, 2011 No. of Slides:20

1. PayamHanafizadeh, PhD Department of Industrial Management, School of Management and Accountancy, AllamehTabataba'i University, Tehran, Iran Email: hanafizadeh@gmail.com URL: www.hanafizadeh.com Volume 54,Number 1-2.July 2011 Mathematical and Computer Modelling 54(2011)233-242 Robust Net Present Value , 2011 No. of Slides:20

2. Agenda Abstract Introduction Literature review Robust net present value Robust net present value analysis Simulation of the robust net present value Discussion Conclusion

3. Abstract • Historical data • Investor's characteristics • risk-taking • risk-aversion -New approach to computing Net Present Value (NPV). • high significance in analyzing the sensitivity • The model is highly reliable • Variance • Correlation -Define a closed and convex region for the changes of the uncertain parameters. -Determine the size and shape of the uncertainty region. -Present the mathematical formulation for computing the robust NPV.

4. Introduction Variance Correlation One of the most important and frequent managerial decision is to evaluate the attractiveness of the investment projects. uncertainty region • It is of paramount importance to use precise data in calculating NPV, because the feasibility of a project may change by fluctuation of data. NPV One project Two or more projects Highest ROR MARR ≤ ROR

5. Literature review dealing with uncertainty

6. Robust net present value an-1 an a1 a2 The standard equation to calculate NPV : -c0 0 1 2 n-1 n F Robust Net Present Value : a1 a2 Region U μa

7. Robust net present value • Uncertain region : W is an n×n symmetric positive definite matrix:

8. RNPV For each arbitrary x, we have inf(x) = -sup (-x), therefore : According to norm function properties we have:

9. RNPV Based on the definition of the dual norm • = • , and we can write

10. Robust net present value analysis The robust NPVformulation always obtains an NPV which is smaller than NPV. U(2,3) RROR ROR - c i = ∞ i

11. impressive elements that affect difference between NPV and RNPV choosing a greaterqleads to a greater uncertainty region. and Proposition 1 : A greater uncertainty region obtains a smaller RNPV.

12. impressive elements that affect difference between NPV and RNPV

13. impressive elements that affect difference between NPV and RNPV The bigger the radius of uncertainty region, the less the amount of RNPV will be.

14. impressive elements that affect difference between NPV and RNPV Considering a greater covariance matrix leads to a smaller RNPV.

15. Simulation of the robust net present value n = 4 r = 2 q = 2 ROR = 25.31% RROR = 14.23%

16. Simulation of the robust net present value A : C : both approaches will suggest the investor not accept the project • B :

17. Discussion • Positive skewness • The number of scenarios, whose ROR is less • than the mean value is more than 50%. • Negative skewness • The number of scenarios, whose ROR is less • than the mean value is less than 50%.

18. Conclusion • The robust approach was presented to how we deal with random and dependent net income of a cash flow. • A smaller robust NPV is acquired as the uncertainty region gets bigger and bigger. • The simulation indicates that the robust approach is more reliable than the traditional NPV

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