关于公式使用

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：

17.60%

15.73%

14.67%

解释：

C is correct.

考点：Capital Structure Theory: with tax

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

V_L = V_U + T*D = 3.5 + 30%*2 = $4.1 million

E = V_L –D = 4.1 – 2 = $2.1 million

根据公式 $r_e=r_0+(r_0-r_d)\ast(1-T)\ast\frac DE$

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

这道题是要把Proposal1和2的公式结合起来用吗两个proposal不是相互独立吗？

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1 个答案

王琛_品职助教 · 2021年07月17日

嗨，从没放弃的小努力你好：

是有题目要结合两个 proposal 的公式的

比如这道题，写出 re 的公式很简单，但是会发现公式中的 E 题干并没有告诉我们，所以需要通过 Vu 和 Vl 的钩稽关系倒推出来

也请参考：https://class.pzacademy.com/qa/57937

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加油吧，让我们一起遇见更好的自己！

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NO.PZ2018101501000067 Company M now is all equity-financeanthe cost of capitis 12%. EBIT of Company M is $0.6 million. Management is consiring changing the capitstructure so they intento issue 2 million new to repurchase outstanng shares. The trate is 30% anthe before-tcost of is 8%. What’s the cost of equity after changing the capitstructure accorng to the MM`s proposition with tax? 17.60% 15.73% 14.67% C is correct. 考点CapitStructure Theory: with t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\%}VU=r0EBIT(1−T)=12%0.6∗(1−30%) = $3.5 million VL = VU + T*= 3.5 + 30%*2 = $4.1 million E = VL –= 4.1 – 2 = $2.1 million 根据公式 re=r0+(r0−r∗(1−T)∗r_e=r_0+(r_0-r_\ast(1-T)\ast\frre=r0+(r0−r)∗(1−T)∗E = 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？

2021-05-26 13:51 1 · 回答

Company M now is all equity-financeanthe cost of capitis 12%. EBIT of Company M is $0.6 million. Management is consiring changing the capitstructure so they intento issue 2 million new to repurchase outstanng shares. The trate is 30% anthe before-tcost of is 8%. What’s the cost of equity after changing the capitstructure accorng to the MM`s proposition with tax? 17.60% 15.73% 14.67% C is correct. 考点CapitStructure Theory: with t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\%}VU=r0EBIT(1−T)=12%0.6∗(1−30%) = $3.5 million VL = VU + T*= 3.5 + 30%*2 = $4.1 million E = VL –= 4.1 – 2 = $2.1 million 根据公式 re=r0+(r0−r∗(1−T)∗r_e=r_0+(r_0-r_\ast(1-T)\ast\frre=r0+(r0−r)∗(1−T)∗E = 12% + (12% -8%) * (1-30%) * (2/2.1) = 14.67% 老师，如果已知中没有repurchase outstanng shares这个条件，对计算过程有影响吗？

2020-09-15 14:36 1 · 回答

Company M now is all equity-financeanthe cost of capitis 12%. EBIT of Company M is $0.6 million. Management is consiring changing the capitstructure so they intento issue 2 million new to repurchase outstanng shares. The trate is 30% anthe before-tcost of is 8%. What’s the cost of equity after changing the capitstructure accorng to the MM`s proposition with tax? 17.60% 15.73% 14.67% C is correct. 考点CapitStructure Theory: with t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\%}VU=r0EBIT(1−T)=12%0.6∗(1−30%) = $3.5 million VL = VU + T*= 3.5 + 30%*2 = $4.1 million E = VL –= 4.1 – 2 = $2.1 million 根据公式 re=r0+(r0−r∗(1−T)∗r_e=r_0+(r_0-r_\ast(1-T)\ast\frre=r0+(r0−r)∗(1−T)∗E = 12% + (12% -8%) * (1-30%) * (2/2.1) = 14.67% 如果8%是after tcost of bt，该如何做？是要先用8%除以1-t，求出税前bt成本再带入公式么？

2020-02-17 21:49 1 · 回答

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2019-03-21 19:50 1 · 回答

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