# The Paper LBO in 5 Steps – The Ultimate Guide (2022)

The **Paper LBO, **a full LBO analysis completed with pen and paper, is an **increasingly common question** in** ****Investment Banking** and **Private Equity** interviews. Understandably, the thought of doing **mental math on the spot and walking through an entire LBO** analysis is **intimidating**. But Paper LBOs do not need to be such a scary prospect.

In this guide, we will walk you through **the common variations of Paper LBOs** (**+ Mental Math tricks**) to help you **nail this question and get the job**!

In this article, you will learn:

- The
**Basics of Paper LBO**Interview Questions (typical prompt, most common variations, timing, interviewer goals). - The
**most Common Pitfalls**when working through a Paper LBO. - The
**Critical Mental Math Hacks**needed to fly through these Interview Questions. - The
**5 Step Process**to nail the**core Paper LBO**(solving for IRR). - A separate
**5 Step Process**to master the**Reverse Paper LBO**(solving for required EBITDA Growth based on Target Return).

Estimated reading time: 39 minutes

**TL;DR**

- A
**Paper LBO**requires an**Interview Candidate**to walk through a**full LBO analysis**with just**Pen and Paper**(no calculator allowed). - The
**Paper LBO**can be a**daunting Interview Question**but can be**mastered with a 5 Step Process**. **Mental Math shortcuts****are essential**to mastering Paper LBO questions.

**A Little Context on the ‘Paper LBO’**

Just the **mention of a Paper LBO** question can **strike fear in the hearts** of aspiring **Investment Banking** and **Private Equity** candidates.

And it is **no surprise** that’s the case!

*LBO Mechanics + Mental Math + Lots of Moving Pieces + Numerous Variations = Lots of Stress*

We **cannot eliminate all of the stress** involved in a **Paper LBO**, but we can help you **massively reduce it**.

Before we jump ahead, it is **worth mentioning** that **Paper LBOs** are **not just an ****Interview Question**.

**Private Equity and ****Investment Banking professionals**** use these ‘ back of the envelope’** calculations every day

**on the job**

**to**

**quickly assess the attractiveness of an LBO transaction**.

**Now let’s dive into what a Paper LBO typically looks like in real life.**

**Want To Learn More About Finance?**

**Check out all of our (free) deep-dive articles in our** **Analyst Starter Kit**:

**What is a Paper LBO?**

A Paper LBO is an **Interview Question** in which the **Interviewer asks **you to complete an **entire LBO analysis with just pencil (or pen) and paper**.

In most cases, you are **not allowed to use a calculator**. Instead, you must do all of the **math in your head**.

**Most Paper LBOs** must be completed in **10-15 minutes**.

And Interviewees **must write out and show all of their calculations**.

For most candidates, the **two scariest aspects** of the process are:

- On-the-spot Mental Math
- Mixing up LBO model mechanics

But there are **a few Mental Math tricks **that you can use to **mitigate most of the stress with Item #1 above**.

For **Item #2**, we will provide a **simple, 5 Step framework** **to keep you anchored** when working through these problems.

We have now **covered the basics of Paper LBOs**. Let’s quickly **clarify the difference between the Paper LBO** **and another common LBO-related Interview Question**.

**Paper LBO vs. Walk Me Through an LBO**

Before we dive in here, we must **clarify a common point of confusion**.

A **common question** around **Paper LBOs** is how they **differ** **from** the ‘**Walk Me Through an LBO**’ **Interview Question**.

The **big difference** between these two questions is that you are **typically not working through LBO calculations on the spot** with ‘**Walk Me through an LBO**.’

With ‘**Walk Me Through an LBO,’** an interviewee **typically only **provides a **high-level overview** of the **LBO process**.

**If you are new to LBOs** and preparing for interviews, we **recommend checking out** our ‘**Walk Me Through an LBO**’ deep-dive article.

With that point clarified, **let’s look at what interviewers when job candidates work through a Paper LBO.**

**What are Interviewers Looking For?**

When an **Interviewer asks you to complete a Paper LBO**, they are **testing you on a few factors**.

The items below are the core items interviewers are testing:

**Knowledge of LBOs (and Key Drivers**): Do you have a strong understanding of an LBO model’s mechanics, key steps, and underlying drivers?**Composure Under Pressure**: Can you keep your cool while working through a tricky problem with someone looking over your shoulder?**Mental Math**: Can you quickly work through various mental math calculations without getting tripped up?**Organization**: Can you keep all of the bits and pieces organized when working through this problem?

You will be in **great shape** if you **exhibit all four factors above** and **complete the exercise with accuracy**!

**If you fumble on any of the four**, you will have difficulty** landing the job, particularly in Private Equity**.

With those points covered, let’s look at **common pitfalls** when answering **Paper LBO questions**.

**5 Common Paper LBO Mistakes (and Solutions)**

There are **five common mistakes** to avoid **when working through a Paper LBO** problem in an interview.

**Mistake #1 – Losing Sight of the Big Picture**

There are many moving pieces in an LBO model, and it is easy to get lost.

__Solution__*: To avoid getting lost, you need a ‘North Star.’ Your North Star is the 5 Step Process laid out below for a Paper LBO. Whenever you get lost, always anchor back to the framework.*

**Mistake #2 – Mixing Up Numbers in Your Analysis**

Even with a solid grasp of the big picture, you will need to manage numerous details during a Paper LBO.

__Solution__*: The key here is to keep your work as neat as possible. If you try to write everything out too quickly and have sloppy handwriting, you are bound to mix up your numbers.*

**Mistake #3 – Complicating Calculations**

In a Paper LBO exercise, **interviewees often feel they need to be incredibly precise** with their calculations.

**Unnecessary complexity or precision in a Paper LBO exercise is your archenemy.**

This **desire for precision** leads to **extra information you have to manage**, which **in turn leads to getting stuck** in your calculations.

Clearly, **calculation errors are never OK** in a Paper LBO. However, you **do not need** to calculate every number to the **third decimal place**.

__Solution (Part 1)__*: The first thing to note is that you should round numbers wherever possible.*

*For example, let’s say we need to calculate 10% Revenue growth on $121 of Revenue.*

*The exact answer is: $121 * 1.1 = $133.1.*

*But in a case like this, it’s entirely acceptable to round to $133.*

__Solution (Part 2)__*: With any set of calculations in the Paper LBO process, you should always look for ways to reduce the number of calculations (and thus your mental load).*

*All else equal, the more calculations you make, the more likely you are to make a mistake.*

*For example, when a prompt assumes constant Revenue Growth, you can shortcut the number of calculations by simply growing any item that will remain at a constant Percentage of Sales by Revenue Growth.*

*We show an example of this trick later in the article.*

**Mistake #4 – Stumbling on Mental Math**

The thought of **performing numerous quick calculations in your head** during an Interview is **understandably intimidating**.

** Solution**:

*Mental Math, when performed well, can look like magic to an outside observer.*

*But no, most*

**people in Finance are**.__not__human calculators*Rather most Finance professionals learn a set of Mental Math shortcuts (listed above) to make mental calculations quickly.*

*This article will help you to shortcut that process and learn those tricks now.*

**Mistake #5 – Not Enough Practice**

It is **not enough to complete one or two Paper LBO practice problems** before an interview.

__Solution__*: You should practice working through Paper LBOs as many times as possible (ideally ten times or more).*

*As you work through additional problems, you will begin to see the common threads as well as the shortcuts that permeate most Paper LBO questions.*

*Learning these things can help you go on autopilot for stretches of the exercise to give your brain a break (or allow for background processing of an upcoming problem).*

*In short, Practice!*

Now that we have **covered the common pitfalls** let’s **carry on to the most common Paper LBO Variations**.

**Enjoying the Article?Check out our LBO Modeling Course**.

**Common Variations of the Paper LBO**

Before we dive into our first Paper LBO example, we must **clarify a few common variations of Paper LBO problems**.

Below are the **most common Paper LBO variations** you are likely to encounter:

**The Core Paper LBO:**- Includes all necessary assumptions
- Assumptions are constant over the projection period
- Purchase Price based on LTM
**EBITDA** - Only one layer (‘tranche’) of Debt
**Solve for IRR**

**The Reverse Paper LBO:**- Reverse engineer the Core Paper LBO to determine the level of EBITDA growth required to achieve a
**Targeted IRR**.

- Reverse engineer the Core Paper LBO to determine the level of EBITDA growth required to achieve a

You may encounter more **advanced variations (NTM Multiples, Multiple Debt Tranches, Debt Amortization, Assumptions that Vary over the Projection Period, etc.)** to the Paper LBO, which we will cover in **future iterations of this article**. (see more **here**)

To begin here, we will **focus on the Core Paper LBO**, which is the version you are **most likely to see in an Interview**.

**Let’s dive in!**

**The Paper LBO in 5 Steps**

To **work through a Paper LBO**, we’ll use the following **5 Step Process**:

**Organize Assumptions**Organize given assumptions by category. The key here is to have a system to track which pieces of data you have and what is missing (if anything).

**Create Sources & Uses Table**Create a table to work from Purchase Price (

**Enterprise Value**) to Debt Funding, and ultimately to the ‘**Sponsor Equity**’ Investment (i.e., the money the Private Equity Firm will need to contribute).**Calculate Cumulative Cash Flow**Work from

to the**EBITDA****Levered Free Cash Flow**for each year to determine the cumulative Cash Flow that will be used to pay down Debt.**Create Exit Analysis**Calculate Exit Sale Value and work to Exit

**Equity**Proceeds.**Assess Returns**Calculate the

**Multiple of Invested Capital**(MOIC) and approximate**Internal Rate of Return**(IRR) from the Deal.

Below, we will **work through the 5 Steps above** using **sample a prompt based on examples of real-life Paper LBOs**.

**Core Paper LBO (Process + Example)**

To help make this **a little more tangible**, we will **walk through this question as if you were in the Interview**.

We will **imagine that you have landed an interview** for your dream Private Equity role.

**As we progress through the article**, the Interviewer will **add additional twists and turns** to throw you off track.

And **the first question the Interviewer asks after the initial ‘***Tell Me About Yourself***’ question** is the following Paper LBO question.

**The Paper LBO Prompt**

To kick things off, the **Interviewer shares the details below**:

The Interviewer says you can assume that the **Purchase Multiples will be based on LTM EBITDA**. And that you should **assume no Debt is paid down until Exit**.

Let’s jump ahead and see how we can tackle this.

**Paper LBO Step #1: Organize Assumptions**

**First of all. Holy moly! That’s a lot of information!**

**Let’s start by getting organized.**

Below are **the critical items** we will need for the **Core Paper LBO** the relevant categories to help you stay organized.

Let’s **organize the provided data into the relevant categories** **above** to ensure we have everything we need.

To **help you keep track of the major categories**, you can use the **PD-REIT-CDN mnemonic**:

- Purchase Price & Debt Funding Details (‘PD’ or ‘Police Department’)
- Revenue, EBITDA, Interest, Taxes (‘REIT’ or ‘Real Estate Investment Trust’)
- CapEx, D&A, and Net Working Capital (‘CDN’ or ‘Canadian Currency’)

**You’re laughing!** **We get it**.

It is a **funny shorthand**, but it will **ease the mental burden** of completing your Paper LBO and make sure you don’t miss anything!

Now let’s **fill in the missing pieces** based on the information provided.

**Purchase Price and Debt Funding**

With the information provided, we can now **determine the Purchase Price and Debt Funding**

As we noted in our **Walk Me Through an LBO** article, we calculate purchase in the **Private Equity** world with **EBITDA** * **EV/EBITDA Multiple**.

The **Interviewer provided the Purchase Multiple of 8.0x**, but we **still need EBITDA** to calculate **Purchase Price**.

**To arrive at EBITDA**, we’ll multiply the provided **Revenue of $100 * EBITDA Margin of 15%**.

We **have $15 of EBITDA**, so our **Purchase Price will be $120** ($15 EBITDA * 8.0x EV/ LTM EBITDA).

Now, we can move on to **Debt Funding**.

Debt is typically expressed as a **multiple of LTM EBITDA** in the LBO world.

We were told that the **Funding would be 4.0x Debt / EBITDA** in the prompt.

We **have $15 of EBITDA**, so our **Debt Funding will be $60** ($15 EBITDA * 4.0x Debt / LTM EBITDA).

Now that we **have organized our Assumptions**, we will create our **Sources and Uses table**.

**Paper LBO Step #2: Create Sources & Uses Table**

The **Sources and Uses** table for a Paper LBO typically **contains very basic**:

- Purchase Price of the Target
- Debt and Equity Funding

When working through this step, **always start by figuring out Uses first (in this or any LBO exercise)**.

In other words, first, **figure out how much money you need to come up with** to buy the Business. **Then figure out how you will pay for it.**

Our **only ‘Use of Funds’ in the Core Paper LBO problem** is the **Purchase Price** of the Business.

In the prior step, we said that the **Purchase Price of the Business (Enterprise Value) is $120**.

So we will **need to come up with $120 **using a **combination of Debt and Equity funding**.

Leveraged Buyouts are first **funded with Debt. **The **Private Equity firm covers the rest** of the **Purchase Price**.

In the **prior step**, we determined that we **needed $120 of total Funding** to Purchase the Business and we said that **Lenders would offer us $60 of Debt**.

**The difference** is what the **Private Equity Fund will need to contribute** (also called ‘** Sponsor Equity**’).

So as the **Private Equity**** Investor**, we **must come up with $60 of Funding** ($120 Purchase Price – $60 of Debt Funding).

Note that the **Private Equity funding amount** **is often called the ‘Plug,’** because it **funds the gap** **between the Purchase Price and any Debt** in an LBO transaction.

With the **Sources and Uses completed**, we will now **calculate the Cash Flow Generated** by the Business over the five-year projection period.

**Paper LBO Step #3: Calculate Cumulative Cash Flow**

First, we need to clarify what Cash Flow we are calculating here.

Broadly speaking, there are **two types of Cash Flow**: Levered and Unlevered.

In a standard **Discounted Cash Flow** analysis, we typically calculate to __Unlevered__**Free Cash Flow** because we want to value **the Business as a whole (i.e. ‘****Enterprise Value****’)**, absent the **impact of Debt**.

In an **LBO analysis**, however, we are **looking at** everything from the **value attributable to the Equity Investor** (a Private Equity firm in this case).

And **Equity Value **sits **below Debt **in the capital hierarchy.

As a result, we look at __Levered__**Free Cash Flow**, which **incorporates the impact of Debt**.

To calculate to **Levered Free Cash Flow**, we will typically follow the path laid out below:

Now that we have laid out the **path to Levered Free Cash Flow**, we will **work through each** **item one-by-one**.

Before we begin, we need to **review a few Mental Math Shortcuts** that will help us to **fly through this exercise**.

**A Few Mental Math Shortcuts**

**Mental Math Hack #1: Constant Growth Rate Tables**

**When we have constant growth rates in a Paper LBO**, we can **simplify growth calculations by using the rules of thumb below**.

**First, most LBO deals** involve later-stage companies with **growth below 15% per year, so we’ll focus on calculating Revenue growth from 0-15%**.

Further, **Paper LBO prompts** **often utilize even numbers (e.g., 5%, 10%, etc.).**

So you can **memorize the growth factors for five years of growth at typical growth rates** to help you complete a Paper LBO.

As you will see shortly, you can **use percentages in the tables below with the original (Year 0) Revenue** **to quickly assess Revenue in each year**.

At the very least, we **strongly recommend** memorizing the **10% Annual Growth factors below** because that growth rate is relatively common.

Now, **instead of manually calculating** each year’s Revenue, we simply **apply the ‘Rounded Factor’** **Growth %** in each year **to the Original (‘Year 0’) Revenue**.

As you can see above, the **cumulative Revenue with this approximate approach is incredibly close to the actual calculation**.

Let’s now **try something a bit more complicated**.

Let’s say **Revenue starts at $250**.

If we know the factors, we can **complete quick percentage calculations** to get to Revenue for each year.

__Another Constant Revenue Growth Shortcut__

__Another Constant Revenue Growth Shortcut__

There’s yet another trick to keep in mind when **we have a constant** **Revenue Growth Rate assumption.**

**Constant Revenue growth **allows us to **reduce the number of calculations **we need to make in a Paper LBO.

If we **use our Constant Growth Rate tables** above, we could **calculate Revenue for each year and then EBITDA and Capital Expenditures; **we would **need to make 15 calculations**.

However, **for any item that stays at a constant percentage of Revenue**, **the growth of that line item will grow in line with Revenue Growth**.

**Since EBITDA and Capital Expenditures remain constant** **as a percentage of sales**, they will simply **grow in line with the rate of Revenue Growth**.

As a result, we can **skip calculating Revenue altogether** and use the **Constant Growth Rate Factors** above to **grow EBITDA** and **Capital Expenditures** in our Levered Free Cash Flow calculation.

As you can see above, we **can still calculate the EBITDA and Capital Expenditure** value needed for the Paper LBO, but we **eliminated five calculations** in the process.

Now, let’s **move on to the final Mental Math trick** you should have in your toolkit for a Paper LBO exercise.

**Mental Math Hack #2: Rule of 1s, 5s, and 10s**

Let’s imagine **you are in an interview**.

You have been **asked to complete the calculation in the image above** as part of a Paper LBO exercise.

**This doesn’t have to be a daunting task!**

**When working through percentage calculations, break down numbers into 1%, 5%, and 10% increments.**

For example:

**3% of any number is**: 3 * 1%

**15% of any number is**: 1 * 10% and 1 * 5%

**47% of any number is**: 4 * 10% + 1 * 5% + 2* 1%

We can **use this to our advantage** when working through a **Paper LBO** (or any quick calculation involving percentages).

**To work through the example above**, we would:

**Calculate the 10% increment**– move the decimal place. For example, 10% of $35 billion is $3.5 billion.**Calculate the 1% increment**– move the decimal place again. 10% of $3.5 billion is $350 million.**If needed, calculate the 5% increment**– divide $3.5 billion by 2 to arrive at $1.75 billion.

To begin with, **3 *$350 million = $1.05 billion**.

We can then **add $1.05 billion to $3.5 billion** to arrive at **$4.55 billion**.

**In short, you can create the building blocks to calculate any percentage using the Rule above.**

**Below are a few different examples of percentage calculations** we could create using these building blocks as additional examples.

Now that we have **covered the core Mental Math hacks** you will need to complete this section, let’s **work from Revenue to Free Cash Flow**.

**Revenue and EBITDA Projections**

To kick things off here, we’ll **need to project out Revenue**.

The prompt stated **that Revenue would grow at 10% over the time horizon**.

As stated above, though, **when we have constant Revenue growth**, we **can skip the Revenue calculation altogether** as long as the **operating assumptions** in the model **remain the same percentage of sales** over the projections period.

We were told that the **EBITDA Margin would remain constant at 15%** over the projection period.

So, we can **move down** and **calculate EBITDA using the Constant Growth Factors** from above.

**What if Revenue and EBITDA Margin Assumption Aren’t Constant?**

If **Revenue Growth or EBITDA margin varies over the projection period**, you will need to use the **Rule of 1s, 5s, and 10s**.

And, as always, **round where you can**.

**Calculate All Remaining Cash Flow Items**

Now that we have **calculated EBITDA,** we need to work from **EBITDA to Levered Free Cash Flow**.

**Below **we’ve laid out the calculations for **each item through to Levered Free Cash Flow**.

**Depreciation and Amortization Expense**

To begin with, we will need to **deduct Depreciation and Amortization** (‘D&A’) to get to Profit Before Tax.

Even though it’s a **non-cash charge**, D&A **lowers the Company’s tax bill** (via the ‘**Depreciation Tax Shield**’).

The **Paper LBO prompt** stated that **Depreciation would be constant at $4 per year,** which keeps things simple.

The **image below** reflects the deduction of **D&A Expense**.

W**e have incorporated D&A** into our **Levered Free Cash Flow calculation** and can move onto interest expense.

**Interest Expense Calculations**

In **Step #1**, we determined that **Lenders would offer $60 of Debt funding**.

Our **Paper LBO prompt** stated that the **Interest Rate** **on Debt would be 5% **and to assume no Debt paydown until the Sale of the Business.

As such, we will have a **constant dollar value** **of** **Interest Expense** each year.

Below is the quick calculation for Interest Expense:

Now that we can see that **Interest Expense will be $3 per year** in all years, we can **subtract Interest Expense** to calculate **Profit Before Tax (PBT)**.

**Income Tax Calculation**

The **Paper LBO prompt** stated that **Income Tax Rate is 20%**.

We will **apply the 20% Rate** to our **Profit Before Tax** (i.e., ‘Taxable Income’) to **calculate** **our Taxes Owed (‘**Income Tax Expense’).

Once again, we **can use the Rule of 1s, 5s, and 10s** to calculate Income Tax Expense.

With Income Tax Expense calculated, we **can calculate Net Income**.

From this point, we need to make **just a few more adjustments** to get to **Levered Free Cash Flow**.

**D&A, Capital Expenditures, and Net Working Capital**

Going back to an earlier step, we **deducted D&A Expense because it lowers our tax bill**, but D&A is a **non-cash charge**.

So we now **need to add back D&A Expense** to calculate Levered Free Cash Flow.

With **Capital Expenditures (‘CapEx’)**, we could **use the percentage of sales calculation** provided in the prompt.

**But remember that we didn’t project out Revenue.**

And **CapEx remains constant** as a **percentage of sales** over the projection period.

So we can **apply the same growth factors** as before **to project CapEx**.

Finally, the **Paper LBO prompt** stated that **Net Working Capital would use up $2 of Cash each year**.

We **can now complete the calculation down to Levered Free Cash Flow**, which you can see below.

In total, **you will have $28 of Cumulative Levered Free Cash Flow to pay down Debt at the Exit** (at the end of Year 5).

**Curious as to what you would have calculated if you were working in a spreadsheet? **

Drum roll…

**$29 of Cumulative Levered Free Cash Flow. **

As you can see, **even with a little bit of rounding**, you arrive at **nearly the same exact answer**!

On that note, we will **take this a step further** and **just say the business will generate $30 of Cumulative Levered Free Cash Flow** to make our lives easier as we move ahead.

**Congrats, you’ve completed step #3!**

**Before we continue to Step #4**, let’s talk about a **few common complications** that can arise with **Levered Free Cash Flow calculations in a** **Paper LBO exercise**.

**Calculation Note #1: CapEx and Depreciation**

For a **Paper LBO**, we will typically **calculate Capital Expenditures and Depreciation** as a **percentage of Sales unless a constant number is provided**.

But **sometimes**, the prompt will **only provide one of the two items**.

**Here’s how to deal with that situation.**

For a mature Business, **Capital Expenditures** should roughly equal **Depreciation**.

And **most LBO transactions** will **involve a mature business**.

*For more on why Leveraged Buyouts typically occur with mature businesses, check out this *

*Animated Explainer Video**.*

So, it is **generally reasonable** in a **Paper LBO exercise** to assume that the **target business is mature**.

As such, **if the Interviewer does not provide D&A**, you can usually **assume that CapEx = D&A**.

And **vice versa**, if you are **only given D&A**, you could assume that **D&A roughly approximates CapEx**.

**Before making this assumption,** you should **always say** something like, ‘** I’m going to assume CapEx = D&A. Is that OK?**’

**Calculation Note #2: Income Taxes**

**Prior to the ****Tax Reform in 2017**, the **US Corporate Tax Rate** was in the **range of 35-40%,** depending on a Company’s Taxable Income.

Since 2018, the **Federal Tax Rate has been 21%. Additional State and Local Taxes** often lead to an **all-in 25%-26% Tax Rate**.

To keep it simple, we **recommend using a 20% Tax Rate** if the tax rate is not provided for a Paper LBO.

Despite the changes above, **some Paper LBO cases** will **use the 40% Tax Rate**.

In that case, you can **just use (4 * 10% Tax Rate)** to calculate Income Taxes.

**Calculation Note #3: NWC – Source & Uses of Cash**

**Net Working Capital (NWC) is a bit different** than the other items in the calculations, as you can see.

In short, we are **calculating** whether the **aggregate of working Capital** is a net **Source of Cash** or **Use of Cash**.

**If you’re not familiar** with the mechanics of these calculations, **check out this video** on **Net Working Capital**.

**Calculation Note #4: NWC – The Assumption**

In **most Paper LBO cases**, the **Interviewer will provide** a **Net Working Capital** as a **Percentage of Sales assumption or a Constant Dollar Value**.

In the event that the **Interviewer doesn’t provide that assumption**, you could say: ‘*For simplicity’s sake, can we assume that Net Working Capital equals zero?’*

If they say **yes**, **life is easy**.

However, if they say **no**, then **ask what a reasonable assumption** should be. Then off you go!

One last note here.

**Some businesses** can have **Negative Working Capital****,** which results in a **Cash Inflow as a business grows**.

If you are **not familiar** with the **concept of Negative Working Capital**, check out this **Quick Video walkthrough** of all of the mechanics.

Once you **have incorporated all of the above items**, you’ll arrive at **Cash Flow** for each year of the Paper LBO.

With those points covered, we can move on to the **next step,** which is our **Exit Analysis**.

**Paper LBO Step #4: Create Exit Analysis**

We will assume that the **Private Equity Fund sells the Business at the end of the five-year projection period**, as noted in the prompt.

In this step, we **need to determine the Sale Value** of the Business (again, ‘**Enterprise Value**’).

From there, we will **incorporate both Debt and Cash** to **calculate the Net Proceeds (‘Equity Value’) to the PE Fund**.

When the PE fund puts a Business up for sale, a **Prospective Buyer** will typically **use the same valuation approach we saw earlier**.

In other words, **the Buyer will assess** the Company’s **EBITDA at the time of Sale**, typically for the **most recent ****‘Last Twelve Months’ or ‘LTM’**** period**.

**Calculating the Enterprise Value at Sale**

In our Paper LBO, the **LTM period** would be **EBITDA in the final year of our projections**.

Once we have **calculated the Sale Value,** we can then **calculate the Net Sale Proceeds** (i.e., Exit Equity Value) to the **Private Equity Fund**.

To **get to Net Proceeds**, we need to **subtract Debt and add Cash** at the time of the sale (i.e., the end of Year 5).

So, we’ll **take the Debt we initially used to fund the Transaction** and **subtract** the

**Cumulative Cash Flow**generated by the Business over the projection period.

The **net of Debt and Cumulative Cash Flow **is what the Private Equity fund will **have to pay down before collecting and Sale Proceeds**.

Below, you can see the **complete calculation from the Exit Sale Value to Net Proceeds (‘Equity Value**‘).

Now that **we have determined how much money the PE firm will take home**, we can **move on to Step #5 and assess the returns** from the deal.

**Paper LBO Step #5: Assess Returns**

**After we calculate the net proceeds**, we can then **assess the returns of the Deal to the Private Equity Investors**!

We will need the two items for this calculation: the **Dollars Invested** (‘Sponsor Equity’ from Step #2) and **Dollars Returned** (‘Net Proceeds’ from Step #4).

In Private Equity, there are **two standard return metrics**: **Internal Rate of Return** (IRR) and **Multiple of Invested Capital** (MOIC).

**MOIC** reflects purely **Dollars Returned vs. Dollars Invested**.

In contrast, **IRR** reflects an **implied annualized percentage return for the Investors**.

*Note: There is a more complicated calculation for IRR, but it is beyond the scope of a Paper LBO discussion.*

Below are the summary calculations for each:

At this point, you might be thinking, ‘**I think I can do MOIC, but how am I supposed to calculate IRR in my head?!?!**’

**You’re in luck. You don’t have to!**

**Mental Math Hack #3: MOIC to IRR Table**

We can use a well-known rule of thumb to **approximate to IRRs based on the MOIC of a Deal**.

**Nearly everyone who works on the ‘****Buy-Side****’ commits these tables to memory.**

But of course, **they will not tell you that before you Interview**.

With these tables, you can **roughly approximate the 3 and 5-Year IRR for an LBO using the MOIC**.

For example, in our case, **MOIC is 2.8x ($170 Equity Returned / $60 Equity Invested).**

So, you could say that the **IRR is about three-quarters of the way between 2.5x (20% IRR) and 3.0x (25% IRR). **

And, so, the **approximate IRR is 23-24%****.**

**The actual, calculated IRR is 22% so, again, we are not far off.**

As you can see above, you can **get very close to the IRR without crazy mental math**.

**The Reverse Paper LBO**

Let’s now imagine that **you’ve passed the initial Core Paper LBO test**.

You have **calculated the Approximate IRR as 23-24%.**

At this point, you are **feeling pretty proud of yourself**.

Then the Interviewer says, “**What level of EBITDA growth would you need to get to a 25% IRR?**”

**You can’t create a sensitivity analysis on the spot. You’re not a supercomputer!**

As **you would probably guess **at this point, you **do not need to be a computer**.

Jump ahead to see how to nail this exercise with ease!

Again, before we dive in, it is worth mentioning that **the exercise we are about to work** through is **constantly used on the job in Private Equity**!

**The 5 Steps for a Reverse Paper LBO**

To work through this exercise, you’ll need to complete the following steps:

**Calculate Target Equity at Exit**– work from Starting Equity to Ending Equity using the T arget MOIC.**Calculate Net Debt at Exit**– work to Ending Net Debt by taking Debt from the Sources & Uses and Subtracting the Cumulative Cash Flow from the Core Paper LBO.**Calculate Exit Enterprise Value**– add Ending Equity and Ending Net Debt.**Determine Exit EBITDA**– divide Exit Enterprise Value by the Entry Multiple to determine the required Exit EBITDA.**Calculate Implied Annual EBITDA Growth**– approximate to an annual growth rate in EBITDA.

**This probably looks like quite a lot at first glance.**

But **it is just the flip of the Core Paper LBO** we just completed.

Lets’ dive in!

**Reverse Paper LBO Step #1: Calculate Target Equity at Exit**

If we target** a return of 3.0x (or 25% IRR)**, then **every dollar we invest** needs to **become three dollars at the end of Year 5**.

So, the first step here is to **multiply the Initial Equity Investment by 3.0x** to arrive at the **required Exit Equity of $180**, which you can see below:

**Reverse Paper LBO Step #2: Calculate Net Debt at Exit**

Next, we need to** calculate the value of Debt and Cash at the end of Year 5**.

We can **take the starting Debt from our Sources and Uses from Step #2 of the Core LBO.**

And we can take the **Cumulative Cash Flow** **from Step #3 of the Core LBO.**

We would then **subtract cumulative Cash Flow from Debt** to arrive at the **level of Debt that the Private Equity Fund must pay down at Exit**.

**Reverse Paper LBO Step #3: Calculate Exit Enterprise Value**

We then **combine Exit Equity and Exit Net Debt** to arrive at the **required Exit Enterprise Value** at the time of Sale.

In other words, this is the **Valuation (in dollar terms)** that we would **need to sell at to achieve the target return of 3.0x (25% IRR)**.

Next, we will **use this Targeted Exit Enterprise** value to **determine the required EBITDA at Exit**.

**Reverse Paper LBO Step #4: Determine Exit EBITDA**

To **find the required EBITDA at Exit**, we will **divide the Exit Enterprise Value** by our expected **EV/EBITDA Multiple** at the end of Year 5.

In Private Equity, it is **generally accepted practice** to **assume the Exit EV/EBITDA Multiple** is the **same as the Entry EV/EBITDA multiple**.

And while there are exceptions to this Rule in real life, you **can safely make this assumption in a Paper LBO exercise**.

**Below we make that assumption**, and you can see that the **Business will need to generate about $25M of EBITDA** to achieve the targeted return.

**Reverse Paper LBO Step #5: Calculate Implied Annual EBITDA Growth**

At this point, we can **take the starting EBITDA and the Ending EBITDA** and **determine the approximate annual growth**.

For **low growth rates**, you could likely get away with a **simple average**.

For example, if **Exit EBITDA is 15% higher than at Entry**, we could say…**roughly 3% per year (15% / 5)**.

**The actual answer is 2.8%, which is not far off from our estimate.**

For **high growth rates (10% or more)**, you can **anchor back to the MOIC to IRR table** we used earlier.

Below we **added a threshold for 10% as a point of reference** for the **typical five-year time horizon**.

In our case, you would ** need to believe that EBITDA grows** from

**$15 to $25 over five years**, or about 1.7x.

Looking at the table above, we see that **10% growth is a 1.6x increase**.

So, **EBITDA would need to grow** **just over 10%** per year to achieve a **3.0x (25% IRR Return)**.

The **fully** **calculated answer is 12% per year**.

As you can see, we were **very close with our rules of thumb**.

**From this point**, you should discuss** the two key drivers that would get you there**:

- Revenue Growth
- EBITDA Margin Expansion

As a **final note**, we are **anchoring** to the **Cash Flow** generated in the **original case**.

So, while this **approach is approximately correct**, the **further the Target Return **is from the IRR of the Original Case provided, the **more you’ll be off from a properly calculated answer**.

**More Advanced Paper LBO Variations**

So…we **have worn ourselves out writing everything you see in this article**.

So, we’re taking a little break for now.

From here, there are **quite a few additional topics** to cover **related to Paper LBOs**.

**A few sample topics are:**

- How to cut Levered Free Cash Flow Calculation time down by ~60%
- How to convert IRR to MOIC
- LTM vs NTM Multiples
- Inconsistent projections in the case prompt
- Multiple pieces of Debt Funding with annual Paydown
- Preferred Equity
- Management Option Pools

We also plan to put together a **comprehensive Paper LBO Excel Template**.

**We** **will accelerate Part 2 of this article** (plus the template) to elaborate on the topics **above if we get enough interest**.

**Once we cross 500 sign-ups below, we get to work on the topics above.**

**In the meantime, we hope you’ve found this helpful.**

**Wrap-Up: The Paper LBO**

**Hopefully**, you now have a **much better understanding of** the **Paper LBO Process**.

And also understand the **underlying idea** behind each of the steps.

**Let us know if you have any questions in the comments below. We’d love to hear from you!**

**About the Author**

**Mike Kimpel** is the **Founder and CEO** of **Finance|able**, a next-generation Finance Career Training platform. Mike has worked in Investment Banking, Private Equity, Hedge Fund, and Mutual Fund roles during his career.

He is an **Adjunct Professor** in **Columbia Business School’s Value Investing Program** and leads the Finance track at **Access Distributed**, a non-profit that creates access to top-tier Finance jobs for students at non-target schools from underrepresented backgrounds.

**Frequently Asked Questions**

*What is a Paper LBO?*A **Paper LBO** is the process in which you complete a **full LBO analysis with just pen and paper**.

*How long should a Paper LBO take?*In **most cases, you will be given 10-15 minutes **to work through the Paper LBO. However, this can vary depending on the difficulty of the case.

*Can you use a calculator or a Paper LBO?*You are **generally not allowed to use a calculator**. The trick here is to **learn a few mental math tricks** (see above) that help you work through complicated calculations.

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