Minnesota’s largest companies have started to reveal how dramatically their taxes will shrink under the new federal tax law.

3M Co. executives said last month that they believe the company’s effective tax rate, which was 35.5 percent in 2017, will settle in a range of 20 percent to 22 percent later this year. U.S. Bancorp in January estimated that its tax rate would fall to 21.9 percent from 29.8 percent.

While it’s too soon to say precisely how much money the changes will save the two companies on their tax obligations, their most recent fiscal years indicate the savings could be in the hundreds of millions: Last year, U.S. Bancorp reported income tax expense of $1.5 billion, while 3M paid $2.7 billion.

The tax cut fulfilled a pledge that President Donald Trump and congressional Republicans made during the 2016 campaign. They hope that lower rates will stimulate companies and individuals to spend and invest in ways that drive economic growth, while making U.S. businesses more globally competitive.

“When you’re an organization where 85 percent of your business is in the U.S., having the tax rate change is pretty meaningful,” Dan Florness, chief executive of Winona-based Fastenal Co., said at the company’s annual meeting last month.

The cut does not only benefit businesses. Most Americans have already seen a bump in their paychecks as tax withholding requirements changed when the law took effect. Some big companies also made headlines shortly after the law’s passage by announcing they would spend a portion of their tax savings on employee bonuses.

But as publicly held companies around the country announced quarterly results in recent weeks, many projected huge future savings from the law as the corporate tax rate falls to 21 percent from 35 percent, a sharper drop than for individuals at any level of income.

A number of them have said they plan to return a large portion of the savings to shareholders through dividends and share buybacks. “The first thing we do is we reinvest back into the business,” Florness told shareholders, “and if there’s some dollars left over, we share it with the folks in this room.”

Initially, the biggest economic effect of the law, formally called the Tax Cut and Jobs Act, is an increase in the government’s budget deficit and related long-term debt. The Congressional Budget Office is projecting the federal deficit will rise by $139 billion this fiscal year to $804 billion. CBO is estimating annual deficits will top $1 trillion starting in 2020 and the national debt will rise from $21 trillion to $33 trillion by 2028.

Trump and backers of the tax cuts are betting that higher economic growth from the cuts will spur enough new tax collection to offset the forecast hit to the government’s revenue.

Beyond the numbers that big public companies are reporting, accountants and tax lawyers say the new law will have even more profound effects on smaller firms. Many of them will reevaluate the way their businesses are structured for tax purposes in the next year or two, as avenues to lower tax bills become evident.

“This is by far the most change we’ve seen in a long time,” said Amy Roberts, tax partner in the Minneapolis office of the accounting firm Grant Thornton. “It’s sometimes hard to get your arms around.”

The wave of first-quarter results announcements that began in mid-April reflected many publicly traded companies’ first stab at estimating the law’s eventual impact. Some estimated their new effective tax rate, a figure that includes state, local and international rates as well.

For some companies, the law’s initial impacts include a big one-time jump in the tax expense they are reporting, chiefly to account for changes in previous assumptions they made about taxes. In coming months, many will revisit those assumptions as they further analyze the most sweeping rewrite of American tax law since the Reagan administration.

At 3M, for example, the effective tax jumped to 37.2 percent in the first quarter as the Maplewood-based company accounted for several provisions in the new law, including the elimination of a manufacturing-related deduction.

Mosaic Co. executives last week said the company’s effective tax rate will climb this year because the new law eliminated its ability to deduct the taxes it pays in Brazil, where it has a growing presence.

“At this point, we’ve optimized our operations under the old tax laws,” James O’Rourke, chief executive of the Plymouth-based fertilizer producer, told investment analysts on a conference call. “And although we’re going to change that and try to optimize against the new tax laws, in the transition, there are some quirks that will drive higher taxes.”

Executives at Minneapolis-based U.S. Bancorp said last month that they saw another effect — their business customers were borrowing less money. With a tax savings windfall, businesses paid down debt at a faster than usual rate, the bankers said.

Altogether the law contains hundreds of changes — such as how a company’s repayment of moving expenses to an employee will now count as income for that person, or how a company can no longer deduct entertainment expenses — many of them have gotten little attention.

“The 2017 tax law has a lot of things in it that are under the radar,” said Kim Severson, who chairs the tax practice at Minneapolis law firm Dorsey & Whitney. “It’s jam-packed with changes.”

The law’s biggest effect on business may play out beyond the eyes of investors, analysts and media. Most businesses in the United States are privately owned, and many owners — from farmers to storekeepers to partners in white-shoe law firms — are reconsidering how those firms are structured.

The vast majority of American businesses are structured as pass-through entities, tax lingo that covers forms such as limited liability companies or S-corporations in which corporate income “passes through” or “flows through” to the owner. The business’ income is taxed at the rate of the individual owner rather than the corporate rate.

“The trend for 30 years has been a preference for pass-through corps, where the business doesn’t pay the tax, the individual does,” said Christine Powers, Mankato-based partner of Abdo Eick & Meyers, an accounting firm that also has offices in the Twin Cities. “It was more advantageous for most businesses.”

But the new corporate rate of 21 percent is sharply below the highest individual rate of 37 percent. Business owners are flooding tax accountants and lawyers seeking advice about qualifying for the corporate rate by reshaping as a C-corporation, the structure used by most big firms.

Roberts, of Grant Thornton, worked on a team at the accounting firm that spent six weeks at the start of the year building a data tool to help business owners weigh their options. She said that it’s the first time in her career that she’s seen S-corporations switch to the C-corporation structure.

Business owners face numerous considerations, such as how many people share in a firm’s profits and whether a sale may be in the offing. There is no rush to decide, though no business owner wants to pay more taxes if it’s possible to pay less.

“They’re not forced to make a particular decision by a particular time,” John Erhart, who leads the tax practice at Fredrikson & Byron, a Minneapolis law firm. “But over a period of a year or two, I think every business is going to have to ask, ‘Is this the best way of operating the business from a tax perspective?’ ”

Many other issues tied to the new law remain unsettled. The Internal Revenue Service has provided little guidance so far as it works to define its implementation of the law’s hundreds of provisions. And the Minnesota Legislature is still writing its own bill to conform to the changes on the federal level.

Powers estimates it will be 18 months to two years before businesses adjust to all the changes. “It makes business owners apprehensive,” she said.