Question

On January 1, 2027, Ajax Corporation had 10 million shares of common stock, issued and outstanding. On October 1, 2027 Ajax issued an additional 1 million shares of common stock. Ajax also has $40 million face value, 6.25% convertible bonds outstanding for the entire year. The bonds are convertible into 2 million common shares. Ajax has a tax rate of 40% and net income of $14 million in 2027. What is Ajax’s diluted earnings per share for 2027?

	$1.35
	$1.27
	$1.22
	$1.37

Answer 1

Solution:

Calculation of after tax interest :

As per the information given in the question we have

Face value of convertible bonds = $ 40,000,000 ; Coupon rate of the bonds = 6.25 % ;

Tax rate = 40 % ;

Thus after tax interest = ( Face value of convertible bonds * Coupon rate of the bonds ) * ( 1 – tax rate )

= ( $ 40,000,000 * 6.25 % ) * ( 1 – 0.40 )

= $ 2,500,000 * 0.60 = $ 1,500,000 ;

Thus after tax Interest = $ 1,500,000 ;

Calculation of Weighted Average common shares outstanding :

No. of shares of common stock at the beginning of the year = 10,000,000 ;

Thus 10,000,000 shares were held for a period of 12 months.

Issue of additional shares of common stock on October 1, 2027 = 1,000,000 ;

Thus 10,000,000 additional shares were held for a period of 3 months i.e., October 1,2027 to December 31, 2027

Thus the weighted average common shares outstanding = ( 10,000,000 * ( 12 / 12 ) ) + ( 1,000,000 * (3/12 ) )

= 10,000,000 + 250,000 = 10,250,000

Calculation of diluted earnings per share :

As per the information available we have

The bonds are convertible into 2 million common shares. Thus No. of Dilutive common shares = 2,000,000 ;

Weighted average number of shares of common stock = $ 10,250,000 ;

Net income = $ 14,000,000 ; After tax Interest = $ 1,500,000 ;

The formula for calculating the Diluted Earnings per share is

= ( Net Income + After tax Interest ) / ( Weighted Average common shares outstanding + No. of Dilutive common shares )

Applying the above information in the formula we have the diluted earnings per share :

= ( $ 14,000,000 + $ 1,500,000 ) / ( 10,250,000 + 2,000,000 )

= $ 15,500,000 / 12,250,000

= $ 1.265306

= $ 1.27 ( when rounded off to two decimal places )

Thus Ajax's Diluted Earnings per share for 2027 = $ 1.27

The solution is option 2 = $ 1.27