{"title":"实物期权分析中利率不确定性的定量评估","authors":"L. Ballestra, G. Pacelli, Radi Davide","doi":"10.22495/CPR19A1","DOIUrl":null,"url":null,"abstract":"The discounting cash flow (DCF) technique is the most popular approach for valuing firms' projects. Basically, it consists of discounting the values of the forecasted future cash flows by some interest rate, for example the so-called weighted average cost of capital (WACC), or an Enterprise's rate of return (measured by the annual growth of the firm's total assets), or, eventually, a required (desired) rate of return. DCF calculations have been widely criticized since they do not fully consider uncertainty. In particular, when a firm decides to undertake a project, if it is a complex project with a long time horizon, future revenues and costs are not exactly known. Then, during the project lifetime, depending on the realized economic and financial scenarios, managers have the option of making changes to the project, or even of abandoning it. The DCF approach does not allow one to consider such an option, which is instead accounted for by the so-called real option analysis (ROA). Specifically, due to its flexibility to cope with future uncertainty, ROA has become a very usual procedure for valuing firms' strategic projects, see, for example, Amram and Kulatilaka (1999), Baldi and Trigeorgis (2009), Cobb and Charnes (1994), Copeland and Antikarov (2003), Dixit and “Corporate Governance: Search for the Advanced Practices” Rome, February 28, 2019 23 Pindyck (1994), McDonald and Siegel (1986), Mun (2006), Schulmerich (2010). The real option approach is almost always applied by considering flat interest rates. Nevertheless, if the time horizon of a firm’s project is long (say several years), assuming that the interest rate remains constant over all the project’s life does not seem very realistic. In particular, one could argue that, if the ROA is used in order to cope with unknown future scenarios, then the uncertainty of future interest rates should be taken into account as well. A ROA approach that also takes into account stochastic interest rates has been pursued by Schulmerich (2010). However, the effect of the interest rate on the projects’ evaluation is not completely explored. In this work, we discuss the effect of the uncertainty of future interest rates on real option valuation. In particular, we assume that the interest rate follows the Vasicek model: which may be regarded as the continuous version of the AR(1) time series: rt+1 = θ + α(rt − θ) + εt (1) (for a suitable value of α). Furthermore, the interest rate specification (1) is coupled with the common real option approach based on the famous Black-Scholes model (see Black and Scholes, 1973). By doing that it is possible to derive a simple analytical formula to evaluate firms’ projects. Then, the ROA model with stochastic interest rates can be tested against a simpler ROA model with constant interest rate. The results obtained, some of which are contained in Ballestra et al. (2017), will be discussed in the talk.","PeriodicalId":193680,"journal":{"name":"Corporate Governance: Search for the advanced practices","volume":"340 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A quantitative assessment of interest rate uncertainty in real option analysis\",\"authors\":\"L. Ballestra, G. Pacelli, Radi Davide\",\"doi\":\"10.22495/CPR19A1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The discounting cash flow (DCF) technique is the most popular approach for valuing firms' projects. Basically, it consists of discounting the values of the forecasted future cash flows by some interest rate, for example the so-called weighted average cost of capital (WACC), or an Enterprise's rate of return (measured by the annual growth of the firm's total assets), or, eventually, a required (desired) rate of return. DCF calculations have been widely criticized since they do not fully consider uncertainty. In particular, when a firm decides to undertake a project, if it is a complex project with a long time horizon, future revenues and costs are not exactly known. Then, during the project lifetime, depending on the realized economic and financial scenarios, managers have the option of making changes to the project, or even of abandoning it. The DCF approach does not allow one to consider such an option, which is instead accounted for by the so-called real option analysis (ROA). Specifically, due to its flexibility to cope with future uncertainty, ROA has become a very usual procedure for valuing firms' strategic projects, see, for example, Amram and Kulatilaka (1999), Baldi and Trigeorgis (2009), Cobb and Charnes (1994), Copeland and Antikarov (2003), Dixit and “Corporate Governance: Search for the Advanced Practices” Rome, February 28, 2019 23 Pindyck (1994), McDonald and Siegel (1986), Mun (2006), Schulmerich (2010). The real option approach is almost always applied by considering flat interest rates. Nevertheless, if the time horizon of a firm’s project is long (say several years), assuming that the interest rate remains constant over all the project’s life does not seem very realistic. In particular, one could argue that, if the ROA is used in order to cope with unknown future scenarios, then the uncertainty of future interest rates should be taken into account as well. A ROA approach that also takes into account stochastic interest rates has been pursued by Schulmerich (2010). However, the effect of the interest rate on the projects’ evaluation is not completely explored. In this work, we discuss the effect of the uncertainty of future interest rates on real option valuation. In particular, we assume that the interest rate follows the Vasicek model: which may be regarded as the continuous version of the AR(1) time series: rt+1 = θ + α(rt − θ) + εt (1) (for a suitable value of α). Furthermore, the interest rate specification (1) is coupled with the common real option approach based on the famous Black-Scholes model (see Black and Scholes, 1973). By doing that it is possible to derive a simple analytical formula to evaluate firms’ projects. Then, the ROA model with stochastic interest rates can be tested against a simpler ROA model with constant interest rate. The results obtained, some of which are contained in Ballestra et al. 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引用次数: 0
摘要
贴现现金流(DCF)技术是评估公司项目最流行的方法。基本上,它包括用某种利率对预测的未来现金流的价值进行贴现,例如所谓的加权平均资本成本(WACC),或者企业的回报率(由公司总资产的年增长率衡量),或者最终是所需的(期望的)回报率。DCF计算由于没有充分考虑不确定性而受到广泛批评。特别是,当一个公司决定承担一个项目时,如果它是一个复杂的项目,具有很长的时间跨度,未来的收入和成本是不确切知道的。然后,在项目生命周期中,根据已实现的经济和财务情况,管理人员可以选择对项目进行更改,甚至放弃它。DCF方法不允许人们考虑这样的期权,而是由所谓的实物期权分析(ROA)来解释。具体而言,由于其应对未来不确定性的灵活性,ROA已成为评估公司战略项目的一种非常常用的程序,例如,参见Amram和Kulatilaka (1999), Baldi和Trigeorgis (2009), Cobb和Charnes (1994), Copeland和Antikarov (2003), Dixit和“公司治理:寻找先进实践”罗马,2019年2月28日23 Pindyck (1994), McDonald和Siegel (1986), Mun (2006), Schulmerich(2010)。实物期权方法几乎总是通过考虑固定利率来应用。然而,如果公司项目的时间跨度很长(比如几年),假设利率在项目的整个生命周期中保持不变似乎不太现实。特别是,有人可能会争辩说,如果使用ROA是为了应对未知的未来情景,那么未来利率的不确定性也应该考虑在内。Schulmerich(2010)也采用了考虑随机利率的ROA方法。然而,利率对项目评价的影响并没有得到充分的探讨。在本研究中,我们讨论了未来利率的不确定性对实物期权估值的影响。特别地,我们假设利率遵循Vasicek模型:它可以看作是AR(1)时间序列的连续版本:rt+1 = θ + α(rt−θ) + εt(1)(对于合适的α值)。此外,利率规范(1)与基于著名的Black-Scholes模型(参见Black and Scholes, 1973)的常见实物期权方法相结合。这样就有可能推导出一个简单的分析公式来评估公司的项目。然后,将随机利率下的ROA模型与更简单的固定利率下的ROA模型进行比较。所获得的结果,其中一些包含在Ballestra et al.(2017)中,将在讲座中讨论。
A quantitative assessment of interest rate uncertainty in real option analysis
The discounting cash flow (DCF) technique is the most popular approach for valuing firms' projects. Basically, it consists of discounting the values of the forecasted future cash flows by some interest rate, for example the so-called weighted average cost of capital (WACC), or an Enterprise's rate of return (measured by the annual growth of the firm's total assets), or, eventually, a required (desired) rate of return. DCF calculations have been widely criticized since they do not fully consider uncertainty. In particular, when a firm decides to undertake a project, if it is a complex project with a long time horizon, future revenues and costs are not exactly known. Then, during the project lifetime, depending on the realized economic and financial scenarios, managers have the option of making changes to the project, or even of abandoning it. The DCF approach does not allow one to consider such an option, which is instead accounted for by the so-called real option analysis (ROA). Specifically, due to its flexibility to cope with future uncertainty, ROA has become a very usual procedure for valuing firms' strategic projects, see, for example, Amram and Kulatilaka (1999), Baldi and Trigeorgis (2009), Cobb and Charnes (1994), Copeland and Antikarov (2003), Dixit and “Corporate Governance: Search for the Advanced Practices” Rome, February 28, 2019 23 Pindyck (1994), McDonald and Siegel (1986), Mun (2006), Schulmerich (2010). The real option approach is almost always applied by considering flat interest rates. Nevertheless, if the time horizon of a firm’s project is long (say several years), assuming that the interest rate remains constant over all the project’s life does not seem very realistic. In particular, one could argue that, if the ROA is used in order to cope with unknown future scenarios, then the uncertainty of future interest rates should be taken into account as well. A ROA approach that also takes into account stochastic interest rates has been pursued by Schulmerich (2010). However, the effect of the interest rate on the projects’ evaluation is not completely explored. In this work, we discuss the effect of the uncertainty of future interest rates on real option valuation. In particular, we assume that the interest rate follows the Vasicek model: which may be regarded as the continuous version of the AR(1) time series: rt+1 = θ + α(rt − θ) + εt (1) (for a suitable value of α). Furthermore, the interest rate specification (1) is coupled with the common real option approach based on the famous Black-Scholes model (see Black and Scholes, 1973). By doing that it is possible to derive a simple analytical formula to evaluate firms’ projects. Then, the ROA model with stochastic interest rates can be tested against a simpler ROA model with constant interest rate. The results obtained, some of which are contained in Ballestra et al. (2017), will be discussed in the talk.