# LBO Model Concept Card: [Your name, elective or deal, and date] > An elective-level concept card for the full leveraged buyout (LBO) model: the spreadsheet a private equity deal team > builds after the paper LBO says a deal is worth a closer look. It builds on mba/mba-paper-lbo (sources and uses, > debt paydown, MOIC, IRR and the value bridge) and does not re-teach it. This card adds what the paper version leaves > out: several debt tranches with different terms, mandatory amortisation and a cash sweep, a revolving credit > facility, minimum cash, working capital, financing fees, management incentives, the interest circularity, limits on > interest deductibility, payment-in-kind (PIK) debt, credit statistics, downside cases and the maximum price. It is > for second-year MBA students in a private equity or advanced corporate finance elective and for candidates preparing > for a modelling test. Worked example A rebuilds the Northfield Outdoor Co. deal from the paper LBO card as a full > model and reconciles the two answers, Worked example B is a half-solved downside case, and Exercise C asks for the > maximum price and the effect of PIK notes. Source basis: Jensen (1986), Kaplan and Stein (1993), Kaplan and > Stromberg (2009), Axelson, Stromberg and Weisbach (2009), Axelson, Jenkinson, Stromberg and Weisbach (2013), written > up in original words with fictional numbers. Replace every [bracketed] value and every row marked *Example*. This is > a learning aid, not investment, credit, legal or tax advice. ## Document control | Field | Value | |---|---| | Learner | [Your name] | | Elective or deal | [Private equity elective, modelling test, deal name] | | Model file and version | [File name, v0.1] | | Base case date | YYYY-MM-DD | | Reviewed by | [Learning team member, teaching assistant or deal-team mentor] | | Version | [0.1] | | Last updated | YYYY-MM-DD | ## Contents - [When to use it](#when-to-use-it) - [The idea in plain language](#the-idea-in-plain-language) - [Formulas and notation](#formulas-and-notation) - [Assumptions and limits](#assumptions-and-limits) - [How deal teams use the model](#how-deal-teams-use-the-model) - [The model build step by step](#the-model-build-step-by-step) - [Worked example A (fully solved): Northfield Outdoor Co. as a full model](#worked-example-a-fully-solved-northfield-outdoor-co-as-a-full-model) - [Worked example B (half solved): a downside case](#worked-example-b-half-solved-a-downside-case) - [Exercise C (unsolved): maximum price and PIK notes](#exercise-c-unsolved-maximum-price-and-pik-notes) - [Connections to other cards](#connections-to-other-cards) - [Common mistakes and misconceptions](#common-mistakes-and-misconceptions) - [Self-test questions](#self-test-questions) - [My notes and next steps](#my-notes-and-next-steps) - [Sources and further reading](#sources-and-further-reading) - [Answer key](#answer-key) ## When to use it Use a full LBO model when: - a deal has passed the paper LBO screen and the team must set a bid, so a few points of IRR now change the decision; - the financing has more than one tranche (a term loan, notes, a revolver, perhaps PIK debt or preferred equity) and the tranches repay in a different order and at different rates; - lenders need credit statistics (leverage and interest cover by year) and a downside case to commit to the financing, and the deal team needs to know whether a covenant could be tested; - working capital, capital expenditure, cash taxes or fees are large enough that the paper shortcuts mislead; - you must answer the investment committee's standard questions: what is the maximum price, which assumption breaks the deal, and how much of the return depends on the exit multiple. Do not build a full model to answer an interview question that the paper LBO answers, and do not let the precision of a model hide the fact that its two most important inputs (the operating plan and the exit multiple) are judgements. ## The idea in plain language The paper LBO treats debt as one block that absorbs all free cash flow. Real buyouts are financed with a stack of claims, each with its own price, its own rank and its own rules for repayment. A senior term loan is cheaper because it is repaid first and is secured; it usually amortises by a small fixed amount each year and must also be repaid from a share of excess cash (the sweep). Unsecured or subordinated notes are more expensive and are usually repaid only at maturity or at exit. A revolving credit facility sits at the top of the stack as a liquidity line: it is often undrawn at closing, costs a commitment fee while undrawn, and is drawn when cash runs short. Some deals add PIK debt, whose interest is not paid in cash but added to the principal, which helps cash flow today and costs more at exit. The model follows each claim through time. Each year, the operating model produces EBITDA; the company pays cash interest, fees, tax, capital expenditure and the investment in working capital; what is left is the free cash flow available to repay debt. The model pays the mandatory amortisation first, keeps a minimum cash balance, repays any revolver drawings, and sweeps the rest to the term loan. At exit, the enterprise value is shared by the claims in order of rank, and the equity gets what is left after management's incentive plan takes its share of the gain. Two features make the model harder than its paper cousin. The first is circularity: if interest is charged on the average balance of the year, interest depends on how much debt is repaid, which depends on interest. The second is that the tax line depends on how much interest is deductible, which many tax systems now cap. Both are small effects in a good deal and large ones in a marginal deal. Why use so much debt at all? Jensen (1986) argued that debt commits managers to pay out free cash flow instead of investing it in low-return projects. Kaplan and Stein (1993) documented how buyout prices and leverage rose in the late 1980s and how deals with aggressive structures defaulted more often. Axelson, Stromberg and Weisbach (2009) explain why buyout funds finance deals with debt raised deal by deal, and Axelson, Jenkinson, Stromberg and Weisbach (2013) find that buyout leverage tracks credit market conditions more than company characteristics, and that higher leverage goes with higher prices and lower fund returns. Kaplan and Stromberg (2009) summarise the financial, governance and operational engineering that private equity applies. The model is the tool that tests whether a particular structure is one the company can carry. ## Formulas and notation Free cash flow available to repay debt in year $t$ (the paper LBO's $FCF_t$, now with fees, a tax line of its own and working capital; it is after interest, so it is not the project-finance CFADS, which is measured before debt service): $$ FCF_t = EBITDA_t - I^{cash}_t - F_t - T_t - CapEx_t - \Delta NWC_t $$ Cash tax, with deductible interest $I^{ded}_t$: $$ T_t = \tau \cdot \max\left(0,\; EBITDA_t - DA_t - I^{ded}_t\right) $$ Mandatory amortisation, sweep and the term loan balance (minimum cash $C_{min}$, sweep share $s$, revolver repayment $R_t$): $$ A_t = \min(a \cdot TL_0,\; TL_{t-1}) \qquad S_t = \min\left(s \cdot \max(0,\; Cash_{t-1} + FCF_t - A_t - C_{min} - R_t),\; TL_{t-1} - A_t\right) \qquad TL_t = TL_{t-1} - A_t - S_t $$ Interest on opening balances (no circularity) or on average balances (circular): $$ I_t = r \cdot D_{t-1} \qquad \text{or} \qquad I_t = r \cdot \frac{D_{t-1} + D_t}{2} $$ PIK notes accrue instead of paying cash interest: $$ PIK_t = PIK_{t-1} \cdot (1 + r_{PIK}) $$ Interest limitation with a carryforward $CF$ of disallowed interest (cap share $\kappa$ of tax EBITDA): $$ I^{ded}_t = \min\left(I_t + CF_{t-1},\; \kappa \cdot EBITDA_t\right) \qquad CF_t = I_t + CF_{t-1} - I^{ded}_t $$ Exit, management incentive plan (share $\varphi$ of the equity gain) and returns: $$ E_N = m_{exit} \cdot EBITDA_N - (TL_N + N_N + PIK_N + RCF_N - Cash_N) \qquad MIP = \varphi \cdot \max(0,\; E_N - E_0) $$ $$ MOIC = \frac{E_N - MIP}{E_0} \qquad IRR = MOIC^{1/N} - 1 \quad \text{(no interim flows)} $$ Credit statistics lenders read each year: $$ \text{Total leverage}_t = \frac{TL_t + N_t + PIK_t + RCF_t}{EBITDA_t} \qquad \text{Interest cover}_t = \frac{EBITDA_t}{I_t + F_t} $$ | Symbol | Meaning | Note | |---|---|---| | $EBITDA_t$ | Earnings before interest, tax, depreciation and amortisation | From the operating model | | $I^{cash}_t$, $I_t$ | Cash interest and total interest | PIK interest is in $I_t$ but not in $I^{cash}_t$ | | $F_t$ | Revolver commitment fee | Fee rate times the undrawn commitment | | $T_t$, $\tau$ | Cash tax and tax rate | Tax base after deductible interest | | $DA_t$, $CapEx_t$, $\Delta NWC_t$ | Depreciation and amortisation, capital expenditure, increase in net working capital | $\Delta NWC$ is negative when working capital is released | | $TL_t$, $a$ | Term loan balance and mandatory amortisation rate | $a$ applies to the original balance $TL_0$ | | $FCF_t$ | Free cash flow available to repay debt | After cash interest, fees, tax, capex and working capital | | $S_t$, $s$ | Cash sweep amount and sweep share | Credit agreements often step the share down as leverage falls | | $R_t$ | Revolver repayment | Zero in Worked example A, where the revolver is never drawn | | $N_t$, $PIK_t$, $RCF_t$ | Notes, PIK notes, revolver drawings | Notes and PIK usually repaid at exit | | $C_{min}$, $Cash_t$ | Minimum and actual cash | Minimum cash is funded at closing | | $\kappa$, $CF_t$ | Interest cap share and carryforward of disallowed interest | Rules differ by jurisdiction | | $\varphi$, $MIP$ | Management incentive share and its value at exit | Paid out of the sponsor's exit equity | | $E_0$, $E_N$, $m_{exit}$, $N$ | Sponsor equity at entry, equity at exit, exit multiple, years | As in mba/mba-paper-lbo | Excel: build each formula once in the year 1 column with named inputs, then copy across. With named cells, the sweep is `=MIN(Sweep_share*MAX(0,Cash_open+FCF-Amort-Min_cash-RCF_repay),TL_open-Amort)`, the tax is `=Tax_rate*MAX(0,EBITDA-DA-Int_deductible)`, and the circuit-breaker version of interest is `=IF(Circ_switch=1,TL_rate*AVERAGE(TL_open,TL_close),TL_rate*TL_open)`. Average-balance interest needs iterative calculation (File, Options, Formulas, Enable iterative calculation); the switch lets you break the loop when the workbook shows errors. ## Assumptions and limits - **Interest on opening balances** in the base case. It avoids the circularity and slightly understates the benefit of early repayment; Worked example A shows the size of the difference. - **Floating rates as a fixed all-in rate.** Term loans in most markets pay a floating benchmark plus a spread. For US dollar loans the benchmark is now SOFR or Term SOFR: according to the Alternative Reference Rates Committee (ARRC), all USD LIBOR panel settings ceased on 30 June 2023 (as of October 2026, see https://www.newyorkfed.org/arrc/sofr-transition); sterling and euro loans use SONIA and EURIBOR or €STR based rates. This card uses a fixed all-in rate to keep the arithmetic visible. In a real model, project the benchmark from the forward curve, add the spread and any floor, and show a rate sensitivity or the effect of an interest rate hedge. - **Cash sweep at 100%.** Many credit agreements sweep 50% of excess cash flow, stepping down as leverage falls, and allow voluntary prepayment. A lower sweep leaves cash on the balance sheet; the exit equity counts it, but the return is lower because cash earns less than the debt costs. - **Interest fully deductible** in the base case. As of October 2026 the IRS states that the US limit on business interest (section 163(j)) is business interest income plus 30% of adjusted taxable income plus floor plan financing interest, that depreciation, amortisation and depletion are again added back to adjusted taxable income for tax years beginning after 31 December 2024, and that disallowed interest carries forward (IRS FS-2026-14, https://www.irs.gov/newsroom/questions-and-answers-about-the-limitation-on-the-deduction-for-business-interest-expense). In the EU, Article 4 of Council Directive (EU) 2016/1164 sets a limit of 30% of tax-adjusted EBITDA for exceeding borrowing costs; member states may set a lower percentage and may allow full deduction up to EUR 3 million (an optional safe harbour), among other national options, so the rules differ by member state (http://data.europa.eu/eli/dir/2016/1164/oj). Worked example A models a stylised 30% of EBITDA cap with an unlimited carryforward. Check the current rules with a tax adviser before you rely on them. - **Financing fee amortisation** is ignored for tax and book income. In practice debt issuance costs reduce the carrying amount of the debt and are amortised; their tax treatment depends on the jurisdiction. - **Notes repaid at par at exit.** Notes often have call protection, so early repayment costs a premium (a call premium or a make-whole amount) that the exit waterfall must include. - **Management incentive plan** modelled as 10% of the equity gain above the sponsor's entry equity. Real plans use options, ratchets or "sweet equity" with different strike prices and vesting; treat the share as an illustrative assumption to state, not a benchmark. - **No dividends, no add-on acquisitions, no refinancing.** Each would need its own lines, and each changes both the credit statistics and the timing of equity cash flows. ## How deal teams use the model The deal team, the lenders and the investment committee read the same model for different reasons. | Reader | Question | Outputs they look at | |---|---|---| | Deal team | What can we bid and what must go right? | Maximum price at the target IRR and MOIC, value bridge, sensitivity tables | | Investment committee | Is the return worth the risk, and what breaks the deal? | Base, upside and downside cases, exit multiple dependence, equity cheque and fund concentration | | Arranging banks and credit funds | Can the company service and repay the debt? | Leverage and interest cover by year, minimum liquidity, covenant headroom, downside case | | Management | What does the plan require of us, and what do we earn? | Operating plan, capital expenditure, management incentive value under each case | | Rating agencies and later buyers | How quickly will the company deleverage? | Free cash flow to debt, leverage path | Lenders usually test the sponsor's downside case and then build their own. The sponsor's model is usually linked to the quality of earnings work (finance/quality-of-earnings-scope) and to the due diligence findings (finance/due-diligence-request-list), which adjust the starting EBITDA and the working capital target. The output goes into the investment memo (finance/private-equity-investment-memo) and the committee paper (finance/investment-committee-memo). Broadly syndicated term loans are often "covenant-lite": they have no maintenance covenant, and the only financial covenant sits in the revolver and "springs" into force when drawings exceed a threshold set in the credit agreement. Private credit loans more often carry a maintenance covenant tested every quarter. Either way, the model must show the headroom: how far EBITDA can fall before a covenant is breached (finance/covenant-compliance-certificate shows the reporting side). ## The model build step by step Build the workbook in the same order every time: inputs and cases, sources and uses, operating model, debt schedule and interest, tax, cash sweep and balances, exit waterfall and returns, then the outputs that readers use (credit statistics, sensitivity tables, value bridge). The only loop is between interest and debt repayment, and it is controlled by a switch. ```mermaid flowchart TD A["Inputs and case selector: base, upside, downside"] --> B["Sources and uses: price, fees, minimum cash, tranches, equity plug"] B --> C["Operating model: revenue, EBITDA, capex, working capital"] C --> D["Interest and fees by tranche"] D --> E["Tax with deductible interest and carryforward"] E --> F["FCF: EBITDA less cash interest, fees, tax, capex, working capital"] F --> G["Mandatory amortisation, then revolver, then sweep"] G --> H["Closing balances by tranche and cash"] H -->|"Average-balance interest, switch on"| D H --> I["Exit: enterprise value less net debt by rank"] I --> J["Management incentive plan"] J --> K["Sponsor MOIC and IRR"] K --> L["Credit statistics, sensitivities, value bridge, maximum price"] ``` ## Worked example A (fully solved): Northfield Outdoor Co. as a full model *Example* inputs (USD m): last-twelve-month revenue 800 and EBITDA 100 (margin 12.5%); revenue growth 5% a year with a constant margin, so EBITDA follows the paper LBO path; depreciation and amortisation 15 and capital expenditure 15 a year; net working capital 10% of revenue; tax 25%; entry and exit at 8.0x; holding period 5 years. Financing: term loan B (TLB) 3.5x EBITDA at an all-in 7.5%, 1% a year mandatory amortisation, 100% cash sweep; senior unsecured notes 1.5x EBITDA at 9.0%, repaid at exit; revolver of 75 undrawn at closing with a 0.375% commitment fee (7.0% if drawn); transaction fees 2% of enterprise value; financing fees 2% of funded debt; minimum cash 20 funded at closing; management incentive plan 10% of the equity gain. ### Step 1: sources and uses (USD m) | Uses | Amount | Sources | Amount | |---|---|---|---| | Purchase enterprise value (8.0 x 100) | 800.00 | Revolver (75 commitment) | 0.00 | | Transaction fees (2% x 800) | 16.00 | Term loan B (3.5 x 100) | 350.00 | | Financing fees (2% x 500) | 10.00 | Senior notes (1.5 x 100) | 150.00 | | Cash to balance sheet | 20.00 | Sponsor equity (plug) | 346.00 | | Total uses | 846.00 | Total sources | 846.00 | Equity is 40.9% of sources (`=346/846`), against 38.7% in the paper LBO, because the financing fees and the minimum cash are funded with equity. ### Step 2: operating model and free cash flow available to repay debt (USD m) | Year | Revenue | EBITDA | Increase in NWC | TLB interest | Notes interest | Commitment fee | Cash tax | FCF | |---|---|---|---|---|---|---|---|---| | 1 | 840.00 | 105.00 | 4.00 | 26.25 | 13.50 | 0.28 | 12.49 | 33.48 | | 2 | 882.00 | 110.25 | 4.20 | 23.74 | 13.50 | 0.28 | 14.43 | 39.10 | | 3 | 926.10 | 115.76 | 4.41 | 20.81 | 13.50 | 0.28 | 16.54 | 45.22 | | 4 | 972.41 | 121.55 | 4.63 | 17.42 | 13.50 | 0.28 | 18.84 | 51.88 | | 5 | 1,021.03 | 127.63 | 4.86 | 13.52 | 13.50 | 0.28 | 21.33 | 59.13 | Year 1 in Excel: revenue `=800*(1+5%)`; EBITDA `=840*12.5%`; increase in NWC `=10%*(840-800)`; TLB interest `=7.5%*350`; notes interest `=9%*150`; commitment fee `=0.375%*75`; cash tax `=25%*(105-15-26.25-13.5-0.28125)` = 12.49; FCF `=105-26.25-13.5-0.28125-12.49-15-4` = 33.48. ### Step 3: debt schedule and credit statistics (USD m) | Year | Mandatory amortisation | Sweep | Closing TLB | Notes | Cash | Total leverage | Interest cover | |---|---|---|---|---|---|---|---| | 0 | | | 350.00 | 150.00 | 20.00 | 5.00x | | | 1 | 3.50 | 29.98 | 316.52 | 150.00 | 20.00 | 4.44x | 2.62x | | 2 | 3.50 | 35.60 | 277.43 | 150.00 | 20.00 | 3.88x | 2.94x | | 3 | 3.50 | 41.72 | 232.21 | 150.00 | 20.00 | 3.30x | 3.35x | | 4 | 3.50 | 48.38 | 180.32 | 150.00 | 20.00 | 2.72x | 3.90x | | 5 | 3.50 | 55.63 | 121.19 | 150.00 | 20.00 | 2.12x | 4.67x | Year 1: amortisation `=1%*350`; sweep `=MIN(33.48-3.5,350-3.5)` = 29.98; closing TLB `=350-3.5-29.98` = 316.52; leverage `=(316.52+150)/105` = 4.44x; interest cover `=105/(26.25+13.5+0.28)` = 2.62x. Total debt repaid over five years is 228.81 (`=350-121.19`), all of it from the term loan: the notes are untouched until exit. ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Northfield full LBO model: closing debt by tranche, USD m, computed example", "width": 420, "height": 240, "data": { "values": [ {"year": "0", "tranche": "Term loan B", "debt": 350.0}, {"year": "0", "tranche": "Senior notes", "debt": 150.0}, {"year": "1", "tranche": "Term loan B", "debt": 316.5}, {"year": "1", "tranche": "Senior notes", "debt": 150.0}, {"year": "2", "tranche": "Term loan B", "debt": 277.4}, {"year": "2", "tranche": "Senior notes", "debt": 150.0}, {"year": "3", "tranche": "Term loan B", "debt": 232.2}, {"year": "3", "tranche": "Senior notes", "debt": 150.0}, {"year": "4", "tranche": "Term loan B", "debt": 180.3}, {"year": "4", "tranche": "Senior notes", "debt": 150.0}, {"year": "5", "tranche": "Term loan B", "debt": 121.2}, {"year": "5", "tranche": "Senior notes", "debt": 150.0} ] }, "mark": "bar", "encoding": { "x": {"field": "year", "type": "ordinal", "title": "Year"}, "y": {"field": "debt", "type": "quantitative", "title": "Closing debt (USD m)", "stack": "zero"}, "color": {"field": "tranche", "type": "nominal", "title": "Tranche"} } } ``` ### Step 4: exit and returns (USD m) | Item | Computation | Result | Excel formula | |---|---|---|---| | Exit enterprise value | 8.0 x 127.63 | 1,021.03 | `=8*100*1.05^5` | | Less TLB and notes, plus cash | 121.19 + 150.00 - 20.00 | 251.19 | `=121.19+150-20` | | Exit equity before incentives | 1,021.03 - 251.19 | 769.83 | `=1021.03-251.19` | | Gross MOIC and IRR | 769.83 / 346.00 | 2.22x, 17.3% | `=RRI(5,346,769.83)` | | Management incentive plan | 10% x (769.83 - 346.00) | 42.38 | `=10%*MAX(0,769.83-346)` | | Sponsor exit proceeds | 769.83 - 42.38 | 727.45 | `=769.83-42.38` | | Sponsor MOIC | 727.45 / 346.00 | 2.10x | `=727.45/346` | | Sponsor IRR | 2.102^(1/5) - 1 | 16.0% | `=RRI(5,346,727.45)` | ### Step 5: walk from the paper LBO to the full model Each line adds one modelling choice to the line above, so the IRR change is the cost of that choice. | Step | Sponsor equity | Sponsor exit proceeds | MOIC | IRR | |---|---|---|---|---| | Paper LBO (one tranche 5.0x at 8%, as in mba/mba-paper-lbo) | 316.00 | 776.30 | 2.46x | 19.7% | | Two tranches: TLB 3.5x at 7.5% with 1% amortisation, notes 1.5x at 9% | 316.00 | 775.62 | 2.45x | 19.7% | | Revolver commitment fee | 316.00 | 774.44 | 2.45x | 19.6% | | Working capital at 10% of revenue | 316.00 | 749.83 | 2.37x | 18.9% | | Financing fees and minimum cash funded by equity | 346.00 | 769.83 | 2.22x | 17.3% | | Management incentive plan (10% of the gain) | 346.00 | 727.45 | 2.10x | 16.0% | The tranche mix barely matters here because the blended rate (7.95% at entry) is close to 8%. Working capital costs almost a point because growth ties up 22.10 of cash over five years. The larger cheque costs one and a half points: the minimum cash comes back at exit, but it earns nothing for five years, and the financing fees are gone. The incentive plan costs another 1.3 points. A candidate who quotes the paper answer of about 20% to an investment committee is almost four points too optimistic. ### Step 6: three modelling choices tested | Variant | Sponsor exit proceeds | MOIC | IRR | What it shows | |---|---|---|---|---| | Base: interest on opening balances | 727.45 | 2.10x | 16.0% | Reference | | Interest on average balances (circular, iterated) | 734.04 | 2.12x | 16.2% | Opening-balance interest overstates interest slightly when debt falls quickly | | Interest deduction capped at 30% of EBITDA, carryforward allowed | 726.86 | 2.10x | 16.0% | Disallowed interest of 8.53 in year 1 builds to a carryforward of 13.25 in year 3, then is used as interest falls | With the cap, year 1 deductible interest is `=MIN(40.03,30%*105)` = 31.50, so cash tax rises from 12.49 to 14.62. The carryforward is fully used by year 5, so the cap shifts tax payments in time rather than adding to them, and the IRR falls by only about 0.02 points. In a deal that deleverages slowly, or where the carryforward cannot be used before exit, the cost is permanent and much larger. ### Step 7: sensitivity tables (sponsor MOIC and IRR after the incentive plan) Entry multiple against exit multiple (debt fixed at 5.0x EBITDA, so equity absorbs the price change): | Entry \ exit multiple | 7.0x | 8.0x | 9.0x | |---|---|---|---| | 7.0x (equity 244.00) | 2.47x / 19.8% | 2.94x / 24.1% | 3.41x / 27.8% | | 8.0x (equity 346.00) | 1.77x / 12.1% | 2.10x / 16.0% | 2.43x / 19.5% | | 9.0x (equity 448.00) | 1.39x / 6.8% | 1.65x / 10.5% | 1.90x / 13.7% | Total leverage against revenue growth (notes fixed at 1.5x, term loan varied): | Total leverage \ growth | 0% a year | 5% a year | 8% a year | |---|---|---|---| | 4.0x | 1.40x / 6.9% | 1.93x / 14.0% | 2.29x / 18.0% | | 5.0x | 1.42x / 7.3% | 2.10x / 16.0% | 2.57x / 20.8% | | 6.0x | 1.47x / 8.0% | 2.42x / 19.3% | 3.07x / 25.2% | ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Northfield full LBO model: sponsor IRR after the incentive plan against the exit multiple, entry 8.0x", "width": 420, "height": 240, "data": { "values": [ {"exit": 6.0, "irr": 7.5}, {"exit": 6.5, "irr": 9.9}, {"exit": 7.0, "irr": 12.1}, {"exit": 7.5, "irr": 14.1}, {"exit": 8.0, "irr": 16.0}, {"exit": 8.5, "irr": 17.8}, {"exit": 9.0, "irr": 19.5}, {"exit": 9.5, "irr": 21.1}, {"exit": 10.0, "irr": 22.6} ] }, "mark": {"type": "line", "point": true}, "encoding": { "x": {"field": "exit", "type": "quantitative", "title": "Exit multiple (x EBITDA)", "scale": {"domain": [6, 10]}}, "y": {"field": "irr", "type": "quantitative", "title": "Sponsor IRR (%)"} } } ``` Read the tables as an investment committee would. At the base exit multiple, a turn of entry price moves the IRR by five and a half to eight points (10.5% at 9.0x, 24.1% at 7.0x); a turn of exit multiple is worth about three and a half to four. Leverage helps only when the business grows: at 0% growth, two extra turns of debt add about one point, because the extra interest absorbs the cash that would have repaid debt, while the downside gets worse. That is the pattern Axelson et al. (2013) warn about: cheap debt makes it easy to pay more, and paying more lowers returns. ### Step 8: value bridge (USD m, equity before the incentive plan) | Source | Computation | Contribution | |---|---|---| | EBITDA growth | (127.63 - 100) x 8.0 | 221.03 | | Multiple expansion | (8.0 - 8.0) x 127.63 | 0.00 | | Debt paydown | 500.00 - 271.19 | 228.81 | | Fees paid at entry | 16.00 + 10.00 | -26.00 | | Equity gain | 769.83 - 346.00 | 423.83 | The minimum cash of 20 is in both the entry cheque and the exit equity, so it does not appear in the bridge. The judgement to state: this is still a cash-flow deal, with slightly more of the gain from deleveraging than from growth, and the 8.0x exit assumption carries the risk. ## Worked example B (half solved): a downside case Same deal as Worked example A. Year 1 is on plan (EBITDA 105.00). In year 2 a recession cuts revenue and EBITDA by 20% (EBITDA 84.00, revenue 672.00 at the same 12.5% margin); from year 3 both grow 5% a year again. The exit multiple falls to 7.0x. | Item, year 2 | Computation | Result | |---|---|---| | Increase in NWC | `=10%*(672-840)` | [ ] | | Total interest and fee | 23.74 + 13.50 + 0.28 | 37.52 | | Cash tax | `=25%*(84-15-37.52)` | [ ] | | FCF | 84 - 37.24 - 0.28 - [tax] - 15 - [NWC] | [ ] | | Closing TLB | 316.52 - 3.50 - [sweep] | [ ] | | Total leverage | [closing TLB + 150] / 84 | [ ] | | Interest cover | 84 / 37.52 | 2.24x | | Item, exit | Computation | Result | |---|---|---| | Year 5 EBITDA | 84 x 1.05^3 | 97.24 | | Closing TLB, year 5 | from the model | 184.93 | | Exit equity before incentives at 7.0x | 7.0 x 97.24 - 184.93 - 150 + 20 | [ ] | | Sponsor MOIC and IRR after the incentive plan | | [ ] | | Same downside with exit at 8.0x: MOIC and IRR | | 1.30x, 5.5% | Questions to answer: why does FCF in year 2 rise even though EBITDA falls by 20%? Would a lender with a springing revolver covenant be worried in this case? What is the main lesson for the equity? [ ] ## Exercise C (unsolved): maximum price and PIK notes C1. Keep the base case of Worked example A with debt fixed at 5.0x EBITDA (so the extra price is all equity). The fund needs a 20% IRR after the incentive plan. What is the maximum entry multiple, the maximum enterprise value and the sponsor equity cheque at that price? Excel hint: Goal Seek the IRR cell to 20% by changing the entry multiple. C2. Replace the 9.0% cash-pay senior notes with 150 of PIK notes at 11.0%, repaid with accrued interest at exit. Find the PIK balance at exit, the closing TLB in year 5, the sponsor MOIC and IRR, and the year 5 total leverage. Explain why the term loan falls faster but the equity return is lower. C3. In one paragraph, say which of the base, downside and PIK variants you would present to the investment committee as the "lender case", and why. ## Connections to other cards | Card or template | Connection | |---|---| | mba/mba-paper-lbo | The mental-math version; its Worked example A is this card's base deal | | mba/mba-private-equity-guide | The elective this card belongs to, with a buyout mini-case and teaching note | | mba/mba-pe-fund-economics-card | How the deal IRR becomes the fund's net IRR after fees and carried interest | | mba/mba-pe-value-creation-card | How to build and defend the operating plan that drives EBITDA growth | | mba/mba-deal-structuring-card | Earn-outs, rollover equity, vendor notes and other structure choices | | mba/mba-capital-structure-card | Tax shields, distress costs and why leverage has limits (Modigliani and Miller) | | mba/mba-dcf-valuation-card | Intrinsic value against the sponsor's return-based price | | mba/mba-three-statements-card, mba/mba-cash-flow-statement-card | Why FCF starts from EBITDA and subtracts working capital and capex | | finance/credit-memo, finance/covenant-compliance-certificate | The lender's view of the same model | | finance/private-equity-investment-memo, finance/investment-committee-memo | Where the outputs go | ## Common mistakes and misconceptions 1. **Sweeping cash that is not there.** The sweep must come after mandatory amortisation, minimum cash and revolver repayment; otherwise the model repays debt with cash the company needs to operate. 2. **Applying the amortisation rate to the opening balance** each year instead of to the original principal, which makes the mandatory payment shrink when it should stay fixed. 3. **Forgetting the minimum cash and financing fees** in uses, so the equity cheque is too small and the IRR too high. 4. **Ignoring working capital** in a growing business. In Worked example A it costs almost a point of IRR. 5. **Taxing EBITDA or using total instead of deductible interest** when an interest cap applies, or forgetting the carryforward, which can turn a timing effect into an apparent permanent loss. 6. **Leaving the circularity unprotected.** A circular model without a switch can fill with errors that never clear; always add a circuit breaker. 7. **Treating PIK interest as free.** It saves cash today but compounds at a high rate and is repaid at exit before the equity. 8. **Reporting the gross IRR as the sponsor's return**, before the management incentive plan, and then also quoting it as the fund's net return, which is lower again after fees and carried interest. 9. **Using the exit multiple as a plug.** If the deal only works at an exit above entry, say so; do not hide it in a case labelled "base". 10. **Sensitising only one variable at a time.** Downside cases come in combinations: lower EBITDA, a lower multiple and a higher rate tend to arrive together. 11. **Confusing covenant-lite with risk-free.** No maintenance covenant means fewer early warnings for lenders, not that the company can carry more debt. 12. **Hard-coding numbers inside formulas** in a model others must audit; every input belongs on the inputs sheet. ## Self-test questions 1. List, in order, the uses of cash from FCF in Worked example A's debt schedule. 2. Why does equity rise from 316.00 in the paper LBO to 346.00 in the full model? 3. Which single modelling choice in the walk from the paper LBO costs the most IRR, and why? 4. In Worked example A, what is the revolver commitment fee each year, and why does it fall to zero in a year the revolver is fully drawn? 5. Explain the interest circularity in two sentences and how a circuit breaker works. 6. With a 30% of EBITDA cap, what is year 1 deductible interest in Worked example A, and why does the IRR barely move? 7. Why can a PIK note raise the speed of term loan repayment but lower the equity return? 8. What is a springing covenant, and why is the downside case still important in a covenant-lite deal? 9. A sponsor receives 2.2x in four years with no interim flows. What is the IRR? Give the Excel formula. 10. From the entry and exit sensitivity table, which is worth more: one turn lower entry price or one turn higher exit multiple? Why? 11. Why does extra leverage add almost nothing to the IRR at 0% growth in the leverage table? 12. What does the incentive plan cost the sponsor in Worked example A, in USD and in IRR points? ## My notes and next steps | Date | Model or exercise | Time (minutes) | Errors found | Next step | |---|---|---|---|---| | *Example:* YYYY-MM-DD | Worked example A from blank sheet | 75 | Swept cash before amortisation | Rebuild the debt block in under 20 minutes | | [YYYY-MM-DD] | [ ] | [ ] | [ ] | [ ] | ## 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. - Kaplan, S. N. and Stein, J. C. (1993). The evolution of buyout pricing and financial structure in the 1980s. *The Quarterly Journal of Economics*, 108(2), 313-357. - Kaplan, S. N. and Stromberg, P. (2009). Leveraged buyouts and private equity. *Journal of Economic Perspectives*, 23(1), 121-146. - Axelson, U., Stromberg, P. and Weisbach, M. S. (2009). Why are buyouts levered? The financial structure of private equity funds. *The Journal of Finance*, 64(4), 1549-1582. - Axelson, U., Jenkinson, T., Stromberg, P. and Weisbach, M. S. (2013). Borrow cheap, buy high? The determinants of leverage and pricing in buyouts. *The Journal of Finance*, 68(6), 2223-2267. - 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. Official pages for dated facts (checked 2026-10-28): - Internal Revenue Service (2026). Questions and answers about the limitation on the deduction for business interest expense (FS-2026-14), https://www.irs.gov/newsroom/questions-and-answers-about-the-limitation-on-the-deduction-for-business-interest-expense. - Council Directive (EU) 2016/1164 of 12 July 2016 (Anti-Tax Avoidance Directive), Article 4, http://data.europa.eu/eli/dir/2016/1164/oj. - Alternative Reference Rates Committee, SOFR transition page, https://www.newyorkfed.org/arrc/sofr-transition. Textbooks (further reading, by name only): Rosenbaum and Pearl, *Investment Banking: Valuation, LBOs, M&A, and IPOs*; Berk and DeMarzo, *Corporate Finance*; Koller, Goedhart and Wessels, *Valuation*. Open resource: OpenStax, *Principles of Finance* (CC BY-NC-SA 4.0), https://openstax.org. ## Answer key Worked example B (year 2): increase in NWC -16.80 (working capital is released as revenue falls); cash tax 7.87; FCF 40.41 (`=84-37.24-0.28-7.87-15-(-16.8)`); sweep 36.91, closing TLB 276.11; total leverage 5.07x (`=(276.11+150)/84`). Exit at 7.0x: enterprise value 680.68, exit equity before incentives 365.75 (`=680.68-184.93-150+20`), incentive plan 1.98, sponsor proceeds 363.78, MOIC 1.05x, IRR 1.0% (`=RRI(5,346,363.78)`). FCF rises because the fall in revenue releases 16.80 of working capital, a one-off cushion that reverses when growth returns (year 3 FCF is 25.67). Leverage peaks at 5.07x, just above entry, and interest cover stays above 2.2x; the revolver is never drawn, so a springing covenant would not be tested, but a maintenance covenant set tightly against the base case could be. The lesson for the equity: the debt survives, the equity return almost disappears, because the same downside hits EBITDA and the multiple together. Exercise C: - C1: maximum entry multiple 7.45x, enterprise value 745.20, sponsor equity 290.10, for an IRR of exactly 20.0% after the incentive plan. - C2: PIK balance at exit 252.76 (`=150*1.11^5`); closing TLB in year 5 36.12; exit equity before incentives 752.15, incentive plan 40.61, sponsor proceeds 711.53, MOIC 2.06x, IRR 15.5% (against 16.0% in the base); year 5 total leverage 2.26x (`=(36.12+252.76)/127.63`). The term loan falls faster because no cash goes to the notes, but the PIK compounds at 11%, above the 7.5% the sweep saves on the term loan, so the claim ahead of equity at exit is larger. - C3: present the downside of Worked example B, perhaps with the higher rate of C2, as the lender case: lenders care whether the company can service and refinance the debt when EBITDA and the multiple fall together, not about the base case IRR. Self-test: 1. Cash interest and fees and tax are already deducted in FCF; then mandatory amortisation (3.50), then keep minimum cash (20), then repay any revolver drawings, then sweep the rest to the term loan. 2. Financing fees of 10.00 and minimum cash of 20.00 are funded with equity. 3. Funding the financing fees and minimum cash, about 1.5 points (18.9% to 17.3%), because the cheque grows while the cash earns nothing; next is the incentive plan (1.3 points) and working capital (0.8 points). 4. 0.375% x 75 = 0.28 a year (`=0.375%*75`); the fee is charged only on the undrawn commitment. 5. Interest on average debt depends on the year's repayment, which depends on cash after interest. A circuit breaker is a switch that replaces average-balance interest with opening-balance interest, breaking the loop when needed. 6. `=MIN(40.03,30%*105)` = 31.50; the disallowed 8.53 is carried forward and used in years 4 and 5 as interest falls, so the cap delays tax savings rather than removing them. 7. PIK interest is not paid in cash, so more cash is swept to the term loan, but the PIK principal compounds at a rate above the term loan rate and is repaid ahead of equity at exit. 8. A financial covenant, usually in the revolver, that applies only when drawings exceed a threshold. The downside still decides whether the company can pay interest, refinance and avoid drawing the revolver; the equity bears the loss first. 9. `=2.2^(1/4)-1` or `=RRI(4,1,2.2)`, 21.8%. 10. One turn lower entry price: it is worth about eight points of IRR (16.0% to 24.1%) because it cuts the equity cheque at once, while one turn higher exit multiple is worth about three and a half points (16.0% to 19.5%) and arrives only in year 5. 11. Without growth, the extra interest consumes the cash that would otherwise repay debt, so the equity gains little from the smaller cheque while the risk of distress rises. 12. 42.38 of exit proceeds; IRR falls from 17.3% to 16.0%, about 1.3 points. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First build of Worked example A from the inputs | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Added downside case and interest cap switch | ## Standard and licence note Based on standard leveraged finance and private equity modelling practice and the primary works listed above, with dated facts on interest deductibility and benchmark rates taken from the official pages named in the sources and checked on 2026-10-28. The text, the model, the numbers and the exercises are original; no textbook, bank training material or published case is copied or paraphrased, and Northfield Outdoor Co. and every number in this card are fictional. The template is independent and not affiliated with or endorsed by any private equity firm, bank, lender, business school or publisher. Check current tax rules, credit market terms and benchmark rates before you rely on them. Template licence: MIT.