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大太阳 · 2021年05月26日

老师这个思路有什么错吗？

  1. CFA II
  2. Corporate Issuers

NO.PZ2018101501000067

问题如下：

Company M now is all equity-financed and the cost of capital is 12%. EBIT of Company M is $0.6 million. Management is considering changing the capital structure so they intend to issue 2 million new debt to repurchase outstanding shares. The tax rate is 30% and the before-tax cost of debt is 8%. What’s the cost of equity after changing the capital structure according to the MM`s proposition with tax?

选项：

A.

17.60%

B.

15.73%

C.

14.67%

解释：

C is correct.

考点：Capital Structure Theory: with tax

解析：VU=EBIT(1−T)r0=0.6∗(1−30%)12%V_U=\frac{EBIT(1-T)}{r_0}=\frac{0.6\ast(1-30\%)}{12\%} = $3.5 million

VL = VU + T*D = 3.5 + 30%*2 = $4.1 million

E = VL –D = 4.1 – 2 = $2.1 million

根据公式re=r0+(r0−rd)∗(1−T)∗DEr_e=r_0+(r_0-r_d)\ast(1-T)\ast\frac DE

                = 12% + (12% -8%) * (1-30%) * (2/2.1) = 14.67%

在原来全投资的情况下Equity=0.6/12%=5, 债券回购股票2million，这样Equity就是3million，而不是答案的2.1million，想知道思路哪里错了？

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1 个答案

王琛_品职助教 · 2021年05月26日

嗨，努力学习的PZer你好：


同学的思路中，有两个地方错了哈

1）在原来全投资假设时，Vu，即 Equity 的价值，并不是同学计算的 5，而是解析中的 3.5。同学使用的计算公式中，分子要乘以税率的。虽然没有债务，但是有税。

2）同学后半部分的思路，是想用计算出来的 3.5 m，直接减去发债回购的 2 m，得到 1.5 m.

但是还没完，因为对于股东来说，发债要交利息，而利息是税前列支，有税盾作用，相当于因为缴税而产生的好处是 DxT，即 2 x 0.3 = 0.6，所以最后，Equity 为 1.5 + 0.6 = 2.1

思路，也请参考：https://class.pzacademy.com/qa/61193

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

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2021-07-15 10:23 1 · 回答

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