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johnny · 2021年08月01日

答案最后那个公式是怎么来的?

NO.PZ2018101501000031

问题如下:

Company M has invested $20 million in fixed capital and another $5 million in working capital in a ten-year project. The equipment will be depreciated straight-line to zero over five years. It will generate additional annual revenues of $1.5 million and reduce annual cash operating expenses of $0.5 million. After ten years, the equipment will be sold for $3 million. The tax rate and the required rate of return are 25% and 10% respectively. However, after reappraising the project, the fixed capital investment will be adjusted downward by $2 million with no change in salvage value. What will happen on the project NPV?

选项:

A.

It will increase $2.38 million.

B.

It will decrease $1.62 million.

C.

It will increase $1.62 million.

解释:

C is correct.

考点:Cash Flow Projections: Expansion Project

解析固定资产投资下降$2 million,折旧会下降$0.4 million,相对应的depreciation tax saving会下降 0.25*($2 million/5) = $0.1 million

所以NPV最终会增加2 - t=150.11.1t\sum_{t=1}^5\frac{0.1}{1.1^t} = $1.62 million

答案最后那个公式是从哪儿来的?

难道不是把变化前变化后的npv都算出来然后相减吗

1 个答案
已采纳答案

王琛_品职助教 · 2021年08月02日

嗨,努力学习的PZer你好:


1

这道题有两种解题思路

第一种是像同学分析的,分别算出变化前后的 NPV,然后做差。但是这个思路有个缺点,就是计算量过大

2

第二种是只考虑对 NPV 有变化的因素。题干说期初的固定资产投入减少了,所以这个变量的变化,会影响 NPV 计算过程中的两个地方

第一个地方就是 Initial Outlay 中的固定资产投入 FCInv

第二个地方就是折旧,间接影响了期间现金流 OCF,因为 OCF=(S-C)(1-T)+D*T

第二种思路,要求我们对 NPV 的计算过程有更深入的了解,这样仅通过分析有影响的变量的变化,可以又快速又简单的得到答案

3

两种思路,分别的计算过程,请参考:https://class.pzacademy.com/qa/50168

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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