能给出其具体的证明? 我现在手上有篇《关于内部收益率概念中隐含假定的辨析》，作者是武汉大学 商学院 孙续元。发表于武汉大学学报（人文社会科学版）2000年1月。因不会上传文件，还清大家搜一下，看看这篇文章有何不托之处？

没有这个假设。

六楼的朋友的回答有问题。在本质上，NPV方法与IRR方法是一致的，也就是说，ＮＰＶ与ＩＲＲ的评判结果是一致的，是一个方程等式的不同解释。

对于NPV、ＩＲＲ方法而言，其一个基本假设是现金流的符号只变化一次。根据柯西规则，符号变化一次，内部收益率就只有唯一解。如果现金流符号变化两次（即在项目运营期内出现再投资），那么就会出现两个解。在出现两个解的情况下，IRR判断准则就失去意义。

如何解决再投资现象，至少有一种方法来解决这个问题，即将每一次投资视为一个单独的项目，采用复合项目的方法来分析，并具体问题具体分析。

建议读者看一看有关于工程经济学这方面的经典教材。现在的一些教材太简单，基本不讨论这些个问题，在1980年代、1990年代初讨论这个问题很多。

IRR是算PROJECT的，用所有的FUTURE CASH FLOW来算IRR。 IRR本身是个非常简单的MODEL，并不考虑再投资不再投资的问题，直接把一个PROJECT的所有EXPECTED CASH FLOW算就好了。再投资不再投资的问题，是涉及到 CORPORATE REAL OPTION的计算。当计算REAL OPTION的时候，连NPV都要从新算，更不要说IRR。

所以要看你说的IRR是考虑不考虑REAL OPTION的，不考虑的话，就不要想的太复杂了。如果你觉得再投资要考虑，那就是算REAL OPTION。这个已经超过普通的IRR计算了。

我自己都说糊涂了，反正就是 那个书上说的是最简单的IRR计算，前提假设是不考虑再投资。如果你认为应该考虑再投资，那当然不能用书上说的方法计算IRR。

The only thing your need to know is what the question is. The thing he asked is what the underlying assumption in this model not what the result is from these two methods. What you said is true but doesn't answer the question.

Here are some definitions from my previous papers.

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Define NPV and IRR.

· NPV: Net present value is a capital-budgeting concept defined as the present value of the project’s annual net cash flows less the project’s initial outlay. It can be obtained by discounting the all cash flows on the project, including the initial investment at the appropriate hurdle rate.

· Decision Rule: Accept if NPV > 0

· Preference: if a business has substantial funds on hand, access to capital, limited surplus value projects, and more certainty on its project cash flow, it is much more likely to use NPV

· IRR: Internal rate of return is a capital-budgeting technique that reflects the rete of return a project earns. This internal rate of return is the discount rate that sets the net present value equal to zero. The IRR rule assumes that intermediate cash flows on the project get reinvested at the IRR. The implication of this assumption is that the firm has an infinite stream of projects yielding similar IRR

· Decision Rule: Accept if IRR > hurdle rate

· Preference: if a business has limited access to capital, has a stream of surplus value projects and faces more uncertainty in its project cash flows, it is much more likely to use IRR.

Define MIRR

Modified internal rate of return (MIRR) is the rate of return which equates the initial investment with a project’s terminal value, where the terminal value is the future value of the cash inflows compounded at the required rate of return (the opportunity cost of capital).

Benefit:

It provides a measurement of project return in percentage.

It avoids the upward bias as it assumes that any cash flows from the project will be reinvested at cost of capital, which is more appropriate in real world.

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下面这两个是网上的信息. 你可以查查. 说得再清楚不过了.

Damodaran, http://pages.stern.nyu.edu/~adamodar/pdfiles/ovhds/ch5.pdf, P198

Reinhart: http://www.departments.bucknell.edu/management/apfa/Dundee%20Papers/37Reinhart.pdf, P3

建议读者看一看有关于工程经济学这方面的经典教材。现在的一些教材太简单，基本不讨论这些个问题，在1980年代、1990年代初讨论这个问题很多。

可以推荐几本教材么？