Advanced LBO Modeling: Paper LBOs, Sensitivity Analysis, and What Interviewers Really Want

The interviewer slides a piece of paper across the table. "Build me an LBO. You have 15 minutes. No calculator."

This is the paper LBO—the rite of passage for private equity recruiting. Everyone knows it's coming. Most candidates still struggle with it.

The challenge isn't the math. Basic LBO mechanics are straightforward. The challenge is demonstrating investment judgment under pressure while performing mental arithmetic accurately.

Here's how to master advanced LBO concepts—from paper LBOs to complex sensitivity analysis—and what interviewers actually want to see.

---

The Paper LBO: Fundamentals

What It Tests

Paper LBOs assess multiple skills simultaneously:

Mental math: Can you compute quickly and accurately without a calculator?

LBO mechanics: Do you understand how the model works conceptually?

Time management: Can you structure your approach to finish within the time limit?

Communication: Can you explain your thinking while you calculate?

Judgment: Do you make reasonable assumptions when information is missing?

The Standard Setup

Most paper LBOs follow this format:

Given:

• Purchase price or EBITDA multiple
• EBITDA (often $100M for easy math)
• Debt structure (or leverage multiple)
• Interest rate
• Revenue/EBITDA growth rate
• Hold period (usually 5 years)
• Exit multiple

Asked:

• Calculate equity returns (IRR and/or MOIC)
• Sometimes: determine maximum purchase price for target returns

The Step-by-Step Framework

Step 1: Calculate purchase price and sources/uses

If given: EV = $1,000M, Debt = 5x EBITDA ($500M)

Sources:

• Debt: $500M
• Equity: $500M

Step 2: Project EBITDA through hold period

If EBITDA grows 5% annually from $100M:

• Year 1: $105M
• Year 2: $110M
• Year 3: $116M
• Year 4: $122M
• Year 5: $128M

(Shortcut: 5% growth for 5 years ≈ 28% total growth)

Step 3: Calculate exit enterprise value

Exit EBITDA × Exit Multiple = Exit EV

$128M × 10x = $1,280M

Step 4: Calculate debt paydown

Simple approach: Assume 100% of free cash flow goes to debt paydown.

FCF ≈ EBITDA - Interest - Taxes - Capex - Working Capital Changes

Rough estimate for stable businesses: FCF ≈ 40-50% of EBITDA

If FCF is ~$50M annually × 5 years = $250M debt paydown

Remaining debt: $500M - $250M = $250M

Step 5: Calculate exit equity value

Exit EV - Remaining Debt = Exit Equity

$1,280M - $250M = $1,030M

Step 6: Calculate returns

MOIC = Exit Equity / Entry Equity = $1,030M / $500M = 2.06x

IRR: For 5-year hold, use rule of 72 or memorized approximations:

• 2.0x in 5 years ≈ 15% IRR
• 2.5x in 5 years ≈ 20% IRR
• 3.0x in 5 years ≈ 25% IRR

So 2.06x ≈ 15-16% IRR

---

Mental Math Shortcuts

Growth Calculations

Compound growth shortcuts:

Annual Growth	5-Year Total
3%	~16%
5%	~28%
7%	~40%
10%	~61%
15%	~100% (doubles)

The Rule of 72: Years to double = 72 / Growth Rate

At 10% growth, doubles in ~7 years. At 15% growth, doubles in ~5 years.

IRR Approximations

Memorize these benchmarks:

MOIC	3-Year IRR	5-Year IRR	7-Year IRR
1.5x	14%	8%	6%
2.0x	26%	15%	10%
2.5x	36%	20%	14%
3.0x	44%	25%	17%
4.0x	59%	32%	22%

Quick IRR formula (approximation): IRR ≈ (MOIC^(1/years) - 1)

For quick mental math: IRR ≈ (MOIC - 1) / Years × Adjustment Factor

Percentage Calculations

Quick multiplications:

• x × 5% = x × 10% ÷ 2
• x × 15% = x × 10% + x × 5%
• x × 25% = x ÷ 4
• x × 33% = x ÷ 3

Divisions:

• ÷ 4 = × 25%
• ÷ 5 = × 20%
• ÷ 8 = × 12.5%

---

Advanced Paper LBO Scenarios

Scenario 1: Maximum Purchase Price

Question: "Target has $50M EBITDA. Assuming 5x leverage, 5% interest rate, 5% EBITDA growth, and 10x exit multiple in 5 years, what's the maximum purchase price for a 20% IRR?"

Approach:

Work backward from required returns:

1. 20% IRR over 5 years ≈ 2.5x MOIC
2. Calculate exit value: $50M × 1.28 (5% growth for 5 years) × 10x = $640M exit EV
3. Estimate debt paydown: ~$100M (rough estimate)
4. Exit equity: $640M - (Entry debt - $100M) = $640M - Entry debt + $100M
5. If entry equity × 2.5 = exit equity, and debt = 5x EBITDA = 5 × $50M = $250M
6. Entry debt: $250M, Remaining debt: $150M, Exit equity: $490M
7. Entry equity for 2.5x: $490M / 2.5 = $196M
8. Maximum purchase price: $196M + $250M = $446M, or ~8.9x EBITDA

Scenario 2: Debt Paydown Sensitivity

Question: "How does the deal change if the company pays down 50% more debt?"

Approach:

Original: $250M paydown → $250M remaining → $1,030M exit equity → 2.06x

50% more paydown: $375M paydown → $125M remaining → $1,155M exit equity → 2.31x

Delta: +0.25x MOIC, ~2-3% additional IRR

Scenario 3: Multiple Contraction

Question: "What if exit multiple compresses from 10x to 8x?"

Approach:

Original: $128M × 10x = $1,280M exit EV

New: $128M × 8x = $1,024M exit EV

Exit equity: $1,024M - $250M = $774M

MOIC: $774M / $500M = 1.55x

IRR: ~9% (down from ~15%)

This illustrates why multiple contraction is a significant risk in LBOs.

---

Sensitivity Analysis in Full Models

The Three Key Sensitivities

Every LBO should be sensitized on:

1. Entry multiple sensitivity: Shows how returns vary with purchase price.

Entry Multiple	MOIC	IRR
8x	2.8x	23%
9x	2.4x	19%
10x	2.1x	15%
11x	1.8x	12%

2. Exit multiple sensitivity: Shows risk of multiple compression.

Exit Multiple	MOIC	IRR
8x	1.6x	9%
9x	1.8x	12%
10x	2.1x	15%
11x	2.4x	18%

3. EBITDA growth sensitivity: Shows importance of operational performance.

EBITDA CAGR	Exit EBITDA	MOIC	IRR
0%	$100M	1.5x	8%
5%	$128M	2.1x	15%
10%	$161M	2.7x	22%

Building a Sensitivity Table

Standard format for presentation:

IRR Sensitivity: Entry Multiple vs. Exit Multiple

	Exit 8x	Exit 9x	Exit 10x	Exit 11x
Entry 8x	14%	18%	22%	26%
Entry 9x	10%	14%	18%	21%
Entry 10x	6%	10%	14%	18%
Entry 11x	3%	7%	11%	14%

The diagonal (entry = exit) shows returns from operational improvement alone.

What Sensitivities Reveal

Margin of safety: How much can go wrong before returns become unacceptable?

Risk/reward profile: What's the upside if things go well? The downside if they don't?

Key value drivers: What matters most—growth, margins, multiple, debt paydown?

Deal breakers: Under what assumptions does this deal not work?

---

Value Creation Bridges

The Returns Attribution

Understanding where returns come from:

Source	Contribution	Calculation
Revenue growth	+X%	Revenue CAGR impact on EBITDA
Margin expansion	+Y%	Basis points of margin improvement
Multiple expansion	+Z%	Exit multiple vs. entry multiple
Debt paydown	+W%	Leverage reduction benefit
Total IRR	Sum

Building the Bridge

Sample attribution:

Entry: $500M equity at 10x on $100M EBITDA

Exit (Year 5): $1,030M equity

Component	Contribution
Base case (no growth, same multiple)	8% IRR
EBITDA growth (5% CAGR)	+5% IRR
Multiple expansion (10x to 10.5x)	+1% IRR
Debt paydown ($250M)	+3% IRR
Total	17% IRR

This shows that operational improvement (EBITDA growth) drives most of the return.

---

What Interviewers Actually Want

Beyond the Math

Technical accuracy is table stakes. Interviewers are really assessing:

Commercial judgment: Do you understand what makes this a good or bad deal? Can you identify risks and opportunities beyond the numbers?

Investment instinct: Would you invest in this? Why or why not? What would you need to believe?

Communication: Can you explain complex concepts clearly? Do you think out loud in a structured way?

Poise under pressure: How do you handle being challenged? Do you panic when stuck, or work through it calmly?

The Questions Behind the Questions

"Walk me through this paper LBO" Really asking: Can you structure your thinking and communicate clearly?

"What are the key risks?" Really asking: Do you have commercial judgment beyond the model?

"How would you improve returns?" Really asking: Do you think like an investor, not just a modeler?

"What assumptions would make you not do this deal?" Really asking: Can you identify deal-breakers and protect against downside?

Demonstrating Judgment

After completing calculations, add commentary:

On risks: "The main risk here is multiple compression. If we buy at 10x and exit at 8x, returns drop to single digits. We'd need to underwrite meaningful EBITDA growth to justify this entry price."

On value creation: "Returns are heavily dependent on the operational plan. The 5% EBITDA growth assumes successful margin improvement. I'd want to understand what specific initiatives drive that and how realistic they are."

On deal structure: "At 5x leverage, we have reasonable cushion. But if the business is cyclical, we might want lower leverage to survive a downturn."

This shows you're thinking like an investor, not just executing calculations.

---

Common Mistakes and How to Avoid Them

Calculation Errors

Mistake: Forgetting to account for debt paydown.

Fix: Always calculate ending debt = starting debt - cumulative FCF.

Mistake: Confusing entry equity with entry enterprise value.

Fix: Clearly label each line. EV = Equity + Debt.

Mistake: Using wrong growth periods (4 years instead of 5).

Fix: Count carefully. Entry Year 0, Exit Year 5 = 5 years of growth.

Structural Errors

Mistake: Spending too long on early steps, running out of time.

Fix: Practice pacing. Allocate time for each section before starting.

Mistake: Not showing work, making it impossible to follow your logic.

Fix: Write out each step. If you make an error, they can see where and may give partial credit.

Mistake: Getting stuck and freezing.

Fix: State your assumptions and keep moving. "I'm not sure of the exact number, but assuming X, I'll continue..."

Judgment Errors

Mistake: Only presenting the math without interpretation.

Fix: Always conclude with what the numbers mean for the investment decision.

Mistake: Not acknowledging limitations of your analysis.

Fix: Note key assumptions and what would need to be verified in full diligence.

---

Practice Problems

Problem 1: Basic Paper LBO

Setup:

• EBITDA: $100M
• Purchase multiple: 10x ($1,000M EV)
• Debt: 5x ($500M)
• Interest rate: 6%
• Tax rate: 25%
• D&A: $30M
• Capex: $25M
• No working capital change
• EBITDA growth: 5%/year
• Exit: Year 5 at 10x

Calculate: IRR and MOIC

Solution approach:

Year 5 EBITDA: $100M × 1.28 = $128M

FCF calculation (Year 1):

• EBITDA: $105M
• Interest: $30M (on $500M)
• EBT: $75M
• Tax: $19M
• Net income: $56M
• Add back D&A: $30M
• Subtract capex: $25M
• FCF: $61M

Total FCF over 5 years: ~$350M (growing with EBITDA)

Exit EV: $128M × 10x = $1,280M Exit debt: $500M - $350M = $150M Exit equity: $1,130M

MOIC: $1,130M / $500M = 2.26x IRR: ~17-18%

Problem 2: Multiple Expansion Scenario

Same setup, but exit at 11x instead of 10x.

Exit EV: $128M × 11x = $1,408M Exit equity: $1,258M MOIC: 2.52x IRR: ~20%

Problem 3: Downside Case

Same setup, but 0% EBITDA growth and exit at 9x.

Exit EV: $100M × 9x = $900M FCF over 5 years: ~$275M (lower without growth) Exit debt: $225M Exit equity: $675M MOIC: 1.35x IRR: ~6%

This shows the downside case barely returns cost of capital.

---

Key Takeaways

Paper LBOs and advanced modeling separate candidates who understand private equity from those who've just memorized formulas.

Master the mechanics:

• Sources and uses
• EBITDA projection
• Debt paydown
• Exit valuation
• Returns calculation

Develop shortcuts:

• Growth approximations
• IRR benchmarks
• Quick mental math techniques

Show judgment:

• Interpret what the numbers mean
• Identify risks and sensitivities
• Think like an investor

Practice relentlessly:

• Timed paper LBOs
• Verbal walkthroughs
• Sensitivity analysis
• Returns attribution

The key insight:

The paper LBO tests whether you can think like a PE investor under pressure. The math is just the medium. What they're really evaluating is your judgment, communication, and investment instinct.

Master the mechanics so thoroughly that they become automatic. Then you can focus on demonstrating the commercial thinking that actually gets you hired.