ROIC when stockholders' equity is negative

Nontarget, you are incorrect. When calculating ROIC you want to use book value of equity and debt, as these are measures of the dollars of investment that debt and equity holders have put into the business (whereas market value is the assessed valuation of those investments). For an alternate measure, one can also use tangible capital (PP&E + Net Working Capital + [other relevant investments]), which will not include (as much of) an impact from acquisition adjustments. I could go on for hours about the various potential issues that can affect even clean-looking ROIC calculations, but it isn't directly relevant for grosse's (excellent) question.

To grosse: this can certainly happen, and in fact should happen with any capital light business (think: tobacco, consumer staples, franchisor restaurants). Really the only thing that should keep these businesses' book equity positive are deals, which create new book equity.

The issue is that ROIC simply isn't that relevant a concept for capital light businesses. Return on invested capital is a useful model when your growth depends on putting more capital in the ground. For instance, opening new physical restaurants, building new factories, etc. But when a business does not actually use capital to grow (e.g., price increases, new franchise licences, etc.), the ROIC approach just isn't that relevant. The amount of capital "in the ground" has only the loosest of relationships with the size of the business, and thus the accounting system just doesn't give you very meaningful answers. The classic example: if the fund you work at bought new office space and equipment with retained profits, doubling the book equity invested in the fund, would you expect its profits to double as well?

To walk through what is technically happening: debt holders care about cash flow, which is growing without new capital investment (or with trivial capital investment). As the cash flows grow, the business can take on more debt, of course, but the book value of equity does not have to rise, as no earnings need be retained. However, the accounting statement "thinks" that the business has not grown, and thus "interprets" the payout of the dividend as a liquidation, rather than a distribution of gains. For this reason, the accounting statements just can't "handle" the situation. Accounting statements were born in an era of heavy industry; the idea of "capital light" just wasn't that relevant, and thus we have an accounting system that isn't well calibrated for such businesses. It is a limitation of accounting that you have run into, and one that might not ever be fully dealt with using a three statement approach.

So when you see negative equity for the reason you described, the answer is "this business does not use capital to grow and therefore ROIC is not a relevant metric for the business." Note that there are some other ways to think about ROIC. For instance, you can look at the ROIC of a "franchise system" as a whole, including the invested capital of the franchisees. If you can find or estimate that number, then that ROIC number will inform you of the health and growth prospects of the entire system of restaurants, which does have an impact on the future profitability of the franchisor.

EDIT: One additional thought. This scenario can also occur if there is capital invested in the business, but the return on that capital is extremely high. The logic is the same: cash flows are growing much faster than book equity, permitting the business to take on debt and pay out more than book equity.