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金融知识学习笔记(二)——FV PV NPV IRR等等概念

(2011-04-13 15:40:35)
标签:

杂谈

1.FV(未来值)
未来价值(FV)是现在一项投资在支付复利的投资产品上未来能得到的价值。未来价值也被
称为复合价值,就是一个计算复利的简单例子。
data:image/png;base64,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PV NPV IRR等等概念" />
在这个公式中,
PV=今天投资的资金数额(即the present value)
1/Y=每一个计复利期间的回报率(rate of return per compounding period)
N = 总共的计复利的期数(total number of compounding periods)

2.PV(现值)
单笔货币的现在价值,是将来一个时间点将要得到的一笔现金流的现在价值。换句话说,
就是计算在给定的回报率(rate of return)下,为了在将来得到一个确定的价值FV,现在
需要投资的金额。
data:image/png;base64,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PV NPV IRR等等概念" />
计算PV 的过程是折现(discounting,即将未来价值折现到现在价值)。
在折现过程中用到的利率通常称为折现率(discount rate),也称为机会成本(opportunity
cost),要求的回报率(required rate of return),或者资本的成本(cost of capital)。
不管怎么命名,都表示一项投资上面可以取得的,按年计复利的回报率(annual compound
rate of return)

3.NPV(净现值)
一个投资项目的净现值(NPV),是这个项目带来的预期现金流流入(expected cash
inflows)的现在价值,减去该项目预期现金流流出(expected cash outflows)的现在价值。
所有的现金流都按照一个合适的资本成本(appropriate cost of capital)折现。
data:image/png;base64,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PV NPV IRR等等概念" />
CFt = t 时刻预期的净现金流(the expected net cash flow at time t)
N =该项投资的预期时间长度(the estimated life of the investment)
r =折现率/机会成本(discount rate=opportunity cost)
注:NPV 其实就是后面年度的现金流的现在价值,减去初始的现金流支出。

4.IRR(内部回报率)
在该回报率下,一项投资的所有的
期望现金流入的现值,与该投资所有的期望现金流出的现值相同。即在该回报率下,这个投
资的净现值(NPV)为0
data:image/png;base64,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PV NPV IRR等等概念" />
初始的现金流CF0,表示一个投资机会的初始现金投入,因此是一个负数。所以,任何的比IRR 大的折现率下,得到的NPV 都是负数。当折现率为IRR 时,这个投资的净现值(NPV)为0

5.投资决策规则
NPV 决策规则总结如下:
  • 如果一个项目有正的 NPV,就应该投资这个项目。正的NPV 的项目将会增加股东价值。
  • 如果一个项目有负的 NPV,就不应该投资这个项目。负的NPV 的项目将会减小股东价值。

IRR 决策规则总结如下:
  • 如果一个项目的 IRR,大于公司(投资者)要求的回报率,应该投资于这个项目
  • 如果一个项目的 IRR,小于公司(投资者)要求的回报率,不应该投资于这个项目
注:,对于一个单一的项目,NPV 与IRR 规则得到的决策结果(投资/不投资于该项目)是一
致的。如果一个项目的IRR,大于公司(投资者)要求的回报率,NPV 一定是正数;如果一
个项目的IRR,小于公司(投资者)要求的回报率,NPV 一定是负数。

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