Anti-dilution clauses can keep an investor’s original ownership percentage intact, thus, the conversion ratio should rise because of the declaration of dividend.
Think of it this way.
Say the company only had a 300 shares pre-stock split.
Your convert ggave yiou the right to by 20 more @ $50 each.
After conversion you would own 20/320 = 6.25% of the firm,
You are paying a $1000 for a 6.25% stake.
It is this last line we are trying to preserve,
If the company has a 10% stock dividend there wil be 330 shares pre coversion of convert.
You now want to buy 22 shares when you convert (22/352 = 6,25% ) you stake will be 6.25%
So you are going to spend $1000 to buy 22 shares
$1,000/22 = $45.45
We get the quicker with 50 / 1.1
Mathematically
20 x $50 = $1000
(20 x 1.1 ) x ($50/1.1) = $1000