تجزیه و تحلیل حساسیت در ارزیابی پروژه های سرمایه گذاری

This paper discusses the sensitivity analysis of valuation equations used in investment decisions. Since financial decision are commonly supported via a point value of some criterion of economic relevance (net present value, economic value added, internal rate of return, etc.), we focus on local sensitivity analysis. In particular, we present the differential importance measure (DIM) and discuss its relation to elasticity and other local sensitivity analysis techniques in the context of discounted cash flow valuation models. We present general results of the net present value and internal rate of return sensitivity on changes in the cash flows. Specific results are obtained for a valuation model of projects under severe survival risk used in the industry sector of power generation.

In this paper, we discuss the sensitivity analysis (SA) of valuation equations used in investment project valuation. Investment project decision making involves the use of valuation models that require the estimation of the investment cash flows (CF), that feed into the equation of the economic criterion (net present value—“NPV”—or internal rate of return—“IRR”) that supports the decision (Taggart, 1996). We denote the valuation criterion as Y, and write equation(1) where is the set of the model input parameters. The decision often relies on the value of the criterion that is obtained when the input parameters are fixed at the so-called base-case values. Such values reflect the analyst/decision maker knowledge of the investment assumptions. We write equation(2) where denotes the base-case value of the parameters. The decision making process is integrated by SA, where the analyst assesses the effect on Y0 of changes in the input parameters. Such sensitivity is usually tested through, what is called, a “one way” or a combined SA scheme, where the analyst registers the change in , obtained when a parameter or a combination of parameters is varied by a rationally assumed range. Such analysis is used to draw conclusions on the consistency and correctness of the valuation model, as well as, in some cases, it integrates risk analysis giving information on the investment risk consequent to changes in the assumptions. The decision maker is often lead by this analysis to infer a relative importance of the parameters/assumptions and to rank them according to their influence on Y0 (the classical “Tornado diagram” scheme ( Clemen, 1998)). However, while this SA scheme is appropriate for the first and second task, it should not be used to infer parameter importance, since the parameter changes (Δxi) are not taken into consideration ( Borgonovo and Apostolakis 2001a and Borgonovo and Apostolakis 2001b; Borgonovo, 2001b). Several local SA techniques have been recently developed in the literature to infer parameter importance (Borgonovo and Apostolakis, 2001a; Borgonovo, 2001b; Cheok et al., 1998; Helton, 1993; Turanyi and Rabitz, 2000; Koltai and Terlaky, 2000). We focus on the differential importance measure (DIM), a SA technique recently proposed (Borgonovo, 2001a; Borgonovo and Apostolakis 2001a and Borgonovo and Apostolakis 2001b). We highlight its relationship to other local SA techniques, with particular reference to elasticity. We consider the application of DIM on NPV valuation equations. We show that through DIM the analyst is able to obtain the importance of any arbitrary change in the magnitude of the CFs. Besides, the importance of the CFs for NPV equations has an intuitive interpretation, which we will discuss. We, then, focus on the SA of IRR equations. We apply the results obtained for NPV and IRR equations to the local SA of a specific model, developed for the evaluation of projects under survival risk and used in the energy sector (Beccacece et al., 2000). In Section 2, we present the definition of DIM, its computation and its relationship with other local SA techniques. In Section 3, we discuss the application of DIM to NPV and IRR valuation equations. In Section 4, we present an overview of the model for project evaluation, we discuss application and results of the local SA of the model through DIM and elasticity. Conclusions are offered in Section 5.

We have discussed the sensitivity analysis of valuation equations used in investment project valuation. Since financial decisions are often based on the nominal value of the project economics chosen as valuation criterion (NPV, IRR etc.), we have focused on the use of local SA techniques. We have based our analysis on the differential importance measure. We have discussed its relation to other local SA techniques, with particular reference to Elasticity. We have shown that DIM and Elasticity differ for a normalization factor under the assumption of proportional parameter changes (H2). Thus, Elasticity can be seen as producing the importance of parameters for proportional changes. We have then applied DIM to NPV and IRR equations. We have derived an analytical expression for the CF importance on both NPV and IRR. We have seen that if the NPV is the valuation criterion, for uniform changes (H1), the importance of the CFs depends only on the CF profile and not on the CFs magnitude. For proportional changes (H2), the CF DIM is the fraction of the NPV associated with the CFs. If the IRR is the valuation criterion, for proportional changes (H2), the total change in IRR is zero. In this case, the ranking can be obtained for the individual CFs using their elasticity. As far as the importance of CFs with respect to timing is concerned, it has been possible to derive the conditions under which CFs that come early in time are the more relevant than CF coming at a later time. We have then applied DIM to a specific model for the valuation of projects under serious survival risk utilized in a real case investment. Results for the project NPV, IRR and value at time have been discussed. They confirm the general results illustrated above.