Q:

Usage of "estimate" as a noun

Morgan Stanley, the best-performing stock this year among the five
largest Wall Street banks, reported profit that beat estimates on
a smaller drop in fixed-income trading revenue than analysts
projected.
Second-quarter net income rose to $1.94 billion, or 94 cents a share,
from $980 million, or 41 cents, a year earlier, the New York-based
company said today in a statement. Excluding an accounting adjustment
tied to the firm’s own debt and a tax benefit, profit was 60 cents a
share, topping the 56-cent average estimate of 24 analysts
surveyed by Bloomberg.
-- Source

I've always run across "estimate of something" rather than "estimate on something". Does on here mean based on? Any other alternative prepositions could be used here?
And can I say "greater than the averaged 56-cent estimate" or "greater than the averaged estimate at 56-cent" in place of that part in bold?

A:

An estimate of X means that the estimated value = X.
In your first sentence, on heads a preposition phrase which modifies beat. It means that the smaller-than-projected drop was the cause of profits beating the before-the-fact estimate.
You first paraphrase is accurate: the average estimate was $0.56, and profit, at $0.60 was greater than that. Your second, however, is not: X was greater than Y at Z is understood to mean that X=Z, not Y=Z.

