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🐚 · 2022年10月15日

rd怎么算出来的

NO.PZ2021091701000017

问题如下:

Happy Resorts Company currently has 1.2 million common shares of stock outstanding, and the stock has a beta of 2.2. It also has $10 million face value of bonds that have five years remaining to maturity and an 8% coupon with semiannual payments and are priced to yield 13.65%. If Happy issues up to $2.5 million of new bonds, the bonds will be priced at par and will have a yield of 13.65%; if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16%. Happy has learned that it can issue new common stock at $10 a share. The current risk-free rate of interest is 3%, and the expected market return is 10%. Happy’s marginal tax rate is 30%. If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio, its weighted average cost of capital will be closest to

选项:

A.

14.5%

B.

15.5%

C.

16.5%

解释:

B is correct. The capital structure is as follows:

Market value of debt: FV = $10,000,000, PMT = $400,000, N = 10, and I/YR = 6.825%. Solving for PV gives $7,999,688.

Market value of equity: 1.2 million shares outstanding at $10 = $12,000,000


To raise $7.5 million of new capital while maintaining the same capital structure, the company would issue $7.5 million × 40% = $3.0 million in bonds, which results in a before-tax rate of 16%.

rd(1 – t) = 0.16(1 – 0.3) = 0.112, or 11.2%.

re = 0.03 + 2.2(0.10 − 0.03) = 0.184, or 18.4%.

WACC = 0.40(0.112) + 0.6(0.184) = 0.0448 + 0.1104 = 0.1552, or 15.52%

rd为什么=0.16

2 个答案

王琛_品职助教 · 2023年06月12日

嗨,从没放弃的小努力你好:


@醉清风

老师,这个资本比例D/E=4/6是从哪里看出来的,谢谢 

1

D/E 比例,并不是案例背景直接告诉我们的,而是要分别计算 debt 和 equity 的 market value,然后再计算得出来的哈

同学可以先看一下解析中,对股债市场价值的计算过程,看是否能理解

如果有疑问,可以追问或者评论,我再回答同学的后续疑问哈

2

关于这道题的备考建议

一级的题目短小精干,考试不会遇到这种巨无霸式的题目的

我个人对这道题的备考建议是:因为计算量太大了,综合考查了资本成本的计算,至少可以拆成三道题目,相当于把几个知识点放到一起考查了

所以了解一下思路即可,关键是掌握几个知识点,比如用 YTM approach 计算税后债务成本,用 CAPM 计算股权成本,WACC 的公式等

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王琛_品职助教 · 2022年10月16日

嗨,从没放弃的小努力你好:


1

首先,背景交代:债券融资规模不同,适用的融资成本不同

如果融资规模小于 2.5 m,融资成本是 13.65%

如果融资规模大于 2.5 m,融资成本是 16%

所以我们需要了解债券的融资规模

2

其次,背景交代:现在要融资 7.5m,保持当前的资本结构

所以,要先算出当前的资本结构,D 40%,E 60%

所以融资 7.5m,债券的融资规模是 7.5x40% = 3m

大于 2.5m,所以税前债务资本成本 rd 为 16%

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加油吧,让我们一起遇见更好的自己!

醉清风 · 2023年06月10日

老师,这个资本比例D/E=4/6是从哪里看出来的,谢谢

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NO.PZ2021091701000017 问题如下 Happy Resorts Company currently h1.2 million common shares of stooutstanng, anthe stoha beta of 2.2. It also h$10 million favalue of bon thhave five years remaining to maturity an8% coupon with semiannupayments anare priceto yiel13.65%. If Happy issues up to $2.5 million of new bon, the bon will pricepanwill have a yielof 13.65%; if it issues bon beyon$2.5 million, the expecteyielon the entire issuanwill 16%. Happy hlearnethit cissue new common sto$10 a share. The current risk-free rate of interest is 3%, anthe expectemarket return is 10%. Happy’s margintrate is 30%. If Happy raises $7.5 million of new capitwhile maintaining the same bt-to-equity ratio, its weighteaverage cost of capitwill closest to A.14.5% B.15.5% C.16.5% B is correct. The capitstructure is follows: Market value of bt: FV = $10,000,000, PMT = $400,000, N = 10, anI/YR= 6.825%. Solving for PV gives $7,999,688. Market value of equity: 1.2 million shares outstanng $10 = $12,000,000To raise $7.5 million of new capitwhile maintaining the same capitstructure, the company woulissue $7.5 million × 40% = $3.0 million in bon, whiresults in a before-trate of 16%. r1 – t) = 0.16(1 – 0.3) = 0.112, or 11.2%. re = 0.03 + 2.2(0.10 − 0.03) = 0.184, or 18.4%. WA= 0.40(0.112) + 0.6(0.184) = 0.0448 + 0.1104 = 0.1552, or 15.52% 想问一下这个为什要用PV的值来算债券的占比呢,谢谢老师

2023-10-27 18:51 1 · 回答

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2023-09-29 10:01 1 · 回答

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2023-04-19 15:31 1 · 回答

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2023-03-20 09:11 1 · 回答

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