NEW YORK >> Square, the 6-year-old company known for its white, cube-shaped credit and debit card readers that plug into smartphones, is boosting its planned initial public offering value by 47 percent in what has become a tough market for new companies trying to raise cash.

The San Francisco financial services startup was founded and is led by Jack Dorsey, who co-founded Twitter and recently returned to that company. Dorsey, 38, who owns 24.4 percent of Square, did not give up the CEO job at Square when he returned to his former company.

The traditional manner of valuing a company, done by multiplying the total outstanding shares by the price of each share, puts Square’s worth at $4.2 billion if the top end of the pricing range is used. That is substantially lower than a $6 billion valuation by the private investors in connection with the $150 million Series E fundraising in October 2014.

Square Inc. plans to offer about 30 million shares at a maximum of $13 apiece for total value of up to $403.7 million.

Shares will trade under the symbol SQ on the New York Stock Exchange. Square helps small businesses process credit card payments on phones and tablet computers, turning them into electronic sales terminals.