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添晴 · 2025年03月18日

解析的公式

NO.PZ2023081403000026

问题如下:

Q. For its fiscal year-end, Calvan Water Corporation (CWC) reported net income of USD12 million and a weighted average of 2,000,000 common shares outstanding. The company paid USD800,000 in preferred dividends and had 100,000 options outstanding with an average exercise price of USD20. CWC’s market price over the year averaged USD25 per share. CWC’s diluted EPS is closest to:

选项:

A.USD5.33

B.USD5.54

C.USD5.94

解释:

B is correct. The formula to calculate diluted EPS is as follows:

Diluted EPS = (Net income – Preferred dividends)/[Weighted average number of shares outstanding + (New shares that would have been issued at option exercise – Shares that could have been purchased with cash received upon exercise) × (Proportion of year during which the financial instruments were outstanding)].

The underlying assumption is that outstanding options are exercised, and then the proceeds from the issuance of new shares are used to repurchase shares already outstanding:

Proceeds from option exercise = 100,000 × USD20 = USD2,000,000Shares repurchased = USD2,000,000/USD25 = 80,000

The net increase in shares outstanding is thus 100,000 – 80,000 = 20,000. Therefore, the diluted EPS for CWC = (USD12,000,000 – USD800,000)/2,020,000 = USD5.54.

解析中的公式,(portion of year during ……outstanding),指的是option行权后的shares 也要来、考虑weighted的意思吗?

1 个答案

王园圆_品职助教 · 2025年03月18日

同学你好,是的,解析确实是这个意思

但是注意,既然我们要计算的是diluted EPS,那必然要计算的是最大稀释效果下的EPS的值

而option,可转债,可转换优先股等只有在期初(也就是第一天)就全部转换的时候,weight才是1才能获得最大的稀释效果,所以碰到这类可转换证券,都是默认期初第一天就全额发生转普通股的,也就是不需要做时间加权

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