Pomiar ryzyka w kalkulacji opłacalności inwestycji rzeczowych
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Opublikowane:
mar 31, 2023
Słowa kluczowe:
NPV, CFaR, NPVaR, ES (NPV), opcje realne
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Abstrakt
W artykule przedstawiono model kalkulacji opłacalności inwestycji rzeczowych. Jest on oparty na koncepcji kwantylowych miar ryzyka i wycenie opcji realnych. Zastosowanie symulacji Monte Carlo pozwala otrzymać rozkład prawdopodobieństwa wartości zaktualizowanej netto (Net Present Value – NPV) i wdrożyć miary ryzyka, takie jak przepływy pieniężne narażone na ryzyko (Cash Flow at Risk – CFaR), wartość zaktualizowana netto narażona na ryzyko (Net Present Value at Risk – NPVaR) czy oczekiwana strata (Expected Shortfall – ES) w stosunku do NPV – ES (NPV). Głównym wkładem artykułu jest implementacja ES (NPV), która pokazuje średnią najgorszych strat względem NPV. ES (NPV) informuje inwestorów, jaki może być najgorszy wynik projektu.
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Szczepańska, J. (2023). Pomiar ryzyka w kalkulacji opłacalności inwestycji rzeczowych. Kwartalnik Nauk O Przedsiębiorstwie, 67(1), 98–114. https://doi.org/10.33119/KNoP.2023.67.1.6
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Oficyna Wydawnicza SGH posiada autorskie prawa majątkowe do wszystkich treści czasopisma. Zamieszczenie tekstu artykuły w repozytorium, na stronie domowej autora lub na innej stronie jest dozwolone o ile nie wiąże się z pozyskiwaniem korzyści majątkowych, a tekst wyposażony będzie w informacje źródłowe (w tym również tytuł, rok, numer i adres internetowy czasopisma).
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Bibliografia
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Anas, A. V., Amalia R., Qaidahiyani N. F., Djamaluddin N. and Herin S. (2020), Sensitivity Analysis of Net Present Value Due to Optimal Pit Limit in PT Ceria Nugraha Indotama, Kolaka Regency, Southeast Sulawesi Province, “IOP Conference Series: Materials Science and Engineering”, 875 (1), https://doi.org/10.1088/1757-899X/875/1/012050.
Andros, S., Akimov, O., Akimova, L., Chang, S. and Gupta, S. K. (2021), Scenario Analysis of the Expected Integral Economic Effect from an Innovative Project, “Marketing and Management of Innovations”, pp. 237–51. https://doi.org/http://doi.org/10.21272/mmi.2021.3–20.
Anysz, H. and Rogala W. (2019), Sensitivity Analysis of the Contractor’s Financial Effects Achieved on a Single Building Site, “Scientific Review Engineering and Environmental Sciences”, 28 (2), 183–91, https://doi.org/10.22630/PNIKS.2019.28.2.17.
Appadoo, S. S. (2014), Possibilistic Fuzzy Net Present Value Model and Application, “Mathematical Problems in Engineering”, 2, pp. 1–11, https://doi.org/10.1155/2014/865968.
Artzner, P., Delbaen F., Eber J. M. and Heath D. (1999), Coherent Measures of Risk, “Mathematical Finance”, 9 (3), 203–28, https://doi.org/10.1111/1467–9965.00068.
Balen, R. M., Mens H-Z. and Economides M. (1988), Applications of the Net Present Value (NPV) in the Optimization of Hydrauic Fractures, “Proceedings of SPE Eastern Regional Meeting”, Society of Petroleum Engineers SPE Eastern Regional Meeting, https://doi.org/10.2523/18541‑ms.
Bieliński, J., (ed.). (2004), Zarządzanie wartością przedsiębiorstwa a alokacja kapitału, Warszawa: Wyd. CeDeWu Sp. z o.o.
Birbilis, G. and Mitra, G. (2003), Using @Risk to Calculate Portfolio Performance – ISSSP for Lean Six Sigma, Centre for the Analysis of Risk and Optimisation Modelling Application, https://www.sarisma.brunel.ac.uk/papers/GBpalisade_risk.pdf (15.03.2004)
Blaset K., Anastasia N., and Yu Kulakov N. (2020), A Risk-Adjustment Technique for Negative Cash Flows, “Proceedings of the 2020 IISE Annual Conference”, pp. 37–42, https://www.proquest.com/docview/2511386663/fulltextPDF/87928A2BD24F4C2BPQ/1? accountid=13075 (24.05.2022)
Brandão, L. E., Dyer J. S. and Hahn W. J. (2005), Using Binomial Decision Trees to Solve Real- Option Valuation Problems, “Decision Analysis”, 2 (2), pp. 69–88, https://doi.org/10.1287/deca.1050.0040.
Brealey, R. A. and Myers S. C. (1999), Podstawy finansów przedsiębiorstw, Warszawa: Wyd. Naukowe PWN.
Brigham, E. F. and Gapenski L. C. (2000), Zarządzanie finansami, Warszawa: PWE.
Brzakovic, T., Brzakovic A. and Petrovic J. (2016), Application of Scenario Analysis in the Investment Projects Evaluation, “Ekonomika Poljoprivrede”, 63 (2), pp. 501–13, https://doi.org/10.5937/ekopolj1602501b.
Chiu, C. Y. and Park C. S. (1994), Fuzzy Cash Flow Analysis Using Present Worth Criterion, “Engineering
Economist”, 39 (2), pp. 113–38, https://doi.org/10.1080/00137919408903117.
Filho, A. C. S., Vellasco M. and Tanscheit R. (2012), Modified Net Present Value under Uncertainties: An Approach Based on Fuzzy Numbers and Interval Arithmetic, in: Communications in Computer and Information Science, Greco R. R., Bouchon-Meunier S., Coletti B., Fedrizzi G., Matarazzo M., Yager B. (eds), 300 CCIS, pp.10–19. Berlin, Heidelberg: Springer, https://doi.org/10.1007/978-3-642-31724-8_2.
Gaspars-Wieloch, H. (2019), Project Net Present Value Estimation under Uncertainty, “Central European Journal of Operations Research”, 27 (1), pp. 179–97, https://doi.org/10.1007/ s10100-017-0500-0.
Liao, S-H. and Ho S-H. (2010), Investment Project Valuation Based on a Fuzzy Binomial Approach, “Information Sciences”, 180 (11), pp. 2124–33, https://doi.org/10.1016/j.ins.2010.02.012.
Liu, Q. (2022), Sensitivity Analysis and Investment Decision Making Under Uncertainty Based on NPV Method, “Advances in Economics, Business and Management Research”, 648, pp. 1861– 65, Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022), https://www.atlantis-press.com/article/125971983.pdf (26.06.2022).
Marchioni, A. and Magni C. A. (2018), Investment Decisions and Sensitivity Analysis: NPV–Consistency of Rates of Return, “European Journal of Operational Research”, 268 (1), pp. 361–72, https://doi.org/10.1016/J.EJOR.2018.01.007.
Maric, B. and Grozdic V. (2016), Monte Carlo Simulation in Valuation of Investment Projects in: “Annals of DAAAM and Proceedings of the International DAAAM Symposium”, 27, pp. 686–92, https://doi.org/10.2507/27th.daaam.proceedings.099.
Mentari, D., and Daryanto W. M. (2018), Capital Budgeting Model and Sensitivity Analysis of the Project Feasibility in Vietnam for the Period of 2019–2037, “International Journal of Business, Economics and Law”, 17 (2), pp. 21–28, https://www.ijbel.com/wp-content/uploads/2019/01/BUS-55.pdf (10.02.2024).
Miller, K. D. and Waller H. G. (2003), Scenarios, Real Options and Integrated Risk Management,
“Long Range Planning”, 36 (1), pp. 93–107, https://doi.org/10.1016/S0024-6301(02)00205-4.
Mills, R. W., Weinstein B. and Favato G. (2006), Using Scenario Thinking to Make Real Options Relevant to Managers: A Case Illustration, “Journal of General Management”, 31 (3), pp. 49–74, https://doi.org/10.1177/030630700603100304.
Nwanekezie, O. F., Iroegbu A. N., Wogu C. L. and Okorocha K. A. (2014), Sensitivity Analysis: A Technique for Investigating the Impact of Changes in Project Variables, pp. 1–13, http://www.globalacademicgroup.com/journals/approaches/Sensitivity Analysis.pdf (30.06.2022).
Pluta, W. (2000), Budżetowanie Kapitałów, Warszawa: PWE.
Ranosz, R. (2016), The Decision Tree in the Valuation of Mining Investments, “Inżynieria Mineralna”, 17 (1), 75–78.
Ren, J. (2022), The Scenario Analysis for NPV and IRR in Mutually Exclusive Projects, “Advances in Economics, Business and Management Research”, 648, pp. 2964–68. Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022), https://www.atlantis-press.com/article/125971628. pdf (26.06.2022).
Reyck, B. D., Degraeve Z. and Vandenborre R. (2008), Project Options Valuation with Net Present Value and Decision Tree Analysis, “European Journal of Operational Research”, 184 (1), pp. 341–55, https://doi.org/10.1016/j.ejor.2006.07.047. RiskMerics Group (1999), Corporate Metrics: The Benchmark for Corporate Risk Management, https://www.msci.com/documents/10199/8af520af-3e63-44b2-8aab-fd55a989e312 (10.09.2009).
Rivers, G., Foo J., Ilic D., Nicklen P., Reeves S., Walsh K. and Maloney S. (2015), The Economic
Value of an Investment in Physiotherapy Education: A Net Present Value Analysis, “Journal of Physiotherapy”, 61 (3), pp. 148–54, https://doi.org/10.1016/j.jphys.2015.05.015.
Rockafellar, R. T. and Uryasev S. (2002), Conditional Value-at-Risk for General Loss Distributions, “Journal of Banking & Finance”, 26 (7), pp. 1443–71, https://doi.org/10.1016/S0378-4266 (02)00271-6.
Rodriges Amorim, F., Ferreira Silveira B. C., Alves Dos Santos E., Camargo de Abreu P. H., and
Tostes J. R. (2017), Analysis of the Economic Viability of a Rural Tourism Enterprise in Brazil: An Application of the Monte Carlo Method, “Independent Journal of Management & Production”, 8 (4), pp. 1365, https://doi.org/10.14807/ijmp.v8i4.662.
Saługa, P. W. (2019), Risk-Adjusted Discount Rate and Its Components in Evaluating Hard Coal Projects at the Feasibility Stage, “Gospodarka Surowcami Mineralnymi / Mineral Resources Management”, 35 (3), pp. 63–74, https://doi.org/10.24425/gsm.2019.128530.
Saługa, P. W., Zamasz K., Dacko-Pikiewicz Z., Szczepańska-Woszczyna K. and Malec M. (2021), Risk-Adjusted Discount Rate and Its Components for Onshore Wind Farms at the Feasibility Stage, “Energies”, 14 (20), pp. 1–12, https://doi.org/10.3390/en14206840.
Shaffie, S. S. and Jaaman S. H. (2016), Monte Carlo on Net Present Value for Capital Investment in Malaysia, “Procedia – Social and Behavioral Sciences”, 219, pp. 688–93, https://doi.org/10.1016/j.sbspro.2016.05.052.
Tibiletti, L. (2022), One-Size Risk-Adjusted Discount Rate Does Not Fit All Risky Projects, “Journal Of Risk Finance”, 23 (3), pp. 289–302, https://doi.org/https://doi.org/10.1108/JRF-03-2021-0035.
Trzpiot, G. (2008), Wybrane modele oceny ryzyka. Podejście nieklasyczne, Katowice: Prace Naukowe AE im. Karola Adamieckiego w Katowicach.
Tsao, C. T. (2012), Fuzzy Net Present Values for Capital Investments in an Uncertain Environment, “Computers & Operations Research”, 39 (8), pp. 1885–92, https://doi.org/10.1016/J. COR.2011.07.015.
Wang, A. (2010), Comparison of Real Asset Valuation Models: A Literature Review, “International Journal of Business and Management”, 5 (5), pp. 14–24, https://doi.org/10.5539/ijbm.v5n5p14.
Wicaksono, F. D., Arshad, Y. B. and Sihombing H. (2019), Monte Carlo Net Present Value for Techno-Economic Analysis of Oil and Gas Production Sharing Contract, “International Journal of Technology”, 10 (4), pp. 829–40, https://doi.org/10.14716/ijtech.v10i4.2051.
Wiśniewski, T. (2006), Zastosowanie metody Monte Carlo do oceny ryzyka specyficznego projektu inwestycyjnego, in: “Zeszyty Naukowe Uniwersytetu Szczecińskiego”, 416, Szczecin, Prace Instytutu Ekonomiki i Organizacji Przedsiębiorstw, No. 47.
Yao, J. and Jaafari A. (2003), Combining Real Options and Decision Tree, “The Journal of Structured Finance”, 9 (3), pp. 53–70, https://doi.org/10.3905/jsf.2003.320320.
Yousefi, V., Yakhchali S. H., Saparauskas J. and Kiani S. (2018), The Impact Made on Project Portfolio Optimisation by the Selection of Various Risk Measure, “Inzinerine Ekonomika-Engineering Economics”, 29 (2), pp. 168–75.
Zahid, H. (2019), Implementing Monte Carlo Simulation Model for Revenue Forecasting under the Impact of Risk and Uncertainty, “Management and Production Engineering Review”, 10 (4), pp. 81–89, https://doi.org/10.24425/mper.2019.131448.
Zenad, Y. S. (2015), Sensitivity Anaysis to Know the Project’s Ability to Continue, “European Journal of Accounting, Auditing and Finance Research”, 3 (11), pp. 60–66.
Zhang, Z. (2010), Certainty Equivalent, Risk Premium and Asset Pricing, “Frontiers of Business Research in China”, 4 (2), pp. 325–39, https://doi.org/10.1007/s11782-010-0015–1.
Žižlavský, O. (2014), Net Present Value Approach: Method for Economic Assessment of Innovation Projects, “Procedia – Social and Behavioral Sciences”, 156 (4), pp. 506–12, https://doi.org/10.1016/j.sbspro.2014.11.230.
Acerbi, C. and Tasche D. (2002), On the Coherence of Expected Shortfall, “Journal of Banking & Finance”, 26 (7), pp. 1487–1503, https://doi.org/10.1016/S0378–4266 (02) 00283–2.
Anas, A. V., Amalia R., Qaidahiyani N. F., Djamaluddin N. and Herin S. (2020), Sensitivity Analysis of Net Present Value Due to Optimal Pit Limit in PT Ceria Nugraha Indotama, Kolaka Regency, Southeast Sulawesi Province, “IOP Conference Series: Materials Science and Engineering”, 875 (1), https://doi.org/10.1088/1757-899X/875/1/012050.
Andros, S., Akimov, O., Akimova, L., Chang, S. and Gupta, S. K. (2021), Scenario Analysis of the Expected Integral Economic Effect from an Innovative Project, “Marketing and Management of Innovations”, pp. 237–51. https://doi.org/http://doi.org/10.21272/mmi.2021.3–20.
Anysz, H. and Rogala W. (2019), Sensitivity Analysis of the Contractor’s Financial Effects Achieved on a Single Building Site, “Scientific Review Engineering and Environmental Sciences”, 28 (2), 183–91, https://doi.org/10.22630/PNIKS.2019.28.2.17.
Appadoo, S. S. (2014), Possibilistic Fuzzy Net Present Value Model and Application, “Mathematical Problems in Engineering”, 2, pp. 1–11, https://doi.org/10.1155/2014/865968.
Artzner, P., Delbaen F., Eber J. M. and Heath D. (1999), Coherent Measures of Risk, “Mathematical Finance”, 9 (3), 203–28, https://doi.org/10.1111/1467–9965.00068.
Balen, R. M., Mens H-Z. and Economides M. (1988), Applications of the Net Present Value (NPV) in the Optimization of Hydrauic Fractures, “Proceedings of SPE Eastern Regional Meeting”, Society of Petroleum Engineers SPE Eastern Regional Meeting, https://doi.org/10.2523/18541‑ms.
Bieliński, J., (ed.). (2004), Zarządzanie wartością przedsiębiorstwa a alokacja kapitału, Warszawa: Wyd. CeDeWu Sp. z o.o.
Birbilis, G. and Mitra, G. (2003), Using @Risk to Calculate Portfolio Performance – ISSSP for Lean Six Sigma, Centre for the Analysis of Risk and Optimisation Modelling Application, https://www.sarisma.brunel.ac.uk/papers/GBpalisade_risk.pdf (15.03.2004)
Blaset K., Anastasia N., and Yu Kulakov N. (2020), A Risk-Adjustment Technique for Negative Cash Flows, “Proceedings of the 2020 IISE Annual Conference”, pp. 37–42, https://www.proquest.com/docview/2511386663/fulltextPDF/87928A2BD24F4C2BPQ/1? accountid=13075 (24.05.2022)
Brandão, L. E., Dyer J. S. and Hahn W. J. (2005), Using Binomial Decision Trees to Solve Real- Option Valuation Problems, “Decision Analysis”, 2 (2), pp. 69–88, https://doi.org/10.1287/deca.1050.0040.
Brealey, R. A. and Myers S. C. (1999), Podstawy finansów przedsiębiorstw, Warszawa: Wyd. Naukowe PWN.
Brigham, E. F. and Gapenski L. C. (2000), Zarządzanie finansami, Warszawa: PWE.
Brzakovic, T., Brzakovic A. and Petrovic J. (2016), Application of Scenario Analysis in the Investment Projects Evaluation, “Ekonomika Poljoprivrede”, 63 (2), pp. 501–13, https://doi.org/10.5937/ekopolj1602501b.
Chiu, C. Y. and Park C. S. (1994), Fuzzy Cash Flow Analysis Using Present Worth Criterion, “Engineering
Economist”, 39 (2), pp. 113–38, https://doi.org/10.1080/00137919408903117.
Filho, A. C. S., Vellasco M. and Tanscheit R. (2012), Modified Net Present Value under Uncertainties: An Approach Based on Fuzzy Numbers and Interval Arithmetic, in: Communications in Computer and Information Science, Greco R. R., Bouchon-Meunier S., Coletti B., Fedrizzi G., Matarazzo M., Yager B. (eds), 300 CCIS, pp.10–19. Berlin, Heidelberg: Springer, https://doi.org/10.1007/978-3-642-31724-8_2.
Gaspars-Wieloch, H. (2019), Project Net Present Value Estimation under Uncertainty, “Central European Journal of Operations Research”, 27 (1), pp. 179–97, https://doi.org/10.1007/ s10100-017-0500-0.
Liao, S-H. and Ho S-H. (2010), Investment Project Valuation Based on a Fuzzy Binomial Approach, “Information Sciences”, 180 (11), pp. 2124–33, https://doi.org/10.1016/j.ins.2010.02.012.
Liu, Q. (2022), Sensitivity Analysis and Investment Decision Making Under Uncertainty Based on NPV Method, “Advances in Economics, Business and Management Research”, 648, pp. 1861– 65, Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022), https://www.atlantis-press.com/article/125971983.pdf (26.06.2022).
Marchioni, A. and Magni C. A. (2018), Investment Decisions and Sensitivity Analysis: NPV–Consistency of Rates of Return, “European Journal of Operational Research”, 268 (1), pp. 361–72, https://doi.org/10.1016/J.EJOR.2018.01.007.
Maric, B. and Grozdic V. (2016), Monte Carlo Simulation in Valuation of Investment Projects in: “Annals of DAAAM and Proceedings of the International DAAAM Symposium”, 27, pp. 686–92, https://doi.org/10.2507/27th.daaam.proceedings.099.
Mentari, D., and Daryanto W. M. (2018), Capital Budgeting Model and Sensitivity Analysis of the Project Feasibility in Vietnam for the Period of 2019–2037, “International Journal of Business, Economics and Law”, 17 (2), pp. 21–28, https://www.ijbel.com/wp-content/uploads/2019/01/BUS-55.pdf (10.02.2024).
Miller, K. D. and Waller H. G. (2003), Scenarios, Real Options and Integrated Risk Management,
“Long Range Planning”, 36 (1), pp. 93–107, https://doi.org/10.1016/S0024-6301(02)00205-4.
Mills, R. W., Weinstein B. and Favato G. (2006), Using Scenario Thinking to Make Real Options Relevant to Managers: A Case Illustration, “Journal of General Management”, 31 (3), pp. 49–74, https://doi.org/10.1177/030630700603100304.
Nwanekezie, O. F., Iroegbu A. N., Wogu C. L. and Okorocha K. A. (2014), Sensitivity Analysis: A Technique for Investigating the Impact of Changes in Project Variables, pp. 1–13, http://www.globalacademicgroup.com/journals/approaches/Sensitivity Analysis.pdf (30.06.2022).
Pluta, W. (2000), Budżetowanie Kapitałów, Warszawa: PWE.
Ranosz, R. (2016), The Decision Tree in the Valuation of Mining Investments, “Inżynieria Mineralna”, 17 (1), 75–78.
Ren, J. (2022), The Scenario Analysis for NPV and IRR in Mutually Exclusive Projects, “Advances in Economics, Business and Management Research”, 648, pp. 2964–68. Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022), https://www.atlantis-press.com/article/125971628. pdf (26.06.2022).
Reyck, B. D., Degraeve Z. and Vandenborre R. (2008), Project Options Valuation with Net Present Value and Decision Tree Analysis, “European Journal of Operational Research”, 184 (1), pp. 341–55, https://doi.org/10.1016/j.ejor.2006.07.047. RiskMerics Group (1999), Corporate Metrics: The Benchmark for Corporate Risk Management, https://www.msci.com/documents/10199/8af520af-3e63-44b2-8aab-fd55a989e312 (10.09.2009).
Rivers, G., Foo J., Ilic D., Nicklen P., Reeves S., Walsh K. and Maloney S. (2015), The Economic
Value of an Investment in Physiotherapy Education: A Net Present Value Analysis, “Journal of Physiotherapy”, 61 (3), pp. 148–54, https://doi.org/10.1016/j.jphys.2015.05.015.
Rockafellar, R. T. and Uryasev S. (2002), Conditional Value-at-Risk for General Loss Distributions, “Journal of Banking & Finance”, 26 (7), pp. 1443–71, https://doi.org/10.1016/S0378-4266 (02)00271-6.
Rodriges Amorim, F., Ferreira Silveira B. C., Alves Dos Santos E., Camargo de Abreu P. H., and
Tostes J. R. (2017), Analysis of the Economic Viability of a Rural Tourism Enterprise in Brazil: An Application of the Monte Carlo Method, “Independent Journal of Management & Production”, 8 (4), pp. 1365, https://doi.org/10.14807/ijmp.v8i4.662.
Saługa, P. W. (2019), Risk-Adjusted Discount Rate and Its Components in Evaluating Hard Coal Projects at the Feasibility Stage, “Gospodarka Surowcami Mineralnymi / Mineral Resources Management”, 35 (3), pp. 63–74, https://doi.org/10.24425/gsm.2019.128530.
Saługa, P. W., Zamasz K., Dacko-Pikiewicz Z., Szczepańska-Woszczyna K. and Malec M. (2021), Risk-Adjusted Discount Rate and Its Components for Onshore Wind Farms at the Feasibility Stage, “Energies”, 14 (20), pp. 1–12, https://doi.org/10.3390/en14206840.
Shaffie, S. S. and Jaaman S. H. (2016), Monte Carlo on Net Present Value for Capital Investment in Malaysia, “Procedia – Social and Behavioral Sciences”, 219, pp. 688–93, https://doi.org/10.1016/j.sbspro.2016.05.052.
Tibiletti, L. (2022), One-Size Risk-Adjusted Discount Rate Does Not Fit All Risky Projects, “Journal Of Risk Finance”, 23 (3), pp. 289–302, https://doi.org/https://doi.org/10.1108/JRF-03-2021-0035.
Trzpiot, G. (2008), Wybrane modele oceny ryzyka. Podejście nieklasyczne, Katowice: Prace Naukowe AE im. Karola Adamieckiego w Katowicach.
Tsao, C. T. (2012), Fuzzy Net Present Values for Capital Investments in an Uncertain Environment, “Computers & Operations Research”, 39 (8), pp. 1885–92, https://doi.org/10.1016/J. COR.2011.07.015.
Wang, A. (2010), Comparison of Real Asset Valuation Models: A Literature Review, “International Journal of Business and Management”, 5 (5), pp. 14–24, https://doi.org/10.5539/ijbm.v5n5p14.
Wicaksono, F. D., Arshad, Y. B. and Sihombing H. (2019), Monte Carlo Net Present Value for Techno-Economic Analysis of Oil and Gas Production Sharing Contract, “International Journal of Technology”, 10 (4), pp. 829–40, https://doi.org/10.14716/ijtech.v10i4.2051.
Wiśniewski, T. (2006), Zastosowanie metody Monte Carlo do oceny ryzyka specyficznego projektu inwestycyjnego, in: “Zeszyty Naukowe Uniwersytetu Szczecińskiego”, 416, Szczecin, Prace Instytutu Ekonomiki i Organizacji Przedsiębiorstw, No. 47.
Yao, J. and Jaafari A. (2003), Combining Real Options and Decision Tree, “The Journal of Structured Finance”, 9 (3), pp. 53–70, https://doi.org/10.3905/jsf.2003.320320.
Yousefi, V., Yakhchali S. H., Saparauskas J. and Kiani S. (2018), The Impact Made on Project Portfolio Optimisation by the Selection of Various Risk Measure, “Inzinerine Ekonomika-Engineering Economics”, 29 (2), pp. 168–75.
Zahid, H. (2019), Implementing Monte Carlo Simulation Model for Revenue Forecasting under the Impact of Risk and Uncertainty, “Management and Production Engineering Review”, 10 (4), pp. 81–89, https://doi.org/10.24425/mper.2019.131448.
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