Chapter 4 of 5 · 14 min

The paper LBO

The whole buyout on a notepad: entry, five years of cash repaying debt, exit, MOIC and IRR.

By the end of this chapter you can

Build a year of free cash flow: EBITDA less interest, tax and capex
Carry the debt paydown through five years
Calculate exit equity, MOIC and IRR, and check them with the rules of thumb
Work out the highest entry multiple that still meets a target return

The intuition

You buy a flat to rent out, mostly with a mortgage. Each year the rent comes in; you pay the mortgage interest, the tax on your profit and the repairs, and put every dollar that is left toward the mortgage. The loan shrinks, so next year's interest is smaller and there is even more left over.

After five years you sell. The price, less the mortgage still owed, is what you walk away with. A paper LBO is exactly this, for a company, done by hand in an interview.

The key idea

Each year: free cash flow = EBITDA − interest − taxes − capex, and all of it repays debt. At exit: equity = exit EBITDA × exit multiple − the debt left. Paydown feeds itself, because less debt means less interest.

Why it works

The conventions, stated in every question: a five-year hold, D&A equal to capex, interest on the debt at the start of each year, tax charged after interest, flat working capital, all free cash flow repays debt, no fees.
Each year. Interest = opening debt × rate. EBIT = EBITDA − D&A, and D&A = capex. Taxes = (EBIT − interest) × t. Free cash flow = EBITDA − interest − taxes − capex. Closing debt = opening debt − free cash flow.
Tax comes after interest because this is the cash left for the owners after paying the lenders. The tax saving on interest is real cash in an LBO.
At exit, enterprise value = year-5 EBITDA × exit multiple; subtract the debt still owed to get exit equity. MOIC and IRR follow.
Rules of thumb over five years: 2.0x is about 15% a year, 2.5x about 20%, 3.0x about 25%.
The most you can pay. Debt is sized off EBITDA, so paying more adds only equity. Exit equity ÷ target MOIC is the most equity you can put in; add the debt and divide by EBITDA for the highest entry multiple.

Year one: EBITDA $100M; opening debt $500M at 8%; capex = D&A = $15M; tax 25%

Interest: 500 × 8%	40.0
EBIT: 100 − 15	85.0
Taxes: (85 − 40) × 25%	11.25
Free cash flow: 100 − 40 − 11.25 − 15	33.75
Closing debt: 500 − 33.75	466.25

Checks on the rules of thumb: 2.0^(1/5) − 1 = 14.9%, 2.5^(1/5) − 1 = 20.1%, 3.0^(1/5) − 1 = 24.6%.

The formulas

Entry: TEV = EBITDA₀ × multiple; debt = turns × EBITDA₀; equity = TEV − debt

What is bought, borrowed and put in.

Year i: interest = opening debt × rate; EBIT = EBITDA − capex (D&A = capex)

Interest on the start-of-year balance.

Taxes = (EBIT − interest) × t; FCF = EBITDA − interest − taxes − capex

Cash left after lenders, tax and reinvestment.

Closing debt = opening debt − FCF

Every dollar repays debt.

Exit equity = EBITDA₅ × exit multiple − closing debt₅; MOIC = exit ÷ entry; IRR = MOIC^(1/5) − 1

Sell, repay, measure.

Max entry multiple = (exit equity ÷ target MOIC + entry debt) ÷ EBITDA₀

The most you can pay for a required return.

Worked example

One year of the model. Interest first, then tax on what is left after interest, then capex.

Drawing the numbers…

See it move

Same deal. Change the growth, the interest rate, the capex, the leverage and the exit multiple.

Drawing the numbers…

Try this

Raise the interest rate. Year-one interest rises, taxes fall by the tax rate × that rise, so free cash flow falls by only the after-tax part of it.
Raise capex. EBITDA does not move, but free cash flow falls, less debt is repaid, and IRR drops.
Add leverage. The equity check shrinks, but more interest leaves less free cash flow every year.
Change the exit multiple. Nothing in the five years changes; only exit equity moves, by the change in multiple × year-5 EBITDA.

Run it backwards

Same deal, reversed: the fund needs a target multiple of money. What is the highest entry multiple you can pay?

Drawing the numbers…

The lenders lend the same turns of EBITDA whatever the price, so the debt, the five years of cash flow and the exit equity do not depend on the entry multiple. Exit equity ÷ target MOIC is the most equity you can put in. Add the debt for the most enterprise value, and divide by EBITDA.

This is why the winner of a competitive auction often earns the lowest return: every turn it bids above the others is paid entirely in equity.

Traps

Taxing EBIT before interest.

This is the cash left for the owners, so tax is charged on EBIT after interest. The interest shield is real cash.

Forgetting capex.

D&A is added back through EBITDA, but capex is real cash spent. Subtract it.

Charging interest on the closing balance.

These questions charge interest on the debt at the start of the year. Using the closing balance makes the model circular.

Paying the whole exit enterprise value to the sponsor.

Repay the debt still owed first. Only the rest is exit equity.

Computing IRR as MOIC ÷ 5.

IRR compounds: take the fifth root of MOIC and subtract one, or use the rules of thumb.

Say it in the interview

The interviewer asks

“Walk me through a paper LBO.”

Say yours out loud first, then compare.

Check yourself

4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.

Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.

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Drawing your questions…

Remember

FCF = EBITDA − interest − taxes after interest − capex.
All FCF repays debt; less debt means less interest next year.
Exit equity = EBITDA₅ × exit multiple − debt left.
5 years: 2x ≈ 15%, 2.5x ≈ 20%, 3x ≈ 25%.