In this article, we go through a standard paper LBO example problem set that you’ll encounter in pre-MBA private equity Associate interviews.
This one is very similar to the ones you’ll encounter in most interviews.
You should do this problem set on a piece of paper and pen.
If you haven’t read our guide to crush paper LBO in private equity interviews, you should do that first. There, we lay out the structure you should follow along with tips to avoid the common mistakes. You can find that article here.
Paper LBO Example – The Prompt
The company has a Year 0 revenue of $500, growing at a rate of 10% every year. EBITDA margin is 20% in Year 0 and remains constant throughout the holding period. We’re buying it at the end of Year 0 at 10x LTM EBITDA multiple. We’re financing it with 4x of bank debt @ 5% and an additional 2x of bond @ 10%. As a reminder, if you haven’t read our step-by-step guide, you should assume bullet payment at the end and confirm it with the interviewer. Assume $20 of D&A in Year 0, growing by $5 every year. CapEx = D&A. Fixed working capital changes of $10 every year. 40% tax rate. Exit at the end of Year 5 with the same multiple as at entry.
Paper LBO Example – The Structure
Just like you’d have a structured approach towards deal discussion, you should also have a structured approach for paper LBOs.
This is a recurring theme in private equity interviews.They expect you to have a structured thought process and not be all over the place. If you don’t have a structured approach, you come off as disorganized and scattered, which will penalize you even if you ultimately get the answer right.
Here’s the simple 3-step structure that you should follow.
First, set up Sources & Uses table. The purpose of this step is to calculate the Entry Equity Check. The goal of a paper LBO is to calculate IRR and MOIC and you can’t calculate them without the Entry Equity Check.
Second, project out Levered Free Cash Flow. This step gives you the numbers (i.e. exit EBITDA and cash) that you need to calculate your Exit Equity Value.
Third, calculate the IRR and MOIC (Multiple on Invested Capital) based on the inputs from the first two steps.
Step 1: Sources & Uses
First, calculate the Enterprise Value. The Company has $500 in Revenue with 20% EBITDA margin, so that implies $100 in EBITDA. The interviewer told you that the purchase multiple is 10x LTM EBITDA. Therefore, your Enterprise Value is $1,000.
Assuming that the transaction is cash-free & debt-free, the $1,000 Enterprise Value is also your Equity Purchase Price. This is the cash that you’re paying to the selling shareholders. As we laid out in the guide, keep things simple here and don’t voluntarily add in complexities (i.e. fees).
Second, calculate the debt & equity financing split. The interviewer just told you that the deal is being financed with 4x bank debt and 2x bond. In PE, leverage multiples are usually based off of LTM EBITDA, which is $100. So 4x bank debt translates to $400 (4 * $100 LTM EBITDA). 2x Bond translates to $200 (2 * $100 LTM EBITDA). That’s a total of $600 in debt.
The Total Uses is $1,000, which is the purchase price assuming no additional fees & expenses. If the banks are lending you $600 of debt, then you’ll have to pay the remainder out of your own pocket. So Entry Equity Check is $400 ($1,000 of total uses – $600 of total debt).
Here’s what your sources & uses should look like:
Step 2: Projecting Levered Free Cash Flow
Our next step in this paper LBO example is to project out Levered Free Cash Flow over our holding period.
The interviewer had told you that you enter at the end of year 0 and exit at the end of Year 5. So that’s a 5-year holding period.
Step 2.1: Calculate EBITDA First
You might be tempted to project Revenue out first by growing it at 10% a year and then applying a 20% margin to derive EBITDA.
Can you think of a better way to do that?
Why do 2-steps of math, when you can simplify and just grow EBITDA at 10% a year? Since the EBITDA margin stays constant at 20%, you can just grow EBITDA by 10% a year.
You should just grow EBITDA at 10% instead of doing it in 2-steps for two reasons. First, it takes up valuable interview time, time that you need to show that you can think like an investor. Second, it increases your chances of messing up. Remember, you don’t have a calculator so all of these are mental math. Your interviewer isn’t going to give you extra credit for taking the long route.
Quite the opposite – they might even discount you because you couldn’t see the straightforward solution to solve the problem.
So simply grow EBITDA at 10% a year if margin is constant.
And confirm with interviewer that you can round the numbers to the nearest whole number. In most instances, they’d prefer you to round the numbers to the nearest whole number. That’s because they need to do the math in their head to follow you and having decimal points complicates things for them.
While you can sacrifice calculating other line items (i.e. revenue, operating expenses), you must calculate EBITDA because you need this number to calculate your exit value.
Your 5-year EBITDA projection, rounded to whole numbers, should look like this:
Once you have calculated these numbers, say each year’s EBITDA number out loud. Do this so that the interviewers can follow your math. Make things simple for them – they’ll appreciate it.
Step 2.2: Derive Net Income
You might be also be tempted to bridge directly from EBITDA to Levered Free Cash Flow.
Don’t. Reasons are laid out in our paper LBO guide, so refer to that first if you haven’t.
You should always go from EBITDA to Net Income first, and then from Net Income to Levered Free Cash Flow.
So from EBITDA, you’d subtract D&A to get EBIT. Then you’d subtract Interest to get EBT. Finally, subtract Taxes to get Net Income.
For D&A, the interviewer had initially told you that it was $20 for Year 0 and increases by $5 every year. So that’s simple math. Add $5 to the previous year D&A for every year and subtract it from EBITDA to get EBIT:
For Interest, interviewer told you that bank debt interest is 5% and bond interest is 10%. You calculated the bank debt and bond’s dollar amount in Step 1 so simply apply the respective interest rates.
First, there’s 400 of bank debt at 5% interest rate, so that’s $20 of bank debt interest expense. Then, you also have $200 of bond at 10%, so that’s an additional $20 of bond interest expense. In total, you deduct $40 of interest expense. So it should look like this:
This is one of the key parts of any LBO. The investment is getting a tax-shield by stripping out taxable income through interest expenses to minimize company’s cash tax payments.
Finally, for Taxes, the prompt mentioned a 40% tax rate. Remember what we said about simple math above? Don’t apply 40% of taxes to EBT and then subtract that to get Net Income. That’s a 2-step math. Just multiply EBT by (1 – 40%). In this case, you simply multiply the EBT by 60%.
After you’re finished, your financials so far should look like this:
Step 2.3: Project Levered Free Cash Flow
Once you have calculated Net Income, it’s time to bridge to Levered Free Cash Flow.
First, add back D&A because it’s a non-cash expense. You’ve already calculated it above so you have the numbers.
Second, subtract out Capital Expenditures. Prompt told you that the annual CapEx is the same as the D&A amount. So the net impact from these two steps is zero.
Finally, adjust for Changes in Working Capital. Interviewer told you that Working Capital needs is fixed at $10 a year. Working Capital needs usually mean negative cash flow impact. So subtract $10 from Net Income.
That’s it! Once you’ve made these calculations, then your projected Levered Free Cash Flow during the holding period should look something like this:
Step 3: Calculate MOIC and IRR
Now that you have the Initial Equity Check and the projected financials, it’s time to calculate the returns.
First, calculate the Exit Enterprise Value. The interviewer had told you that you’re exiting at the same multiple as at entry so that’s 10x LTM EBITDA. You’re exiting in year 5 so that’s 10x Year 5 EBITDA of $161, which equals to $1,610 of Enterprise Value.
Now bridge that Exit Enterprise Value to Exit Equity Value by subtracting debt and adding cash.
You haven’t repaid any debt so debt quantum is the same as at entry. At the same time, all the Levered Free Cash Flow accrued to your balance sheet. This means that at exit, your cash balance is the sum of the Levered Free Cash Flow over the 5-year period.
So $1,610 of Enterprise Value minus $600 of debt plus $129 of cash. That’s $1,139 of Exit Equity Value.
Then, calculate MOIC by dividing Exit Equity Value by Entry Equity Check. So divide $1,139 by $400, which is about 2.8x MOIC.
Finally, you can derive the IRR based on the MOIC over a 5-year period. You can’t mentally calculate IRR so the trick is to memorize the corresponding IRR to MOIC over a 5-year period (table below). Yes, you absolutely need to memorize this. The standard private equity holding period is 5-years so most interviewers expect you to know it.
A MOIC of 3.0x over 5-year holding period is ~25% IRR. 2.5X MOIC is ~20% IRR. The investment is 2.8x MOIC, which is slightly above 2.75x or the midpoint of 2.5x and 3.0x. So the IRR must be slightly above 22.5%. Round it to the nearest whole number and that’s ~23% IRR.
So there you have it! 2.8x MOIC and 23% IRR. There’s all there is to the paper LBO.
For the Ambitious Ones
Now that you have went through the above paper LBO example, try to create a prompt like the one we laid out above on your own. Change the numbers a bit and then practice it yourself based on our proposed structure. Also keep in mind to avoid the bad habits we’ve highlighted and stay with the best practices.
We recommend that you get to a level where this is second nature to you before you walk into the interview.
The above paper LBO example is a standard problem set. Most private equity interviews’ problem sets are similar to this.
However, we’ve seen some of the large-cap private equity firms give out more challenging paper LBOs. See why you should work with us for your PE recruiting process here.
Questions? Leave a comment below and we’ll get back to you.
For Further Reading
North America Pre-MBA Private Equity Associate Recruiting Process
Private Equity Paper LBO Guide
How to Answer “Why Private Equity”
How to Talk About Deals in Private Equity Interviews
What It Means to Think Like an Investor
About 10X EBITDA
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