Hold'em: Odds on the flop

[Raza]

Hi, I've recently been reading and studying Small Stakes Hold'em and wanted to ask specifically about the necessary odds to call when you have a backdoor flush draw. On the flop, after a bet to you, you can call for .5BB. On the turn, if you miss your flush card you fold (-.5BB total, odds are 37/47). If you do catch your flush card, you will continue, but may have to call a bet in the process. On the river, if you miss you flush card you fold. (-1.5BB total, odds are 10/47 * 37/46). If you catch you flush, you will win the pot. (odds are 10/47 * 9/46).

So this is what I have:

37/47 = .787
10/47 * 37/46 = .171
10/47 * 9/46 = .0416

EV = (.787)*(-.5BB ) + (.171)*(-1.5BB) + (.0416)*(final pot size not including your bets since the flop)

Break-even pot size: 15.625BB. So in practice, on the flop, you would add the size of the pot plus any future bets by your opponents and go from there. Is this analysis correct?

Thanks.