基于利率期限结构模型的项目投资决策研究
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摘要
净现值分析指标是现代项目投资决策的一个重要研究内容,已广泛应用于经济与管理领域。而折现率是决定净现值的关键因素,直接影响着投资决策结果的可靠性和准确性,如何使折现率更加符合投资项目评价和财务管理的实际是一个值得深入研究的问题。本文在前人研究成果基础上,提出用利率期限结构模型来确定折现率,修正净现值计算公式,进而改进盈亏平衡分析、实物期权分析中对净现值公式的应用,变静态分析为动态分析,并将以上研究成果应用于项目投资决策。主要工作及创新之处如下：
(1)针对净现值中折现率一成不变的弊端,充分发挥利率期限结构模型在拟合和估计利率变动行为方面的优势,修正净现值中的折现率,弥补其静态被动性分析的缺陷,使其具备动态性,更合理有效地反映项目现金流的风险特性,更加符合现实情况,并设置不同情况下的算例对其进行应用验证。
(2)传统盈亏平衡分析以盈利为零作为盈亏平衡点,没有考虑资金的时间价值,是一种静态分析。动态盈亏平衡分析以净现值等于零的状态作为盈亏平衡状态,将资金的时间价值考虑在内,但在应用净现值公式计算时仍采用固定折现率,本文通过运用线性规划利率期限结构模型来确定动态折现率,使动态盈亏平衡分析的动态性更具有实际意义,并结合适当算例验证该方法的有效性。
(3)很多情况下实物期权分析都局限于B-S模型,由于实物期权分析在一定程度上是对NPV方法的扩展,本文将利率期限结构模型引入实物期权,运用遗传算法优化的SV模型修正传统的基于B-S模型的实物期权定价公式,改进实物期权分析中对净现值公式的运用,提高评价结果的可信度。并将这种理论上的创新应用到清洁发展机制(CDM)项目的投资决策中,令该投资项目的经济评价更切合实际。
Net present value analysis accounts an important position in project decision-making problems. It has been widely used in economic, management and other fields. The rate used to discount future cash flows to the present value is a key variable of this process, which directly impacts on the accuracy and reliability of the decision-making results, and how to obtain the more effective discount rate which is suitable for projects assessment and financial management is a very significant research field.
Based on previous research results, the paper uses interest rates term structure model to determine the discount rate, and amends the calculation formula of net present value, thereby improving the application of net present value calculation formulas during the solving process of breakeven analysis and real option analysis, changing the static analysis into dynamic analysis. At the same time, this paper applies the above results to the field of project investment decision-making. The main work and innovative results are as follows:
(1) For the common pitfalls of static discount rates used in the net present value calculation formula, this paper giving full play to the superiority of interest rates term structure models in fitting and estimating the randomness of rates change introduces interest rates term structure models, which can amend the calculation formula of net present value and change the static analysis into dynamic analysis, in order to make the net present value analysis more reasonable and effective to reflect the risk characteristics of the project cash flow and more in line with reality.
(2) Traditional breakeven analysis is a static analysis, which makes profit to be zero as the break-even point, without considering the time value of capital. Dynamic breakeven analysis considers the time value of capital by making net present value to be zero as the break-even point. This paper will make the dynamic breakeven analysis more practical by using the linear programming interest rate term structure model to determine the dynamic discount rate and verify the effectiveness of the method with appropriate examples.
(3) In many cases real option analysis is limited to B-S model. Since real option analysis is the expansion of NPV method to some extent, this paper introduces interest rates term structure models into the real option, uses SV interest rates term structure models optimized by genetic algorithm to amend the real option pricing formula based on the traditional B-S model, so that to improve the application of NPV formula in the real option analysis, which will make the evaluation results more believable.The paper applies the theoretical innovation to the investment decision of clean development mechanism (CDM) projects, so as to make the projects assessment more in line with the actual situation.
(1)针对净现值中折现率一成不变的弊端,充分发挥利率期限结构模型在拟合和估计利率变动行为方面的优势,修正净现值中的折现率,弥补其静态被动性分析的缺陷,使其具备动态性,更合理有效地反映项目现金流的风险特性,更加符合现实情况,并设置不同情况下的算例对其进行应用验证。
(2)传统盈亏平衡分析以盈利为零作为盈亏平衡点,没有考虑资金的时间价值,是一种静态分析。动态盈亏平衡分析以净现值等于零的状态作为盈亏平衡状态,将资金的时间价值考虑在内,但在应用净现值公式计算时仍采用固定折现率,本文通过运用线性规划利率期限结构模型来确定动态折现率,使动态盈亏平衡分析的动态性更具有实际意义,并结合适当算例验证该方法的有效性。
(3)很多情况下实物期权分析都局限于B-S模型,由于实物期权分析在一定程度上是对NPV方法的扩展,本文将利率期限结构模型引入实物期权,运用遗传算法优化的SV模型修正传统的基于B-S模型的实物期权定价公式,改进实物期权分析中对净现值公式的运用,提高评价结果的可信度。并将这种理论上的创新应用到清洁发展机制(CDM)项目的投资决策中,令该投资项目的经济评价更切合实际。
Net present value analysis accounts an important position in project decision-making problems. It has been widely used in economic, management and other fields. The rate used to discount future cash flows to the present value is a key variable of this process, which directly impacts on the accuracy and reliability of the decision-making results, and how to obtain the more effective discount rate which is suitable for projects assessment and financial management is a very significant research field.
Based on previous research results, the paper uses interest rates term structure model to determine the discount rate, and amends the calculation formula of net present value, thereby improving the application of net present value calculation formulas during the solving process of breakeven analysis and real option analysis, changing the static analysis into dynamic analysis. At the same time, this paper applies the above results to the field of project investment decision-making. The main work and innovative results are as follows:
(1) For the common pitfalls of static discount rates used in the net present value calculation formula, this paper giving full play to the superiority of interest rates term structure models in fitting and estimating the randomness of rates change introduces interest rates term structure models, which can amend the calculation formula of net present value and change the static analysis into dynamic analysis, in order to make the net present value analysis more reasonable and effective to reflect the risk characteristics of the project cash flow and more in line with reality.
(2) Traditional breakeven analysis is a static analysis, which makes profit to be zero as the break-even point, without considering the time value of capital. Dynamic breakeven analysis considers the time value of capital by making net present value to be zero as the break-even point. This paper will make the dynamic breakeven analysis more practical by using the linear programming interest rate term structure model to determine the dynamic discount rate and verify the effectiveness of the method with appropriate examples.
(3) In many cases real option analysis is limited to B-S model. Since real option analysis is the expansion of NPV method to some extent, this paper introduces interest rates term structure models into the real option, uses SV interest rates term structure models optimized by genetic algorithm to amend the real option pricing formula based on the traditional B-S model, so that to improve the application of NPV formula in the real option analysis, which will make the evaluation results more believable.The paper applies the theoretical innovation to the investment decision of clean development mechanism (CDM) projects, so as to make the projects assessment more in line with the actual situation.
引文
[1]Myers S. Determinants of Corporate Borrowing[J]. Journal of Financial Economics,1977, (5), 147-175.
[2]McCulloch, J. Huston. Measuring the term structure of interest rates[J]. Journal of Business, 1971,44:19-31.
[3]McCulloch J H. The tax-adjusted yield curve[J]. Journal of Finance,1975,30:811-830.
[4]Nelson C, Siegel, A. Parsimonious modelling of yield curves[J]. Journal of Business,1987, 60(4):473-489.
[5]Svensson, L.E.O. Estimating and Interpreting Forward Interest Rates:Sweden 1992-1994[R]. International Monetary Fund Working Papers,1994,94-114.
[6]Svensson,L.E.O. Estimating Forward Interest Rates with the Extended Nelson&Siegel Method[J].Sveriges Riksbank Quarterly Review,1995(3):13-26.
[7]Ioannides Michalis. A comparison of yield curve estimation techniques using UK data[J].Journal of Banking & Finance,2003,27:1-26.
[8]Allen D.E., Thomas L.C., Zheng, H. Stripping coupons with linear programming[J]. Journal of Fixed Income,2000,10(2):80-87.
[9]Vasicek O.A. An equilibrium characterization of the term structure[J].Journal of Financial Economics,1977,5(2):177-188.
[10]Cox J.C., Ingersoll J.E., Ross S.A. A theory of the term structure of interest rates[J]. Econometrica,1985,53(2):385-407.
[11]Ho,T.S.Y., Lee,S.B. Term Structure Movements and Pricing Interest Rate Contingent Claims [J]. Journal of Finance,1986,41(5):1011-1029.
[12]Hull J, White A. Pricing interest rate derivative securities[J].Review of Financial Studies,1990,3(4):573-592.
[13]Heath, D., Jarrow, R., Morton, A. Bond Pricing and the Term Structure of Interest Rate:A New Methodology for Contingent Claim Valuations[J]. Econometrica,1992,60:77-105.
[14]Kennedy, D.P. The Term Structure of Interest Rates as a Gaussian Random Field[J]. Mathematical Finance,1994,4:247-258.
[15]Goldstein, R.S. The Term Structure of Interest Rates as a Random Field[J]. Review of Financial Studies,2000, (5):365-384.
[16]Duffie, D., Kan, R. A Yield-Factor Model of Interest Rates[J]. Mathematical Finance,1996, 6:376-406.
[17]Dai, Q., Singleton, K.J. Specification Analysis of Affine Term Structure Models[J]. Journal of Finance,2000,55(5):1943-1978.
[18]Damir F. A General Characterization of One Factor Affine Term Structure Models[J]. Finance Stochastic,2001, (5):389-412.
[19]Duffee, G.R. Term Premia and Interest Rate Forecasts in Affine Models[J]. The Journal of Finance,2002,57:405-443.
[20]Duffie, D., Filipovinc, D., Schachermayer, W. Affine Processes and Applications in Finance[J]. Annals of Applied Probability,2003,13:984-1053.
[21]Ang,A., Piazzesi,M. And Wei,M. What Does the Yield Curve Tell us About GDP Growth[M].manuscript, Columbia University and UCLA,2003.
[22]Sergei, L. Consistency Conditions for Affine Term Structure Models[J].Stochastic Processes and Their Applications,2004,(109):225-261.
[23]范龙振,张国庆.仿射模型、广义仿射模型与上交所利率期限结构[J].管理工程学报,2005,19(3)：97-101.
[24]陈盛业,陈宁,王义克.银行间国债利率期限结构的三因子仿射模型[J].运筹与管理,2006,1 5(6)：87-90.
[25]Stefano, D.A., Axel, H. K. International Stock-Bond Correlations in a Simple Affine Asset Pricing Model[J]. Journal of Banking and Finance,2006,30:2747-2765.
[26]Patrick, C., Damir, F., Kimmel, R.L. Market Price of Risk Specifications for Affine Models: Theory and Evidence[J]. Journal of Financial Economics,2007,83:123-170.
[27]Ruslan Bikbov, Mikhail Chernov. Unspanned Stochastic Volatility in Affine Models:Evidence from Eurodollar Futures and Options [J]. Management Science,2009,55(8):1292-1305.
[28]陈雯,陈浪南.国债利率期限结构：建模与实证[J].世界经济,2000,8：24-28.
[29]李仲飞,汪寿阳,邓小铁.摩擦市场的利率期限结构的无套利分析[J].系统科学与数学,2002,7：285-295.
[30]周建新,于鸿福,张千云.以线性规划法估计台湾公债市场利率期限结构之实证研究[J].管理科学研究,2003,1(1)：31-47.
[31]周荣喜,邱菀华.基于多项式样条函数的利率期限结构模型实证比较[J].系统工程,2004,22(6)：39-43.
[32]唐革榕.我国利率期限结构的静态拟合实证研究.[D].厦门：厦门大学博士学位论文,2006.
[33]林海,郑振龙,利率期限结构研究述评[J].管理科学学报,2007,10(1)：79-98.
[34]孙甜.利率期限结构理论的最新研究述评[J].统计与决策,2009,4：159-161.
[35]邓飞琼.利率期限结构理论与研究方法综述[J].现代商业,2010,29：159-161.
[36]白小莹,杨丰梅,周荣喜.基于线性规划和多项式样条函数的利率期限结构模型[J].运筹与管理,2009,18(2)：30-34.
[37]张景,石琳,李妍.基于插值函数的利率期限结构分析[J].兰州大学学报(自然科学版),2010,46：2020-208.
[38]董皓舒.基于智能神经网络组合预测的国债利率期限结构建模与实证[J].中国市场, 2010,44：47-49.
[39]宋巍.我国国债利率期限结构的实证分析[J].商业时代,2010,295：5-56.
[40]周子康,王宁,杨衡.中国国债利率期限结构模型研究与实证分析[J].金融研究,2008,(3)：131-150.
[41]白小莹,周荣喜,杨丰梅.基于遗传算法的多项式样条函数利率期限结构模型[J].系统工程,2009,27(7)：22-27.
[42]石峰,秦磊.中国债券市场动态利率模型及其实证检验[J].运筹与管理,2010,19(5)：135-148.
[43]周荣喜,刘雯宇,牛伟宁.基于SV参数利率期限结构模型的国债信用价差研究[J].北京化工大学学报(自然科学版),2011,38(3)：129-133.
[44]Bichler, Shimshon; Nitzan, Jonathan.Systemic Fear, Modern Finance and the Future of Capitalism[J]. Jerusalem and Montreal,2010,7:8-11.
[45]Karl Claxton, Mike Paulden, Hugh Gravelle, Werner Brouwer, Anthony J. Culyer.Discounting and decision making in the economic evaluation of health-care technologies [J].Health Economics,2011,12(1):2-15.
[46]George Saravacos, Zacharias Maroulis. Food Process Economics[J]. Food Engineering Interfaces,2011,1:219-236.
[47]Mohammad A. Ammar. Optimization of Project Time-Cost Trade-Off Problem with Discounted Cash Flows[J]. Construction Engineering and Management,2011,137(1):65-72.
[48]吴联生.评内含报酬率求解数学模型[J].会计研究,1996.12：36-38.
[49]李苹莉,王斌.净现值法和内含报酬率法的比较分析及理性选择[J].会计研究,1996.12：38-40.
[50]吕长江.净现值法与内含报酬率法冲突的协调[J].数量经济技术经济研究,1998,15(4)：51-53.
[51]李心愉.净现值法和内部收益率法的比较法分析[J].数量经济技术经济研究,1998,15(12)：31-33.
[52]陶亚文,余波.贴现原理的再认识—对净现值和内含报酬率理性选择的新思考[J].会计研究,1998.12：29-34.
[53]张信东.调整净现值法和内含报酬率法的冲突方法探析[J].南开管理评论,1999,2(6)：29-33.
[54]Sugata Roychowdhury. Discussion of:Acquisition profitability and timely loss recognition by J. Francis and X. Martin[J]. Accounting and Economics,2010,49(1-2):179-183.
[55]王玉春.关于净现值的计算模型及概念的修正[J].财贸研究,1999,(6)：48-49.
[56]郭树声.净现值指数法在方案选择中的错误和危害[J].数量经济技术经济研究,2005,22(9)：91-95.
[57]许仁青.对净现值法中折现率的一点思考[J].经济问题探索,2003,(5)：107-108.
[58]陶菊春.风险性投资决策的一种分析方法[J].数量经济技术经济研究,1993,10(11)：52-55.
[59]邓敏.一种新的财务评价指标：基于可靠性分析的净现值法的改进[J].当代财经,2001,(6)：69-70.
[60]罗福周,孔凡楼.带投资风险度的随机净现值分析方法[J].西安建筑科技大学学报(自然科学版),2006,38(3)：441-444.
[61]王岩,蔡小军,净现值指标的进一步分析及其修正算法研究[J].数量经济技术经济研究,2004,21(12)：70-75.
[62]Hazen, G. B. A new perspective on multiple internal rates of return[J].Engrg. Economist 2003,48(1)31-51.
[63]Hazen, G. B. An Extension of the Internal Rate of Return to Stochastic Cash Flows[J]. Mangement Science,2009,55(6):1030-1034.
[64]Christian Gollier. Expected net present value, expected net future value, and the Ramsey rule[J]. Environmental Economics and Management,2010,59(2):142-148.
[65]徐增标,郑垂勇,刘卫国,动态盈亏平衡分析在商业银行网点建设中的应用[J].金融理论与实践,2008,(6)：62-64.
[66]Laura K. James, Scott M. Swinton, and Kurt D. Thelen. Profitability Analysis of Cellulosic Energy Crops Compared with Corn[J]. Agronomy Journal,2010,102(2):675-687.
[67]John E. Murdock,Ceib Phillips,Richard Beane,Rocio Quinonez.Break-even analysis of Medicaid vs fee for service in orthodontic practice [J]. Orthodontics & Dentofacial Orthopedics.2010,137 (3):334-339.
[68]Michael E. Chernew, Iver A. Juster, Mayur Shah, Evidence That Value-Based Insurance Can Be Effective[J]. Health Affairs,2011,30(1):109-117.
[69]饶莉,关于二次型非线性盈亏平衡的分析[J].重庆大学学报,2003,26(4)：152-154.
[70]牛建高,李义超,动态盈亏平衡分析方法及其在企业投资决策中的应用[J].2004,27(4)：399-403.
[71]章晓霞,谈项目投资决策中的现值盈亏平衡分析法[J].财会月刊.2006,(3)：75.
[72]王军,李英慧,动态盈亏平衡分析[J].辽宁石油化工大学学报,2005,25(4)：94-97.
[73]许弘.本量利分析方法改造浅析[J].经济研究导刊,2009,(17)：74-75.
[74]陈金龙.实物期权定价理论与方法研究[D].天津：天津大学博士论文,2003.
[75]Enric O. Pennings, Onno Lint, Marketentry. Phased Rollout or Abandonment A Real Option Approach[J].European Journal of Operational Research,2002,124:125-138.
[76]李洪江,曲晓飞,冯敬海.阶段性投资最优比例问题的实物期权方法[J].管理工程学报,2003,6(1)：20-26.
[77]何启志,何建敏,马立成.基于利率期限结构和博弈论的R&D投资决策分析[J].管理学报,2007,4(5)：580-583.
[78]何启志,何建敏.无风险利率和折现率变化时的R&D投资实物期权方法[J].东南大学学报(英文版),2008,24(1)：119-123.
[79]刘照云.基于实物期权的房屋拆迁价格评估研究.[D].长沙：中南大学硕士学位论文,2009.
[80]张津源.基于实物期权理论的企业并购价值的研究.[D].天津：天津商业大学硕士学位论文,2010.
[81]周荣喜,车君.基于利率期限结构模型的净现值公式[J].北京化工大学学报(自然科学版),2010,37(1)：130-134.
[82]于艳萍,钱争鸣.投资项目现金流量估计和风险度量研究[J].厦门大学学报(哲学社会科学版),2002,(4)：38-43.
[83]周荣喜,张汉鹏.项目管理数量方法[M].北京：化学工业出版社,2010：28-50.
[2]McCulloch, J. Huston. Measuring the term structure of interest rates[J]. Journal of Business, 1971,44:19-31.
[3]McCulloch J H. The tax-adjusted yield curve[J]. Journal of Finance,1975,30:811-830.
[4]Nelson C, Siegel, A. Parsimonious modelling of yield curves[J]. Journal of Business,1987, 60(4):473-489.
[5]Svensson, L.E.O. Estimating and Interpreting Forward Interest Rates:Sweden 1992-1994[R]. International Monetary Fund Working Papers,1994,94-114.
[6]Svensson,L.E.O. Estimating Forward Interest Rates with the Extended Nelson&Siegel Method[J].Sveriges Riksbank Quarterly Review,1995(3):13-26.
[7]Ioannides Michalis. A comparison of yield curve estimation techniques using UK data[J].Journal of Banking & Finance,2003,27:1-26.
[8]Allen D.E., Thomas L.C., Zheng, H. Stripping coupons with linear programming[J]. Journal of Fixed Income,2000,10(2):80-87.
[9]Vasicek O.A. An equilibrium characterization of the term structure[J].Journal of Financial Economics,1977,5(2):177-188.
[10]Cox J.C., Ingersoll J.E., Ross S.A. A theory of the term structure of interest rates[J]. Econometrica,1985,53(2):385-407.
[11]Ho,T.S.Y., Lee,S.B. Term Structure Movements and Pricing Interest Rate Contingent Claims [J]. Journal of Finance,1986,41(5):1011-1029.
[12]Hull J, White A. Pricing interest rate derivative securities[J].Review of Financial Studies,1990,3(4):573-592.
[13]Heath, D., Jarrow, R., Morton, A. Bond Pricing and the Term Structure of Interest Rate:A New Methodology for Contingent Claim Valuations[J]. Econometrica,1992,60:77-105.
[14]Kennedy, D.P. The Term Structure of Interest Rates as a Gaussian Random Field[J]. Mathematical Finance,1994,4:247-258.
[15]Goldstein, R.S. The Term Structure of Interest Rates as a Random Field[J]. Review of Financial Studies,2000, (5):365-384.
[16]Duffie, D., Kan, R. A Yield-Factor Model of Interest Rates[J]. Mathematical Finance,1996, 6:376-406.
[17]Dai, Q., Singleton, K.J. Specification Analysis of Affine Term Structure Models[J]. Journal of Finance,2000,55(5):1943-1978.
[18]Damir F. A General Characterization of One Factor Affine Term Structure Models[J]. Finance Stochastic,2001, (5):389-412.
[19]Duffee, G.R. Term Premia and Interest Rate Forecasts in Affine Models[J]. The Journal of Finance,2002,57:405-443.
[20]Duffie, D., Filipovinc, D., Schachermayer, W. Affine Processes and Applications in Finance[J]. Annals of Applied Probability,2003,13:984-1053.
[21]Ang,A., Piazzesi,M. And Wei,M. What Does the Yield Curve Tell us About GDP Growth[M].manuscript, Columbia University and UCLA,2003.
[22]Sergei, L. Consistency Conditions for Affine Term Structure Models[J].Stochastic Processes and Their Applications,2004,(109):225-261.
[23]范龙振,张国庆.仿射模型、广义仿射模型与上交所利率期限结构[J].管理工程学报,2005,19(3)：97-101.
[24]陈盛业,陈宁,王义克.银行间国债利率期限结构的三因子仿射模型[J].运筹与管理,2006,1 5(6)：87-90.
[25]Stefano, D.A., Axel, H. K. International Stock-Bond Correlations in a Simple Affine Asset Pricing Model[J]. Journal of Banking and Finance,2006,30:2747-2765.
[26]Patrick, C., Damir, F., Kimmel, R.L. Market Price of Risk Specifications for Affine Models: Theory and Evidence[J]. Journal of Financial Economics,2007,83:123-170.
[27]Ruslan Bikbov, Mikhail Chernov. Unspanned Stochastic Volatility in Affine Models:Evidence from Eurodollar Futures and Options [J]. Management Science,2009,55(8):1292-1305.
[28]陈雯,陈浪南.国债利率期限结构：建模与实证[J].世界经济,2000,8：24-28.
[29]李仲飞,汪寿阳,邓小铁.摩擦市场的利率期限结构的无套利分析[J].系统科学与数学,2002,7：285-295.
[30]周建新,于鸿福,张千云.以线性规划法估计台湾公债市场利率期限结构之实证研究[J].管理科学研究,2003,1(1)：31-47.
[31]周荣喜,邱菀华.基于多项式样条函数的利率期限结构模型实证比较[J].系统工程,2004,22(6)：39-43.
[32]唐革榕.我国利率期限结构的静态拟合实证研究.[D].厦门：厦门大学博士学位论文,2006.
[33]林海,郑振龙,利率期限结构研究述评[J].管理科学学报,2007,10(1)：79-98.
[34]孙甜.利率期限结构理论的最新研究述评[J].统计与决策,2009,4：159-161.
[35]邓飞琼.利率期限结构理论与研究方法综述[J].现代商业,2010,29：159-161.
[36]白小莹,杨丰梅,周荣喜.基于线性规划和多项式样条函数的利率期限结构模型[J].运筹与管理,2009,18(2)：30-34.
[37]张景,石琳,李妍.基于插值函数的利率期限结构分析[J].兰州大学学报(自然科学版),2010,46：2020-208.
[38]董皓舒.基于智能神经网络组合预测的国债利率期限结构建模与实证[J].中国市场, 2010,44：47-49.
[39]宋巍.我国国债利率期限结构的实证分析[J].商业时代,2010,295：5-56.
[40]周子康,王宁,杨衡.中国国债利率期限结构模型研究与实证分析[J].金融研究,2008,(3)：131-150.
[41]白小莹,周荣喜,杨丰梅.基于遗传算法的多项式样条函数利率期限结构模型[J].系统工程,2009,27(7)：22-27.
[42]石峰,秦磊.中国债券市场动态利率模型及其实证检验[J].运筹与管理,2010,19(5)：135-148.
[43]周荣喜,刘雯宇,牛伟宁.基于SV参数利率期限结构模型的国债信用价差研究[J].北京化工大学学报(自然科学版),2011,38(3)：129-133.
[44]Bichler, Shimshon; Nitzan, Jonathan.Systemic Fear, Modern Finance and the Future of Capitalism[J]. Jerusalem and Montreal,2010,7:8-11.
[45]Karl Claxton, Mike Paulden, Hugh Gravelle, Werner Brouwer, Anthony J. Culyer.Discounting and decision making in the economic evaluation of health-care technologies [J].Health Economics,2011,12(1):2-15.
[46]George Saravacos, Zacharias Maroulis. Food Process Economics[J]. Food Engineering Interfaces,2011,1:219-236.
[47]Mohammad A. Ammar. Optimization of Project Time-Cost Trade-Off Problem with Discounted Cash Flows[J]. Construction Engineering and Management,2011,137(1):65-72.
[48]吴联生.评内含报酬率求解数学模型[J].会计研究,1996.12：36-38.
[49]李苹莉,王斌.净现值法和内含报酬率法的比较分析及理性选择[J].会计研究,1996.12：38-40.
[50]吕长江.净现值法与内含报酬率法冲突的协调[J].数量经济技术经济研究,1998,15(4)：51-53.
[51]李心愉.净现值法和内部收益率法的比较法分析[J].数量经济技术经济研究,1998,15(12)：31-33.
[52]陶亚文,余波.贴现原理的再认识—对净现值和内含报酬率理性选择的新思考[J].会计研究,1998.12：29-34.
[53]张信东.调整净现值法和内含报酬率法的冲突方法探析[J].南开管理评论,1999,2(6)：29-33.
[54]Sugata Roychowdhury. Discussion of:Acquisition profitability and timely loss recognition by J. Francis and X. Martin[J]. Accounting and Economics,2010,49(1-2):179-183.
[55]王玉春.关于净现值的计算模型及概念的修正[J].财贸研究,1999,(6)：48-49.
[56]郭树声.净现值指数法在方案选择中的错误和危害[J].数量经济技术经济研究,2005,22(9)：91-95.
[57]许仁青.对净现值法中折现率的一点思考[J].经济问题探索,2003,(5)：107-108.
[58]陶菊春.风险性投资决策的一种分析方法[J].数量经济技术经济研究,1993,10(11)：52-55.
[59]邓敏.一种新的财务评价指标：基于可靠性分析的净现值法的改进[J].当代财经,2001,(6)：69-70.
[60]罗福周,孔凡楼.带投资风险度的随机净现值分析方法[J].西安建筑科技大学学报(自然科学版),2006,38(3)：441-444.
[61]王岩,蔡小军,净现值指标的进一步分析及其修正算法研究[J].数量经济技术经济研究,2004,21(12)：70-75.
[62]Hazen, G. B. A new perspective on multiple internal rates of return[J].Engrg. Economist 2003,48(1)31-51.
[63]Hazen, G. B. An Extension of the Internal Rate of Return to Stochastic Cash Flows[J]. Mangement Science,2009,55(6):1030-1034.
[64]Christian Gollier. Expected net present value, expected net future value, and the Ramsey rule[J]. Environmental Economics and Management,2010,59(2):142-148.
[65]徐增标,郑垂勇,刘卫国,动态盈亏平衡分析在商业银行网点建设中的应用[J].金融理论与实践,2008,(6)：62-64.
[66]Laura K. James, Scott M. Swinton, and Kurt D. Thelen. Profitability Analysis of Cellulosic Energy Crops Compared with Corn[J]. Agronomy Journal,2010,102(2):675-687.
[67]John E. Murdock,Ceib Phillips,Richard Beane,Rocio Quinonez.Break-even analysis of Medicaid vs fee for service in orthodontic practice [J]. Orthodontics & Dentofacial Orthopedics.2010,137 (3):334-339.
[68]Michael E. Chernew, Iver A. Juster, Mayur Shah, Evidence That Value-Based Insurance Can Be Effective[J]. Health Affairs,2011,30(1):109-117.
[69]饶莉,关于二次型非线性盈亏平衡的分析[J].重庆大学学报,2003,26(4)：152-154.
[70]牛建高,李义超,动态盈亏平衡分析方法及其在企业投资决策中的应用[J].2004,27(4)：399-403.
[71]章晓霞,谈项目投资决策中的现值盈亏平衡分析法[J].财会月刊.2006,(3)：75.
[72]王军,李英慧,动态盈亏平衡分析[J].辽宁石油化工大学学报,2005,25(4)：94-97.
[73]许弘.本量利分析方法改造浅析[J].经济研究导刊,2009,(17)：74-75.
[74]陈金龙.实物期权定价理论与方法研究[D].天津：天津大学博士论文,2003.
[75]Enric O. Pennings, Onno Lint, Marketentry. Phased Rollout or Abandonment A Real Option Approach[J].European Journal of Operational Research,2002,124:125-138.
[76]李洪江,曲晓飞,冯敬海.阶段性投资最优比例问题的实物期权方法[J].管理工程学报,2003,6(1)：20-26.
[77]何启志,何建敏,马立成.基于利率期限结构和博弈论的R&D投资决策分析[J].管理学报,2007,4(5)：580-583.
[78]何启志,何建敏.无风险利率和折现率变化时的R&D投资实物期权方法[J].东南大学学报(英文版),2008,24(1)：119-123.
[79]刘照云.基于实物期权的房屋拆迁价格评估研究.[D].长沙：中南大学硕士学位论文,2009.
[80]张津源.基于实物期权理论的企业并购价值的研究.[D].天津：天津商业大学硕士学位论文,2010.
[81]周荣喜,车君.基于利率期限结构模型的净现值公式[J].北京化工大学学报(自然科学版),2010,37(1)：130-134.
[82]于艳萍,钱争鸣.投资项目现金流量估计和风险度量研究[J].厦门大学学报(哲学社会科学版),2002,(4)：38-43.
[83]周荣喜,张汉鹏.项目管理数量方法[M].北京：化学工业出版社,2010：28-50.