When RadioShack Corp. filed for bankruptcy protection last year, it raised more than $170 million by selling such holdings as real estate, leases and inventories of smartphones, computer cables and cameras.

But the retailer’s books didn’t acknowledge two of its most valuable assets: its brand and its customer data.

How do you attach a price tag to something you can’t see or touch?

The question is increasingly significant for investors as more companies collect information about their customers and use it to develop products and services. Some companies rely on the hipness of their brands to propel sales.

Assigning a value to a physical asset like a store or equipment is relatively easy. But, in the murky world of intangible assets, the calculations are squishy. The problem of how to value such assets has vexed accountants for decades.

Under current accounting rules, U.S. companies don’t record those items on their books as assets. “It’s 19th-century accounting,” said Baruch Lev, an accounting and finance professor at New York University’s Stern School of Business.

The absence of abstractions like brand value on corporate balance sheets prevents investors from properly gauging their risks, said Mr. Lev. “It’s an incredibly important issue,” he said. “Investment in intangibles is almost completely obscured from investors.”

Altogether, companies in the U.S. could have more than $8 trillion in intangible assets, according to Leonard Nakamura, an economist at the Federal Reserve Bank of Philadelphia. That’s nearly half of the combined $17.9 trillion market capitalization of the S&P 500 index.

These days, companies put far more money into nonphysical assets, such as customer databases, than they do in building new factories. Companies invested the equivalent of 14% of the private sector’s gross domestic product in intangibles in 2014, according to research by economist Carol Corrado. The investment in physical assets was about 10% of that sum. That’s essentially the reverse of 40 years ago, when 13% of private-sector GDP went to tangibles and 9% to intangible assets.

Last month a small group of researchers at the nation’s accounting standards-setter began grappling with the idea of updating its rules to recognize the growing importance of intangibles. The effort is still in its early stages, but the Financial Accounting Standards Board is considering adding the topic to its rule-making agenda. That could lead to a new rule requiring companies to bring those assets onto their books.

The FASB has weighed the question before, but got hung up on key issues: For example, should the value of intangibles be based on how much they cost to create, or should company management have to estimate the fair value of those assets?

Companies also need to measure value over time. While there are well-established ways to determine the depreciating value of a computer, it’s much harder to do so for such things as trademarks, patents or customer relationships. So far, the FASB hasn’t been able to find a solution in which the benefits of reporting intangibles outweigh the costs, according to a spokesman.

“It’s definitely possible to value intangibles,” said John Rainey, chief financial officer of digital-payments company PayPal Holdings Inc. “But it represents another burden. The question is: how much incremental work does it take?”

If the FASB adds intangibles to its agenda, it could be years before it comes up with a new rule. It took a decade of debate and revisions to overhaul rules for lease accounting that go into effect for public companies at the end of 2018. That rule, which requires companies to bring operating leases onto their books, could swell U.S. corporate balance sheets by $2 trillion overall, according to some estimates.

The addition of intangibles would likely have much greater impact, said PJ Patel, co-chief executive of Valuation Research Corp.

Sometimes, such as after an acquisition, companies are required to value intangible assets. The buyer must itemize intangibles like brand value and client lists, and update their value annually.

The accounting department at Perrigo Co., spends weeks at the end of every year valuing and auditing intangibles that the Dublin-based pharmaceutical company has purchased over the past several years. Doing the same every quarter for earnings reports would be “a huge undertaking,” said finance chief Judy Brown.

Businesses that file for bankruptcy value their intangibles, because those assets can be sold for millions. That, too, is a cumbersome process.

Putting a value on RadioShack’s intangibles and selling them took about eight weeks, said David Peress, an executive vice president of valuation firm Hilco Streambank, who advised the company on the sale. Its brand and itscustomer data fetched $26.2 million.

Corporate borrowers also often use their brands to backstop loans. Ford Motor Co., for example, borrowed $23.6 billion in 2006 by putting up virtually all of its assets—including its blue Ford logo—as collateral.

Some investors and analysts say they don’t need to know the specific value of intangible assets like data. They say a company’s stock price reflects the market’s appraisal of those assets.

Take Facebook Inc. The stock market values the social-networking company at nearly $320 billion. As of Dec. 31, its assets minus liabilities totaled $44.2 billion. The difference between the two could serve as a proxy for the value of Facebook’s vast troves of user data, the algorithms it creates to mine that data and its brand.

That would put the value of Facebook’s intangibles at about six times that of its tangible assets, such as cash, property and equipment.

But there’s no way to really know, said Ms. Corrado, the economist, who now works for the Conference Board. “You’re leaving a lot to the imagination.”

Write to Vipal Monga at vipal.monga@wsj.com