Diluted EPS, Financial Statement Analysis (2) on CFAI web

The following information is available on a company for the current year.

Net income $1,000,000
Average number of common shares outstanding 100,000

Details of convertible securities outstanding:
Convertible preferred shares outstanding 2,000
Dividend/share $10
Each preferred share is convertible into five shares of common stock

Convertible bonds, $100 face value per bond $80,000
8% coupon
Each bond is convertible into 25 shares of common stock

Corporate tax rate 40%

The company’s diluted EPS is closest to:

  1. $7.72.
  2. $7.57.
  3. $7.69.

The answer is A. $7.72.

Because both the preferred shares and the bonds are dilutive, they should both be converted to calculate the diluted EPS. Diluted EPS is the lowest possible value.

Basic EPS Diluted EPS: Bond Converted Diluted EPS: Preferred Converted Diluted EPS: Both Converted
Net income $1,000,000 $1,000,000 $1,000,000 $1,000,000
Preferred dividends –$20,000 –$20,000 0 0
After-tax cost of interest
8% × $80,000 × (1 – 0.40) $3,840 $3,840
Numerator $980,000 $983,840 $1,000,000 $1,003,840
Average common shares outstanding 100,000 100,000 100,000 100,000
Preferred converted 10,000 10,000
Bond converted 20,000 20,000
Denominator 100,000 120,000 110,000 130,000

EPS $9.80 $8.20 $9.09 $7.72

But I dont understand how the key answer came up with $10,000 preferred converted. I got (2,000*10/100)*5=1,000. Where did I go wrong? Please help me. Thank you so so much

All you need to do is multiply the number of preferred shares by their conversion factor.

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