Paper LBO and Mental Math for PE Superday Interviews

The paper LBO is the PE interview's signature exercise: a partner or VP gives you a napkin, a whiteboard, or five minutes of silence, and asks you to size a buyout, estimate the return, and explain where it comes from — without Excel. It's not testing spreadsheet skills. It's testing whether you understand the mechanics well enough to reason about them in real time. This guide covers the mental math framework that lets you do that cleanly.

The 30-second setup

Every paper LBO starts with four inputs:

1. Entry EBITDA (e.g., $100M)
2. Entry Multiple (e.g., 10x)
3. Leverage (e.g., 5.0x EBITDA = $500M debt on $1B EV)
4. Hold period (e.g., 5 years)

From those four numbers, you can derive everything else:

Entry EV     = EBITDA × Multiple = $100M × 10x = $1,000M
Debt         = EBITDA × Leverage = $100M × 5.0x = $500M
Equity       = EV − Debt = $500M

That's your entry. Now you need three exit assumptions:

5. EBITDA growth (e.g., 5% CAGR → Exit EBITDA ≈ $128M)
6. Exit multiple (e.g., same 10x)
7. Debt paydown (e.g., $200M over 5 years from cash flow)

Exit equity in three lines

Exit EV     = Exit EBITDA × Exit Multiple = $128M × 10x = $1,280M
Exit Debt   = Entry Debt − Paydown = $500M − $200M = $300M
Exit Equity = Exit EV − Exit Debt = $1,280M − $300M = $980M

MoIC = Exit Equity ÷ Entry Equity = $980M ÷ $500M = 1.96x
IRR  ≈ MoIC^(1/5) − 1 ≈ 1.96^0.2 − 1 ≈ 14.4%

Done. You just paper-LBO'd a deal in under two minutes.

Mental math shortcuts

MoIC to IRR conversion (5-year hold)

| MoIC | Approx IRR | |------|-----------| | 1.5x | ~8% | | 2.0x | ~15% | | 2.5x | ~20% | | 3.0x | ~25% | | 4.0x | ~32% |

Memorize this table. For other hold periods, use MoIC^(1/years) − 1. For quick mental math, the rule of thumb for 5 years: IRR ≈ (MoIC − 1) × 15% works reasonably for MoIC between 1.5x and 3.0x.

EBITDA growth shortcuts

| CAGR | 5-Year Multiple | Quick Estimate | |------|----------------|----------------| | 0% | 1.00x | Flat | | 5% | 1.28x | ~$100M → $128M | | 10% | 1.61x | ~$100M → $161M | | 15% | 2.01x | ~$100M → $201M |

For mental math, 5% CAGR over 5 years ≈ 30% total growth (multiply by 1.3). 10% CAGR ≈ 60% growth (multiply by 1.6).

Debt paydown estimation

Without building a full debt schedule, estimate paydown as a fraction of entry debt:

• Strong cash generator (low capex, high margins): 40%–50% of entry debt paid down over 5 years
• Average business: 25%–35% paydown
• Capex-heavy or low-margin: 10%–20% paydown

Quick check: if EBITDA is $100M, margins are 30%, capex is 5% of revenue, and debt costs 6%, annual free cash flow available for sweep might be ~$20M–$25M. Over 5 years, that's $100M–$125M of paydown on $500M of debt — roughly 20%–25%. Adjust up or down based on the business profile.

The three-scenario framework

Interviewers often ask you to bracket the return with upside and downside cases. Build three scenarios mentally:

Base case (as above): 5% EBITDA growth, flat multiple, 40% debt paydown → ~2.0x MoIC

Upside: 10% EBITDA growth, +1 turn multiple, 50% paydown

• Exit EBITDA: $161M, Exit EV at 11x = $1,771M, Exit Debt = $250M → Exit Equity = $1,521M → MoIC = 3.0x

Downside: Flat EBITDA, −1 turn multiple, 20% paydown

• Exit EBITDA: $100M, Exit EV at 9x = $900M, Exit Debt = $400M → Exit Equity = $500M → MoIC = 1.0x (zero return)

Presenting this range shows you understand which assumptions drive the outcome and that the deal has real downside risk if multiples compress.

Returns attribution without a spreadsheet

Once you have entry and exit equity, decompose verbally:

"This is a ~2.0x deal over 5 years. Roughly $200M from debt paydown, $280M from EBITDA growth at the entry multiple, and zero from multiple expansion since we held the multiple flat. It's a deleveraging-and-growth story, not a multiple expansion bet."

The math:

• Deleveraging: $500M − $300M = $200M
• EBITDA growth: ($128M − $100M) × 10x = $280M
• Multiple expansion: $128M × (10 − 10) = $0
• Check: $500M + $200M + $280M = $980M ✓

Common paper LBO questions and how to handle them

"What leverage would you put on this business?" Start with the business profile: stable cash flow, low capex, defensible market → 5.0x–5.5x is reasonable. Cyclical or capex-heavy → 3.5x–4.5x. Always tie leverage to cash flow coverage, not just a rule of thumb.

"What if you can't pay down any debt?" Exit Equity = Exit EV − Entry Debt. If EBITDA grows 5% and multiple is flat: Exit EV = $1,280M − $500M = $780M → MoIC = 1.56x. Still a return, but entirely from EBITDA growth. Shows why deleveraging matters.

"What's the maximum price you could pay and still hit 2.0x?" Work backwards: you need Exit Equity = 2.0 × Entry Equity. With known exit EV and exit debt, solve for entry equity, then entry EV, then implied entry multiple. This reverse-engineering is a common follow-up.

"How does a dividend recap affect this?" A recap pulls forward equity via a special dividend funded by new debt, boosting IRR (earlier distributions) but increasing exit debt (lower exit equity). Net effect on MoIC is often neutral or slightly negative, but IRR improves because capital is returned sooner.

What separates a good paper LBO from a great one

A good candidate gets the math right. A great candidate:

1. States assumptions explicitly before calculating ("I'm assuming 5% EBITDA growth, flat multiple, and 40% debt paydown")
2. Identifies the binding constraint ("This is a deleveraging story — the business doesn't need to grow much if cash generation is strong")
3. Brackets with upside/downside without being asked
4. Connects to the business ("This is a subscription software business with 90% gross margins and low capex, so 5.0x leverage and strong paydown is credible")
5. Knows when the deal doesn't work ("At 12x entry, you'd need significant multiple expansion or EBITDA growth to hit 2.5x — that's a bet on market, not operations")

Practice the framework until it's automatic

The paper LBO isn't about precision — it's about structured thinking under pressure. Practice with random inputs until you can go from "EBITDA $80M, 8x, 4.5x leverage, 5 years" to "~2.2x MoIC, ~17% IRR, deleveraging-heavy" in under three minutes.

Then prove the precision on SheetRank's live LBO deals, where every cell in your debt schedule and returns build is graded against a real answer key. The paper LBO gets you through the interview; the live model gets you the offer.