### Core Financial Modeling

Learn accounting, 3-statement modeling, valuation/DCF analysis, M&A and merger models, and LBOs and leveraged buyout models with 10+ global case studies.

Learn moreIn this tutorial, you’ll learn how to complete a “paper LBO” test in a private equity interview and how to approximate the IRR in a leveraged buyout using pencil and paper.

Paper LBO Definition:In a “paper LBO” test, a private equity firm describes the leveraged buyout of a company and asks you to approximate the IRR or money-on-money multiple in the dealwithout using Excel or a calculator.

Paper LBOs are not true “financial modeling tests” in the same way that other Excel-based exercises are; they’re more like extended mental math questions.

**To succeed with paper LBO tests, you must round and simplify the numbers as much as possible so you can finish the calculations within the time limit (often 30 minutes or less).**

It’s also important to **start with the end in mind** so you can check yourself along the way.

For example, if the PE firm is targeting a 25% IRR over 5 years, you should know that it corresponds to a **3x multiple** of the initial Investor Equity (see: our tutorial on how to calculate IRR manually).

Learn accounting, 3-statement modeling, valuation/DCF analysis, M&A and merger models, and LBOs and leveraged buyout models with 10+ global case studies.

Learn moreIf you finish most of the exercise and you can tell that the deal will generate nothing close to a 3x multiple, you can immediately reject it.

It’s best to **simplify the transaction assumptions** as well, which means “ignore the transaction and financing fees” and “assume all deals are cash-free, debt-free” (i.e., that the target company’s Cash and Debt immediately go to 0 after the deal closes).

Finally, you may assume that the Debt issued to fund the leveraged buyout stays the same or that 100% of the company’s Free Cash Flow is used to repay the Debt principal.

More complicated assumptions, such as “cash flow sweeps,” make it too difficult to track the numbers and calculate everything with pencil and paper.

Click here to get the case study prompt for this exercise.

In short, the PE firm is acquiring a company for 10x EBITDA and using 6x Debt to fund the deal.

They provide numbers for the company’s revenue, EBITDA, cash flow line items, and the details of the Debt funding, such as the interest rates and principal repayments.

The PE firm is targeting a 20% IRR over 5 years, so we have to complete this paper LBO and recommend or reject the deal based on this target.

You can click here to get the full solutions to this exercise, but we’ll present the highlights below:

You should know that a 20% IRR over 5 years is approximately a **2.5x multiple** of invested capital because a 2x multiple is a ~15% IRR over 5 years, and a 3x multiple is a ~25% IRR.

The case document gives us the company’s initial EBITDA of $250 million.

Since the company spends 60% of Revenue on COGS and 15% on SG&A, its EBITDA Margin equals 1 – 60% – 15% = 25%.

So, the company’s Revenue is $250 / 25% = $1,000.

A 10x purchase multiple means a Purchase Enterprise Value of $2,500, and the deal is funded with 6x Debt and 4x Equity, so the Investor Equity is $2,500 * 40% = $1,000.

**Therefore, this deal must generate $1,000 * 2.5x = $2,500 in Equity Proceeds to be viable.**

We need to determine the Year 5 EBITDA and the Year 5 Debt to see if that happens.

The case document gives us the initial numbers:

To project the Revenue figures, we can use approximations. For example:

- $1,000 * 5% –> This is easy; it’s an increase of $50.
- $1,050 * 7.5% –> This is halfway between $52.5 and $105, so we can round it to $80.

Once we have all the Revenue figures, we can use a similar strategy for EBITDA.

For example, if we know the Year 1 Revenue is $1,050 and the EBITDA Margin is 24%, we can approximate the Year 1 EBITDA like this:

$1,050 * 24% –> $1,050 is a bit higher than $1,000, and 24% is a bit lower than 25%, so we can say the EBITDA is still $250.

After completing these steps, we arrive at these estimates for Revenue and EBITDA:

In the context of this simplified “model,” we can define Free Cash Flow like this:

**Free Cash Flow** = EBITDA – Interest – Taxes +/– Change in Working Capital – CapEx – Purchases of Intangibles.

CapEx, Purchases of Intangibles, and the Change in Working Capital are all simple percentages of Revenue, so we can group them together:

FCF = EBITDA – Interest – Taxes – “Other Items.”

CapEx = –8% of Revenue, Intangible Purchases = –4%, and Change in WC = +2%.

The first two are negative, and the Change in WC is positive, **so “Other Items” represents negative 10% of Revenue.**

We can round the numbers to units of 5 or 10, producing this chart:

To calculate the Taxes and Interest, we need the Taxable Income first.

**Taxable Income** = EBIT – Interest, and **EBIT** = EBITDA – D&A.

The D&A is simple, but the Interest changes each year as the company repays Debt.

So, let’s start with the D&A: it’s 5% of Revenue, so we can multiply each of the “Other Items” above by 50% to estimate it.

The Interest Expense is the toughest part because the company **repays** its Term Loan balance over time, and many of the numbers are interdependent:

**Interest:** Depends on the Debt balance, but the Debt balance depends on FCF.

**FCF:** Depends on the Interest and Taxes.

**Taxes:** Depends on the Interest.

We have to complete this process **iteratively**, starting with the Interest in Year 1.

The initial Term Loan is $1,000, or $250 * 4, and the initial Senior Notes are $500, or $250 * 2, so the initial Interest Expense is $1,000 * 5% + $500 * 10% = $100:

The Term Loans have 2% annual principal repayments, which might seem complicated at first.

But since the company’s FCF is higher than 2% * $1000 = $20 per year, we can combine the mandatory and optional repayments and assume that 100% of the company’s FCF is used to repay Debt principal.

The Senior Notes stay the same at $500 per year, so only the Term Loan balance changes.

Once we have the Year 1 numbers, we can continue to Year 2, where Interest = 5% * $975 + 10% * $500.

We round *all* the Interest numbers to units of 5 or 10 to simplify the math.

The company’s FCF never changes by a huge amount, so we use figures such as $25, $30, and $35 in each period.

We also round all the Tax numbers to ones that end in 5 or 0, as shown below:

Once we have the numbers for Years 1 and 2, we go through the same process for each of the following years.

It’s impossible to track all these numbers in your head, so it’s **essential** to write down the whole schedule on paper.

The finished “Debt Schedule” looks like this:

To finish, we need to calculate the Exit Enterprise Value, Exit Equity Value, money-on-money multiple, and IRR.

We know the Year 5 EBITDA is approximately $300 and the Year 5 Exit Multiple is 12x (from the case document):

$300 * 12 = $300 * 10 + $300 * 2 = $3,600 for the Exit Enterprise Value ($3.6 billion).

**We have no information on the Cash balance, but we know it has NOT changed because all the company’s FCF was used to repay the Term Loan**.

Since the remaining Debt in Year 5 is $1,360, the Exit Equity Value = $3,600 – $1,360 = $2,240; we can round this to $2,200 or $2,300.

This range produces a multiple of 2.2x to 2.3x because $2,200 / $1,000 = 2.2x and $2,300 / $1,000 = 2.3x.

To get a 20% IRR over 5 years, we need a 2.5x multiple on the $1,000 of Investor Equity.

Therefore, this deal is **not viable**.

The exact IRR here is probably between 15% and 20%, so it’s not a bad outcome – but it’s also below what the PE firm was targeting.

If you want to “see” this paper LBO in Excel format, click here to download the Excel recreation, which has the exact numbers rather than approximations.

**Note that it’s completely pointless to build this model in Excel because the purpose of a paper LBO test is to finish it using pencil and paper and mental math.**

If you use Excel, you might as well try a full-blown LBO modeling test that takes 2-3 hours to complete.

Some private equity firms like to administer paper LBO tests, but you’re more likely to get *real* Excel-based modeling tests and case studies.

So, if you’re going through the private equity interview process, it’s worth practicing a few paper LBO tests, but don’t go through dozens of exercises or spend days on them.

You should spend that time improving your story, reviewing and discussing your deal experience, and practicing real LBO modeling tests.

Paper LBOs, when they do come up, tend to occur in earlier rounds of interviews and are mostly used to *eliminate* candidates.

You’re never going to win a private equity job offer because you ace a paper LBO test.

But if you perform poorly, you could easily *lose* a job offer.

Brian DeChesare is the Founder of Mergers & Inquisitions and Breaking Into Wall Street. In his spare time, he enjoys lifting weights, running, traveling, obsessively watching TV shows, and defeating Sauron.