Paper LBO Concept Card and Practice Cases Template

Paper LBO Concept Card: [Your name, target firms and interview date]

A concept card and drill book for the paper leveraged buyout (LBO): the pen-and-paper LBO that private equity interviewers ask candidates to solve in 10 to 30 minutes without a spreadsheet. It is for MBA candidates recruiting for private equity, growth equity, leveraged finance and investment banking, and for any MBA student who wants to understand how a financial sponsor thinks about price, leverage and return. It covers sources and uses of funds, debt paydown from free cash flow, the exit, the multiple of invested capital (MOIC) and the internal rate of return (IRR), the shortcuts that make the arithmetic fast (the rule of 72 and a MOIC to IRR table), and the value creation bridge. Worked example A is fully solved, Worked example B is half solved, and two original practice cases have full answers in the answer key. Source basis: Jensen (1986 and 1989), Kaplan and Stromberg (2009) and Gompers, Kaplan and Mukharlyamov (2016), written up in original words with fictional companies (Northfield Outdoor Co. and invented targets). Replace every [bracketed] value and every row marked Example. This is a learning aid, not investment or tax advice.

Document control

Contents

• When to use it
• The idea in plain language
• Formulas and notation
• Assumptions and limits
• How investors and interviewers use it
• The method step by step
• Worked example A (fully solved): Northfield Outdoor Co.
• Shortcuts for the arithmetic
• Worked example B (half solved): a dividend recapitalisation
• Practice case 1: Brindlemoor Packaging
• Practice case 2: Oxley Lane Laboratory Services
• Connections to other cards
• Common mistakes and misconceptions
• Self-test questions
• My notes and next steps
• Sources and further reading
• Answer key

When to use it

Use a paper LBO when:

• an interviewer gives you a target's EBITDA, an entry multiple, a leverage multiple, a growth rate and an exit multiple and asks for the return;
• you need the maximum price a financial sponsor can pay for a target return (the LBO floor in a banking football field, see mba/mba-banking-technical-prep);
• you want a first view of a deal before building a full model, for example in the screening section of finance/private-equity-investment-memo;
• a case discussion in class asks whether a buyout price was justified.

Do not use it as a substitute for a full model when the capital structure has several debt tranches with different amortisation, when cash taxes differ materially from book taxes, or when working capital swings are large. The paper LBO is a sketch: it is right to within a few percentage points of IRR when its assumptions hold.

The idea in plain language

A financial sponsor buys a company using a large amount of borrowed money and a smaller cheque of its own equity. The company's cash flow pays the interest and repays the debt over a holding period of typically three to seven years. At exit the sponsor sells the company; whatever is left after repaying the remaining debt belongs to the equity. Because the equity cheque is small relative to the price, every unit of value gained at exit is a large percentage gain on the equity.

Returns come from three sources:

1. EBITDA growth: the company earns more, so it is worth more at the same multiple.
2. Multiple expansion: the exit multiple is higher than the entry multiple. Prudent cases assume none.
3. Debt paydown (deleveraging): free cash flow repays debt, so a larger share of the enterprise value belongs to the equity at exit.

Jensen (1986) argued that debt disciplines managers by committing free cash flow to interest and repayment instead of low-return projects; Jensen (1989) extended the argument to the buyout organisation. Kaplan and Stromberg (2009) describe the financial, governance and operational engineering that private equity firms apply, and Gompers, Kaplan and Mukharlyamov (2016) report from a survey that investors rely mainly on IRR and MOIC rather than discounted cash flow when they evaluate deals.

Formulas and notation

Excel equivalents: IRR without interim flows =(E_N/E_0)^(1/N)-1 or =RRI(N,E_0,E_N); with interim flows =IRR(range) on the equity cash flows (entry as a negative number, then each year's flow); exact doubling time =LN(2)/LN(1+IRR).

Assumptions and limits

• Interest on opening debt. Using opening balances avoids the circularity of interest on average debt. The error is small at moderate rates.
• All free cash flow repays debt. The "cash sweep". In reality minimum cash is kept and some debt cannot be prepaid.
• Interest is fully deductible. Many jurisdictions cap the deduction. As general examples, as of October 2026: Article 4 of Council Directive (EU) 2016/1164 (the Anti-Tax Avoidance Directive) caps deductible exceeding borrowing costs at 30% of the taxpayer's tax-adjusted EBITDA, with options for member states such as a de minimis amount, so national rules differ (http://data.europa.eu/eli/dir/2016/1164/oj); in the United States, section 163(j) of the Internal Revenue Code generally limits business interest expense to business interest income plus 30% of adjusted taxable income, which the IRS says again adds back depreciation and amortisation for tax years beginning after 31 December 2024 (IRS FS-2026-14, checked 28 October 2026, https://www.irs.gov/newsroom/questions-and-answers-about-the-limitation-on-the-deduction-for-business-interest-expense). Check the current rules before you rely on them. At high leverage a cap raises cash taxes and lowers the return. State the assumption in interviews.
• Exit multiple equals entry multiple. Prudent, but not neutral in every market: entry at a cyclical peak makes even "no expansion" optimistic.
• Fees and transaction costs are funded by equity, which lowers MOIC.
• No management equity or options; in practice management dilution of 5% to 15% of exit equity is common and reduces the sponsor's return. Treat that range as an illustrative assumption to state, not a benchmark.
• IRR is a rate, MOIC is a multiple. IRR rewards speed; MOIC rewards size. Investors look at both, and limited partners also look at time-weighted and public-market-equivalent measures.

How investors and interviewers use it

Investors use a paper LBO at the screening stage to decide whether a deal can meet the fund's return target (often stated as a minimum IRR and MOIC), to set the maximum entry price, and to see which lever matters most. Interviewers use it to test arithmetic under time pressure, the logic of the three statements (free cash flow after interest and tax), and judgement: the best candidates finish the arithmetic and then say what would worry them (customer concentration, cyclicality, covenant headroom, refinancing risk at exit).

A good answer has four parts: the sources and uses table, the debt schedule, the exit and returns, and two or three sentences of judgement. Interviewers usually give round numbers precisely so that the arithmetic stays manageable; use them, and round consistently.

The method step by step

Every paper LBO follows the same eight moves: inputs, sources and uses, EBITDA projection, free cash flow, debt repayment, exit value, exit equity and returns, then a short judgement. Rehearse the routine until the order is automatic, so your attention is free for the arithmetic and the judgement.

Worked example A (fully solved): Northfield Outdoor Co.

Example inputs: last-twelve-month EBITDA USD 100m; entry multiple 8.0x; debt 5.0x EBITDA at 8% interest; transaction fees 2% of enterprise value; EBITDA growth 5% a year; depreciation and amortisation USD 15m a year equal to capital expenditure; no change in working capital; tax 25%; holding period 5 years; exit at 8.0x; all free cash flow repays debt.

Step 1: sources and uses (USD m)

Equity is 38.7% of total sources (=316/816).

Step 2: debt schedule (USD m)

Because depreciation equals capital expenditure and working capital is flat, free cash flow equals net income. Excel for year 1: interest =8%*500, free cash flow =(105-15-40)*(1-25%), closing debt =500-37.5. Total paydown over five years is 255.28 (=500-244.72).

Mental-math version: year-5 EBITDA is 100 x 1.05^5, about 127.6 (1.05^5 = 1.276). Free cash flow grows from about 37 to about 66; an average of about 51 over five years repays about 255.

Step 3: exit and returns

Shortcut check: 2.5x over five years is 20.1% in the MOIC to IRR table; 2.46x is a little lower, so about 19.7%.

Step 4: value creation bridge (USD m)

Slightly more than half the gain comes from deleveraging: this is a "cash flow" deal rather than a growth deal. That is the judgement to state, with its risk: if EBITDA falls, interest still has to be paid, and the paydown slows.

Step 5: sensitivity (MOIC and IRR)

One turn of exit multiple moves IRR by about four percentage points at 5% growth; five points of annual growth moves it by about ten. In this deal, growth is the bigger lever, and the multiple is the bigger risk if the market falls.

Shortcuts for the arithmetic

MOIC to IRR table

IRR equals MOIC^(1/N) - 1 when there are no interim cash flows (Excel =RRI(N,1,MOIC)), computed exactly:

Anchors worth memorising: 2x in 5 years is about 15%; 2.5x in 5 years is about 20%; 3x in 5 years is about 25%; 2x in 3 years is about 26%.

Rule of 72

Money doubles in about 72 / (100 x rate) years. It is a good approximation at the rates sponsors target, and slightly optimistic at high rates:

Use it backwards: if equity doubles in about 3.6 years, the IRR is about 20%; if it doubles and then doubles again (4x) in about 7.2 years, the IRR is about 20% too. That is why the 4.0x and 7-year cell (21.9%) is close to 20%.

Other mental-math aids

• Growth factors: 1.05^5 = 1.28, 1.06^4 = 1.26, 1.08^5 = 1.47, 1.10^5 = 1.61.
• Required entry equity for a target return: exit equity / (1 + IRR)^N; 1.20^5 = 2.49 and 1.25^5 = 3.05.
• Tax on interest: after-tax cost = rate x (1 - tax rate); at 8% and 25%, 6%.

Worked example B (half solved): a dividend recapitalisation

Start from Worked example A. In year 3 Northfield raises new debt and pays the sponsor a dividend of USD 100m. To keep the arithmetic simple, assume the new debt is repaid out of exit proceeds, so exit equity falls by exactly 100 and the extra interest is ignored (a simplification you would state in an interview).

Question to answer in one sentence: why does a sponsor like a dividend recap even when MOIC does not rise? [ ]

Practice case 1: Brindlemoor Packaging

Brindlemoor Packaging is a fictional maker of recyclable food trays with last-twelve-month EBITDA of USD 50m. A sponsor proposes:

• entry at 10.0x EBITDA, fees 2% of enterprise value;
• debt of 6.0x EBITDA at 9% interest, all free cash flow used to repay debt;
• EBITDA growth of 6% a year for four years;
• depreciation and amortisation USD 8m a year, capital expenditure USD 10m a year, no change in working capital;
• tax 25%; exit after four years at 10.0x.

Questions:

1. Build the sources and uses table.
2. Build the four-year debt schedule.
3. Compute exit equity, MOIC and IRR.
4. The exit multiple falls to 9.0x. What are MOIC and IRR now?
5. What exit multiple would the sponsor need for a 20% IRR?
6. Give two sentences of judgement: what drives the return and what is the main risk?

Practice case 2: Oxley Lane Laboratory Services

Oxley Lane Laboratory Services is a fictional provider of outsourced testing for food producers, with last-twelve-month EBITDA of USD 40m. Lenders will provide debt of 4.5x EBITDA at 8%, regardless of the price. Other assumptions: EBITDA growth 8% a year; depreciation and amortisation equal to capital expenditure at USD 6m a year; no change in working capital; tax 25%; no fees (to keep the case short); holding period five years; exit at 9.0x; all free cash flow repays debt. The fund needs an IRR of 25%.

Questions:

1. Build the debt schedule. (Hint: because debt does not depend on the price, neither does the schedule.)
2. Compute exit equity.
3. What is the maximum entry equity for a 25% IRR, and so the maximum entry enterprise value and multiple?
4. The seller asks for 9.0x. What MOIC and IRR would the sponsor earn?
5. Name two ways the sponsor could still meet 25% at 9.0x, and the risk each one adds.

Connections to other cards

Common mistakes and misconceptions

1. Forgetting fees in uses, so the equity cheque and the MOIC denominator are too small.
2. Computing interest on closing debt or on entry debt every year instead of on opening debt each year.
3. Forgetting tax on pre-tax income, or taxing EBITDA instead of income after depreciation and interest.
4. Adding back depreciation but forgetting to subtract capital expenditure, which overstates free cash flow.
5. Subtracting entry debt instead of remaining debt at exit.
6. Treating IRR as MOIC divided by years (2.5x in 5 years is not 30%; it is about 20%).
7. Assuming multiple expansion without saying so; a prudent base case exits at the entry multiple.
8. Believing that more leverage always raises the return: it raises IRR only while the business can service the debt, and the downside case gets worse.
9. Ignoring limits on interest deductibility at high leverage, which raise cash taxes.
10. Finishing the arithmetic without any judgement about risks and levers.

Self-test questions

1. Name the three sources of return in an LBO.
2. A sponsor invests 200 and receives 500 after five years with no interim flows. What are MOIC and IRR?
3. Using the rule of 72, roughly how many years does it take to double money at 18%?
4. Why does a higher leverage multiple raise IRR, and when does it stop helping?
5. In Worked example A, what share of the equity gain came from debt paydown?
6. Why is interest charged on opening debt in a paper LBO?
7. A deal returns 2.0x in three years or 2.5x in five years. Which has the higher IRR?
8. Write the Excel formula for the IRR of a 2.4x MOIC over four years without interim flows.
9. What happens to MOIC and to IRR when a sponsor receives a dividend recap in year 2, other things equal?
10. Why is the LBO value usually the lowest bar in a banking football field?

My notes and next steps

Sources and further reading

Primary works:

• Jensen, M. C. (1986). Agency costs of free cash flow, corporate finance, and takeovers. American Economic Review, 76(2), 323-329.
• Jensen, M. C. (1989). Eclipse of the public corporation. Harvard Business Review, 67(5), 61-74.
• Kaplan, S. N. and Stromberg, P. (2009). Leveraged buyouts and private equity. Journal of Economic Perspectives, 23(1), 121-146.
• Gompers, P., Kaplan, S. N. and Mukharlyamov, V. (2016). What do private equity firms say they do? Journal of Financial Economics, 121(3), 449-476.
• Council Directive (EU) 2016/1164 of 12 July 2016 laying down rules against tax avoidance practices that directly affect the functioning of the internal market, Article 4, http://data.europa.eu/eli/dir/2016/1164/oj.
• Internal Revenue Service (2026). Questions and answers about the limitation on the deduction for business interest expense (FS-2026-14), checked 2026-10-28, https://www.irs.gov/newsroom/questions-and-answers-about-the-limitation-on-the-deduction-for-business-interest-expense.

Textbooks (further reading, by name only): Rosenbaum and Pearl, Investment Banking: Valuation, LBOs, M&A, and IPOs; Berk and DeMarzo, Corporate Finance; Brealey, Myers and Allen, Principles of Corporate Finance.

Open resource: OpenStax, Principles of Finance (CC BY-NC-SA 4.0), https://openstax.org.

Answer key

Worked example B: equity flows -316, 0, 0, +100, 0, +676.30; total distributions 776.30; MOIC 2.46x (unchanged); IRR 21.1% (=IRR on the six flows) against 19.7% without the recap. IRR is higher and MOIC the same because cash comes back earlier; sponsors like recaps because they lock in part of the return and raise IRR, at the cost of higher leverage.

Practice case 1 (Brindlemoor Packaging, USD m):

1. Uses: enterprise value 500.00 (10.0 x 50) plus fees 10.00 = 510.00. Sources: debt 300.00 (6.0 x 50), sponsor equity 210.00 (41.2%).
2. Debt schedule (free cash flow = net income + 8 - 10):

3. Exit EV 10.0 x 63.12 = 631.24; exit equity 631.24 - 233.57 = 397.66; MOIC 1.89x; IRR 17.3% (=RRI(4,210,397.66)).
4. Exit EV 568.11; exit equity 334.54; MOIC 1.59x; IRR 12.3%.
5. Needed exit equity 210 x 1.2^4 = 435.46; needed EV 435.46 + 233.57 = 669.03; multiple 669.03 / 63.12 = 10.60x.
6. High entry price and heavy interest (9% on 6.0x) leave little free cash flow, so paydown is slow (66.43 over four years) and the return depends on EBITDA growth and holding the multiple. The main risk is multiple compression: one turn lower costs about five points of IRR.

Practice case 2 (Oxley Lane Laboratory Services, USD m):

1. Debt 180.00 (4.5 x 40). Free cash flow equals net income because depreciation equals capital expenditure.

2. Exit EV 9.0 x 58.77 = 528.96; exit equity 528.96 - 53.86 = 475.10.
3. Maximum entry equity 475.10 / 1.25^5 = 475.10 / 3.052 = 155.68; maximum EV 155.68 + 180.00 = 335.68; maximum multiple 335.68 / 40 = 8.39x. Excel: =475.10/(1+25%)^5.
4. Entry equity 360.00 - 180.00 = 180.00; MOIC 475.10 / 180.00 = 2.64x; IRR 21.4% (=RRI(5,180,475.10)).
5. More debt (raises IRR but adds default and covenant risk), faster growth or margin improvement (operating risk if the plan slips), or a dividend recap (refinancing risk). A higher exit multiple assumption is not a plan.

Self-test:

1. EBITDA growth, multiple expansion, debt paydown.
2. MOIC 2.5x; IRR 20.1% (=RRI(5,200,500)).
3. About 4 years (exact 4.19).
4. A smaller equity cheque means each unit of value gained is a larger percentage of equity. It stops helping when interest absorbs the free cash flow, when interest caps raise taxes, or when the default risk and lenders' price rise.
5. Debt paydown 255.28 of a 460.30 gain, about 55%.
6. To avoid circularity: interest on average debt depends on the repayment, which depends on interest.
7. 2.0x in three years (26.0%) beats 2.5x in five (20.1%).
8. =2.4^(1/4)-1 or =RRI(4,1,2.4), which gives 24.5%.
9. MOIC is unchanged (if the recap debt is simply repaid at exit, ignoring its interest) and IRR rises because cash arrives earlier; with the extra interest, MOIC falls slightly.
10. A sponsor has no synergies and a high return target, so it can pay less than a strategic buyer.

Revision history

Standard and licence note

Based on standard leveraged buyout and corporate finance practice and the primary works listed above. The text, examples, numbers and practice cases are original; no textbook, guide or published interview case is copied or paraphrased, and Northfield Outdoor Co., Brindlemoor Packaging and Oxley Lane Laboratory Services are fictional. The template is independent and not affiliated with or endorsed by any private equity firm, bank, business school or publisher. Check current tax rules on interest deductibility before you rely on them. Template licence: MIT.