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冬冬Liu~💫💫 · 2023年07月21日

这道题的分子不太理解

  1. CFA I
  2. FRA

NO.PZ2016012102000039

问题如下：

Given the following information, calculate the company's diluted EPS:

company has net income of $200,000 and 150,000 common shares outstanding from the beginning of the year. Company also has 1,000, 8%, $1,000 par bonds convertible into 24 shares each,

outstanding as of the beginning of the year. The tax rate is 35%.

选项：

A.

$1.1.

B.

$1.3

C.

$2.17.

解释：

Basic EPS = $200,000150,000=$1.3\frac{\$200,000}{150,000}=\$1.3

Check if the convertible bonds are dilutive:

Impact of numerator= (1,000 x 1,000 x 0.08) x (1 - 0.35) = $52,000

Impact of denominator = (1,000 x 24) = 24,000 shares

Impact per share =

$52,00024,000shares=$2.17\frac{\$52,000}{24,000shares}=\$2.17

$2.17 > basic EPS of $1.3, so the bonds are antidilutive. Then the diluted EPS = basic EPS = $1.3.

考点：股票稀释

假设把所有的债权转为股权

Net income = 200,000+1,000×1,000×8%×(1-35%) =252,000

share = 150,000+1,000×24 =174,000

EPS = [200,000+1,000×1,000×8%×(1-35%)]/(150,000+1,000×24)=1.45

大于basic EPS，因此没有稀释作用，diluted EPS=basic EPS=1.3

分子应该是200000+1000x0.8x65%吧。怎么会是200000x1000x1000x0.8x65%呢

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1 个答案

王园圆_品职助教 · 2023年07月21日

同学你好，你再仔细看下解析呢

要使用加入了可转换债券的EPS作为最终的diluted EPS，起码要确认这个convertible bond确实对EPS有稀释作用才能加入

可是根据计算可转换债券的稀释作用：

”Impact of numerator= (1,000 x 1,000 x 0.08) x (1 - 0.35) = $52,000——这是求税后利息费用的减少对NI的增加作用的

Impact of denominator = (1,000 x 24) = 24,000 shares——这是求可转债可以转换成的股数

Impact per share =$52,000/24,000=$2.17——分子除分母可以算实际这个可转债对basic EPS是会使其增大还是缩小"

2.17是大于basic EPS的值（1.3）的，说明这个可转债没有稀释作用，那就不能把可转债算入计算diluted EPS的分子分母里，也就是本题其实basic EPS就等于diluted　EPS哦

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