Paper LBO: Setup, Execution, and Worked Examples

Introduction

The paper LBO mental math framework article covers the underlying mechanics and the core IRR approximation rules. This article takes those foundations and applies them to two fully worked examples at different complexity levels, so you understand not just the process but also how to adapt when the numbers get harder.

If you have not read the framework article first, do that now. This article assumes you are familiar with MOIC-to-IRR approximation shortcuts (2x = 15%, 3x = 23-25%, 4x = 30%) and the Rule of 72.

Before you see a single number, you need a mental template. Every paper LBO has the same skeleton:

Write this structure on paper before any numbers appear. The format itself buys you confidence. For a detailed walkthrough of the verbal LBO answer, see Walk Me Through an LBO. For the three value creation levers (EBITDA growth, debt paydown, multiple expansion), see the dedicated article.

Paper LBO

A simplified LBO analysis performed with pen, paper, and mental math during a private equity or investment banking interview. The candidate receives a set of assumptions (entry multiple, leverage, EBITDA growth, exit multiple, holding period) and must calculate the sponsor's returns (MOIC and approximate IRR) within 5-10 minutes. The paper LBO tests three skills simultaneously: understanding of LBO mechanics, comfort with mental math under pressure, and the ability to communicate clearly while calculating. For more on mental math shortcuts, see our blog post on paper LBOs.

The prompt: A private equity firm is considering acquiring a manufacturing company with $100 million in LTM EBITDA. The entry multiple is 8x. The deal is financed with 5x leverage. The company grows EBITDA at 8% per year. CapEx is $10 million per year and net working capital changes are minimal. The tax rate is 30%. All FCF is used to repay debt. The firm plans to exit at 8x EBITDA after five years. What is the approximate IRR?

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Step 1: Entry

Step 2: Project EBITDA at exit

EBITDA grows 8% per year for 5 years. Mental shorthand: 8% for 5 years compounds to roughly 1.47x. $100M x 1.47 = approximately $147 million exit EBITDA. Round to $150 million for ease.

Free Cash Flow for Debt Repayment (Paper LBO Context)

In a paper LBO, the simplified free cash flow available for debt repayment is approximately: EBITDA minus taxes on EBIT minus CapEx minus working capital changes. This is NOT the same as UFCF (which uses EBIT x (1-t) as the starting point) but is a close enough approximation for mental math. The key simplification: ignore interest expense for the FCF calculation (since the paper LBO typically states "all FCF goes to debt repayment" without modeling the interest explicitly). If the prompt says interest is $30 million per year, subtract it from FCF before calculating debt repayment.

Step 3: Estimate annual FCF for debt repayment

Total debt repaid over 5 years: $77M x 5 years = roughly $385 million.

Step 4: Exit

Step 5: MOIC and IRR

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This example layers in a more complex debt structure and a changing exit multiple, representing a harder interview prompt.

The prompt: A PE firm is evaluating a business services company with $80 million EBITDA. Entry multiple is 9x. The deal uses 4.5x total leverage, split between a $250 million term loan repaid pro rata over 5 years and a $110 million second lien that is interest-only (no amortization). EBITDA grows at 10% per year. CapEx is 6% of EBITDA annually. Tax rate is 30%. No significant working capital changes. Exit after 5 years at 8x EBITDA (multiple compression of 1 turn). What is the approximate IRR?

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Step 1: Entry

Step 2: Exit EBITDA

10% per year for 5 years: 1.1^5 is approximately 1.61. $80M x 1.61 = $129 million. Round to $130 million.

Step 3: FCF and debt repayment

Second lien is interest-only, so only the term loan of $250M amortizes. Straight-line over 5 years: $50M per year in mandatory amortization.

Check FCF supports this: midpoint EBITDA roughly $105M, CapEx 6% = $6.3M, taxes (EBIT roughly $99M, tax $30M). FCF approximately $69M, well above the $50M minimum. Excess cash after amortization is $19M per year, which could be used for additional debt paydown. Conservative approach: assume only mandatory amortization.

Step 4: Exit

Step 5: MOIC and IRR

After delivering your headline IRR, show that you understand what drives it by running a brief sensitivity. In a paper LBO, you can do this verbally:

"If we assume the exit multiple holds at 9x instead of compressing, exit EV becomes $1,170M, exit equity $1,060M, MOIC 2.9x, and IRR climbs toward 24%. Alternatively, if EBITDA growth is 7% instead of 10%, exit EBITDA would be closer to $112M, exit EV at 8x would be $896M, exit equity $786M, MOIC 2.2x, and IRR roughly 17%."

This takes 30 seconds and signals to the interviewer that you think in ranges, not point estimates, which is exactly how a real private equity investor thinks.

The target is to complete the full exercise, including IRR estimation and one sensitivity comment, in under 10 minutes. Break it down:

If you are consistently taking 12-15 minutes in practice, the bottleneck is almost always the FCF calculation. Simplify: use a single representative FCF figure for the entire hold period rather than building a year-by-year schedule. Precision is the enemy of completion in a paper LBO.

Practice with different entry multiples, leverage levels, and growth rates until the arithmetic feels automatic. The goal is not to be a calculator. The goal is to demonstrate that you think like an investor who can quickly frame whether a deal generates acceptable returns.