Thursday was a huge day for Twitter as it went public on the New York Stock Exchange and closed at $44.90 or 73 percent higher, after hitting a peak of $49.45. However, now several analysts are taking a cautious approach and wondering whether the company should be valued at $24.4billion. 

Wedbush Securities have given a "neutral" rating to the San Francisco-based social network, while Hudson Square has given a "sell" rating. The careful attitude comes from concerns expressed by a number of analysts and investors that the young and unprofitable company is overvalued in its 73 percent jump above the initial public offering.

According to Twitter's IPO paperwork, it has not turned a profit for at least the last three years. The chairman for financial analysis firm Sageworks Brian Hamilton also took a cautious approach.

"That valuation is simply far too high for a company that's losing money and seeing their rate of sales growth decrease," Hamilton said. 

Brian Wieser, Pivotal Research Group senior analyst, was also worried. Wieser downgraded his rating on the stock to "sell" from "buy" less than one hour after Twitter began trading. Wieser said its per-share price would be justified only if Twitter could earn more than $6 billion in annual sales by 2018 compared to the $422 million in sales in the first nine months of this year.

Wedbush analyst Michael Pachter has set a 12-month price target of $37 on Twitter using a complex series of assumptions. 

"We believe that Twitter is in the early innings of its growth," wrote Pachter. "We believe that the majority of the world's 2.4 billion Internet users have great potential to find something or someone on Twitter that they are interested in."   

While Pachter was cautious, the head of equity strategy at Saxo Bank, Peter Garnry, didn't mince his words. 

"The valuation at these price levels is disconnected from any logical calculation," wrote Garnry to clients Thursday. "and reflects a huge downside risk for investors if Twitter does not meet expectations at every quarterly earnings release from now on."

Despite the cautious note, Twitter started on a bullish note on Friday, soaring as much as $46.82, before settling at $44.10 around noon and finally closed at $41.65 or 7.24 percent down.

The company will report the fourth quarter and 2013 full year results in January.