Private companies can choose whether to consolidate onto their balance sheets an interest in another entity that they control—known as variable interest entities—under a rule change intended to make the accounting simpler.

The updates that the Financial Accounting Standards Board announced Oct. 31 are intended to reduce the cost and complexity for private companies to report on variable interest entities. Consolidation accounting stands among the most complicated areas of financial reporting.

“It provides private companies the choice to not apply...