Which creates more value in an LBO: one turn of multiple expansion or one more turn of leverage?

I would show it with a simple example. Say the company has $100M of EBITDA and is bought at 10 times, so $1,000M, funded with 5 times debt, $500M, and $500M of equity. To isolate the effect, assume EBITDA stays flat, no debt is repaid and interest is ignored.

With one turn of multiple expansion, the company exits at 11 times, or $1,100M. After repaying the $500M of debt, equity is worth $600M, so the investor gets 1.2 times its money. With one more turn of leverage instead, debt is $600M and equity only $400M. If the exit is at the same 10 times, enterprise value is $1,000M, equity is still $400M, and the multiple is 1.0 times. Nothing was created, because leverage does not change the value of the business.

So in this setup multiple expansion creates more value. Leverage magnifies whatever happens to enterprise value. If EBITDA grew to $120M and the exit was at 10 times, equity would be $700M on $500M invested with 5 times debt, 1.4 times, versus $600M on $400M with 6 times debt, 1.5 times. But in a downturn extra leverage hurts returns more and adds interest cost and default risk.