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Katherine · 2023年09月20日

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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

可以解释一下1000，8%，还有一个啥是什么意思

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1 个答案

王园圆_品职助教 · 2023年09月20日

同学你是想问“Company also has 1,000, 8%, $1,000 par bonds convertible into 24 shares”是什么意思是吗？——这个条件是用来计算diluted　EPS中NI加回的金额的

如果你已经学过fixed income这门课了，这里会更好理解，这就是一个可转债。在以债券形式存在的时候，有1000份面值为1000美元，coupon rate是8%，就可以算出每年需要支付的coupon payment = 1000*1000*8% = 80000

如果一旦转换成股票，那这个80000的coupon payment就不用支付了，所以在计算diluted EPS的时候，相当于分子NI要加回这笔费用，但是由于coupon payment有税盾作用，所以实际加回的是80000*(1-t）这么多的金额

convertible into 24 shares是指每一份可转换债券可以转换成24份股票，所以有1000份，就可以1000*24 = 24000份股票——这是计算diluted EPS的时候分母增加的股份数

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