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wowo · 2024年11月08日

rWACC = CF(1 – t)/V这个公式在哪里提到的啊?

NO.PZ2023090507000002

问题如下:

A financial analyst is evaluating the capital structure for Plover, Inc., a European-based unleveraged firm with a constant (perpetual) cash flow of EUR10.0 million per year before taxes. The firm has a market value of EUR100.0 million and a corporate tax rate of 20%. Plover plans to issue EUR35.0 million in debt to retire an equivalent amount of equity, so the size of the firm will remain unchanged. The debt will have a cost of 4.5%. Assume the cost of financial distress is close to zero.

After the debt issuance and change in the capital structure, Plover’s WACC is closest to:

选项:

A.

5.47%.

B.

7.48%.

C.

8.82%.

解释:

B is correct. The calculations to determine the WACC are as follows:

The after-tax cash flows for the company are EUR10.0 million (1 – 0.20) = EUR8.0 million. Since the cash flows are assumed to be perpetual, WACC for the unlevered firm is calculated as

rWACC = CF(1 – t)/V = EUR8.0 million/EUR100.0 million = 8.0%.

The market value of Plover with the debt financing is EUR107 million:

VL = VU + tD = EUR100.0 million + 0.20(EUR35.0 million) = EUR107.0 million.

To find the cost of equity, we first need to find the market value of equity:

VL = D + E, where D and E are market values of debt and equity, respectively.

E = EUR107.0 million – EUR35.0 million = EUR72.0 million.

The cost of equity is given by

re = r0 + (r0 − rd)(1 − t)D/E

= 8.0% + (8.0% – 4.5%)(0.80)(EUR35.0 million/EUR72.0 million) = 9.36%.

Plover’s WACC is calculated as follows:

WACC = (Weighting of debt × Cost of debt) + (Weighting of equity × Cost of equity)

= (EUR35 million/EUR107.0 million)(4.5%)(1 – 0.2) + (EUR72.0 million/ EUR107.0 million)(9.36%) = 7.48%, which is lower than the 8.0% for the unlevered firm.

为什么是rWACC而不是r0,而且为什么要乘(1-t)?

2 个答案

Kiko_品职助教 · 2024年11月12日

嗨,爱思考的PZer你好:


是的。

是要无杠杆的情况下才成立得。这道题目我们求出来的rWACC8%也是在all equity的情况下的。题目中最开始说了,a European-based unleveraged firm with a constant (perpetual) cash flow of EUR10.0 million per year before taxes. 最开始这家公司是all equity的。后来是他要发债来赎回股权,所以资本结构改变了,在计算有债务融资后的股权成本的时候,r0是无杠杆公司的股权成本,也就是无杠杆公司的 WACC,前面计算为 8.0%。所以就有了解析的公式。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Kiko_品职助教 · 2024年11月11日

嗨,从没放弃的小努力你好:


这个公式在 MM 理论的部分老师上课讲的一道例题。即计算企业价值时,题目假设了是永续现金流(with a constant (perpetual) cash flow of EUR10.0 ……),所以可以使用现金流折现求现值,这道题因为告诉了税率,所以分子就使用税后现金流,即 CF(1-T),同时告诉了公司价值V,求wacc,代入公式rWACC = CF(1 – t)/V 即可。

请参考基础班讲义墨迹版 P339

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努力的时光都是限量版,加油!

wowo · 2024年11月12日

请问r0是等于rWACC吗所以才用这个公式?例题上的re=r0=rWACC不是只有在初始全equity的特殊情况才是吗

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