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Private Equity puzzles, solved step by step

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All topicsCredit and PIK maths8Returns maths10Mental paper LBOs8Operating levers and margin maths8Valuation riddles10Fund economics numeracy9Market sizing and estimation9Compounding and time value7Mental maths8Probability and expected value in deals8Leverage and capital structure9Logic and brainteasers6
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  1. 064Revenue is 1,000 at a 25% EBITDA margin. Depreciation and amortisation are 40, interest is 60, tax is 25%, capex is 50, and working capital is 10% of the revenue growth of 100. Walk from revenue to levered free cash flow.Operating levers and margin mathsCoreVista Equity PartnersAustin · 2025

    Try it first

    What is levered free cash flow?

    Show the worked solution

    Levered free cash flow is 92.5. EBITDA is 250. Take off D&A of 40 and interest of 60 to get pre-tax profit of 150, tax of 37.5 and net income of 112.5. Add back the 40 of D&A because it is not cash, then subtract capex of 50 and the 10 of working capital the growth absorbs. What remains, 92.5, is cash the owners could take out.

    Why does depreciation come off and then go back on?

    Think of a delivery van bought last year. Each year the accounts charge a slice of its cost as depreciation, but no money leaves the business that year: the van was paid for already. Depreciation reduces taxable profit, which saves real tax, but it is not a cash payment, so it is subtracted to work out tax and then added back to reach cash. The cash cost of assets enters through capex instead, here 50, which is more than the 40 of depreciation because the business is growing.

    From EBITDA to levered free cash flow: lenders, taxman, reinvestment250EBITDA-60Interest-37.5Tax-50Capex-10Moreworking capital92.5Levered FCFTax is on profit after D&A:250 - 40 - 60 = 150 taxablex 25% = 37.5; D&A 40 is no cashRevenue 1,000 x 25% margin
    EBITDA of 250 loses 60 to interest, 37.5 to tax, 50 to capex and 10 to working capital, leaving levered free cash flow of 92.5; depreciation of 40 appears only inside the tax calculation.
    StepAmount
    Revenue1,000
    EBITDA at 25%250
    Less D&A(40)
    EBIT210
    Less interest(60)
    Pre-tax profit150
    Less tax at 25%(37.5)
    Net income112.5
    Add back D&A40
    Less capex(50)
    Less increase in working capital(10)
    Levered free cash flow92.5
    Net income of 112.5 plus D&A of 40, less capex of 50 and a working capital increase of 10, gives levered free cash flow of 92.5, the same answer the EBITDA route gives.

    What makes it levered, and why does a buyout investor want that version?

    Levered means after interest: the lenders have been paid. Levered free cash flow is the cash left for the equity holders after the lenders, the taxman and the business's own reinvestment, which is exactly the cash that repays debt in a buyout. Check it a second way from EBITDA: 250 less 60 less 37.5 less 50 less 10 is 92.5. The limit worth saying: working capital is modelled here as 10% of growth, and a real business can swing by far more in a single year.

    Where candidates lose it

    The most common slip is forgetting to add back depreciation, which gives 52.5 and treats the van as paid for twice, once through depreciation and again through capex.

    The second is using the whole working capital balance, 10% of revenue, instead of the increase, 10% of the growth. Only the change in working capital uses cash in the year.

    What the interviewer asks next

    • What is unlevered free cash flow here, and why is it higher?
    • Revenue falls instead of growing. What happens to the working capital line?
    • Capitalised software development of 30 sits inside capex. Should a software buyer treat it differently?

    Asked at Vista Equity Partners, Private Equity, Austin, 2025 (Wall Street Oasis): I got a question about getting from revenue to levered free cash flow

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