It's been an exciting week for mobile-payment processor Square (NYSE:SQ). The company has traveled a long and winding road to going public, and Square's exciting technology has maintained a certain level of hype around the start-up. Square's IPO has been notable because it serves as potential evidence that start-up valuations are beginning to cool off a bit.

Square's most recent private valuation was at $6 billion a little over a year ago. Square filed its official S-1 Registration Statement with the SEC just last month, and the company subsequently expected to price the offering at $11 to $13 per share. The offering ended up pricing at $9, valuing Square at $2.9 billion.

Why so low?
On the first day of trading, Square shares surged 45% and closed at $13 and change, near the high end of the initially expected range. That makes the $9 offer price seem conservative in hindsight, but investors often judge the "success" of an IPO by the performance of it first day trading on the secondary market. In that regard, Square's IPO was a success.

The flip side of the offer is that by pricing so conservatively, Square may left some money on the table. After underwriting fees and expenses, Square raised $218.2 million in fresh capital to add to its coffers. Insiders and early investors also sold $11.5 million through the offering. It's a tricky balance to strike. It goes without saying that Square wanted to raise as much money as possible, but it also didn't want to risk pricing the offering too high and deal with the possibility of negative headlines if shares plunged on the first day.

Oh, and as far as those late-stage investors that bought in at a $6 billion valuation, I wouldn't worry about them (I know you're concerned about how the venture capitalists fared). They protected themselves with a ratchet, which guarantees a certain return if the IPO prices below a certain threshold. Square issued an additional $93 million worth of shares to these investors to compensate them.

What's next?
Now that Square's IPO is in the rear view mirror, the real question going forward will be whether or not the company can represent meaningful competition with larger rivals like PayPal (NASDAQ:PYPL) and Intuit (NASDAQ:INTU).

PayPal's biggest advantage over Square is its scale. PayPal processes far more payments volume on a global basis and has been able to translate that volume into cost efficiencies. PayPal's transaction expense rate is roughly half of Square's, making PayPal much more profitable. Intuit's sophisticated financial accounting and tax software also appeals to small businesses more than Square's offerings. Anecdotally, I recently spoke with a building contractor that cited this as precisely the reason his company chooses Intuit over Square.

Better safe than sorry
The fact that investors bid shares up by 45% on the first day shows that Square might have been able to get away with a higher price. But the market's been rather choppy lately, and some companies have even withdrawn IPOs due to "market conditions." Square figured it was better to move forward with a conservatively priced IPO. Even though Square may have left some money on the table, sometimes it's better safe than sorry.

Evan Niu, CFA, has no position in any stocks mentioned. The Motley Fool owns shares of and recommends Intuit and PayPal Holdings. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.