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

CFA Level I FRA
#1

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

#2

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

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#3

[SOLVED BELOW]

Hi - on the same question, I have one simple doubt. Everything flows for me except for the fact that the preferred dividends are not included in the Diluted EPS: Both Converted scenario.

In other words, why is the numerator:
1,000,000 + 3,840

Instead of:
1,000,000 +3,840 - 20,000 ?

The answer prompt simply mentions “Preferred dividends were included after preferred conversion (see table).” but I simply don’t get it -_-

EDIT

For future readers, the reason is the following:

Since to calculate the diluted EPS for companies with preferred shares in their capital structure you have to use the if-converted method, you have to consider that, if the preferred shares had been originally converted, the company would not have to pay the preferred dividends on those. Therefore, the Net Income available to common shareholders (i.e., the numerator in the Diluted EPS calculation) is greater than with the basic EPS calculation. In the question above, the 20,000 $ are not subtracted because of this reason: the company is assumed not to have paid such dividends.

Hope this helps someone.

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