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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 and 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.

[2]

N. Bollen, Valuing option in regime-switching models, Journal of Derivatives, 6 (1998), 38-49. 

[3]

N. Bollen, Real options and product life cycles, Management Science, 45 (1999), 670-684. 

[4]

R. A. Brealey and S. C. Myers, Principles of Corporate Finance, McGraw-Hill, New York, 1992.

[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. 

[6]

P. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, Journal of Finance, 47 (1992), 271-293. 

[7]

P. P. Boyle, Option valuation using a three-jump process, International Options Journal, 3 (1986), 7-12. 

[8]

P. P. Boyle, A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23 (1988), 1-12. 

[9]

J. C. CoxS. A. Ross and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7 (1979), 229-263. 

[10]

M. G. ColomboA. Croce and S. Murtinu, Ownership structure, horizontal agency costs and the performance of high-tech entrepreneurial firms, Small Business Economics, 42 (2014), 265-282. 

[11]

R. E. Caves, Industrial organization and new findings in the turnover and mobility of firms, Journal of Economic Literature, 36 (1998), 1947-1982. 

[12]

D. L. DeedsD. 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. 

[13]

P. A. Geroski, What do we know about entry?, International Journal of Industrial Organization, 13 (1995), 450-456. 

[14]

X. HuangN. SongW. K. ChingT. 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.

[15]

B. Kamrad and P. Ritchken, Multinomial approximating models for options with $k$ state variables, Management Science, 37 (1991), 1640-1652. 

[16]

D. Kellogg and J. M. Charnes, Real-options valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 76-84. 

[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. 

[18]

J. Mun, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, 2006.

[19]

S. C. Myers, Finance theory and financial strategy, Interfaces, 14 (1984), 126-137. 

[20]

V. K. Narayanan, Managing Technology and Innovation for Competitive Advantage, Englewood Cliffs, NJ: Prentice Hall, 2001.

[21]

S. RuhrmannJ. Hochdörffer and G. Lanza, A methodological approach to evaluate supplier development based on real options, Production Engineering, 8 (2014), 373-382. 

[22]

E. S. Schwartz and M. Moon, Rational pricing of Internet companies, Financial Analysts Journal, 56 (2000), 62-75. 

[23]

E. S. Schwartz and M. Moon, Rational pricing of Internet companies revisited, The Financial Review, 36 (2001), 7-26. 

[24]

J. E. Smith and R. F. Nau, Valuing risky projects -option pricing theory and decision analysis, Management Science, 41 (1995), 795-816. 

[25]

J. E. Smith and K. F. McCardle, Valuing oil properties: Integrating option pricing and decision analysis approaches, Operations Research, 46 (1998), 198-217. 

[26]

J. Sutton, Gibrat's legacy, Journal of Economic Literature, 35 (1997), 40-59. 

[27]

F. M. TsengY. 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. 

[28]

L. Trigeorgis and S. P. Mason, Valuing managerial flexibility, Midland Corporate Finance Journal, 5 (1987), 14-21. 

[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.

[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. 

[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.

[32]

D. D. WuD. 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. 

[33]

D. D. WuO. 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.

[34]

E. WangT. SuD. 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. 

[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. 

[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. 

[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. 

[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.

[39]

L. Zhu, A simulation based real options approach for the investment evaluation of nuclear power, Computers & Industrial Engineering, 63 (2012), 585-593. 

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.

[2]

N. Bollen, Valuing option in regime-switching models, Journal of Derivatives, 6 (1998), 38-49. 

[3]

N. Bollen, Real options and product life cycles, Management Science, 45 (1999), 670-684. 

[4]

R. A. Brealey and S. C. Myers, Principles of Corporate Finance, McGraw-Hill, New York, 1992.

[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. 

[6]

P. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs, Journal of Finance, 47 (1992), 271-293. 

[7]

P. P. Boyle, Option valuation using a three-jump process, International Options Journal, 3 (1986), 7-12. 

[8]

P. P. Boyle, A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23 (1988), 1-12. 

[9]

J. C. CoxS. A. Ross and M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7 (1979), 229-263. 

[10]

M. G. ColomboA. Croce and S. Murtinu, Ownership structure, horizontal agency costs and the performance of high-tech entrepreneurial firms, Small Business Economics, 42 (2014), 265-282. 

[11]

R. E. Caves, Industrial organization and new findings in the turnover and mobility of firms, Journal of Economic Literature, 36 (1998), 1947-1982. 

[12]

D. L. DeedsD. 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. 

[13]

P. A. Geroski, What do we know about entry?, International Journal of Industrial Organization, 13 (1995), 450-456. 

[14]

X. HuangN. SongW. K. ChingT. 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.

[15]

B. Kamrad and P. Ritchken, Multinomial approximating models for options with $k$ state variables, Management Science, 37 (1991), 1640-1652. 

[16]

D. Kellogg and J. M. Charnes, Real-options valuation for a biotechnology company, Financial Analysts Journal, 56 (2000), 76-84. 

[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. 

[18]

J. Mun, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, 2006.

[19]

S. C. Myers, Finance theory and financial strategy, Interfaces, 14 (1984), 126-137. 

[20]

V. K. Narayanan, Managing Technology and Innovation for Competitive Advantage, Englewood Cliffs, NJ: Prentice Hall, 2001.

[21]

S. RuhrmannJ. Hochdörffer and G. Lanza, A methodological approach to evaluate supplier development based on real options, Production Engineering, 8 (2014), 373-382. 

[22]

E. S. Schwartz and M. Moon, Rational pricing of Internet companies, Financial Analysts Journal, 56 (2000), 62-75. 

[23]

E. S. Schwartz and M. Moon, Rational pricing of Internet companies revisited, The Financial Review, 36 (2001), 7-26. 

[24]

J. E. Smith and R. F. Nau, Valuing risky projects -option pricing theory and decision analysis, Management Science, 41 (1995), 795-816. 

[25]

J. E. Smith and K. F. McCardle, Valuing oil properties: Integrating option pricing and decision analysis approaches, Operations Research, 46 (1998), 198-217. 

[26]

J. Sutton, Gibrat's legacy, Journal of Economic Literature, 35 (1997), 40-59. 

[27]

F. M. TsengY. 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. 

[28]

L. Trigeorgis and S. P. Mason, Valuing managerial flexibility, Midland Corporate Finance Journal, 5 (1987), 14-21. 

[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.

[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. 

[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.

[32]

D. D. WuD. 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. 

[33]

D. D. WuO. 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.

[34]

E. WangT. SuD. 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. 

[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. 

[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. 

[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. 

[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.

[39]

L. Zhu, A simulation based real options approach for the investment evaluation of nuclear power, Computers & Industrial Engineering, 63 (2012), 585-593. 

Figure 1.  Probability distributions of jump time from mature stage to decline stage in Case 3 and Case 4
Figure 2.  (a): Impacts of risk-free interest rate $r$ for investment option valuation, (b): Impacts of risk-free Interest Rate $r$ for divestment option valuation
Figure 3.  (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
Figure 4.  (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
Figure 5.  (a): Impacts of mean of sales for investment option valuation, (b): Impacts of mean of sales for divestment option valuation
Figure 6.  (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
Figure 7.  Four possible paths of $p(t)q(t)$ along the time in the pentanomial tree model
Table 1.  Parameters adopted in the model
$T$ $\sigma^2_p$ $\sigma^3_p$ $\mu^2_q$ $\mu^3_q$ $\sigma^2_q$ $\sigma^3_q$ $r$ $p_{12}$$\gamma$
80.380.30.2-0.20.40.30.00120.850.6
$T$ $\sigma^2_p$ $\sigma^3_p$ $\mu^2_q$ $\mu^3_q$ $\sigma^2_q$ $\sigma^3_q$ $r$ $p_{12}$$\gamma$
80.380.30.2-0.20.40.30.00120.850.6
Table 2.  Different cases for different types of high-tech companies
Case 1Case 2Case 3Case 4
Time $t_{12}$$t_{12}=2$$t_{12}=2$$t_{12}=2$$t_{12}=2$
Time $t_{23}$Fixed timeAny timeAny timeAny time
$t_{23}=a$$t_{23}=t$$t_{23}=t$$t_{23}=t$
${t_{12}}<a<T$${t_{12}}<t<T$${t_{12}}<t<T$${t_{12}}<t<T$
Probability of1 if $t=a$Uniform rateConcave functionConvex function
$t_{23}=t$0 if $t\neq{a}$$1/5$$0.0853\ln{(4t)}$$0.0516e^{0.4t}$
(${t_{12}}<t<T $)
Case 1Case 2Case 3Case 4
Time $t_{12}$$t_{12}=2$$t_{12}=2$$t_{12}=2$$t_{12}=2$
Time $t_{23}$Fixed timeAny timeAny timeAny time
$t_{23}=a$$t_{23}=t$$t_{23}=t$$t_{23}=t$
${t_{12}}<a<T$${t_{12}}<t<T$${t_{12}}<t<T$${t_{12}}<t<T$
Probability of1 if $t=a$Uniform rateConcave functionConvex function
$t_{23}=t$0 if $t\neq{a}$$1/5$$0.0853\ln{(4t)}$$0.0516e^{0.4t}$
(${t_{12}}<t<T $)
Table 3.  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 Value4.086.098.2510.4012.30
Combination of Stages 2 and 3(1, 5)(2, 4)(3, 3)(4, 2)(5, 1)
Option Value4.086.098.2510.4012.30
Table 4.  Investment option values (dollars) in four cases with different probability distributions of the jump time $t_{23}$
Case of $t_{23}$Case 1Case 2Case 3Case 4
Option Value8.258.228.919.78
Case of $t_{23}$Case 1Case 2Case 3Case 4
Option Value8.258.228.919.78
Table 5.  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 Value5.257.269.4111.5613.47
Combination of Stages 2 and 3(1, 5)(2, 4)(3, 3)(4, 2)(5, 1)
Option Value5.257.269.4111.5613.47
Table 6.  Divestment option values (dollars) in four cases with different probability distributions of the jump time $t_{23}$
Case of $t_{23}$Case 1Case 2Case 3Case 4
Option Value9.418.999.7010.61
Case of $t_{23}$Case 1Case 2Case 3Case 4
Option Value9.418.999.7010.61
Table 7.  Impacts of the varying parameters on the optimal times to exercise the options. "-" means that the option is not exercised at any time
InvestDivest
Path 1Path 2Path 3Path 4Path 1Path 2Path 3Path 4
r=0.0001t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.0012t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.0023t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
1-γ= 0.2 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.5 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.8-- t=3- t=4 t=5 t=8 t=6
p12 = 0.04t=2 t=2 t=2 t=2t=8 t=8 t=8 t=8
0.44 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.84 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
μq2= 0.05t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.2t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.35 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
Kin=0.1t=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=-2.5t=5 t=5 t=5 t=5
-0.5t=8 t=8 t=8 t=8
1.5t=8 t=8 t=8 t=8
InvestDivest
Path 1Path 2Path 3Path 4Path 1Path 2Path 3Path 4
r=0.0001t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.0012t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.0023t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
1-γ= 0.2 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.5 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.8-- t=3- t=4 t=5 t=8 t=6
p12 = 0.04t=2 t=2 t=2 t=2t=8 t=8 t=8 t=8
0.44 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.84 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
μq2= 0.05t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.2t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
0.35 t=1 t=1 t=1 t=1t=8 t=8 t=8 t=8
Kin=0.1t=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=-2.5t=5 t=5 t=5 t=5
-0.5t=8 t=8 t=8 t=8
1.5t=8 t=8 t=8 t=8
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