From the stars to a parking lot. A mathematical adventure
The models on which sponsors and banks base their investment decisions in project finance transactions are large, complex and difficult to handle. They usually are spreadsheet models with hundreds of exogenous variables and no analytical expression. Consequently, the model works as a black box and its behaviour as a function of the exogenous variables in unknown to the financial analyst.
Emanuele Borgonovo (Department of Decision Sciences and ELEUSI Bocconi), Stefano Gatti (Department of Finance and CAREFIN Bocconi) and Lorenzo Peccati (Department of Decision Sciences and ELEUSI Bocconi) in What Drives Value Creation in Investment Projects? An Application of Sensitivity Analysis to Project Finance Transactions (European Journal of Operational Research, Vol. 205, Issue 1, August 2010) devise a methodology based on the so-called Differential Importance Measure (D) to enhance the managerial insights obtained by financial models and to overcome the risk of wrongly identifying the key-drivers of investment performance.. "The presence of many exogenous variables", the authors write, "means that sensitivity analysis is usually not performed on all of them. Conversely, to save time and expense, attention is restricted to a subset of inputs, usually pre-selected based on experience or qualitative statements". Their methodology allows decision makers to test the model's robustness and internal consistency, to detect the model's response to changes in the parameters and to determine the influence of each of the model's assumptions on the valuation criterion, i.e., to identify the key performance drivers.
Recent works show that, in the US, the project finance loans market is larger than the Initial Public Offering (IPO) market, that the average value of a project finance investment is about 512 million dollars and that the average debt-to-equity ratio is 4.23. "At the heart of a project finance scheme", Borgonovo, Gatti and Peccati say, "is a nexus of contracts revolving about a Special Purpose Vehicle (SPV), which becomes the counterpart for all the operating and financial contracts. A group of sponsoring firms (the SPV's shareholders), and to a larger extent a bank syndicate headed by a Mandated Lead Arranger, provide the money needed to design, build and operate a new project. Loans are fully guaranteed by all the company's assets, supplemented by a large set of covenants that aims to restrict the SPV's use of the funds (...) Sponsors limit their responsibility to their original equity injection". The success ofthe transaction depends on the project's capacity to generate sufficient cash during its long but finite operating phase so that it matches the cash needed for debt service and dividends paid to the project sponsors. The viability of the initiative must satisfy the valuation criteria of both banks and sponsors, but these criteria generally conflict with each other: shareholders tend to adopt the equity Net Present Value (NPV), while most lenders consider the Debt Service Coverage Ratios (DSCRs).
The methodology introduced in the article is based on the Differential Importance Measure (D), a sensitivity analysis method that was introduced by Borgonovo and Apostolakis in 2001 and that is currently adopted in the risk management procedures of NASA. Di measures the sensitivity of V (a valuation criterion) on the i-th exogenous variable. D possessesthe additivity property, which means that the analyst can compute the sensitivity of V on a group of homogeneous exogenous variables (i.e. all the financial variables or all the macroeconomic variables) simply adding their D values, overcoming any unit of measurement problem. The authors provide an estimation algorithm of D which, as a side effect, tests the model's robustness and internal consistency. Computing the value of D for clusters of exogenous variables, furthermore, the analyst can spot the key performance drivers of a project.
The three Bocconi academics apply their methodology to a real project finance investment, a parking lot which evaluation needed a model with 428 exogenous variables and they observe that exogenous factors affect investors (sponsors and lenders) in different ways, whether exogenous variables are considered individually or by groups. The methodology allows the authors not only to find the individual drivers, but, by clustering the importance meausures, the categories of assumptions that determine investment performance. As far as the sponsor/lenders' perspectives are concerned, thekey performance drivers tend to be the same, with notable discrepancies: as an example, leverage is much more significant for lenders than for sponsors, and the cost of capital is non-significantfor banks using DSCRs as a valuation criterion.