Cost of capital - supermarkets

How should one think about the impact of a large supermarket business's negative cash conversion cycle? Say, for example, I'm looking at a large, privately-owned grocery business which is funded exclusively via equity.

Say, hypothetically, there is a negative working capital balance of similar size to the book value of equity. Is the business therefore not effectively financed by it's suppliers? And using cost of equity only (in CAPM) to determine the business's cost of capital overstates this greatly? Should the negative cash conversion cycle not reduce the implied cost of capital to the business or am I overthinking it?

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