Question

On December 31, 2020, Berclair Inc. had 440 million shares of common stock and 3 million shares of 9%, $100 par value cumulative preferred stock issued and outstanding. On March 1, 2021, Berclair purchased 24 million shares of its common stock as treasury stock. Berclair issued a 5% common stock dividend on July 1, 2021. Four million treasury shares were sold on October 1. Net income for the year ended December 31, 2021, was $650 million. The income tax rate is 25% Also outstanding at December 31 were incentive stock options granted to key executives on September 13, 2016. The options are exercisable as of September 13, 2020. for 30 million common shares at an exercise price of $56 per share During 2021, the market price of the common shares averaged $70 per share. In 2017, $50.0 million of 8% bonds, convertible into 6 million common shares were issued at face value. Required: Compute Berclair's basic and diluted earnings per share for the year ended December 31, 2021. (Enter your answers in millions (ie., 10,000,000 should be entered as 10). Do not round intermediate calculations.) Numerator Denominator - Earnings per Share Basic Diluted

Answer 1

Earnings per share is calculated by dividing the earnings available for distribution by total number of weighted average shares. Diluted EPS takes into potential issue of shares. Each potential share issue has its own merits and viewed accordingly on individual basis.

Numerator (Basic EPS):

Net income = $650 million

Preferred dividends= 3mn * 9% * $ 100 = $ 27 million

since the preferred stock is cumulative, the dividend is deducted whether or not paid)

Denominator (Basic EPS): Weighted average Number of shares

common stock outstanding (1/1 – 12/31)	440 million x (12/12) *1.05	462 million
Treasury shares purchased (3/1 – 12/31)	(24) million x (10/12) *1.05	(21) million
Treasury shares sold (10/1 – 12/31)	(4) million x (3/12)	1
The weighted average number of shares		442 million

Basic EPS = ($650-27) ÷ 442 = $1.41

Now,

Stock Options

The stock options are dilutive because exercise price is lower than market price of $ 70 per share.

Using treasury stock method.

1. Exercise is assumed to take place at the later of the date of issue (9/13/21) or the beginning of the year (1/1/21). Assume exercise 1/1/21
2. The Treasury Stock Method assumes that the proceeds received upon exercise of $1,680 (30 million x $56) are used to buy back stock at the average market price, i.e., $1,680 ÷ $70 = 24 million
3. The net increase in the number of shares = 6 million  (30 million issued upon exercise – 24 million repurchased)

Convertible Bonds

Using method if bonds are converted into common stock. Here is the step by step approach to calculate nature of dilution.

shares issued on conversion = 6 million

Interest paid, net of tax = $3 [(8% x $50) x 75%]

Interest per shares issued = 3/6 = $ 0.5 per share

EPS without assumed conversion = ($650 - $27+3) ÷ (442 + 6+6) = $1.38

The convertible bonds are dilutive because $1.38 is less than $1.41

Hence, diluted EPS = ($650 - $27+3) ÷ (442 + 6+6) = $1.38

Basic EPS =623/442 = 1.41

Diluted EPS = 626/454 = 1.38

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