Now hardly seems the time for a fledgling bank or thrift to introduce new shares to the market-unless, of course, it has something to do with the Internet.

Net.Bank Inc., formerly known as Atlanta Internet Bank, is scheduled Thursday evening to price a secondary offering of 2.37 million shares.

Led by Bear, Stearns & Co., the issue consists of two million Net.Bank shares, plus 370,000 from lead stockholder Carolina First Corp. of Greenville, S.C.

The $283 million-asset Net.Bank, which made its initial public offering in July 1997, would increase its shares outstanding by one-third.

In a filing with the Securities and Exchange Commission, Net.Bank said it expects to raise $58.7 million, assuming a $31.375 per-share offering price. Net.Bank said it would use the proceeds to build its loan portfolio and expand its marketing beyond banners on Internet search engines and down such avenues as cobranded credit cards.

Given the investment community's ravenous appetite for anything related to Internet commerce, it is difficult to predict what value investors will assign the offering. "The 'Net' in their name is probably worth $10 per share alone," said one analyst.

One person familiar with the offering said its scheduling is uncertain because Net.Bank's share price has been so volatile lately.

Net.Bank's share price was $61.9375 last Thursday, a 172% increase since Christmas. It closed Tuesday at $49.50.

Unlike many Internet commerce ventures, Net.Bank actually makes money. It reported third-quarter 1998 earnings of 10 cents a share, compared with a loss of 32 cents a year earlier.

Fourth-quarter earnings have not been released yet. The company trades at 200 times estimated earnings.

Telebanc Financial Corp., an older company that has embraced the Internet banking concept, reported third-quarter income of 1 cent per share, down from 11 cents a year earlier. The Arlington, Va., company's shares trade at $40.25, a 76% increase from about two months ago, or 635 times earnings.

The first widely recognized Internet-based bank, Security First Network Bank of Atlanta, went public at $20 a share on May 23, 1996, and ended that day at $41. The stock traded at $14.875 last Sept. 30, the day it sold its banking operations to Royal Bank of Canada, leaving a publicly traded technology company, Security First Technologies.

Net.Bank's directors include Robin C. Kelton, the former chairman of the London-based investment bank Fox-Pitt Kelton. Chairman T. Stephen Johnson has advised numerous southern banks on mergers. Chief executive officer D.R. Grimes and chief financial officer Richard E. Bowers both hail from Servantis Systems Inc., a software company that has been absorbed into Checkfree Corp.

Mr. Grimes, on the road to pitch his offering to prospective investors, was unavailable to comment.

Net.Bank said it increased customer accounts to 14,600 at Sept. 30, almost 350% more than a year earlier. Its chief attractions are low-cost checking and high-yielding certificates of deposit. The company says it invests deposits in high-quality, single-family home mortgages.

The follow-on offering would bring a measure of regulatory relief to Net.Bank, as well as capital.

Because Carolina First, a bank holding company, owns 19.1% of Net.Bank, it is deemed to be in control, and each company can be held responsible for losses suffered by the other. After the offering, Carolina First's stake should fall to 9.9%, and it would no longer be responsible for any potential loss at Net.Bank, according to the prospectus.

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