How to do a paper LBO in your head

A paper LBO is a leveraged buyout you do with a pen, or in your head, in about ten minutes. Many private equity interviews include one, either as a written test or out loud in the room. The maths is simple. What catches people is the order of steps and the pressure of doing it with someone watching.

Here is the method I'd use, then a full worked example with round numbers.

The five steps, always in this order

1. 01Entry. Purchase price = entry EBITDA × entry multiple. Split it into debt and equity.
2. 02Project EBITDA to the exit year.
3. 03Free cash flow and debt paydown. How much debt is left at exit?
4. 04Exit. Exit enterprise value = exit EBITDA × exit multiple. Equity at exit = exit EV − remaining net debt.
5. 05Returns. MOIC = exit equity ÷ entry equity. Convert to IRR.

Say each step as you go. If you make an arithmetic slip, an interviewer who can follow your steps will often nudge you back. If you go silent and produce a number, they can't.

A worked example

The “FCF is about a third of EBITDA” line is an assumption you'd normally be given or asked to build. If the interviewer gives you interest rates, tax rates and capex, work them through year by year. If they don't, state your shortcut out loud and ask if it's acceptable. Many will say yes and move on.

Know where the returns came from

A very common follow-up is “what drove the return?” There are three sources, and in a paper LBO you can split them exactly.

Interviewers like to hear that the return didn't rely on selling at a higher multiple than you bought at. Multiple expansion is the part of the return you control least. A deal that only works if the exit multiple rises is a weak deal.

MOIC to IRR without a calculator

Nobody expects you to take a fifth root in your head. Memorise a small table and interpolate.

The five-year column is the one you'll use most. 2x in five years is about 15%, 2.5x is about 20%, 3x is about 25%. For 2.25x, halfway between 2x and 2.5x, call it roughly 17 to 18%. That's close enough for any interview, and saying “roughly 17 to 18%, the exact figure is a touch under 18” sounds more confident than guessing to a decimal.

As a cross-check, the rule of 72 says money doubles in about 72 ÷ rate years. At 15%, that's 72 ÷ 15 ≈ 4.8 years, which agrees with 2x in five years being about 15%.

The sensitivities they'll ask for

Once you have a base case, expect “what if?” questions. Don't redo everything. Change one input and follow it through.

One turn of multiple cost about 3.5 points of IRR here. That's worth saying out loud, because it shows you understand how sensitive the deal is to the exit.

The other classic is working backwards: “What exit EBITDA do you need for a 20% IRR?” 20% over five years is about 2.5x, so exit equity needs to be 2.5 × 400 = 1,000. With 400 of debt left, exit EV must be 1,400, so at 10x you need EBITDA of 140. (Higher EBITDA would also mean a bit more debt paid down, so the true figure is slightly lower. Mention that as a refinement, then move on.)

Mistakes that cost marks

1. Forgetting to subtract debt at exit. Exit EV is not your equity.
2. Dividing exit EV by entry EV instead of exit equity by entry equity. That gives an unlevered multiple, not your return.
3. Ignoring fees when they're given. If the case mentions transaction fees, they increase the equity cheque at entry.
4. Skipping the sanity check. If you get a 60% IRR on a mature business bought and sold at the same multiple, something is wrong. Look again before you say it.
5. Not having a view. After the numbers, say whether you'd do the deal and why. “About 17–18% with no multiple expansion, mostly from growth. If the growth case is credible, I'd want to look further.”

The best way to get quick at this is to do the same structure with different inputs ten or fifteen times, out loud, until the steps stop needing thought and your attention can go on the judgement questions at the end.