Private Equity puzzles, solved step by step

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  1. 027A company trades at 10x EV/EBITDA and 2x EV/Sales. What is its EBITDA margin?Valuation riddlesWarm upMid-market buyout fund

    Try it first

    Answer before you write anything down.

    Show the worked solution

    The EBITDA margin is 20%. Both multiples share the same enterprise value on top. Divide EV/Sales by EV/EBITDA and EV cancels, leaving EBITDA divided by sales: 2 over 10, which is 20%. Check it with any EV you like: at 1,000, sales are 500 and EBITDA is 100, and 100 is 20% of 500.

    Why does the enterprise value not matter?

    A cricket bat costs as much as 10 balls, and as much as 2 sets of pads. How many balls is a set of pads worth? Five, and you never needed the price of the bat. When two ratios share the same top line, dividing one by the other cancels it and leaves the ratio of the two bottom lines. Here the shared top line is enterprise value, and the bottom lines are sales and EBITDA.

    The relationship
    EV/SalesEV/EBITDA=EBITDASales=210=20%\frac{EV/\text{Sales}}{EV/\text{EBITDA}} = \frac{\text{EBITDA}}{\text{Sales}} = \frac{2}{10} = 20\%
    EV/Salesenterprise value over revenue, 2x
    EV/EBITDAenterprise value over EBITDA, 10x
    What it says in wordsThe sales multiple divided by the EBITDA multiple is the EBITDA margin.
    Divide one multiple by the other and the enterprise value cancels1,000EVpick any EV500SalesEV / 2.0100EBITDAEV / 10.0EV / SalesEV / EBITDA= EBITDA / Sales2.0 / 10.0 = 20%EBITDA margin 20%The EV of 1,000 is only an illustration.
    Picking any enterprise value, say 1,000, gives sales of 500 at 2x and EBITDA of 100 at 10x, and 100 is 20% of 500; the EV cancels, so the margin is the ratio of the two multiples.

    How do you check the direction of the division?

    A margin must be smaller than 100%, and EBITDA is a slice of sales, so EBITDA has to be the smaller number. The higher multiple sits on the smaller number, so the margin is the low multiple over the high multiple, never the other way. Dividing 10 by 2 gives 5, which would be a 500% margin and is impossible. Dividing 2 by 10 gives 0.2.

    A buyout investor uses this the other way round all the time. If comparable companies trade at 2x sales and the target earns a 10% margin, then 2x sales is 20x EBITDA for this target, which is expensive. Sales multiples hide margin differences; converting to EBITDA puts them back. The limitation: EBITDA multiples carry their own blind spots, such as heavy capital spending that EBITDA leaves out.

    Where candidates lose it

    Candidates freeze because no enterprise value is given and assume the question is missing data. It is not. Saying out loud that EV appears in both ratios and cancels is the whole answer.

    The second loss is dividing the wrong way and saying 5, then not noticing that a margin cannot be 500%. A two-second sense check catches it.

    What the interviewer asks next

    • The company also trades at 25x earnings. What do you learn, and what do you still need?
    • Peers trade at 2x sales with 30% margins. Is this company cheap or expensive on EBITDA?
    • When would you prefer a sales multiple to an EBITDA multiple?
  2. 083A company trades at 15x earnings and 8x EV/EBITDA. Net debt is 200 and net income is 40. What is EBITDA?Valuation riddlesWarm upMid-market buyout fund

    Try it first

    What do you need to find before EBITDA falls out?

    Show the worked solution

    EBITDA is 100. Net income of 40 at 15x gives equity value of 600. Add net debt of 200 to reach enterprise value of 800. The EV/EBITDA multiple of 8x then gives EBITDA of 800 divided by 8, which is 100. Two multiples and the bridge between equity and enterprise value pin down the missing line.

    Why can you not go straight from net income to EBITDA?

    Net income sits below interest, tax, depreciation and amortisation, and the question gives none of them. The two multiples work on different values, P/E on equity and EV/EBITDA on the whole business, so the route runs through value, not through the income statement. It is like knowing a flat's price per square foot and the loan on it: you get to the total value first and then back out what you need.

    P/E gives the equity, net debt bridges to EV, EV/EBITDA gives EBITDA600Equity value+200Net debt800Enterprise value40 x 15100EBITDA/ 8Three steps1. 15 x 40 = 6002. 600 + 200 = 8003. 800 / 8 = 100
    Net income of 40 at 15x gives equity value of 600, net debt of 200 bridges that to enterprise value of 800, and dividing by the 8x EV/EBITDA multiple gives EBITDA of 100.
    The relationship
    EBITDA=15×40+2008=8008=100\text{EBITDA} = \frac{15 \times 40 + 200}{8} = \frac{800}{8} = 100
    15 x 40equity value from the P/E
    200net debt, added to reach enterprise value
    8the EV/EBITDA multiple
    What it says in wordsTurn earnings into equity value, add net debt for enterprise value, and divide by the EBITDA multiple.

    What follow-up can you get ahead of?

    Interviewers often ask what the gap between EBITDA of 100 and net income of 40 is made of. Sixty of EBITDA goes on depreciation, interest and tax, and with net debt of 200 interest is only a modest slice, so depreciation or tax must be large. At an assumed 8% rate, interest would be 16, leaving 44 for depreciation and tax. Saying that shows you read the result, not only compute it.

    State one assumption as you go: net debt here is all the claims that sit between equity and enterprise value. If there were minority interests or preference shares, they would be added too and EBITDA would come out higher.

    Where candidates lose it

    The usual slip is subtracting net debt instead of adding it, which gives EV of 400 and EBITDA of 50. Equity holders stand behind lenders, so the whole business is worth equity plus net debt.

    The other is trying to rebuild EBITDA from net income by adding back guessed interest and tax. The multiples are there so you do not have to guess.

    What the interviewer asks next

    • Net debt is minus 200, a net cash position. What is EBITDA now?
    • If D and A is 30 and interest is 16, what tax rate is implied?
    • What would make the P/E high and the EV/EBITDA low for the same company?