Sales of books and bracelets and other trinkets at Smithsonian museum shops help pay the museums’ ongoing ex­penses, but Smithsonian Inspector General A. Sprightley Ryan has found a confusing and unfair system of revenue-sharing, according to a preliminary report on Smithsonian Enterprises, the organization that oversees the complex’s for-profit businesses.

The museums’ financial agreements are too complex and not transparent enough, harming the share of profits that Smithsonian Enterprises is required to return to the museums, according to the draft report obtained by The Washington Post. The report also found a lack of clarity and collaboration between the museums and Smithsonian Enterprises.

“We believe the way in which SE allocates its overhead costs may be inappropriate,” said the inspector general’s draft report. The total given back to the museums is determined after the museums are charged for SE’s business expenses including overhead, which reduces the museums’ income.

Smithsonian Enterprises, run by President Tom Ott, operates the museum stores and concessions, Smithsonian magazine and other publications, the theaters, the merchandise catalogue and licensing deals. The division also includes Smithsonian Journeys, the educational travel program, and Smithsonian Network, a cable channel.

In fiscal 2010, the division earned a healthy $146.5 million and returned $27.8 million to the Smithsonian. The money given to the museums can be used for many items, including salaries and exhibitions.

The profit-making side of the Smithsonian is important to its financial health, especially in a slow economy. The museums are free and many of the operations are supported by tax dollars. The Smithsonian receives 70 percent of its budget from the federal government. Yet to support research, exhibitions, repairs, expansions and some salaries, it needs to raise millions of dollars privately.

The museums’ finances are a reflection of the larger Smithsonian world. The directors and development officers spend increasingly more time fundraising. However, not knowing exactly how much money they are receiving because the overhead costs fluctuate, the report said, can delay or cancel projects.

“These delays or cancellations lead to a loss of potential revenue and jeopardize relationships with museums,” the report said.

Faulty methodology is cited as a principal cause of the confusion around the money’s distribution. The report asked for reforms of formulas used to measure SE’s costs.

At one point, the draft report quoted a museum director as saying the allocations are “shrouded in mystery.”

The subject of returned revenue share has been a thorny issue at the Smithsonian for years. The inspector general has examined the operations of Smithsonian Enterprises and its predecessor, Smithsonian Business Ventures, in the past.

In 2007, a task force was formed by the Smithsonian management to look at controversies surrounding Smithsonian Business Ventures, the first operation to pull together the money-making departments. After Congress reviewed the business practices, and the misuse of funds by a former official, the Smithsonian moved to correct what it called “gross problems” and renamed the troubled business unit Smithsonian Enterprises.

The task force recommended that the revenue-sharing model between the Smithsonian and the museums be a consistent split at 50/50 after expenses.

Ryan, the Smithsonian inspector general, said many aspects of the draft could change before the report is made final late this summer. In the final statement, the SE managers have an opportunity to respond.

The inspector general’s office reports directly to the Smithsonian Board of Regents.