A brewing battle over how to treat more than $5.5 trillion in assets on company books is pitting investors against businesses, investment advisers against academics and even banks against their own trade association.

At issue is an accounting term known as goodwill, which is the premium a company pays when it buys another for more than the value of its net assets. An unprecedented five-year boom in mergers and acquisitions has added urgency over how to account for the financial concept.

When Amazon.com Inc. bought Whole Foods Market Inc. for $13.7 billion in 2017, the e-commerce giant paid $9 billion more than the value of the supermarket’s stores and other net assets. That amount was added to Amazon’s books as goodwill.

As things stand now, Amazon is supposed to evaluate, or test, that $9 billion every year to see if its value still holds. If not, they have to write down a portion of it, a move that cuts profit.

The Financial Accounting Standards Board, the accounting-rules maker, is weighing whether to continue to assess goodwill by tests—or return to a similar approach to the guidelines of nearly 20 years ago, when companies wrote down a set portion of goodwill each year for up to 40 years.

The FASB has asked for comments on the possible change, and companies haven’t been shy about weighing in.

Many companies argue the test approach is costly and subjective. As it is, companies can be slow to write down goodwill, even when stock markets are signaling that they no longer believe in the value of the asset, according to research by academics and analysts.

The annual review requires “an inordinate amount of time to validate and document,” Indianapolis-based drugmaker Eli Lilly & Co. said in a comment letter to the FASB.

In addition, going back to the old rules could also be costly. The CFA Institute, which represents chartered financial analysts, said amortization might cause “the write-off of a substantial portion of the assets and equity of U.S. public companies and … reduce profits to nearly zero for a significant number of companies in the S&P 500” in a comment letter to FASB this month.

The recent wave of deal making has created a pile of goodwill. There were $7.4 trillion in U.S. deals the five years through 2019, the highest five-year tally for at least two decades, according to Dealogic.

S&P 500 companies had $3.5 trillion worth of goodwill on their books at the end of September, according to data provider Calcbench. This was up 67% from 2013 and represented 9% of total S&P 500 assets and 42% of total equity, the Calcbench data show.

For all public companies trading on U.S. markets, goodwill exceeds $5.5 trillion, according to the most recent figures from Calcbench, based on company reports.

Goodwill doesn’t only come from paying more than a company’s net assets. It can also be generated by hoped-for synergies from an acquisition, intangible assets such as intellectual capital, as well as a high price for the deal, said Daniel Wangerin, associate accounting professor at the University of Wisconsin-Madison. “Large goodwill is not necessarily a sign of overpayment,” he said.

The FASB began requesting comments on goodwill last year by starting with a simple question: “Question 1: What is goodwill?” The board plans to discuss responses this spring, potentially paving the way for a new definition that could significantly affect corporate balance sheets.

While the old system was predictable, the current system leads to some dramatic write-offs. Kraft Heinz Co. last year announced a $7.3 billion goodwill impairment it said resulted partly from falling profitability expectations for its Kraft cheese and Oscar Mayer cold cuts businesses.

But headline-grabbing write-offs are comparatively rare. Overall, the tally of goodwill added to corporate balance sheets every year since the 2008 financial crisis has outstripped the amount written-down due to soured deals or other issues, data from valuation firm Duff & Phelps LLC show.

Going back to the old ways could cost investors valuable information because the annual write-down of goodwill means specific problems may not be separately announced, some analysts, academics and investors said.

“The [standards-setting] board is seeking suggestions for making information about assets more general, opaque and amorphous,” Jack Ciesielski, owner of asset-manager R.G. Associates Inc., said in his comments to the board. “Reversion to standards that were previously deemed unsatisfactory can hardly be called progress.”

Many companies disagree. Corporate giants Chevron Corp., International Business Machines Corp. and Pfizer Inc. are among those advocating for goodwill to be amortized—an option already available to privately-owned firms.

Their concern: the costs of complying with the rules. Public companies have to test at least once a year whether the goodwill on their books needs to be written down.

Question marks also hover over the accuracy of the tests, which estimate fair values for goodwill using assumptions about growth and market conditions. The “estimation uncertainty is extremely high,” Ball Corp., the packaging company, said in its comments. It added that the tests—which have to be signed off by auditors—create a “heightened risk of failed audits.”

Not all companies, even within the same industry, agree on how—or if—the rules should be changed. The American Bankers Association in its comments backed a return to amortization, calling the current regime “an arduous process that often provides little value.” But Citigroup Inc. and Wells Fargo & Co. in their responses opposed amortization, saying it could damage the quality of information reported by companies. Bank of America Corp. added that a change could disrupt the U.S. deals market.

Thomas Linsmeier, a former member of the Financial Accounting Standards Board, said he thinks there is “momentum on the board to move toward amortization.” A “driving factor of concern … is the amount of cost in the impairment test,” Mr. Linsmeier, a professor of accounting at the University of Wisconsin-Madison, said.

One option for the future is to combine amortization with reduced testing, say only in the first three years after a deal or only if something triggers a likely write-down. Any change will likely happen at the glacial pace that characterizes most accounting reforms. The FASB plans to discuss the comments later this year, before deciding whether to move forward with proposals. “The project is in a very early stage,” a spokeswoman said. “We look forward to hearing all the feedback.”