# Weighted Average no. of Shares with Convertible Debt

Hi All,

Hoping someone can clear this up.

CFA Vol. 3 p. 192: “Diluted EPS is calculate as if the convertible debt had been converted at the beginning of the period.” The examples follow this lead. All good.

However,

Schweser 2011 Vol. 3 p. 66 says: “If a dilutive security was ISSUED (my capitals) during the year, the increase in the weighted average number of shares for diluted EPS is based on only the portion of the year the dilutive security was outstanding.” See Concept Checker no. 15 for an example.

The CFA curriculum does not have this extra tweak. Is that something that has changed from 2011?

Thank you,

Mark

Hi Krugermark,

When the CFA curriculum states that the if-converted method calculates diluted EPS as if debt had been converted at the beginning of period it means from the beginning of the period in which the convertible debt was issued. So that means you will still have to measure the time-weighted average that the convertible debt was outstanding for the period.

The reason the following example (Example 16 & Exhibit 12 of page 192-193) appear to not use the time-weighting average method is because the convertible debt was outstanding from day one of the period. So they are being multiplied by a time-weighted factor of 1 for the period. Page 194 of CFA curriculum shows how to calculate the time-weighted average for stock options & warrants so I think you should just refer to that in instances where convertible debt is issued during the period.

I can see why this would appear confusing - if anything, it’s poor form in the curriculum in my opinion. Good thing you picked up on this in Schweser books.

I hope this helps.

Good luck.

Hi, PepeSilvia :

Since you mentioned that page 194 of CFA curriculum shows how to calculate the time-weighted average for stock options & warrants but actually no example of “warrants” was raised on the book,

is it that the calculation for warrants completely same as that for options ?

Hi alpha,

The time-weighted average calculation is the same for options, warrants and convertible debt - ensure that you find the proportion of time that the security is outstanding for the remaining period. The only difference is that convertible debt is assumed to be converted upon issue and stock options/warrants must be exercised to be accounted for in the diluted EPS.

For convertible debt, the if-converted method implies that the moment the debt is issued, it is converted.

For stock options & warrants however, the average market price has to be such that the option/warrants are exercised during the period. So yes, the calculation of the time-weighted average for warrants is the same for stock options assuming that they are being exercised. In the event that the exercise price of the call option/warrant exceeds the average market price - the security should not be exercised, it is said to be antidilutive and is not to be included in the diluted EPS calculation.

I think this can be one of those areas that takes a while to understand if you are not familiar with the application of securities such as this. It is definitely something that I will spend a while reviewing before exam day. FRA is 20% of the exam anyways.

Hope that makes sense.

Hi PepeSilvia,

Thanks for your reply. Always tricky typing this stuff out, much easier to talk…

I don´t get the last sentence of your 1st paragraph…

“When the CFA curriculum states that the if-converted method calculates diluted EPS as if debt had been converted at the beginning of period it means from the beginning of the period in which the convertible debt was issued. So that means you will still have to measure the time-weighted average that the convertible debt was outstanding for the period.”

If we calculate from the beginning of the period, then there is no need to calculate a time-weighted average for the conv. debt outstanding - it is just “1”.

Perhaps the 1st sentence of p. 192 is the key: “When a company has convertible debt outstanding…” Perhaps we are to assume that we are not required to deal with the situation where conv. debt is issued during the year. That would make sense with the fact that, as you rightly pointed out, there are no such examples given.

What do you think?

M.

Exactly. Apologies if that sentence is confusing - from the beginning of the period in which the convertible debt was issued should just read from the date that the convertible debt is issued until the end of the period being examined. So if the convertible debt is outstanding at the beginning of the period - the time-weighted factor is 1 as you stated, and further no computation is required.

As it is not found in the CFA curriculum you may be right in saying that we may not need to compute the time-weighted average for the issue of convertible debt. But yeah, it is interesting how it came up in a Schweser example and it may just be worth keeping in mind - just in case. Stock options and warrants issued during the period in calculating diluted EPS should keep us on our toes anyway.

It maybe worth looking out for in mocks too. I’m sure it is something that we will be able to deal with in any case.

Good luck Mark.

Hi, PepeSilvia :

Thank you so much for your detailed explanation ! I am now much clear !