I sent my prof this e-mail.. Question about Diluted EPS, more specifically Convertible Securities

Professor Klein,

I have a question regarding a problem in the textbook. Specifically, chapter 19 regarding Earnings Per Share. On page 1031-2, the concept review exercise (I won't assume you have the book with you), it states:


Net income for 2009: 180 million
Also, At January 1, 2009, $200 million of 10% convertible notes were outstanding. The notes were converted on April 1 into 16 million shares of common stock.
The tax rate is 40%.
These are the only relevant data.

In the solution, when calculating the Diluted EPS, the textbook has this as their numerator (in millions)::: $180 + [$20 - 40%($20)] x (3/12) = 183. This is net income plus "Assumed after-tax interest savings."

I cannot for the life of me figure out why they multiplied by (3/12). I thought for the numerator we were adding back the "would-have-been" interest expense that was never paid? Wouldn't this mean that we should be multiplying by (9/12) since interest on the notes were not paid from April until year end? Resulting in a final numerator of $189?


Please help, I have been staring at this problem for half an hour, I hope it's just a typo and I'm stressing over nothing


THIS WAS HIS REPLY::
The only show 3 months of interest so we back out the full amount that there is to be backed out.

?

I haven't done diluted EPS since class and my main memory of it is that I hated it. :p So I can't answer you definitively. However, I can dump a thought on you, and if you can answer a question I might know.

If the notes actually were converted April 1, then it seems that no interest was ever charged for 9/12 of the year, meaning it never came out of net income to begin with. So why add it back in?

Interest would have been charged the first 3 months and come out of net income. Are you supposed to be diluting as though conversions took place at the beginning of the year? That would make the 3/12 make sense.

(Of course, if the notes were actually converted, I'm not sure why dilute it to begin with. Isn't the idea supposed to be IF it had been converted, not when it really was converted?)