Banking and private equity
The paper LBO: a ten-minute method
A buyout case with pen and paper: entry, financing, exit, money multiple and IRR, plus the value bridge that explains where the return came from.
الأدلة باللغة الإنجليزية، لغة المقابلات.
What you're given
Usually: EBITDA, entry and exit multiples, how much debt is used, how EBITDA grows, and how much debt is repaid (or the free cash flow that repays it). You're asked for the money multiple (MOIC) and the IRR, and often to explain what drove the return.
The method
- 1
Entry price
Enterprise value = entry EBITDA × entry multiple. If fees are given, they add to what must be funded.
- 2
Financing
Debt = leverage × EBITDA. Equity = price (plus fees) − debt.
- 3
Exit value
Grow EBITDA to the exit year. Exit enterprise value = exit EBITDA × exit multiple.
- 4
Net debt at exit
Starting debt − debt repaid. If all free cash flow repays debt, subtract the cumulative free cash flow.
- 5
Exit equity
Exit enterprise value − net debt at exit.
- 6
Returns
MOIC = exit equity ÷ equity invested. IRR = MOIC1/years − 1, estimated with the table below.
Worked example
مثال محلول · Five-year buyout
تم التحقق برمجيًاEBITDA is $100m. The sponsor pays 10x with 6x debt and holds for five years. EBITDA grows to $150m, the exit is at 10x, and $300m of debt is repaid. What are the MOIC and IRR?
اعرض خطوات الحل
- 1.Price = 10 × $100m = $1,000m. Debt = 6 × $100m = $600m. Equity = $400m.
- 2.Exit enterprise value = 10 × $150m = $1,500m.
- 3.Net debt at exit = $600m − $300m = $300m. Exit equity = $1,500m − $300m = $1,200m.
- 4.MOIC = $1,200m ÷ $400m = 3.0x. From the table, 3.0x over five years is about 25% (exactly 24.6%).
الإجابة3.0x and an IRR of about 25%.
Where the return came from: the value bridge
The $800m gain splits into three drivers. By convention, EBITDA growth is valued at the entry multiple and any change in multiple is applied to exit EBITDA, so the parts add up exactly.
| Driver | Calculation | Value |
|---|---|---|
| EBITDA growth | ($150m − $100m) × 10x | $500m |
| Multiple expansion | (10x − 10x) × $150m | $0m |
| Debt paydown | $600m − $300m | $300m |
| Total gain | $1,200m − $400m | $800m |
مثال محلول · What if the exit multiple is 11x?
تم التحقق برمجيًاSame deal, but the sponsor exits at 11x. What changes?
اعرض خطوات الحل
- 1.Exit enterprise value = 11 × $150m = $1,650m. Exit equity = $1,650m − $300m = $1,350m.
- 2.MOIC = $1,350m ÷ $400m = 3.375x, an IRR of about 27.5%.
- 3.Bridge: growth $500m + multiple expansion 1x × $150m = $150m + paydown $300m = $950m, which equals $1,350m − $400m.
الإجابة3.4x and about 27.5%; multiple expansion adds $150m.
IRR shortcuts to know by heart
| MOIC | 3 years | 4 years | 5 years |
|---|---|---|---|
| 2.0x | 26.0% | 18.9% | 14.9% |
| 2.5x | 35.7% | 25.7% | 20.1% |
| 3.0x | 44.2% | 31.6% | 24.6% |
Computed, not typed: IRR = MOIC1/years − 1.
نصيحةRule of 72: money doubles in about 72 ÷ IRR years. At 15% a year it doubles in about 4.8 years, which is why 2x in five years is about 15%.
Common mistakes
أخطاء شائعة
- Applying the exit multiple to entry EBITDA.
- Subtracting the starting debt at exit instead of what's left after repayments.
- Leaving fees out of the equity check when they're given.
- Giving an IRR without a sanity check: 2x in five years is about 15%, not 20%.
تدرّب على ذلك
طبّق المنهجية على أسئلة جديدة مع تصحيح فوري.
Banking and private equity