I was taking a pass through sample PE interview questions and saw this one from TA Associates:
"They wanted me to mentally tell them that if the target IRR was 25% and revenue growth was 15% while EBITDA margin remained constant with no multiple expansion, what amount of debt will have to be taken to reach the targeted IRR. He mentioned that I could ask for additional data points..."
Thought over this one for a while and quite frankly couldn't come up with an answer without pen & paper / excel. I think I'd ask for FCF conversion, ECF sweep rate, and entry / exit multiple, which I think should be enough to answer the question, but not sure if there's a trick to the mental math that I don't know about. I figured I'm probably thinking of it too mechanically and was curious to see if anyone knew of a less mathematical way to go about it.
Thanks!
ETA: As pointed out by a couple of posters below, the below is wrong. This method works for an investment with a 15% up front YIELD, with NO growth. I am leaving it below unedited, and posted an additional thought separately, further down.
Original post:
It’s basically trying to get you to the fact that IRR is equity return, and with leverage, you can basically do the same thing as a WACC and back into whichever number you need, assuming all of the return is coming from growth. So, as a starting point, if you have a 25% equity return, and you have a 5% cost of debt, if you use a 50/50 debt/equity split that gives you a 15% unlevered return (same concept as a WACC). If you start off knowing that you have a 15% unlevered return, and a 5% cost of debt, you can of course algebraically back into needing a 50/50 split of debt and equity to get a 25% equity return.
In your example, they told you that you have 15% revenue growth, no margin expansion, no multiple expansion. The first question you need to confirm is that you don’t have any change in cash flow conversion. Assuming that is the case, that means that your EBITDA and cash flow is growing 15% a year. Exiting at the same multiple with 15% growth every year will give you a 15% IRR assuming no leverage. Then you need to use leverage to hit your 25%. Your next question is cost of debt. If it is 5%, then as above, you can get to 25% equity by using 50/50 debt equity. If they told you cost of debt was 10%, then you would need to use 2/3 debt, etc…
It isn’t perfect because as the company grows, your leverage profile is changing, but that’s the rough intuition.
How are you translating a 15% revenue growth to 15% IRR? 15% IRR would be if you get 15% per year (no growth) on your initial investment.
To simplify overandout's helpful comment, the base assumption is that if you have a business growing 15% topline at flat margin, flat multiples, your equity value (assuming 0 debt) increases 15% every year, and hence if you exit it, its a 15% IRR, as IRR means the annualized rate of return. If you sell after 2 years, your business would have expanded 15% annually twice, so (100*1.15)*1.15 = 132.25, which is a 15% IRR across 2 years.
If you have 50% leverage at 5% debt cost per year, your equity grows at 30% (i.e. double of 15%) less 5% annual debt service, getting to 25% IRR.
Kind of understand the logic here, but maybe can you expand why it’s fair to treat that 15% cash flow growth as your WACC
You know what, you are both right. I was 100% thinking of situations where you have an up front yield of 15%. I am actually not sure what they would be getting at when they talk about 15% growth. You would definitely need to ask what the up front yield is, and if they tell you it is something like 5%, you would know there isn’t a way to get to the 25% IRR on an unlevered basis because I believe that that unlevered IRR would asymptotically approach 20% (5% yield + 15% growth) as your hold period increases (I don’t have time to put it in a graph and look right now, if someone else wants to, you should go for it). So in that scenario, I guess I would say “okay that will get you to around a 17.5% unlevered return in a five year hold period) which would be a finger in the air guess, and then use the same WACC method I described above, using 17.5% as my unlevered return, caveating that it is less accurate because your capital structure (debt/equity ratio) is shifting as you grow (you are naturally deleveraging your overall capital structure). But honestly not 100% sure what they’re looking for here, other than someone sort of logically hitting those points.
I think your initial response had sound logic until the revenue growth = IRR. My guess is that the interviewee didn’t have a perfect memory and some key points are likely missing… otherwise they might just be looking at how someone would approach the problem rather than a correct response. Super helpful and appreciate the write ups.
I think the question should be solved in the different way.
You gotta ask for a holding period of the investment. Let’s say the holding period is 5Y. If an investor has IRR of 15% over the next 5 years it means MoM is 2x-
EV - 100 in year 1, EV - 200 in year 5
To boost IRR up to 25% the investor should earn 4x by year 5 by taking X amount of debt at year 1 and fully repay it by year 5 -
EV - 100 in year 1, EV - 200 in year 5 Debt - 50 in year 1, debt - 0 in year 5 Equity - 50 at entry, equity - 200 at equity (MoM 4x, IRR c.25%)
So the answer - the investor should take 50 of debt
Thanks for the response. Where are you getting the entry / exit enterprise values from? And 25% IRR is a 3x not 4x pretty sure, 4x will be just under 35%.
I assumed entry and exit values based on 2x MoM for 5 years.
Yea my bad, you are right, 25% over the 5 years is 3.0x of MoM. But you got the idea, the amount of debt should have taken by investor is calculated based on back in calculations that are derived from rules 72 / 114 etc
Isn’t it just like ur unlevered return is 15% so to get to a 25% return assuming a 10% cost of debt (make it easy), I would need to lever up around 2x (again very rough math), so 2/3 debt to cap
Kind of surprised at the answers here. Your return on an unlevered basis is a function of growth and multiple expansion. So if you are growing revs at 15% with NO ebitda margin expansion or multiple expansion that inherently means that your IRR should equate to ur rate of growth. Knowing this fact, you know Unlevered return and levered return is just a function of spread v cost of debt and LTV
Always good to think about stuff outside of the mechanical way it’s tough in excel
Also you guys living on another planet if u think 5% CoD is market today lmao
what would you say market is at (im an intern)?
Amalgamation of all answers:
Note, the above pain in the ass math only applies if there is cashflow yield. The way the question is structured, I would assume that they would actually tell you don't worry about cashflow, and if so, previously referenced levered vs. unlevered math works fine. (so, 15% unlevered return, cost of equity is 25%; 10% cost of debt implies 2/3rd debt funded)
Thanks man very insightful. One thing about this is where do we factor in tax rate? In WACC calculation, CoD is reduced by the tax rate - wouldn't this be the same case?
Nobody is gonna care about this if they're actually asking this interview question. Just say "assume post-tax interest rate of 10%." Analysts love overcomplicating, question is already more complicated than it should be.
Hi,
I think it's just algebra.
IRR quick rules say 25% over 5Y requires 3x MoM
Rules of 72 is divide 72 by your growth rate to get the time for it to double. EBITDA doubles in 5 years (constant margins and 15% topline CAGR).
So you get 2x MoM by taking no debt. Simplify everything (0% interest, no capex, etc.)
Let Debt = D
Let the multiple be 1x
Let EBITDA be V
What is D such that [2V - D] / [V - D] = 3? 2V - D = 3V - 3D, therefore 2D = 2V, so V = D, which can only mean your equity in and debt in are equal.
A massive abstraction here is that I'm ignoring the cash build on the balance sheet. I'm assuming that one of the pieces of additional information deals with that (i.e. capex equals EBITDA in every year).
Just a theory here and I don't have the textbook answer, but if this is a mental maths puzzle, I can't imagine it's too much more complicated.
This is ignoring the cost of debt, which on a IRR-based question you should never, ever do. If you assume EBITDA=CapEx, formula is actually: 15% unlevered = 25%*E + 10% (1-E), if you assume a round 10% cost of debt. So debt would be 2/3rd in this case.
Yes I agree (and hope I made the abstraction of 0% interest clear), but I think that the question is testing how you think - start with a simple case and make it more complex. For sure agree with you that my answer is ignoring major factors
I was looking at it using a MOIC approach. Assuming a five year holding period, a 25% IRR is a 3x MOIC. Applying that same principle to the EBITDA, a 15% compounded growth over five years equates to a 2x "MOIC", or in other words, your EBITDA has doubled over the hold period. That means that on an unlevered basis, purely due to growth in EBITDA (and ignoring the interim cash flows), you are able to get a 2x MOIC assuming no contraction / expansion in the multiple. Now to solve the rest of the problem I'm going to think of everything in terms of an EBITDA multiple (leverage, equity, interest expense, CapEx etc.)
If over five years my EBITDA doubles, I can approximate it linearly (yes I know it's actually exponential) by saying total EBITDA over five years is equal to 5 * 1.5 * EBITDA, where 1.5 is the midpoint. So total EBITDA is 7.5x. We still don't know the leverage, but assuming the interest rate is 10%, we know the interest expense each year is (0.10) * (Dx) where D is a multiple of EBITDA. So over five years we have 0.5Dx. Assuming CapEx is 10% of revenue and margins are 50%, CapEx is 20% of EBITDA over the five years. So the total cash flow over five years is (1 - 0.2) * 7.5 - .5D which is equal to 6 - 0.5D. I'm ignoring change in NWC but you could work that in. The total amount of debt at exit would be Dx - (6x - 0.5Dx) or 1.5Dx - 6x.
So then you can solve for the amount of debt given the purchase EV multiple (P), where x is the starting EBITDA (you can divide the whole thing by x to get rid of that variable). The formula below is saying whatever equity is left at exit must be three times the equity at the start (to get our 25% IRR off the 3x MOIC).
Px - Dx = (P*(2x) - [1.5Dx - 6x]) / 3 ---->>>> D = (P - 6) / 1.5 where the % leverage is D / P
Starting Equity = Ending Equity / 3
I think what people are ignoring is that purchase multiple matters. If I buy a business for 25x versus 8x - the math is not going to work out the same (especially if you're looking at debt as a % of EV - many above were giving percentages). If you're looking at sizing debt in terms of a multiple (which makes more sense), you can work work backwards into what the maximum multiple you could pay is. So if lenders will only give me 4x debt, then I know the maximum I could pay is 12x (33% leverage) to get the 25% IRR. If lenders give me 6x debt, I can pay 15x (40% leverage). Or for 2x debt the max would be 9x (22% leverage).
Even on an unlevered basis the multiple matters, since the interim cash flows are a yield on your investment. In fact, if you buy this business at a 6x multiple unlevered, with the assumptions above you can achieve the 25% IRR.
It's a bit complicated but you can set this up in your head.
Is this really the typical A1 interview question??? Seems kinda hardo for A1, particularly at a sourcing shop ???
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