简单投资中财务收支平衡点的性质

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英文标题：
《Properties of the financial break-even point in a simple investment
  project as a function of the discount rate》
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作者：
Domingo A. Tarzia
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最新提交年份：
2016
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英文摘要：
  We consider a simple investment project with the following parameters: I>0: Initial investment which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0: Price of the product with p>Cv; Cf>0: Annual fixed costs; te: Tax of earnings; r: Annual discount rate. We also assume inflation is negligible. We derive a closed expression of the financial break-even point Qf (i.e. the value of Q for which the net present value (NPV) is zero) as a function of the parameters I, n, Cv, Cf, te, r, p. We study the behavior of Qf as a function of the discount rate r and we prove that: (i) For r negligible Qf equals the accounting break-even point Qc (i.e. the earnings before taxes (EBT) is null) ; (ii) When r is large the graph of the function Qf=Qf(r) has an asymptotic straight line with positive slope. Moreover, Qf(r) is an strictly increasing and convex function of the variable r; (iii) From a sensitivity analysis we conclude that, while the influence of p and Cv on Qf is strong, the influence of Cf on Qf is weak.
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中文摘要：
我们考虑一个具有以下参数的简单投资项目：I>0：初始投资，可在n年内摊销；n： 投资允许年产量不变的生产年数；A> 0：年摊销（A=识别号）；Q> 0：每年销售的产品数量；Cv>0：单位可变成本；p> 0：p>Cv的产品价格；Cf>0：年度固定成本；te：收益税；r： 年贴现率。我们还假设通货膨胀可以忽略不计。我们推导了财务盈亏平衡点Qf（即净现值（NPV）为零的Q值）的闭合表达式，作为参数i、n、Cv、Cf、te、r、p的函数。我们研究了Qf作为贴现率r函数的行为，并证明：（i）对于r，可忽略Qf等于会计盈亏平衡点Qc（即税前收益（EBT）为零）；（ii）当r较大时，函数Qf=Qf（r）的图有一条具有正斜率的渐近直线。此外，Qf（r）是变量r的严格增凸函数；（iii）通过敏感性分析，我们得出结论，虽然p和Cv对Qf的影响很强，但Cf对Qf的影响很弱。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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关键词：收支平衡 平衡点 Quantitative amortization Applications