LBOs - Why repay debt instead of keeping cash flow?

The M&I guide says that "using the company’s cash flows to repay debt principal and pay interest
also produces a better return than keeping the cash flow." Is the intuition that the interest rate on the debt is always higher than the interest income you would get by keeping the cash? Would the exception to this be if reinvesting that cash back into the business and growing its enterprise value would generate an IRR that's higher than the interest rate on the debt principal? Not sure if this is the right way to think about it, so any help is appreciated here.

 
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One (but not the only) explanation is to think about your own credit card balance. The interest payments can become a burden when you are doing nothing to repay debt. And yes you are correct that interest income is generally very minimal. Other reasons include reputation with creditors in terms of being a sponsor that actually pays down debt like they are expected to, as well as increasing refinancing risk (the risk of being unable to refinance the debt that is leftover at exit). Lastly, you would need to consider if you could be in default of any covenants by letting leverage sit / pile on. Particularly risky is the case that you experience a period of EBITDA contraction, making leverage ratio shoot up.

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