# Diluted EPS checking: is the official answer wrong?

I think the official answer is wrong, it should have deducted preferred dividends. Can anyone confirm?

Question:

Net Income \$1m

AVG no. of common shares outstanding 100,000

Convertible preferred shares:

convertible preferred shares outstanding 2,000

dividend/share \$10

each preferred share is convertible into 5 common shares

Preferred dividend: 2000*10=20000

Incremental common shares: 2000*5=10000

Bond:

convertible, \$100 face value per bond, total \$80,000

8% coupon

each bond convertible into 25 common shares

corporate tax rate 40%

After tax cost of interest = 0.08*80000*(1-0.4)=3840

Incremental common shares from bond: (80000/100)*25=20000

Official answer:

NI+after tax cost of interest / common shares + preferred converted + bond converted

[1m + 3840] / (100000 + preferred converted 10000 + bond converted 20000 )= 7.72

Shouldn’t it be

[1m - 20000 pref. div + 3840] / (100000 + preferred converted 10000 + bond converted 20000 )= 7.57

When preferred shares are converted, preferred dividends are not paid so you add them back.

Net Income - Preferred Dividends + Preferred Dividends (because they are converted, they are not paid) + int (1-t)

ah!!! of course…silly mistake.

Thanks for the clarification.