Accounting Due Diligence - understating debt

Hey monkies - my PE prep book says that in accounting due diligence, Accountants make sure that "any outstanding liabilities are categorized properly as debt or working capital. "this is important because debt is subtracted from the purchase price, so sellers have an incentive to classify iffy items as working capital instead of debt"

However, I was under the impression that: -Private Company LBO: Purchase Price = TEV = LTM EBITDA x Entry Multiple -Public Company LBO: Purchase Price = TEV = Market Cap + Net Debt

If anything, assuming the above equations are correct, debt is added to achieve purchase price, not subtracted. (NOTE: Qualitatively, I realize that having lots of debt on a BS can be considered bad, as it increases the cost to the financial sponsor; however, mathematically speaking this should not impact the seller...)

Can someone help clarify?

Thanks!

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