Technical Questions

I got asked these questions during a PE superday and I am still not entirely sure what the answer is. Can anyone provide any guidance as to how to think about answering these questions?

1) If revenue grows by 10% each year, will EBITDA grow more than, as much as or less than 10% each year?

2) If I get cash flows in year 1 at 1 dollar and then every subsequent year (after year 1), my cash flows increases by one additional dollar per year into perpetuity, what would be the value of the cash flows? 

Comments (6)

SOFRsoGood, what's your opinion? Comment below:

1) is a price / volume question. Assuming the only thing that happens is that revenue increases (I.e. no increase to fixed costs), then you have to see whether it was driven by price or volume. If price then the revenue increase drops to the EBITDA line and so you have margin expansion, but you also have less price on the table left to take for the next sponsor. If revenue growth is volume driven then, assuming no change to the variable cost structure, margin stays the same since you're just selling more stuff at the same margin. Generally growth is a mix of these factors and it's important to disaggregate.

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  • Associate 2 in PE - LBOs

Since this is about growth rate not margin % the answer is related to fixed/variable cost structure, not price/volume. Even if growth is 100% volume driven, unless fixed costs are growing, your EBITDA will grow >10%. Price-driven growth will increase by more than volume driven, but both will be higher given the operating leverage over the static fixed costs. 

SOFRsoGood, what's your opinion? Comment below:

2) is interesting. The present value of a perpetual annuity of $x is x/d for discount rate d.

I am sure there is a similarly easy finance answer to the question you were asked, but I was a math major not a finance major so now you have to bear through this:

What you have is a series where the nth term is equal to n/(1+d)^(n-1) for discount rate d.

So 1+2/(1+d)+3/(1+d)^2....+n/d^(n-1)+...

No idea how that's helpful tbh. You can immediately conclude some things - for example, as d->infinity you need the value of the investment to approach 1.

But at least for me, that's not enough to see the answer so someone please provide the answer lol.

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deals1228, what's your opinion? Comment below:

There are a few formulas but I'm not sure if they're relevant here. The value of the last term in a perpetuity growth formula is (value/(growth -discount)), but there is no constant growth factor.

As the series gets larger and larger, the growth rate of the numerator approaches 0 and the denominator gets bigger by the discount rate. Thus, the term approaches 0.For discount rate, I would just use risk free since the way the question is framed, there is no risk to the payout.

You can approximate the answer on excel really quickly. After summing 350 terms, I get $1150 (using 3% as risk free). Curious if anyone has a trick to do this mentally or on paper.

totally_wacc, what's your opinion? Comment below:

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