Every concept, endless questions
Each concept is a small financial model. Read how it works, then draw a real interview question from it: forwards, backwards or what-if, with fresh numbers and a worked solution every time.
Forward runs a concept the usual way. Inverse runs it backwards, which is what separates understanding from memorizing.
LBO Returns
6 conceptsValue creation bridge: growth, multiple and deleveraging
Equity gain in a buyout has exactly three sources. The business earned more (EBITDA growth, valued at the price you paid for it), the market paid more per dollar of earnings (multiple expansion, applied to the bigger exit EBITDA), and the cash the business threw off repaid debt that would otherwise have come out of the equity (deleveraging). Add the three and you get the change in equity to the dollar. Investment committees care about the split because growth and paydown are things the sponsor can plan for; the multiple is a bet on the market.
IRR versus MOIC across hold periods
MOIC says how many dollars came back per dollar in; IRR says how fast. With a single check in and a single check out they are tied together by the hold period alone: the same multiple over fewer years is a higher IRR, and the same IRR over more years needs a bigger multiple. Funds are judged on both. A quick 1.5x flatters the IRR but earns little carry; a 3x that takes eight years earns the carry but drags the IRR the LPs quote. The tension between the two is most of what an exit-timing debate is about.
Dividend recapitalisation
A dividend recap borrows against a business that has deleveraged and hands the proceeds to the sponsor as a dividend. It does not make the company worth more; it moves a slice of the exit proceeds forward in time. Ignoring the extra interest, the sponsor gets the same total dollars — a bigger check early and a smaller one at exit — so MOIC is unchanged. IRR rises because money returned in year two or three is worth more, in IRR terms, than the same money in year five. The recap also takes risk off the table: once the dividend has returned the original equity, the rest of the hold is played with house money.
Entry multiple sensitivity
Lenders size debt off cash flow, not off price. So when a sponsor pays one more turn of EBITDA at entry, every dollar of it is equity — the debt does not move, the exit does not move, and the same exit equity is divided by a bigger check. That is why the entry price is the single most powerful lever on returns, and why "we can fix it with growth" is the most expensive sentence in private equity. Run the price up a turn and read the IRR; run it backwards and you get the most you can pay for a required return.
Management rollover and the incentive pool
When a sponsor buys a business, the managers who own part of it are asked to reinvest a slice of their sale proceeds alongside the sponsor. That rollover buys them a stake in the new deal at the sponsor’s price, and it reduces the check the sponsor has to write. On top of it sits the management incentive plan: a share of exit equity carved out for management before the ordinary equity is divided. Both exist for the same reason — a management team with real money in the deal and a real share of the upside behaves like an owner. The sponsor pays for that alignment with a lower multiple on its own check, and the arithmetic of exactly how much is what this recipe tests.
Bolt-on acquisitions and multiple arbitrage
Small companies trade at lower multiples than large ones. A platform bought at eleven times can buy a competitor at seven, and the moment the two are combined the market values the acquired EBITDA at eleven — the same earnings, re-rated four turns higher simply because they now sit inside a bigger business. That gap is multiple arbitrage. It lowers the blended entry multiple, it lifts the combined return above what the platform alone would earn, and it works whether or not there are synergies. The catch is that the exit multiple has to hold for the combined business: buy enough low-quality EBITDA and the market re-rates the platform down instead of the bolt-on up.
Debt & Leverage
5 conceptsDebt capacity from lender tests
Lenders do not ask how much debt a sponsor wants. They run three tests and lend the smallest answer. Leverage caps debt at a multiple of EBITDA. Coverage caps it at whatever the business can pay interest on with a cushion to spare — which makes it a test of the interest rate as much as the business. Loan-to-value caps it at a share of what the company is worth, so that there is equity underneath the loan. In cheap-money years the leverage test binds; when rates rise the coverage test takes over, and debt capacity falls even though EBITDA has not moved.
Unitranche versus senior plus mezzanine
A buyout can be financed in layers — cheap senior debt on top, expensive mezzanine underneath — or with a single unitranche loan that covers the same total at one blended rate. The layered structure is usually cheaper on paper, because the senior lender is paid only for senior risk. The unitranche costs more per dollar but comes from one lender, closes faster, has one set of covenants and no intercreditor negotiation, and often lets the borrower defer part of the interest. The comparison is a blended-rate calculation; the decision is about certainty, speed and flexibility, and how much the sponsor will pay for them.
Covenant headroom
A leverage covenant says debt may not exceed some multiple of EBITDA. The sponsor cares less about the multiple than about the cushion: how far EBITDA can fall before the test fails. That cushion is set at closing by the gap between actual and permitted leverage, and it moves every year — up as debt is repaid and EBITDA grows, down as the covenant steps down on schedule. A breach hands the lenders control of the conversation. Reading the cushion, and how it changes when the covenant tightens, is the difference between a comfortable capital structure and one that is a bad quarter from default.
PIK toggle and accreting balances
Payment-in-kind interest is not paid; it is added to the loan. That keeps cash in the business, which is the point — but next year’s coupon is charged on the larger balance, so the note compounds. Compare it to paying the same coupon in cash: cash-pay drains free cash flow that would have repaid senior debt, so total debt at exit is higher than if there were no coupon at all, but only by the simple sum of the coupons. PIK costs more than that, by exactly the interest-on-interest. The toggle lets the borrower choose each period, which is why lenders price it and sponsors use it when cash is tight and growth is expected.
Refinancing breakeven
Refinancing swaps an expensive loan for a cheaper one, but the swap is not free: the new lender charges an arrangement fee and the old lender often charges a premium to be repaid early. So the sponsor pays a lump sum today to save a stream of interest tomorrow, and the question is how long the stream has to run before it has covered the lump sum. Run it backwards and you get the rate the new loan must beat for the deal to pay off before the planned exit — which is the number the sponsor takes into the negotiation.
Fund Economics
5 conceptsCarried interest waterfall (European, whole-fund)
Carry is the GP’s share of fund profit, but it is not paid off the top. The waterfall returns the LPs’ capital first, then a preferred return on it, and only then lets the GP catch up — taking most or all of the next distributions until it holds its full carry share of the profit so far. After the catch-up every dollar splits at the carry rate. Two things follow. Below the hurdle the GP earns nothing, however large the fund. And once the catch-up is complete the hurdle has cost the GP nothing at all: it ends up with exactly carry-percent of total profit, as if the hurdle never existed. The hurdle is a gate, not a discount.
Management fee drag
The management fee is paid out of the LPs’ commitments, so a "$500M fund" never invests $500M. Two percent a year on commitments for five years, then a lower rate on what is actually invested for another five, eats a sizeable slice before a single deal is done. The gross multiple is earned only on what was left to invest; the net multiple the LP quotes is measured on everything they committed. The gap between the two is the fee drag, and it is why a fund has to earn well over 2x gross to show 2x net — before carry takes its share.
DPI, RVPI and TVPI
Three multiples describe a fund mid-life. DPI is cash actually returned per dollar paid in — realized, banked, beyond argument. RVPI is what is still held, per dollar paid in — a valuation, and therefore an opinion. TVPI adds the two: total value, realized and unrealised. Early in a fund TVPI is nearly all RVPI and nearly all opinion; by the end RVPI is zero and TVPI equals DPI. LPs read the split, not just the total: a 2.0x TVPI that is 0.3x DPI is a very different fund from one that is 1.5x DPI, even though the headline is the same.
The J-curve
Plot an LP’s cumulative cash position in a fund and it looks like a J. Money goes out first — capital calls for deals, and management fees on the whole commitment from day one — while nothing comes back, because the companies bought in year one are not sold until year five or six. The curve bottoms out when the last deal is bought, then climbs as exits arrive. Two numbers describe it: how deep the trough is, and how long until the LP is back to even. Fees deepen the trough; earlier or larger distributions shorten it. Neither says anything about the fund’s final return, which is why a young fund’s negative IRR is not a verdict.
The GP commitment
Carry is an option: the GP gets a share of the upside and none of the downside. LPs want the GP to have something to lose, so they require it to invest its own money in the fund — the GP commitment, historically one percent and now often two to five. On that money the GP earns what any LP earns, after fees and after its own carry. In a good fund the commitment is a small part of the GP’s economics next to the carry; in a bad fund it is the only part that moves, and it moves against them. That asymmetry is the point.
Deal Structuring
3 conceptsEarnout design
An earnout bridges a valuation gap. The seller believes next year’s EBITDA will be higher than the buyer will pay for today, so the buyer pays a lower price now and promises more if the number is delivered. Three things define it: the threshold below which nothing is paid, the target at which everything is paid, and the line between them. To the buyer the earnout is an expected cost — probability times payout — and the headline price it lets the seller announce is not the price it expects to pay. To the seller it is a bet on their own forecast, which is exactly why it is offered.
Rollover versus cash at close
A seller who rolls part of the proceeds into the new deal is trading certain cash today for a levered bet on the sponsor’s plan. Two things make the trade worth considering. The rolled shares participate in the second exit, which in a good deal is worth several times the cash forgone. And a properly structured rollover defers tax: the seller reinvests pre-tax dollars and is taxed once, at exit, instead of being taxed now and again later. Against that sits concentration, illiquidity and the sponsor’s leverage. The arithmetic says what the rollover has to return to beat the cash; the judgment is whether the seller believes it will.
Preferred structures: liquidation preference and participation
Preferred equity is how an investor buys a share of the upside while keeping first claim on the downside. The liquidation preference says what the investor gets back before the common sees anything — one times its money, sometimes more. Non-participating preferred then makes a choice: take the preference, or convert and take a percentage of everything. Participating preferred does not choose; it takes the preference and then its percentage of the rest, which is why founders call it double-dipping. The exit value at which converting beats the preference is the number that tells you whether the structure is protection or a price cut.
Operating Model
5 conceptsOperating leverage and the margin bridge
When some costs are fixed, profit moves faster than revenue. Every extra dollar of sales brings in its contribution margin — revenue less variable cost — and none of it goes to the fixed base, so the whole contribution drops to EBITDA. The ratio of contribution to EBITDA is the degree of operating leverage: a business at 3x turns 10% revenue growth into 30% EBITDA growth, and a 10% decline into a 30% collapse. Sponsors love it on the way up and fear it on the way down, which is why the fixed-cost base is the first thing an operating partner asks about.
Revenue build: price, volume and mix
Revenue growth is not one number. It is the sum of three things: charging more for the same units (price), selling more units at the old prices (volume), and selling a different blend of units — more of the expensive product, say — at the old prices (mix). Sponsors split growth this way because the three are not equally valuable. Price drops straight to profit and tests pricing power; volume brings variable cost with it; mix can be a strategy or an accident. A plan built on price needs a reason customers will pay; one built on volume needs capacity.
Working capital as a cash lever
Working capital is cash the business has lent to its customers and tied up on its shelves, less cash its suppliers have lent to it. Each day of receivables is a day of revenue the company has not been paid for; each day of inventory is a day of cost of goods sitting in a warehouse; each day of payables is a day of purchases the company has not yet paid. Shorten the first two or lengthen the third and cash comes out — once, permanently, and without touching EBITDA. Sponsors pull this lever in the first hundred days because it repays debt faster than any operating improvement and needs no customers to cooperate.
Maintenance versus growth capex
Not all capex is equal. Maintenance capex is what the business must spend just to stand still — replacing worn machines, refreshing stores — and it is really an operating cost that the accounts happen to capitalize. Growth capex is a choice: spend now to earn more later. The distinction matters because a sponsor can cut growth capex to flatter free cash flow this year, at the cost of EBITDA next year and the exit value that multiplies it. The return on growth capex, measured against the exit multiple, tells you whether the cut is discipline or harvesting.
Cost-out programs
A cost-out program buys a permanent reduction in the cost base with a one-off payment — severance, consultants, plant closures. Three numbers describe it. The run-rate saving is what EBITDA gains every year once the program is complete. The cost to achieve is the one-off bill, usually quoted as a multiple of the run-rate. The phasing says how much of the saving lands in year one, because nobody fires everyone on day one. At exit the saving is capitalized at the multiple, which is why sponsors do it early: a dollar of run-rate saving is worth eight to ten dollars of exit value, against a cost to achieve of one to two.