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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?
  2. 023Two businesses each earn EBITDA of 100 on revenue of 500. A has fixed costs of 50; B has fixed costs of 300. Revenue falls 10% at both. What is each one's EBITDA, and what happens to 4x leverage?Operating levers and margin mathsHardOaktree Capital ManagementLos Angeles · 2024

    Try it first

    After the 10% revenue fall, B's EBITDA is

    Show the worked solution

    A keeps 85 and B keeps 60; leverage goes to 4.7x and 6.7x. A's variable costs are 350, or 70% of revenue, so at 450 they are 315 and EBITDA is 450 less 315 less 50, which is 85. B's variable costs are 100, or 20%, so at 450 they are 90 and EBITDA is 450 less 90 less 300, which is 60. Debt of 400 was 4.0x at both; it is now 4.7x at A and 6.7x at B.

    Why does the same revenue fall hit the two businesses so differently?

    Think of two auto drivers. One rents his vehicle by the day and pays a fixed 300 whatever happens; the other owns his and pays mostly for fuel. On a slow day the owner-driver still goes home with something, while the renter may go home with nothing. Fixed costs do not shrink when revenue shrinks, so the whole of a revenue fall lands on profit after only the variable costs have been saved. At A, 70 of every 100 of lost revenue was variable cost that disappears with it, so profit falls by 30 on 50 of lost revenue. At B only 20 of every 100 was variable, so profit falls by 40 on the same 50.

    The same 10% revenue fall: fixed costs decide how much EBITDA survivesfixed 50variable 350EBITDA 100revenue 500debt 400 = 4.0xbeforefixed 50variable 315EBITDA 85revenue 450debt 400 = 4.7xafterfixed 300variable 100EBITDA 100revenue 500debt 400 = 4.0xbeforefixed 300variable 90EBITDA 60revenue 450debt 400 = 6.7xafterBusiness A: fixed costs 10% of revenueBusiness B: fixed costs 60% of revenueA loses 15% of EBITDA; B loses 40%. Same revenue fall, same debt.
    A 10% revenue fall from 500 to 450 cuts A's EBITDA from 100 to 85 because its fixed costs are only 50, but cuts B's from 100 to 60 because 300 of its costs do not move, so 400 of debt goes from 4.0x to 4.7x at A and 6.7x at B.

    What are the numbers, and what do they do to the lenders?

    A: revenue 450, variable costs 70% of that is 315, fixed 50, EBITDA 85, down 15%. B: revenue 450, variable 20% of that is 90, fixed 300, EBITDA 60, down 40%. Debt of 400 was 4.0x EBITDA at both companies, and after one bad year it is 4.7x at A and 6.7x at B, which is the difference between a conversation with the lender and a covenant breach. The operating leverageThe ratio of the percentage change in profit to the percentage change in revenue. High fixed costs mean high operating leverage. here is 1.5 at A and 4.0 at B: each 1% of revenue lost costs B 4% of EBITDA. Lenders feel it first because their claim is fixed and sits ahead of the equity; the equity feels it hardest because it is what is left.

    The relationship
    EBITDA1=R1(1−v)−FB:450×(1−0.20)−300=6040060=6.7x\text{EBITDA}_1 = R_1(1 - v) - F \qquad B: 450 \times (1 - 0.20) - 300 = 60 \qquad \frac{400}{60} = 6.7x
    R_1revenue after the fall, 450
    vvariable costs as a share of revenue, 0.70 at A and 0.20 at B
    Ffixed costs, 50 at A and 300 at B
    What it says in wordsProfit after the fall is the new revenue less the costs that move with it, less the costs that do not.

    How should a lender and a sponsor use this?

    By sizing the debt to the cost structure, not to the EBITDA alone. Two businesses with identical EBITDA can carry very different debt safely, because the one with high fixed costs needs far less of a downturn to stop covering its interest. B breaks even at revenue of 375, a fall of only 25%, while A breaks even at 167. A lender to B wants lower leverage, a wider cushion in the covenant and a close look at whether any of the 300 can be made variable. The limits: the split of costs into fixed and variable is never clean, fixed costs do move over a long enough horizon, and the same leverage cuts the other way in an upswing, where B's EBITDA would rise 40% on a 10% revenue gain.

    Where candidates lose it

    The common slip is to cut EBITDA by 10% along with revenue, giving 90 at both companies. That treats every cost as variable and misses the whole point of the question.

    The second loss is stopping at 85 and 60. The question says 4x leverage for a reason: convert both numbers into leverage and name which one has become a lender's problem, and say that it is the debt holders who feel operating leverage first because their claim does not shrink.

    What the interviewer asks next

    • What revenue fall would take B to zero EBITDA?
    • Revenue rises 10% instead. What is each EBITDA, and which company would you rather own the equity of?
    • How would you check what share of a target's costs is really fixed during diligence?

    Asked at Oaktree Capital Management, Credit, Los Angeles, 2024 (Wall Street Oasis): How does operating leverage affect debt vs. equity holders