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  1. 087A DCF sets its terminal value at 10x final-year EBITDA. Free cash flow runs at half of EBITDA and the WACC is 10%. What perpetual growth rate is that exit multiple quietly assuming?Valuation riddlesHardElite boutique IBBulge bracket IB

    Try it first

    Roughly what growth rate does 10x EBITDA imply here?

    Show the worked solution

    About 4.8% a year, forever. Write the terminal value both ways. The multiple says 10 x EBITDA. The Gordon formula says 0.5 x EBITDA x (1 + g) / (0.10 - g). Setting them equal, EBITDA cancels: 1.0 - 10g = 0.5 + 0.5g, so g = 0.5 / 10.5 = 4.76%. Every exit multiple implies a growth rate, and the check is whether that rate is believable for this business.

    Why does a multiple contain a growth rate at all?

    If a buyer wants a 5% return and pays 25 times this year's rent for a flat, they are counting on the rent rising: with flat rent, a 5% return supports a price of only 20 times. A multiple is a shorthand price for a stream of future cash flows, so every multiple implies some combination of growth and discount rate. In a DCF the exit multiple sits beside an explicit WACC, which means the growth assumption can be solved for exactly.

    Set the two terminal values equal. The multiple gives 10 x EBITDA. The perpetuity growth method gives next year's free cash flow over (r minus g), and next year's cash flow is 0.5 x EBITDA x (1 + g). EBITDA cancels from both sides, leaving one equation in g, which solves to 4.76%.

    Every exit multiple is a growth assumption in disguiseSolve the Gordon formula for gExit multiple: TV = 10 x EBITDAFree cash flow = 0.5 x EBITDAGordon: TV = FCF x (1 + g) / (r - g)10 = 0.5 x (1 + g) / (0.10 - g)1.0 - 10g = 0.5 + 0.5gg = 0.5 / 10.5implied g = 4.76% a year, foreverWACC 10%: the ceiling-2%0%4%8%4x8x12x16xExit multiple of EBITDA10x: 4.8%5x: 0%
    With free cash flow at half of EBITDA and a 10% WACC, a 10x exit multiple implies perpetual growth of 4.8%, and implied growth rises with the multiple while bending toward the 10% WACC, which it can never reach.
    The relationship
    m=f(1+g)r−g  ⇒  g=mr−fm+f=1.0−0.510+0.5≈4.76%m = \frac{f(1+g)}{r-g} \;\Rightarrow\; g = \frac{mr - f}{m + f} = \frac{1.0 - 0.5}{10 + 0.5} \approx 4.76\%
    mexit multiple of EBITDA, 10x
    ffree cash flow as a share of EBITDA, 0.5
    rWACC, 10%
    gimplied perpetual growth
    What it says in wordsRearranging the perpetuity formula turns any exit multiple into the growth rate it assumes.

    How do you judge whether 4.8% is believable?

    Perpetual growth means growth forever, so it should not exceed the long-run nominal growth of the economy whose currency the cash flows are in, or the business eventually becomes larger than that economy. Whether 4.8% passes depends on that currency's inflation and real growth, so state the benchmark you are using rather than a number from memory. The useful habit is running the check both ways: an exit multiple that implies an unbelievable growth rate is a sign the multiple came from a peer set that does not match this business.

    Say the convention too. If you apply the multiple to final-year EBITDA but take next year's cash flow without the (1 + g) uplift, the answer becomes 10% minus 0.5/10, which is 5.0%. A small difference, but naming the convention shows you know where it comes from.

    Where candidates lose it

    The common answer is that an exit multiple has no growth assumption, which is exactly backwards. Candidates who have only used the multiple method never think to translate it, and the interviewer is testing that translation.

    The second loss is solving the algebra but not commenting on the result. Say the number, then say what you would compare it against and why.

    What the interviewer asks next

    • What exit multiple implies zero growth here?
    • If free cash flow conversion rises to 70% of EBITDA, what growth does 10x imply?
    • Which method would you lead with in a fairness opinion, and why show both?