There’s also operating leverage. This business should trend to 50-80% gross margins and 30-50% profit / free cash flow conversion, similar to Facebook, Google, or other similar businesses.
Further, there’s a bunch of pre- and post- transaction adjustments that hit the financial statements (for example stock based compensation will likely go away in a private company, thus raising profitability), so you can’t just take last years profit and tack on the new debt structure.
Last, the amortization on high yield isn’t necessarily linear. In the most extreme example (where the debt costs >12%) you could have pay-in-kind (PIK) interest where the interest payments accrue to the balance of the loan (like a credit card) and for amortization, it could be anywhere from straight line (1/x periods) to a “bullet” with no amortization at all until a end period where it all comes due at once (you typically refinance in that case).
All-in, it may be risky, but the bankers that committed billions of capital to the deal aren’t exactly brain dead and all have internal credit approval processes which require them to do all the work outlined above and a bunch more.