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ZAA · 2021年04月08日

能写一下计算步骤吗没算对

  1. CFA II
  2. Corporate Issuers

NO.PZ2018101501000021

问题如下：

Company M is investing an equipment of $1 million, which may enable the company to earn a 12% internal rate of return. The equipment will generate operating income after taxes of $150,000 and depreciation of $95,000 annually for the coming four years. The equipment will be sold at the end of the fourth year. The company is in the 25% tax bracket. What`s the terminal selling price?

选项：

A.

$483,273

B.

$452,325

C.

$330,112

解释：

C is correct.

考点：Cash Flow Projections: Expansion Project

解析：CF = (S – C – D)(1 – T) + D = EBIT*(1-T) + D = 150,000+95,000 = $245,000

账面价值BV4 = 1,000,000 – 95000*4 = $620,000

TNOCF = Sal4 +NWCInv−T(Sal4 – B4 ) = Sal4 - 0.25*( Sal4-620,000)

NPV=−1,000,000+∑t=14245,0001.12t+Sal4−0.25×(Sal4−620,000)1.124NPV=-1,000,000+\sum_{t=1}^4\frac{245,000}{1.12^t}+\frac{{Sal_4}-0.25\times{({Sal_4}-620,000)}}{1.12^4}

计算求得Sal4 =$330,112

我看明白答案乐，但是到了最后一步骤

NPV=那步骤，怎么用计算器求解

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1 个答案

王琛_品职助教 · 2021年04月09日

嗨，爱思考的PZer你好：


这道题有两种做法


1) 先说解析的做法，接着最后的公式计算

- 计算前四年 OCF (245000) 的净现值为 -255849.4101，计算器按法

- 清零

- CF0 = -1000000，

- C01 = 245000

- F01 = 4 (t=1 至 t=4 时刻)

- I = 12

- NPV = -255849.4101


- 即 [Sal - 0.25 x (Sal - 620000)]/(1.12^4) = 255849.4101

- Sal - 0.25 x (Sal - 620000) = 402584

- 0.75 Sal + 155000 = 402584

- 0.75 Sal = 247584

- Sal = 330112


2) 再说简便方法，因为这道题是计算题，选项 B 是三个选项的中间数（选项 A 最大，选项 C 最小）

- 思路：所以把选项 B 代入公式，如果算出来的 NPV 大于 0，说明代入的数据大了，就选 C；如果算出来的 NPV 小于 0，说明代入的数据小了，就选 A

- 计算：代入选项 B，则期末总的现金流 Total net CF = 452,325 - (452,325 - 620000) x 0.25 + 245000 = 655406.25

- 计算 NPV，计算器按法

- 清零

- CF0 = -1000000，

- C01 = 245000

- F01 = 3 (t=1 至 t=3 时刻)

- C02 = 655406.25

- F02 = 1 (t=4 时刻) 

- I = 12

- NPV = 4971.181289

- NPV 大于 0，说明代入的 Sal 数据大了，应该选更小的数，所以选 C

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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