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July  2017, 13(3): 1213-1235. doi: 10.3934/jimo.2016069

## A real option approach for investment opportunity valuation

 1 School of Management and Economics, University of Electronic Science and Technology, Chengdu, China 2 College of Economics and Management, Zhejiang University of Technology, China 3 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 4 Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, Australia

Received  January 2016 Revised  April 2016 Published  October 2016

In this paper, the valuation of an investment opportunity in a high-tech corporation using real option theory and modern capital budgeting is studied. Some key characteristics such as high-risk, multi-stage and technology life cycle of a high-tech project are considered in the proposed model. Since a real option is usually not tradable in the market, an actuarial approach is adopted in our study. We employ an irreversible regime-switching Markov chain to model the multi-stage and technology life cycle of the project in the high-tech industry. The valuation of captured real option can be formulated as the valuation of an American option with time-dependent strike price. For the purpose of practical implementation, a novel lattice-based method is developed to value the American option. Numerical examples are given to illustrate the proposed models and methods.

Citation: Na Song, Yue Xie, Wai-Ki Ching, Tak-Kuen Siu. A real option approach for investment opportunity valuation. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1213-1235. doi: 10.3934/jimo.2016069
##### References:
 [1] C. Alexander and X. Chen, A general approach to real option valuation with application to real estate investments, University of Reading, ICMA Centre Discussion Paper No. DP2012-04. Available at SSRN: http://ssrn.com/abstract=1990957. Google Scholar [2] N. Bollen, Valuing option in regime-switching models, Journal of Derivatives, 6 (1998), 38-49.   Google Scholar [3] N. Bollen, Real options and product life cycles, Management Science, 45 (1999), 670-684.   Google Scholar [4] R. A. Brealey and S. C. Myers, Principles of Corporate Finance, McGraw-Hill, New York, 1992. Google Scholar [5] P. P. Boyle and Y. Tian, An explicit finite difference approach to the pricing of barrier options, Applied Mathematical Finance, 5 (1988), 17-43.   Google Scholar [6] P. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, Journal of Finance, 47 (1992), 271-293.   Google Scholar [7] P. P. Boyle, Option valuation using a three-jump process, International Options Journal, 3 (1986), 7-12.   Google Scholar [8] P. P. Boyle, A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23 (1988), 1-12.   Google Scholar [9] J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7 (1979), 229-263.   Google Scholar [10] M. G. Colombo, A. Croce and S. Murtinu, Ownership structure, horizontal agency costs and the performance of high-tech entrepreneurial firms, Small Business Economics, 42 (2014), 265-282.   Google Scholar [11] R. E. Caves, Industrial organization and new findings in the turnover and mobility of firms, Journal of Economic Literature, 36 (1998), 1947-1982.   Google Scholar [12] D. L. Deeds, D. DeCarolis and J. Coombs, Dynamic capabilities and new product development in high technology ventures: an empirical analysis of new biotechnology firms, Journal of Business Venturing, 15 (2000), 211-229.   Google Scholar [13] P. A. Geroski, What do we know about entry?, International Journal of Industrial Organization, 13 (1995), 450-456.   Google Scholar [14] X. Huang, N. Song, W. K. Ching, T. K. Siu and C. K. Yiu, A real option approach to optimal inventory management of retail products, Journal of Industrial and Management Optimization, 8 (2012), 379-389.  doi: 10.3934/jimo.2012.8.379.  Google Scholar [15] B. Kamrad and P. Ritchken, Multinomial approximating models for options with $k$ state variables, Management Science, 37 (1991), 1640-1652.   Google Scholar [16] D. Kellogg and J. M. Charnes, Real-options valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 76-84.   Google Scholar [17] F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation: a simple least-squares approach, The Review of Financial Studies, 14 (2001), 113-147.   Google Scholar [18] J. Mun, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, 2006. Google Scholar [19] S. C. Myers, Finance theory and financial strategy, Interfaces, 14 (1984), 126-137.   Google Scholar [20] V. K. Narayanan, Managing Technology and Innovation for Competitive Advantage, Englewood Cliffs, NJ: Prentice Hall, 2001. Google Scholar [21] S. Ruhrmann, J. Hochdörffer and G. Lanza, A methodological approach to evaluate supplier development based on real options, Production Engineering, 8 (2014), 373-382.   Google Scholar [22] E. S. Schwartz and M. Moon, Rational pricing of Internet companies, Financial Analysts Journal, 56 (2000), 62-75.   Google Scholar [23] E. S. Schwartz and M. Moon, Rational pricing of Internet companies revisited, The Financial Review, 36 (2001), 7-26.   Google Scholar [24] J. E. Smith and R. F. Nau, Valuing risky projects -option pricing theory and decision analysis, Management Science, 41 (1995), 795-816.   Google Scholar [25] J. E. Smith and K. F. McCardle, Valuing oil properties: Integrating option pricing and decision analysis approaches, Operations Research, 46 (1998), 198-217.   Google Scholar [26] J. Sutton, Gibrat's legacy, Journal of Economic Literature, 35 (1997), 40-59.   Google Scholar [27] F. M. Tseng, Y. J. Chiu and J. S. Chen, Measuring business performance in the high-tech manufacturing industry: A case study of Taiwan's large-sized TFT-LCD panel companies, Omega, 37 (2009), 686-697.   Google Scholar [28] L. Trigeorgis and S. P. Mason, Valuing managerial flexibility, Midland Corporate Finance Journal, 5 (1987), 14-21.   Google Scholar [29] L. Trigeorgis and S. Ioulianou, Valuing a high-tech growth company: The case of EchoStar communications corporation, The European Journal of Finance, 19 (2013), 734-759.  doi: 10.1080/1351847X.2011.640343.  Google Scholar [30] B. M. West and J. Bengtsson, Aggregate production process design in global manufacturing using a real options approach, International Journal of Production Research, 45 (2013), 1745-1762.   Google Scholar [31] D. D. Wu and D. L. Olson, Computational simulation and risk analysis: An introduction of state of the art research, Mathematical and Computer Modelling, 58 (2013), 1581-1587.  doi: 10.1016/j.mcm.2013.07.004.  Google Scholar [32] D. D. Wu, D. L. Olson and J. R. Birge, Introduction to special issue on" Enterprise risk management in operations", Internatonal Journal of Production Economics, 134 (2011), 1-2.   Google Scholar [33] D. D. Wu, O. Baron and O. Berman, Bargaining in competing supply chains with uncertainty, European Journal of Operational Research, 197 (2009), 548-556.  doi: 10.1016/j.ejor.2008.06.032.  Google Scholar [34] E. Wang, T. Su, D. Tsai and C. Lin, Fuzzy multiple-goal programming for analyzing outsourcing cost-effectiveness in hi-tech manufacturing, International Journal of Production Research, 51 (2013), 3920-3944.   Google Scholar [35] L. Wu and F. Liou, A quantitative model for ERP investment decision: Considering revenue and costs under uncertainty, International Journal of Production Research, 49 (2011), 6713-6728.   Google Scholar [36] L. Y. Wu, Entrepreneurial resources, dynamic capabilities and start-up performance of Taiwan's high-tech firms, Journal of Business research, 60 (2007), 549-555.   Google Scholar [37] Z. X. Wang and Y. Y. Wang, Evaluation of the provincial competitiveness of the Chinese high-tech industry using an improved TOPSIS method, Expert Systems with Applications, 41 (2014), 2824-2831.   Google Scholar [38] F. Yuen and H. Yang, Option pricing in a jump-diffusion model with regime switching, Astin Bulletin, 39 (2009), 515-539.  doi: 10.2143/AST.39.2.2044646.  Google Scholar [39] L. Zhu, A simulation based real options approach for the investment evaluation of nuclear power, Computers & Industrial Engineering, 63 (2012), 585-593.   Google Scholar

show all references

##### References:
 [1] C. Alexander and X. Chen, A general approach to real option valuation with application to real estate investments, University of Reading, ICMA Centre Discussion Paper No. DP2012-04. Available at SSRN: http://ssrn.com/abstract=1990957. Google Scholar [2] N. Bollen, Valuing option in regime-switching models, Journal of Derivatives, 6 (1998), 38-49.   Google Scholar [3] N. Bollen, Real options and product life cycles, Management Science, 45 (1999), 670-684.   Google Scholar [4] R. A. Brealey and S. C. Myers, Principles of Corporate Finance, McGraw-Hill, New York, 1992. Google Scholar [5] P. P. Boyle and Y. Tian, An explicit finite difference approach to the pricing of barrier options, Applied Mathematical Finance, 5 (1988), 17-43.   Google Scholar [6] P. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, Journal of Finance, 47 (1992), 271-293.   Google Scholar [7] P. P. Boyle, Option valuation using a three-jump process, International Options Journal, 3 (1986), 7-12.   Google Scholar [8] P. P. Boyle, A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23 (1988), 1-12.   Google Scholar [9] J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7 (1979), 229-263.   Google Scholar [10] M. G. Colombo, A. Croce and S. Murtinu, Ownership structure, horizontal agency costs and the performance of high-tech entrepreneurial firms, Small Business Economics, 42 (2014), 265-282.   Google Scholar [11] R. E. Caves, Industrial organization and new findings in the turnover and mobility of firms, Journal of Economic Literature, 36 (1998), 1947-1982.   Google Scholar [12] D. L. Deeds, D. DeCarolis and J. Coombs, Dynamic capabilities and new product development in high technology ventures: an empirical analysis of new biotechnology firms, Journal of Business Venturing, 15 (2000), 211-229.   Google Scholar [13] P. A. Geroski, What do we know about entry?, International Journal of Industrial Organization, 13 (1995), 450-456.   Google Scholar [14] X. Huang, N. Song, W. K. Ching, T. K. Siu and C. K. Yiu, A real option approach to optimal inventory management of retail products, Journal of Industrial and Management Optimization, 8 (2012), 379-389.  doi: 10.3934/jimo.2012.8.379.  Google Scholar [15] B. Kamrad and P. Ritchken, Multinomial approximating models for options with $k$ state variables, Management Science, 37 (1991), 1640-1652.   Google Scholar [16] D. Kellogg and J. M. Charnes, Real-options valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 76-84.   Google Scholar [17] F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation: a simple least-squares approach, The Review of Financial Studies, 14 (2001), 113-147.   Google Scholar [18] J. Mun, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, 2006. Google Scholar [19] S. C. Myers, Finance theory and financial strategy, Interfaces, 14 (1984), 126-137.   Google Scholar [20] V. K. Narayanan, Managing Technology and Innovation for Competitive Advantage, Englewood Cliffs, NJ: Prentice Hall, 2001. Google Scholar [21] S. Ruhrmann, J. Hochdörffer and G. Lanza, A methodological approach to evaluate supplier development based on real options, Production Engineering, 8 (2014), 373-382.   Google Scholar [22] E. S. Schwartz and M. Moon, Rational pricing of Internet companies, Financial Analysts Journal, 56 (2000), 62-75.   Google Scholar [23] E. S. Schwartz and M. Moon, Rational pricing of Internet companies revisited, The Financial Review, 36 (2001), 7-26.   Google Scholar [24] J. E. Smith and R. F. Nau, Valuing risky projects -option pricing theory and decision analysis, Management Science, 41 (1995), 795-816.   Google Scholar [25] J. E. Smith and K. F. McCardle, Valuing oil properties: Integrating option pricing and decision analysis approaches, Operations Research, 46 (1998), 198-217.   Google Scholar [26] J. Sutton, Gibrat's legacy, Journal of Economic Literature, 35 (1997), 40-59.   Google Scholar [27] F. M. Tseng, Y. J. Chiu and J. S. Chen, Measuring business performance in the high-tech manufacturing industry: A case study of Taiwan's large-sized TFT-LCD panel companies, Omega, 37 (2009), 686-697.   Google Scholar [28] L. Trigeorgis and S. P. Mason, Valuing managerial flexibility, Midland Corporate Finance Journal, 5 (1987), 14-21.   Google Scholar [29] L. Trigeorgis and S. Ioulianou, Valuing a high-tech growth company: The case of EchoStar communications corporation, The European Journal of Finance, 19 (2013), 734-759.  doi: 10.1080/1351847X.2011.640343.  Google Scholar [30] B. M. West and J. Bengtsson, Aggregate production process design in global manufacturing using a real options approach, International Journal of Production Research, 45 (2013), 1745-1762.   Google Scholar [31] D. D. Wu and D. L. Olson, Computational simulation and risk analysis: An introduction of state of the art research, Mathematical and Computer Modelling, 58 (2013), 1581-1587.  doi: 10.1016/j.mcm.2013.07.004.  Google Scholar [32] D. D. Wu, D. L. Olson and J. R. Birge, Introduction to special issue on" Enterprise risk management in operations", Internatonal Journal of Production Economics, 134 (2011), 1-2.   Google Scholar [33] D. D. Wu, O. Baron and O. Berman, Bargaining in competing supply chains with uncertainty, European Journal of Operational Research, 197 (2009), 548-556.  doi: 10.1016/j.ejor.2008.06.032.  Google Scholar [34] E. Wang, T. Su, D. Tsai and C. Lin, Fuzzy multiple-goal programming for analyzing outsourcing cost-effectiveness in hi-tech manufacturing, International Journal of Production Research, 51 (2013), 3920-3944.   Google Scholar [35] L. Wu and F. Liou, A quantitative model for ERP investment decision: Considering revenue and costs under uncertainty, International Journal of Production Research, 49 (2011), 6713-6728.   Google Scholar [36] L. Y. Wu, Entrepreneurial resources, dynamic capabilities and start-up performance of Taiwan's high-tech firms, Journal of Business research, 60 (2007), 549-555.   Google Scholar [37] Z. X. Wang and Y. Y. Wang, Evaluation of the provincial competitiveness of the Chinese high-tech industry using an improved TOPSIS method, Expert Systems with Applications, 41 (2014), 2824-2831.   Google Scholar [38] F. Yuen and H. Yang, Option pricing in a jump-diffusion model with regime switching, Astin Bulletin, 39 (2009), 515-539.  doi: 10.2143/AST.39.2.2044646.  Google Scholar [39] L. Zhu, A simulation based real options approach for the investment evaluation of nuclear power, Computers & Industrial Engineering, 63 (2012), 585-593.   Google Scholar
Probability distributions of jump time from mature stage to decline stage in Case 3 and Case 4
(a): Impacts of risk-free interest rate $r$ for investment option valuation, (b): Impacts of risk-free Interest Rate $r$ for divestment option valuation
(a): Impacts of proportion of taxes and various costs with respect to the revenues for investment option valuation, (b): Impacts of proportion of taxes and various costs with respect to the revenues for divestment option valuation
(a): Impacts of successful probability of development of a new product for investment option valuation, (b): Impacts of successful probability of development of a new product for divestment option valuation
(a): Impacts of mean of sales for investment option valuation, (b): Impacts of mean of sales for divestment option valuation
(a): Impacts of one-time cost $K_{in}$ in mature stage for the investment option valuation, (b): Impacts of one-time Cost $K_{di}$ in Mature Stage for the divestment option valuation
Four possible paths of $p(t)q(t)$ along the time in the pentanomial tree model
 $T$ $\sigma^2_p$ $\sigma^3_p$ $\mu^2_q$ $\mu^3_q$ $\sigma^2_q$ $\sigma^3_q$ $r$ $p_{12}$ $\gamma$ 8 0.38 0.3 0.2 -0.2 0.4 0.3 0.0012 0.85 0.6
 $T$ $\sigma^2_p$ $\sigma^3_p$ $\mu^2_q$ $\mu^3_q$ $\sigma^2_q$ $\sigma^3_q$ $r$ $p_{12}$ $\gamma$ 8 0.38 0.3 0.2 -0.2 0.4 0.3 0.0012 0.85 0.6
Different cases for different types of high-tech companies
 Case 1 Case 2 Case 3 Case 4 Time $t_{12}$ $t_{12}=2$ $t_{12}=2$ $t_{12}=2$ $t_{12}=2$ Time $t_{23}$ Fixed time Any time Any time Any time $t_{23}=a$ $t_{23}=t$ $t_{23}=t$ $t_{23}=t$ ${t_{12}}  Case 1 Case 2 Case 3 Case 4 Time$t_{12}t_{12}=2t_{12}=2t_{12}=2t_{12}=2$Time$t_{23}$Fixed time Any time Any time Any time$t_{23}=at_{23}=tt_{23}=tt_{23}=t{t_{12}}
Investment option values (dollars) in five cases with different combinations of the durations for Mature stage and Decline stage
 Combination of Stages 2 and 3 (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) Option Value 4.08 6.09 8.25 10.40 12.30
 Combination of Stages 2 and 3 (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) Option Value 4.08 6.09 8.25 10.40 12.30
Investment option values (dollars) in four cases with different probability distributions of the jump time $t_{23}$
 Case of $t_{23}$ Case 1 Case 2 Case 3 Case 4 Option Value 8.25 8.22 8.91 9.78
 Case of $t_{23}$ Case 1 Case 2 Case 3 Case 4 Option Value 8.25 8.22 8.91 9.78
Divestment option value (dollars) in five cases with different combinations of the durations for the Mature stage and the Decline stage
 Combination of Stages 2 and 3 (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) Option Value 5.25 7.26 9.41 11.56 13.47
 Combination of Stages 2 and 3 (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) Option Value 5.25 7.26 9.41 11.56 13.47
Divestment option values (dollars) in four cases with different probability distributions of the jump time $t_{23}$
 Case of $t_{23}$ Case 1 Case 2 Case 3 Case 4 Option Value 9.41 8.99 9.70 10.61
 Case of $t_{23}$ Case 1 Case 2 Case 3 Case 4 Option Value 9.41 8.99 9.70 10.61
Impacts of the varying parameters on the optimal times to exercise the options. "-" means that the option is not exercised at any time
 Invest Divest Path 1 Path 2 Path 3 Path 4 Path 1 Path 2 Path 3 Path 4 r=0.0001 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.0012 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.0023 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 1-γ= 0.2 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.5 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.8 - - t=3 - t=4 t=5 t=8 t=6 p12 = 0.04 t=2 t=2 t=2 t=2 t=8 t=8 t=8 t=8 0.44 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.84 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 μq2= 0.05 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.2 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.35 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 Kin=0.1 t=2 t=2 t=2 t=2 2.1 t=1 t=1 t=1 t=1 4.1 t=1 t=1 t=1 t=1 Kdi=-2.5 t=5 t=5 t=5 t=5 -0.5 t=8 t=8 t=8 t=8 1.5 t=8 t=8 t=8 t=8
 Invest Divest Path 1 Path 2 Path 3 Path 4 Path 1 Path 2 Path 3 Path 4 r=0.0001 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.0012 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.0023 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 1-γ= 0.2 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.5 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.8 - - t=3 - t=4 t=5 t=8 t=6 p12 = 0.04 t=2 t=2 t=2 t=2 t=8 t=8 t=8 t=8 0.44 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.84 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 μq2= 0.05 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.2 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 0.35 t=1 t=1 t=1 t=1 t=8 t=8 t=8 t=8 Kin=0.1 t=2 t=2 t=2 t=2 2.1 t=1 t=1 t=1 t=1 4.1 t=1 t=1 t=1 t=1 Kdi=-2.5 t=5 t=5 t=5 t=5 -0.5 t=8 t=8 t=8 t=8 1.5 t=8 t=8 t=8 t=8
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