Question

On January 2, 2021, L Co. issued at face value $30,000 of 2% bonds convertible in total into 3,000 shares of L's common stock. No bonds were converted during 2021. Throughout 2021, L had 3,000 shares of common stock outstanding. L's 2021 net income was $12,000. L's income tax rate is 25%. No potential common shares other than the convertible bonds were outstanding during 2021. L's diluted earnings per share for 2021 would be:

Answer 1

Solution:

The formula for calculating the Diluted Earnings per share is

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

As per the information given in the question we have

Face value of convertible bonds = $ 30,000 ; Coupon rate of the bonds = 2 % ; Tax rate = 25 % ;

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

= ( $ 30,000 * 2 % ) * ( 1 – 0.25 )

= $ 600 * 0.75 = $ 450

Thus after tax Interest = $ 450 ;

Net Income = $ 12,000 ;   No. of share of common stock = 3,000 ;

No. of shares of Dilutive common stock = 3,000 ;

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

= ( $ 12,000 + $ 450 ) / ( 3,000 + 3,000 )

= $ 12,450 / 6,000

= $ 2.0750

Thus L’s Diluted Earnings per share for 2021 = $ 2.0750

= $ 2.075 ( when rounded off to three decimal places )

= $ 2.08 ( when rounded off to two decimal places )