一阶偏微分方程及Excel在工程经济敏感性分析中的应用

Application of Partial Differential Equation of First Order and Excel to the Sensitive Analysis in Engineering Economy

传统的IRR敏感性分析存在三个不足之处:计算量繁琐、间断取值以及不能预先判断影响投资项目经济效果的最主要因素。在诸因素变动幅度不大的条件下,将一阶偏微分方程及Excel电子表格结合起来应用于投资项目经济敏感性分析是一个较为理想的选择。为此,推出了一阶偏微分法和Excel求解IRR的原理及一般步骤:建立IRR的隐函数,对隐函数求导,根据偏导数得出相关参数的数学公式原理,利用Excel电子表格快速而准确地建立函数并计算出各个参数值,作出敏感性评价。实例分析表明,在给定的条件下,一阶偏微分法和Excel相结合不但能够圆满解决上述三个问题,而且能够同时解决单纯偏微分法中参数的复杂计算问题。

The traditional IRR sensitivity analysis has three disadvantages： too much calculation, discontinuity of dereferencing and it can＇ t prejudge the primary factor affecting the economic outcomes of investment projects. Within the limited range of all uncertain factors, it is a preferred way for us to replace it with the partial differential equation of first order and Excel. For this purpose, this paper introduces the general steps of solution using the partial differential of first order and Excel method： establishing the implicit function of IRR; solving the derivatives of complicit functions; educing the mathematical formulas principle of some related parameters; quickly and accurately establishing and working out the parameters with Excel; giving the evaluation of IRR sensitivity. Through an example analysis, it has been further shown that： not only the above three problems but also the complexity of computations of the parameters of the single partial differentiation method can be satisfactorily solved by the partial differential equation of first order and Excel.