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  1. 004A portfolio company's revenue grows 10% and its EBITDA grows 30%. The EBITDA margin was 20% before the growth. Assuming costs are either fixed or move in line with revenue, what share of the cost base is fixed?Operating levers and margin mathsHardPortfolio operations teamMid-market buyout fund

    Try it first

    Your instinct: what share of costs is fixed?

    Show the worked solution

    Half the cost base is fixed. Take revenue of 100, so EBITDA is 20 and costs are 80. Revenue grows to 110 and EBITDA to 26, so costs rose by only 4. A 4 rise on 10 of extra revenue means variable costs are 40% of revenue, which is 40. The remaining 40 of the 80 does not move, so fixed costs are 50% of costs.

    Why does profit grow faster than revenue at all?

    A tea stall pays the same rent whether it sells 100 cups or 110. The milk and sugar go up with each cup; the rent does not. When some costs are fixed, every extra unit of revenue only has to cover its own variable cost, and the rest drops straight to profit. The bigger the fixed slice, the more of each new rupee of revenue falls through, and the faster profit grows relative to sales. That gap between the two growth rates is the clue the question hands you.

    So pick round numbers and let the gap tell you the split. Revenue of 100 at a 20% margin means EBITDA of 20 and costs of 80. Ten percent growth takes revenue to 110; thirty percent growth takes EBITDA to 26. Costs are therefore 110 less 26, which is 84, up 4. Those 4 are the variable costs riding on 10 of new revenue, so variable cost is 40% of revenue: 40 of the original 80.

    Revenue up 10, EBITDA up 6: the fixed half of costs does not movevariable 40fixed 40EBITDA 20Year 0: revenue 100variable 44fixed 40EBITDA 26Year 1: revenue 110same 40Where the extra 10 goesVariable cost, 40% of it+4Fixed cost+0EBITDA+66 on a base of 20 = +30%Fixed share: 40 / 80 = 50%Operating leverage = 30% / 10% = 3x
    When revenue rises from 100 to 110, variable cost rises from 40 to 44, fixed cost stays at 40 and EBITDA rises from 20 to 26, a 30% jump, which shows that half of the 80 cost base is fixed.

    Is there a formula you can say out loud to check it?

    Yes. The ratio of profit growth to revenue growth is the degree of operating leverageHow many per cent profit changes for each one per cent change in revenue, equal to contribution divided by profit., here 30 over 10, which is 3. Operating leverage equals contribution divided by EBITDA, so contribution must be three times EBITDA: 60 on revenue of 100. Revenue of 100 less contribution of 60 leaves variable costs of 40, and the cost base of 80 less 40 leaves fixed costs of 40. Two routes landing on the same 50% is the check the interviewer wants to hear.

    The relationship
    DOL=%ΔEBITDA%ΔRevenue=R−VEBITDA=100−4020=3\text{DOL} = \frac{\%\Delta \text{EBITDA}}{\%\Delta \text{Revenue}} = \frac{R - V}{\text{EBITDA}} = \frac{100 - 40}{20} = 3
    Rrevenue, set to 100
    Vvariable costs, which move in line with revenue
    R - Vcontribution, what is left to pay fixed costs and earn profit
    What it says in wordsProfit moves three times as fast as revenue because contribution is three times profit.

    Why would an operating partner care about this number?

    Because it cuts both ways. The same 3x leverage that turned 10% growth into 30% profit growth turns a 10% revenue fall into a 30% profit fall. Say the limitation: real costs are rarely cleanly fixed or variable. Staff can be cut with a lag, rent steps up when a site is added, and a one-year jump can include price rises that carry no variable cost at all, which would make the fixed share look larger than it is.

    Where candidates lose it

    Candidates often reach for the margin and answer 20%, or try to solve with two unknowns in their head and lose the thread. Fix revenue at 100 first; the problem becomes subtraction.

    The other loss is quoting the fixed share of revenue, 40%, rather than of the cost base, 50%. Repeat the question's denominator back before you answer.

    What the interviewer asks next

    • If revenue now falls 10% from 110, what happens to EBITDA?
    • What would the EBITDA growth be if all costs were variable?
    • How would a price increase with no volume change distort this calculation?