run Simulation” icon.

                                                            1 The window depicted here is for the ENPV simulation. The one for the FNPV/K requires analogous inputs.

Input here the base-case NPV as determined in the CBA. The currency and measurement unit can be changed in the adjacent cell if needed (e.g. from “mEUR” to “th.PLN” – Excel cell “E3”).

Input here the base-case value of the Investment, O&M costs and Benefits (or Revenue in the case of FNPV simulation).

The values should be expressed in present value terms, using the same discount rate used to determine the NPV (i.e. social discount rate for the ENPV, financial discount rate for the FNPV).

The figures should be in absolute value terms (i.e. the “-” sign should not be inputted before Investment and O&M costs).

Benefits less Investment less O&M should not necessarily equal the inputted base-case NPV (for example, when residual value or replacement costs also determine the NPV).

For the ENPV simulation, the values inputted in Investment and O&M should be those of the economic analysis. These values can differ from the ones used in the financial analysis when “conversion factors” are used in the economic analysis (e.g. to better reflect the opportunity cost of labour).

Input here the potential variability range for the three variables. The Monte Carlo simulation is here based on “triangular” probability distributions. Triangular distributions are specified based on three parameters: most-likely, minimum and maximum. Normally the Most Likely value of a variable is the one used in the base-case NPV calculations included in the CBA, so only the Minimum and Maximum values need to be inputted.

The values should be expressed as a percentage of the variable’s base-case value. For example, a Minimum of 90 % means that the variable can drop by up to 10 % of its base-case value.

The assumed variability ranges should be sufficiently wide to reasonably encompass all potential values of the three variables.

Where appropriate, asymmetric variability ranges can be specified to reflect asymmetric risks. For example, the risk of investment cost overruns is typically assumed to be higher than the risk of investment costs savings.

This is the number of random values extracted from each specified triangular distribution for the Monte Carlo simulation. Usually there is no need to change the default value.