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Fannie. · 2024年04月18日

关于sensitivity analysis的定义

NO.PZ2018103102000118

问题如下：

Matt is conducting a FCFF sensitivity analysis for Company M`s value. The most recent FCFF of Company M is $100 million. Assuming the tax rate is 35% and a stable capital structure of 40% debt and 60% equity, the company`s value is least sensitive to:

选项：

A.

cost of equity

B.

growth rate

C.

after-tax cost of debt

解释：

C is correct.

考点：Sensitivity Analysis in FCFF and FCFE

解析：1. Cost of equity敏感性分析：保持r_d = 5.5%，g = 5.0%

当r_e = 8.0%时，WACC = 0.4*5.5% + 0.6*8.0% = 7%

$Firm\;Value=\frac{FCFF_0\times\left(1+g\right)}{WACC-g}=\frac{100\times\left(1+5\%\right)}{7\%-5\%}=5250$

当r_e = 12.0%时，WACC = 0.4*5.5% + 0.6*12.0% = 9.4%

$Firm\;Value=\frac{FCFF_0\times\left(1+g\right)}{WACC-g}=\frac{100\times\left(1+5\%\right)}{9.4\%-5\%}=2386.36$

Range = 5250 – 2386.36 = 2863.64

2. After-tax cost of debt敏感性分析：保持r_e = 10%，g = 5%

当r_d = 5.0%时，WACC = 0.4*5.0% + 0.6*10.0% = 8%

$Firm\;Value=\frac{FCFF_0\times\left(1+g\right)}{WACC-g}=\frac{100\times\left(1+5\%\right)}{8\%-5\%}=3500$

当r_d = 6.0%时，WACC = 0.4*6.0% + 0.6*10.0% = 8.4%

$Firm\;Value=\frac{FCFF_0\times\left(1+g\right)}{WACC-g}=\frac{100\times\left(1+5\%\right)}{8.4\%-5\%}=3088.24$

Range = 3500 – 3088.24 = 411.76

3. Growth rate敏感性分析：保持r_e = 10%，r_d = 5.5%

WACC = 0.4*5.5% + 0.6*10.0% = 8.2%

当g = 4%时,

$Firm\;Value=\frac{FCFF_0\times\left(1+g\right)}{WACC-g}=\frac{100\times\left(1+4\%\right)}{8.2\%-4\%}=2476.2$

当g = 6%时,

$Firm\;Value=\frac{FCFF_0\times\left(1+g\right)}{WACC-g}=\frac{100\times\left(1+6\%\right)}{8.2\%-6\%}=4818.2$

Range =4818.2 - 2476.2 = 2342

三者相比，敏感性最弱的是after-tax cost of debt。

印象中，sensitivity analysis是某个因素单位变化所引起的结果变化分析。这题中，三个因素的变化幅度不同，high和low的结果直接相减就OK吗？不用考虑每个因素的变化幅度？

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王园圆_品职助教 · 2024年04月18日

同学你好，不用的哦

这个题目本身的计算量已经超级大了，如果还要剔除每个变量的变化幅度的影响，这个计算难度就远超CFA考试范围了

其次，现实生活中的sensitivity analysis也不可能是按住每个变量变动幅度相同（即要求不同的变量变动幅度一致）来看最终结果的变化大小的

以下是网上助教搜到的sensitivity analysis 的一个样例，同学可以参考一下。由于横轴和纵轴的变量本身变动的底层逻辑就不同，横纵轴的变量的变动幅度是不可能一样的。

所以题目给的变量也没有是每个变量变化幅度一致,这是和现实应用高度一致的

SENSITIVITY ANALYSIS with Data Table in Excel | ExcelJunction.com - YouTube

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2023-08-15 01:25 1 · 回答

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2023-04-24 07:37 1 · 回答

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2023-01-27 17:09 3 · 回答

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2022-08-08 01:59 1 · 回答