If we hypothetically say that LTM EBITDA is $1M, then we buy the company at an enterprise value 10 x $1M = $10M. We borrow 5 x $1M = $5M, so we have to put in $10M – $5M = $5M of equity.
After 5 years, if EBITDA doubled, then ending EBITDA is $2M. If we sell at 10x, we sell at an enterprise value of 10 x $2M = $20M. After paying off the debt of $5M, we have $15M of equity remaining.
We have a multiple of capital of $15M / $5M = 3x. This implies an IRR of 25%, which can be calculated as:
Multiple of capital ^ (1/#of years – 1) = 3 ^ (1/5) – 1 = 25%.