Here's what the Internal Revenue Service says (slightly edited):
"To qualify for the 5% or 15% maximum rate, all of the following
requirements must be met:
1. The dividends must have been paid by a U.S. corporation or a
qualified foreign corporation. (See qualified foreign corporation.)
2. The dividends are not of the type listed later under Dividends
that are not qualified dividends.
3. The proper holding period is met (discussed next).
Generally, to meet the holding period requirement, a shareholder must
have held the stock for more than 60 days during the 121-day period
that begins 60 days before the ex-dividend date. The ex-dividend date
is the first date following the declaration of a dividend on which the
buyer of a stock will not receive the next dividend payment. Instead,
the seller will get the dividend."
So, assuming the holding period is the only issue, the shareholders
who have owned the stock for 20+ years will have no problem. The new
shareholders' dividends will be qualified if they buy the stock before
the ex-dividend date and hold it for 61 days. They would have to buy
the stock before the ex-dividend date anyway to get the dividend at
You said some "will hold stock for only a month." If that means they
will hold it for only a month total and then sell it, they will not
qualify for the 15% rate. However, if it means that they will have
held the stock for a month before the ex-dividend date, then they can
qualify by holding the stock for at least 61 days total.
Fidelity Investments page on Determining Qualified Dividend Eligibility
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