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jane123456 · 2024年08月27日

diluted EPS is equal to or less than its basic EPS

  1. CFA I
  2. FRA

NO.PZ2023081403000027

问题如下：

Q. Laurelli Builders (LB) reported the financial data shown in Exhibit 1 for year-end 31 December:

Exhibit 1:

Laurelli Builders

Which statement about the calculation of LB’s EPS is most accurate?

选项：

A.LB’s basic EPS is USD1.12. B.LB’s diluted EPS is equal to or less than its basic EPS. C.The weighted average number of shares outstanding is 2,210,000.

解释：

B is correct. LB has warrants in its capital structure; if the exercise price is less than the weighted average market price during the year, the effect of their conversion is to increase the weighted average number of common shares outstanding, causing diluted EPS to be lower than basic EPS. If the exercise price is equal to the weighted average market price, the number of shares issued equals the number of shares repurchased. Therefore, the weighted average number of common shares outstanding is not affected and diluted EPS equals basic EPS. If the exercise price is greater than the weighted average market price, the effect of their conversion is anti-dilutive. As such, they are not included in the calculation of basic EPS. LB’s basic EPS is USD1.22 [= (USD3,350,000 – USD430,000)/2,400,000]. Stock dividends are treated as having been issued retroactively to the beginning of the period.

diluted EPS i是否一定是小于等于basic EPS？另外，如何理解warrants不算股份，这不是Option吗？当执行的时候就会转换成分母中的股份数

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1 个答案

lynn_品职助教 · 2024年08月28日

嗨，从没放弃的小努力你好：


diluted EPS i是否一定是小于等于basic EPS？


是的，因为翻译过来叫稀释后EPS，所以一定是小于等于basic EPS。


另外，如何理解warrants不算股份，这不是Option吗？当执行的时候就会转换成分母中的股份数


对的，只是这道题里面哈


warrant是认股权证， 它赋予持有者在一定期限内以行权价购买发行公司一定股份的权利。 一旦投资者行权，企业需要发行新的股份来满足行权要求。


计算行权后公司在外发行股票数量的变化，采用的是treasury stock method。假设企业发行新股获得的资金会以市场平均价回购企业已经发行在外的股票。


分子的计算不受到影响，而计算分母则要考虑两方面，一方面投资者行权后公司需要发行股票，那么在外发行的普通股股数就会增加，另一方面，公司又用收到的钱在市场上以平均价回购股票，因此会减少发行在外的普通股数量。


这道题讨论了warrant的行权价和平均股价的三种关系：


1 行权价小于平均股价，那么新发行的股数就会少于公司回购的股数，其差额就是分母的增加额，这样算的EPS是小于basic EPS的，因此是有稀释作用。


2 行权价等于平均股价，那么新发行的股数就会等于公司回购的股数，两者抵消，最终分母没有变化，算出来的EPS和basic EPS一样。


3 行权价大于平均股价，那么新发行的股数就小于公司回购的股数，因此发行在外的普通股股数减少，分母减少，算出来的EPS是大于basic EPS的，也就是antidilutive。算出来的EPS一旦大于basic EPS，那么就不予考虑，最终的diluted EPS就等于basic EPS。


这道题是原版书后习题，解析写的太复杂，解析认为当行权价大于平均股价时，投资者行权后会导致antidilutive作用，


但是实际上这种情况下正常的投资者是不会选择行权的。


所以这道题在考虑diluted EPS时其实只需要考虑两种情况，一种是行权，会有稀释作用，另一种是不行权，不会有稀释作用。


判断是否行权则要比较行权价和平均股价，因为题目没有相关数据，所以我们只能得出：diluted EPS要么低于basic EPS（行权），要么等于basic EPS（不行权）。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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