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Junqi · 2020年02月23日

问一道题: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

这道题可以把每一期的现金流列出来然后算出NPV再做差么?

那每一期的现金流改变前后是多少呢?能否示范一下。


还有关于折旧下降引起的现金流变化麻烦也解释一下,谢谢

3 个答案
已采纳答案

Debrah_品职答疑助手 · 2020年03月19日

更正一下此前的答案:

变化前后的OCF:

(1)变化前的OCF:

第1-5年OCF=(S-C)*(1-T)+D*T=(1.5-(-0.5))*(1-25%)+20/5*25%=2.5

第6-10年OCF=(S-C)*(1-T)+D*T=(1.5-(-0.5))*(1-25%)+0=1.5

计算出来变化前的NPV=-9.20

(2)变化后的OCF:

第1-5年OCF=(S-C)*(1-T)+D*T=(1.5-(-0.5))*(1-25%)+(20-2)/5*25%=2.4

第6-10年OCF=(S-C)*(1-T)+D*T=(1.5-(-0.5))*(1-25%)+0=1.5

计算变化后的NPV=-7.58

△NPV=1.62

可见固定资产投资下降$2 million,对6-10年的OCF和期末的现金流是没有影响的,因为折旧只有5年,与仅计算变化部分的结果是一样的。

Hugo(Xie Lanzhi) · 2021年03月07日

c是成本,不是应该直接减去吗?为啥c还要加个负号呢?

Debrah_品职答疑助手 · 2021年03月07日

嗨,从没放弃的小努力你好:


Hugo同学,根据题目, It will generate additional annual revenues of $1.5 million and reduce annual cash operating expenses of $0.5 million,revenue增加所以是正值,cost 降低所以是-0.5.

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

Debrah_品职答疑助手 · 2020年02月24日

同学你好!

最快速的做法是仅计算变化部分:

①期初:固定资产投资从-20,变为-18,△=+2,即CF0=2

②期间:折旧抵税部分从20/5*25%=1变为18/5*25%=0.9,△=-0.1,即CF(1-5年)=-0.1

③期末:无现金流变化。

这样按计算器,CF0=2,ENTER,↓,C01=-0.1,ENTER,↓,F01=5,NPV,I=10,ENTER,↓,CPT,NPV=1.62

如果做差的方式,

(1)变化前:

①期初:Initial Outlay=-20-5=-25

②期间:OCF=(S-C)*(1-T)+D*T=(1.5-(-0.5))*(1-25%)+20/5*25%=2.5

③期末:TNOCF=WC+Sal-(Sal-B)*T=5+3-(3-0)*25%=7.25

NPV=-15.52

(2)变化后:

①期初:Initial Outlay=-(20-2)-5=-23

②期间:OCF=(S-C)*(1-T)+D*T=(1.5-(-0.5))*(1-25%)+(20-2)/5*25%=2.4

③期末:TNOCF=WC+Sal-(Sal-B)*T=5+3-(3-0)*25%=7.25

NPV=-13.90

△NPV=1.62

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