As a private, for-profit company, Vanguard Group, the Malvern-based investment giant, doesn't have to release how much it spends or keeps as profits.

But a Securities and Exchange Commission filing this year has shed light on Vanguard's taxable income and its struggles with four northeastern states over their share.

Vanguard hopes to get back $6.5 million in "refund claims filed with the State of Pennsylvania for corporate net income tax," the company's Vanguard Marketing Corp. subsidiary told the SEC in its 2016 annual report, posted on the Vanguard and SEC websites. The company also said Vanguard "is currently under audit by the states of Massachusetts, New York, and New Jersey."

Vanguard declined to comment beyond the filing, spokeswoman Arianna Stefanoni-Sherlock told me.

Given Pennsylvania's 9.9 percent corporate income-tax rate, the filing suggests the company had Pennsylvania taxable income of more than $65 million — and total profits that could top $1 billion if it is similarly profitable in other states, agreed Robert Willens, a widely cited New York-based corporate tax adviser and scholar who reviewed my calculation.

Lee Sheppard, publisher of Tax Notes, warned against assuming Vanguard collects similar profits in other states; it could be less or more. The refund filing could include claims from Pennsylvania taxes that Vanguard paid two or three years ago, two tax practitioners affiliated with the Pennsylvania Institute of CPAs told me.

Vanguard has marketed itself as an "at-cost" company that can provide services with no profit margin because it is owned by the mutual funds it sells. But that doesn't mean the company is run as a nonprofit. Indeed, as a private company with no extra responsibilities to the mutual fund shareholders who "nominally" own it, Vanguard Group's board and management enjoy "unlimited discretion" in deciding what to do with fee income, Yale University law professor John Morley wrote in a 2014 Yale Law Review article.

The company's success brings in piles of cash. While Vanguard assets have quadrupled to $4 trillion since the recession, Vanguard annual fund fees, among the industry's lowest, have dropped by only one-third, to an average 0.12 percentage points, notes Dan Wiener, a New York money manager who advises clients on Vanguard funds. As a result, Vanguard fee income more than doubled in that period, to over $4 billion a year.

David Danon, a former Vanguard tax lawyer, brought attention to Vanguard's profitability starting in 2013. He told the IRS and states including Massachusetts, New York, New Jersey, and Texas that Vanguard's mutual funds were paying the company service fees below market rates, in violation of tax law requiring affiliated companies to charge each other as if they weren't related. Danon said Vanguard manipulated internal payments to minimize reported income and underpay taxes. He also said the company amassed more than $1 billion in cash without paying taxes on it or giving customers a share.

Texas paid Danon $117,000 in 2015 as an "informant" after audits using his information showed Vanguard filed "deficient" tax returns in 2010 to 2014. The company has opposed some other Danon attempts to get paid as a whistleblower. The IRS and other states have declined to say if they acted on Danon's information. Vanguard has lately beefed up its accounting and legal staff.

How likely is it that Vanguard profits top $1 billion a year? Considering that Vanguard's larger rival BlackRock Inc., a public company, reported sales of $11 billion and after-tax profits of $3 billion last year, and that other investment managers are similarly profitable, it would not seem excessive for a private or a public company if Vanguard were to collect $1 billion in profits on sales above $4 billion, said Jane Scaccetti, a partner in Philadelphia-based CPA firm Drucker & Scaccetti.

Vanguard also pays income taxes on foreign profits. For example, a Vanguard subsidiary active in Britain, France, the Netherlands, and Switzerland paid income taxes of 1.5 million British pounds on after-tax profits of 8 million, from revenues of 102 million pounds last year, according to a U.K. regulatory report.