不确定性、最优资本结构与投资期权价值
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摘要
在不确定的假设条件下,研究了债务对企业最优投资时机和最优投资规模的选择问题.以负债企业投资决策的最优化为目标,运用动态规划原理得到了企业投资时机,投资规模以及投资期权价值的表达式,并通过数值仿真求得数值解.研究表明:产品价格的不确定能够影响到企业的最优资本结构选择,并且这两者又同时对企业的最优投资决策和投资期权价值产生影响.
The impacts of debts on the optimal timing and amount of investment are studied in the case of uncertainty. By using stochastic control methods, the expressions for the optimal timing and amount of investment and the option value of investment are obtained. Further, the optimal investment decisions are made by employing numerical simulations. The results show that the uncertainty of product prices has impacts on the optimal capital structure. In addition, both the product price and the optimal capital structure can influence the optimal investment decisions and the option value of investment.
The impacts of debts on the optimal timing and amount of investment are studied in the case of uncertainty. By using stochastic control methods, the expressions for the optimal timing and amount of investment and the option value of investment are obtained. Further, the optimal investment decisions are made by employing numerical simulations. The results show that the uncertainty of product prices has impacts on the optimal capital structure. In addition, both the product price and the optimal capital structure can influence the optimal investment decisions and the option value of investment.
引文
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[2] MacDonald R L. The value of waiting to invest. The Quarterly Journal of Economics, 1986, 101(4):707–727.
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[4] Bellalah M, Jacquillat B. Option Valuation with Information Costs:Theory and Tests. London:Blackwell Publishing Ltd, 1995:617–635.
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[7] Bellalah M. Irreversibility, sunk costs and investment under incomplete information. R&D Management, 2001, 31(2):115–126.
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[9]亢娅丽,朱磊.气候政策不确定条件下的发电投资优化模型.系统工程学报, 2014, 30(2):713–724.Kang Y L, Zhu L. Optimization model of generation investment under uncertainty policy. Journal of Systems Engineering, 2014,30(2):713–724.(in Chinese)
[10] B?ckman T, Fleten S, Juliussen E, et al. Investment timing and optimal capacity choice for small hydropower projects. European Journal of Operational Research, 2008, 190(1):255–267.
[11] Wong K P. The effect of uncertainty on investment timing in a real options model. Journal of Economic Dynamics and Control, 2007,31(7):2152–2167.
[12] Wong K P. The effects of irreversibility on the timing and intensity of lumpy investment. Economic Modeling, 2010, 27(1):97–102.
[13]李应求,刘朝才,彭朝晖.不确定条件下企业的投资规模决策.运筹学学报, 2008, 12(2):121–128.Li Y Q, Liu Z C, Peng Z H. Decision-making on investment capacity under uncertainty. OR Transactions, 2008, 12(2):121–128.(in Chinese)
[14]李强,曾勇.融资能力与技术创新投资决策:一种实物期权方法.系统工程学报, 2009, 24(1):1–8.Li Q, Zeng Y. Financing capabilities and investment decision on technological innovations:A real option approach. Journal of System Engineering, 2009, 24(1):1–8.(in Chinese)
[15]阳军,孟卫东,熊维勤.不确定条件下最优投资时机和最优投资规模决策.系统工程理论与实践, 2012, 32(4):752–759.Yang J, Meng W D, Xiong W Q. Optimal investment timing and investment scale decision making under uncertainty. System Engineering:Theory&Practice, 2012, 32(4):752–759.(in Chinese)
[16] Modigliani F, Miller M H. The cost of capital, corporation finance and the theory of investment. American Economic Review, 1958,48(46):261–297.
[17] Harris M, Raviv A. The theory of capital structure. Journal of Finance, 1991, 46(1):297–355.
[18] Famae F K. Testing tradeoff and pecking order predictions about dividends and debt. Review of Financial Studies, 2002, 15(21):1–33.
[19] Bar-Ilan A, Strange W C. The timing and intensity of investment. Journal of Macroeconomics, 1999, 21(1):57–77.
[20] Sarkar S. Optimal size, optimal timing and optimal financing of an investment. Journal of Macroeconomics, 2011, 33(4):681–689.
1关于价值匹配和平滑粘贴条件的讨论见文献[3].
[2] MacDonald R L. The value of waiting to invest. The Quarterly Journal of Economics, 1986, 101(4):707–727.
[3] Dixit A K, Pindyck R S. Investment under Uncertainty. New Jersey:Princeton University Press, 1994:127–138.
[4] Bellalah M, Jacquillat B. Option Valuation with Information Costs:Theory and Tests. London:Blackwell Publishing Ltd, 1995:617–635.
[5] Cortazar G, Schwartz E S. Implementing a Real Option Model for Valuing an Undeveloped Oil Field. London:Blackwell Publishing Ltd, 1997:125–137.
[6] Farzin Y H, Huisman K J M, Kort P M. Optimal timing of technology adoption. Journal of Economic Dynamics and Control, 1998,22(5):779–799.
[7] Bellalah M. Irreversibility, sunk costs and investment under incomplete information. R&D Management, 2001, 31(2):115–126.
[8] Wong K P. The effects of abandonment options on investment timing and intensity. Economic Modeling, 2012, 15(6):65–73.
[9]亢娅丽,朱磊.气候政策不确定条件下的发电投资优化模型.系统工程学报, 2014, 30(2):713–724.Kang Y L, Zhu L. Optimization model of generation investment under uncertainty policy. Journal of Systems Engineering, 2014,30(2):713–724.(in Chinese)
[10] B?ckman T, Fleten S, Juliussen E, et al. Investment timing and optimal capacity choice for small hydropower projects. European Journal of Operational Research, 2008, 190(1):255–267.
[11] Wong K P. The effect of uncertainty on investment timing in a real options model. Journal of Economic Dynamics and Control, 2007,31(7):2152–2167.
[12] Wong K P. The effects of irreversibility on the timing and intensity of lumpy investment. Economic Modeling, 2010, 27(1):97–102.
[13]李应求,刘朝才,彭朝晖.不确定条件下企业的投资规模决策.运筹学学报, 2008, 12(2):121–128.Li Y Q, Liu Z C, Peng Z H. Decision-making on investment capacity under uncertainty. OR Transactions, 2008, 12(2):121–128.(in Chinese)
[14]李强,曾勇.融资能力与技术创新投资决策:一种实物期权方法.系统工程学报, 2009, 24(1):1–8.Li Q, Zeng Y. Financing capabilities and investment decision on technological innovations:A real option approach. Journal of System Engineering, 2009, 24(1):1–8.(in Chinese)
[15]阳军,孟卫东,熊维勤.不确定条件下最优投资时机和最优投资规模决策.系统工程理论与实践, 2012, 32(4):752–759.Yang J, Meng W D, Xiong W Q. Optimal investment timing and investment scale decision making under uncertainty. System Engineering:Theory&Practice, 2012, 32(4):752–759.(in Chinese)
[16] Modigliani F, Miller M H. The cost of capital, corporation finance and the theory of investment. American Economic Review, 1958,48(46):261–297.
[17] Harris M, Raviv A. The theory of capital structure. Journal of Finance, 1991, 46(1):297–355.
[18] Famae F K. Testing tradeoff and pecking order predictions about dividends and debt. Review of Financial Studies, 2002, 15(21):1–33.
[19] Bar-Ilan A, Strange W C. The timing and intensity of investment. Journal of Macroeconomics, 1999, 21(1):57–77.
[20] Sarkar S. Optimal size, optimal timing and optimal financing of an investment. Journal of Macroeconomics, 2011, 33(4):681–689.
1关于价值匹配和平滑粘贴条件的讨论见文献[3].