I'm on the board of a local chapter of a national nonprofit with an excellent reputation and mission. However, the CEO's book is being sold prominently in the organization's web store. I'm pretty certain that the proceeds of sale are passed through to the CEO. Wouldn’t that be private inurement? Wouldn’t selling the book itself be private inurement?
You think like the Internal Revenue Service! The IRS is very suspicious about charities selling insiders’ books or other products that could constitute private inurement, and it occasionally seeks to revoke an organization’s exemption in egregious cases. But even if the CEO personally benefits from the sales, the arrangement may not rise to the level of private inurement.
The first question is whether the book is related to the purpose of the organization. If the book is unrelated, its sales will generate unrelated business taxable income for the organization, and if substantial could result in loss of the organization’s exempt status. (See Ready Reference Page: “Nonprofits Often Worry About UBIT”) If the book is unrelated, the sale itself could be a form of private inurement, which could jeopardize the exempt status if substantial. If the book sells five copies a year (and there are no other insider deals), I doubt the IRS would get terribly upset about it. If it sells 5000 copies a year, it could be a very different story.
If the content of the book is substantially related to the purpose of the organization, you would need to look at the economic arrangement with the author. Some authors will write the book as a work for hire for the organization so that the organization owns all of the economic value. Some authors will give the copyright to the charity. Some will give all of the proceeds of the sales to the charity (while retaining the right to sell the book for their own benefit in other places). Others may pay a commission to the organization as a sales agent. In the latter case, the sales commission would have to be commercially reasonable or the author could be deemed to be receiving an excess benefit, subject initially to tax on the excess. The organization could also lose its exemption if the practice is continuing and excessive. The charity could pay the author a percentage of the sales price as part of the CEO’s compensation, so long as the total compensation package is reasonable. (See Ready Reference Page: “Charities Must Avoid Excess Benefit Transactions”)
The IRS does not like insiders personally benefiting (beyond reasonable compensation) from activities of a charity that make the insider richer, so you are correct to be concerned. But you have to look at the arrangement and the numbers to determine whether there is a serious risk.