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Olivia · 2022年08月09日

EBIT(1-T) + D = (S-C)(1-T) + DxT,只有D变小了,为何NPV不是decrease而是increase呢?

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

EBIT(1-T) + D = (S-C)(1-T) + DxT,只有D变小了,所以用来discount的cash flow变小了,为何NPV不是decrease而是increase呢?

1 个答案

王琛_品职助教 · 2022年08月10日

嗨,努力学习的PZer你好:


如果仅仅考虑折旧对期间现金流的影响,同学的分析是正确的

可是题目的背景是期初的固定资产减少了,所以这个变量的变化,会影响 NPV 计算过程中的地方有「两」个

不只是折旧对期间现金流的影响;还有 Initial Outlay 中的固定资产投入 FCInv,即解析最后一行公式中的 +2

也请参考:https://class.pzacademy.com/qa/81796

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