Private equity investment simulation : analysing the optimal multiple and leverage ratio using an LBO simulation

University of Twente

Private Equity

Investment Simulation

Analysing the optimal multiple and

leverage ratio using an LBO simulation Master Thesis

T.Q.B. van der Meer

Private Equity Investment

Simulation

Analysing the optimal multiple and leverage ratio using an LBO simulation

by

T.Q.B. van der Meer

Student Number 1741535

University Primary Supervisor: Dr. R.A.M.G. Joosten University Secondary Supervisor Dr. B. Roorda

Company Supervisor: M. van den Heuvel

Institution: University of Twente

Faculty: Behavioural, Management and Social Sciences

Project Duration: February, 2021 ­ July, 2021

Preface

This thesis marks the end of my Master in Financial Engineering, with that it also serves as the final piece of my time as a student. These years have been extraordinary, with all unexpected events, new friends and (almost) unlimited freedom. I did enjoy every bit of it and now I fully understand everyone claiming that ”your student days are the best days of your life”.

After such an extraordinary time, the final year only stepped it up a notch. Where the prospect of not seeing any lecture rooms for a year would seem delightful during my first years, the absence of real­life encounters with fellow students and lecturers did impact the experience of my final year at the University of Twente.

Nevertheless, there was no problem in finding an interesting company and thesis sub­

ject. At Vondel Finance, I could conduct my research and also experience some of the aspects of the typical day­to­day activities at a corporate finance firm. Everyone was helpful and open to any sort of questions, but special thanks go out to Martijn van den Heuvel. His private masterclasses made sure I was quickly up to speed and understood all important concepts.

Support did not only come from within the company, as Reinoud Joosten was my supportive supervisor at the University of Twente. His precise reading, challenging dis­

cussions and extensive feedback enabled me to improve on my research and adjust my course where necessary.

Second opinions are invaluable, for that reason I want to thank Berend Roorda. Hav­

ing made time to read my thesis and provide me with feedback, he helped me delivering a thesis that is at the level that is expected of a Financial Engineering student.

While my thesis was my main focus in the past months and my studies were the focus for the past years, the things happening outside of my academic development were the most important to me. I want to thank all my friends, family and whomever helped me, for all the unplanned adventures, good talks, infallible support and the great nights. Those are the things that make your student days the best days of your life.

T.Q.B. van der Meer Amsterdam, July 2021

i

Management Summary

In this report we focus on the returns realized by Private Equity firms when they invest in companies across different sectors. We offer baseline estimates for the financial structure that enables the highest expected returns on investment, giving investors an indication for the optimal financial deal structure.

The multiple paid for a company and the portion of the deal value that is financed with debt (leverage ratio) are parameters with high impact that can be influenced by investors.

We simulate a Leveraged Buyout model to determine the optimal values for different deal scenarios. The latter represent different business sectors with distinct values for financial ratios as EBITDA margins, capital expenditures, working capital, etcetera. By simulating cash flows, equity and debt positions, we obtain the realized IRR for our simulated invest­

ment. During these simulations, we vary the values for the multiple and leverage ratio to determine their impact on the realized returns for each scenario.

The outcomes of the simulation show a clear relation between the combination of lever­

age ratio and multiple, and the realized returns. The industry motto ”more leverage leads to higher returns” is only partially supported by our results. We find that high leverage ratios should be combined with low multiples and low leverage ratios should be applied to deals with high multiples. There is a clear trade­off between these two parameters, increased risk in one parameter should be offset by the other. This is true for all sectors, while the exact value of the realized return differs. We find the that a 1% increase in leverage ratio should optimally be accompanied with a decrease of 0.66­0.96 % in the multiple, depending on the sector.

Our simulation results indicate a curve governing the optimal ratio between leverage and multiples, which represents a fine line between high and significantly lower returns.

Our research suggests that more conservative deal structures, with less leverage and lower multiples do often lead to comparable, albeit slightly lower, returns. This suggests that going to extremes for high returns in every deal might not be the most sustainable business model.

Our simulation model provides an extensive starting point for investors to assess the impact of deal variables and test investment strategies. While every deal is unique and has its own characteristics, the baseline predictions and relations provided by this model enable understanding of the interplay between deal parameters.

Keywords: Private Equity, Leveraged Buyout, Simulation Study, Leverage ratio, Val­

uation multiple, Financial Structure

ii

Contents

Preface i

Summary ii

Nomenclature v

1 Introduction 1

1.1 Background . . . . 1

1.2 Introduction to the Company . . . . 2

1.3 Management Question . . . . 2

1.4 Research Questions and Report Structure . . . . 4

2 Literature Review 6 2.1 Defining Private Equity . . . . 6

2.2 Impact of Market Conditions . . . . 9

2.3 How do Private Equity Firms create Value? . . . 11

2.4 Leverage used in Private Equity deals . . . 12

2.5 Multiple Arbitrage . . . 14

3 Leveraged Buyout Model 15 3.1 Introduction to the Model . . . 15

3.2 Goal of the Model. . . 16

3.3 Assumptions & Parameters . . . 17

3.4 Model Output . . . 23

3.5 Parameter Summary . . . 24

4 Simulation 25 4.1 Introduction . . . 25

4.2 Scenarios . . . 26

4.3 IIR: the performance indicator . . . 27

4.4 Main input variables . . . 28

4.5 Simulation Results . . . 29

5 Conclusion & Discussion 37 5.1 Multiple­Leverage relationship . . . 37

5.2 Optimal Financial Structure . . . 38

5.3 Other parameters. . . 40

iii

Contents iv

5.4 Model Assumptions . . . 40 5.5 Generalization of model . . . 42

References 46

A Multiple Leverage curves 47

B R Code 48

Nomenclature

Abbreviations

Abbreviation Definition B&B Buy and Build CapEx Capital Expenditures

COGS Cost of goods sold

D&A Depreciation and Amortization

EBITDA Earnings Before Interest, Taxes, Depreciation and Amortization

FCF Free Cash Flow

GBM Geomtric Brownian Motion

GDP Gross Domestic Product

GP General Partner

IRR Internal Rate of Return

LBO Leveraged Buy out

LP Limited Partner

M&A Mergers and Acquisitions

MBI Management Buy in

MBO Management Buy out

NPV Net Present Value

NWC Net Working Capital

PE Private Equity

SBO Secondary Buy out

SDE Stochastic Differential Equation

SG&A Selling, general & administrative expenses SME Small and medium­sized enterprises

v

1

Introduction

Contents

1.1 Background . . . . 1

1.2 Introduction to the Company . . . . 2

1.3 Management Question . . . . 2

1.4 Research Questions and Report Structure . . . . 4

1.1. Background

With the value of assets under management by Private Equity funds rising above $4 trillion since 2018 [1], this sector amounts to a significant part of the global financial system.

Figure 1.1 shows that this growth trend has been present for years, and it may continue for years to come.

Figure 1.1: The development of the total assets under management in the world of Private Equity.

1

1.2. Introduction to the Company 2

The Private Equity industry plays a fundamental role in the capital market. It is an extra source of financing, next to the traditional debt providers such as banks. This is increasingly relevant within the current economic reality, as the global economy tries to overcome the financial consequences of a global pandemic and companies across the globe look for financing and ways to secure their market position [2]. The 2008 crisis led to a so­called ’credit crunch’, where banks tightened their credit supply and businesses had to look for other sources of capital [3]. During this crisis, companies backed by Private Equity behaved counter­intuitively by investing more and ensured themselves increased market shares and revenue growth [4]. The current crisis might present an opportunity to put the capital available to Private Equity firms to use.

We look into the world of Private Equity to determine important factors in the decision making process of Private Equity firms and variables that play a role in the value of a leveraged buyout. This research takes place at the corporate finance and Private Equity firm Vondel Finance in Amsterdam.

1.2. Introduction to the Company

Vondel Finance is an Amsterdam­based firm focused on corporate finance and Private Equity. In this sector, they assist and advise parties on transactions, typically in the mid­

market sector, i.e. with companies valued between €10 and €500 million. These types of deals include takeovers, but also management buy­outs or buy­ins.

Internationally, the company is part of the international Clairfield network, and it is therefore able to use the knowledge and expertise available worldwide in their local part­

ner offices.

Vondel Finance acts as an advisor for Private Equity firms in the broadest sense, it advises on sell­side and buy­side transactions while also assisting management teams of companies owned by these Private Equity firms. This leads to Vondel Finance being well­

connected to virtually all Dutch Private Equity firms. Results from this research enable the company to better service its clients and provide them with the latest Private Equity insights: in this case optimal deal structures.

1.3. Management Question

Which companies are the ’right’ target for a Private Equity acquisition is hard to predict.

Identifying the right target is the core of the game, so to say. Investments in underachiev­

ing companies have led to both high and low returns and sometimes , while the same is true for investments in companies that had a proven business strategy. The ’right’ target for a Private Equity investor should have enough improvement potential to realize an in­

teresting return on investment. There are some theories about fund investments and the

1.3. Management Question 3

optimal points in time to invest. Regarding the timing of the investments, there is a feeling that investments done in times of economic turmoil generate above average returns as a result of the low prices paid for companies in recessions. [5].

As Vondel Finance acts as a corporate finance advisor to numerous clients, it is key for them to know what they should advise clients on the deal structure. Maximising the the return on the investment and the profitability of a deal is an important part of their job, resulting in higher revenues for both their clients as themselves.

Vondel Finance focuses on mid­sized companies, which gives us the incentive to not only focus on large­scale fund performance but also to venture into the world of financial acquisitions in the domain of SMEs. As can be seen in Figure 1.2, about half of the deals done per year are valued below $100 million.

Figure 1.2: The distribution of deal sizes over the total number of deals per year.

Using this focus area, we can phrase the main question in the following way:

Management Question What are important factors in the structuring of

a Private Equity funded buyout deal in the mid­market? Given these factors,

how are they incorporated optimally in a deal?

1.4. Research Questions and Report Structure 4

1.4. Research Questions and Report Structure

We transform the management question posed by the company into a research question and several sub­questions:

Main Research Question What are the decisive conditions of an optimal Private Equity investment and what is the financial structure that results in the highest return on investment?

To find this we define several sub­questions divided over several sections to guide this research. These will serve as the structural backbone of this report.

Section 1 Deal Structure

1. Which parties are involved in transactions?

2. How are deals funded?

3. How do market conditions affect deals?

4. How do market conditions affect companies backed by Private Equity?

These first questions, answered in the first part of Chapter 2, provide an insight in the deal structures present in the Private Equity sector by looking into recent literature and reports.

Section 2 Value creation

1. How do Private Equity firms create value?

2. How does leverage impacts value creation?

3. What is multiple arbitrage and how does it work?

These questions are answered in the second part of Chapter 2, giving an overview of the value­creation methods. This knowledge enables us to focus on the right parameters when designing the simulation model.

Section 3 Simulation Setup

1. Which model is most feasible for a simulation model?

2. Which assumptions are required for this model?

3. Which input parameters are required?

We design our simulation model in Chapter 3. Here we decide on the assumptions,

input parameters and testing scenarios.

1.4. Research Questions and Report Structure 5

Section 4 Simulation

1. Which parameters have the most significant impact in the simulation?

2. What are the optimal values for these parameters?

In Chapter 4 we outline the scenarios that we test and run the simulations. The impact input parameters on the outcomes of the simulation are analyzed.

Section 5 Results

1. What is the relationship between these parameters?

2. What are the values for these parameters leading to the highest IRR?

3. To what extent can these conclusions be generalized?

In Chapter 5 we identify the most important parameters and the optimal values. This

enables us to draw conclusions about an optimal deal structure. We define the extent to

which the result can be generalized to other types of deals.

2

Literature Review

Contents

2.1 Defining Private Equity . . . . 6

2.2 Impact of Market Conditions . . . . 9

2.3 How do Private Equity Firms create Value? . . . 11

2.4 Leverage used in Private Equity deals . . . 12

2.5 Multiple Arbitrage . . . 14

2.1. Defining Private Equity

First, we define what we mean by the term ’Private Equity’. The type of transactions and investments generally associated with Private Equity keep on changing over time, [6].

However, we can see Private Equity as an additional way of raising capital for companies, next to the stock exchange and bank loans.

In its most basic form, Private Equity investors use capital available in their funds to purchase a company, increase its value by improving its performance and then sell it to make a profit. This can be done by investing in targets of all maturity levels, from start­ups to publicly listed companies and by investing small or big amounts of capital.

The private in this type of investing stems from the fact that these firms invest in com­

panies that do not trade publicly. It often entails majority stakes in these private com­

panies. This results in an increased control in the company and illiquid shares for the investor. Some Private Equity investors take public companies private by buying out­

standing shares and de­listing the company.

6

2.1. Defining Private Equity 7

2.1.1. General and Limited Partners

Private Equity firms invest the money available in their funds to generate profit for the investors who filled this fund. The investors in such funds are called Limited Partners (LP), they commit money in exchange for returns. The fund is managed by the General Partner (GP), the PE­firm itself. This GP also invests some amount, amongst others to make sure interests are aligned, but the majority comes from the LPs. The term Limited Partner comes from the fact that the involvement of these LPs in the day­to­day business of the fund is limited. The General Partners do take the business decisions, making them responsible, and liable, for the results of the companies in the portfolio.

During the lifetime of the fund, which is on average 10 years, the GP decides when and in which company to invest. If an opportunity arises, the GP will call upon a part of the capital committed by LPs. Capital that is committed but not yet called upon is known as ’dry powder’. This term is increasingly relevant, as the total amount of dry powder in the industry has been rising tremendously over the past years [7].

When a company is acquired by a PE­firm, the latter will assist with strategic and management decisions, and help the company in all sorts of ways by using its knowledge and its network; an investment strategy with active involvement [8]. An example of a more passive strategy is the investing in stock, where you invest in a company and must rely on the experience and skill of the management in place to put the money to good use. The active investment strategy used by Private Equity investors is more capital and labour intensive, but in general leads to higher returns [9].

2.1.2. Time Horizon

During the first 5 to 6 years the money committed to a Private Equity fund is invested by the GPs [9, 10]. Within the following holding period (between 3­7 years), the investments are managed and the target company is improved in multiple ways (explained in Section 2.3) after which the investments are exited. The exit releases the funds and returns that are divided amongst the GP and the LPs. A schematic drawing of the timeline of an in­

vestment is displayed in Figure 2.1.

Figure 2.1: A schematic representation of the investment lifetime.

2.1. Defining Private Equity 8

2.1.3. Fee Structure

There are different options to exit an investment: the company could be taken to the stock exchange, sold to another company or sold to another investor. This exit liquidizes the value of the company and is the culmination of the GP’s efforts. The revenues of this sale are divided amongst the investors in the fund. Both the GP and the LPs receive their relative share of the returns of the sale, in proportion to their investment. Next to this, the GP receives an annual fee for managing the investments. Most Private Equity firms have an annual management fee of 2% of the committed capital, next to a performance fee of 20% of the profits.

Figure 2.2 shows the general structure of a Private Equity fund, it illustrates the direc­

tions in which money flows and the management relationship between the GP and the PE fund. Of course, a Private Equity fund is not limited to invest in only four companies.

Figure 2.2: General Structure of a Private Equity Fund.

2.1.4. Types of deals

There are multiple relevant types of Private Equity deals that, combined, make up the majority of Private Equity deals. They are commonly referred to by abbreviations such as MBO, MBI, SBO and LBO. There are two distinctive types of deals when looking at the po­

sition of management of the target company. When the management is incumbent in the

firm, we refer to the deal as a Management Buyout (MBO), here the current management

team acquires a stake in the company, often in collaboration with a PE­firm. We refer

to the deal as a Management Buy­In (MBI) when a new management team is brought

into the company as part of the deal, for example as part of the improvement strategy of

the PE­firm [11]. If a company is owned by a Private Equity firm, it can be acquired by

another Private Equity firm. This is called a Secondary Buyout (SBO), which can even

be followed by tertiary or even a quaternary buyout.

2.2. Impact of Market Conditions 9

Leveraged Buyout

When investing in a company, the Private Equity firm usually finances a large part of the value with debt. This is called a leveraged deal. This deal structure requires the investor to only use small amount of own equity. Section 2.4 explains how this enables Private Equity firms to generate high returns on their investment, but also illustrates the dangers of financing the company with debt. The risks associated with LBOs stem from the fact that the debt used for this transaction, and thus the risks, ends up on the balance sheet of the acquired company. As most transactions are labelled as Leveraged Buyouts (LBOs), this research will focus on these type of deals.

2.2. Impact of Market Conditions

Private Equity investments are, like the rest of the economy, impacted by market condi­

tions. We first look into general market correlations, after which we examine the impact of economic crises and evaluate the performance of companies backed by PE firms.

2.2.1. Market correlations

Bernoth and Colavecchio [12] find that, in Western countries, several macro­economic parameters show a significant relationship with PE­activity. GDP per capita and its growth rate are both positively correlated with PE­activity. A negative correlation was found with the inflation rate. These GDP and inflation­related relationships are logical from a macro­

economic perspective, stable and growing economies are interesting to investors [13].

2.2.2. Impact of economic crises

In the period leading up to the global crisis in 2008/2009, Private Equity reported the biggest deals in its history, as Figure 2.3 shows. Of the largest buyouts that took place, almost all were in this period [11].

Figure 2.3: The total number of deals and their aggregate value (in USD bn) since 1990.

2.2. Impact of Market Conditions 10

When this debt market collapsed at the beginning of the crisis, Private Equity firms could not obtain the leverage they required and this was one of the factors that led to the number of deals plummeting at the end of 2008.

Figure 2.3 shows that while the total amount of dollars invested across all deals is not comparable to 2007, the number of deals has grown. The recession that followed did impact the Private Equity firm is their risk­assessment of potential targets [7], but did not lead to fewer deals. Their preferences shifted to deals with smaller investment amount.

Figure 2.4 shows the change in the number and value of deals compared to the same quarter one year earlier. The different ’bubble bursts’ are clearly observed: the dot­com bubble at the beginning of 2000s and the financial crisis of 2008­2009. After these crises, the number and value of deals declined, as can be clearly seen in Figure 2.4 as the values are below 0%. Where the 2016­2017 dip can be explained by the increased competition and the relatively smaller deals done by new entrants [14], the 2019­2020 dip can be explained by the Brexit (as many PE­firms are located in the UK) and Covid­19.

Figure 2.4: Percentage change in the number of deals and aggregate value, compared to the same quarter one year before.

2.2.3. Performance of PE portfolio companies

Post­crisis there was a growing concern that the, highly leveraged, Private Equity deals had created a level of indebtedness at target companies that would pose a risk to the entire economic system

. Studies showed that are both positive and negative aspects of PE­funding. PE­sponsored companies did have capital available in contrast to their non PE­sponsored counterparts, which equipped them to withstand lean years [4, 15]. On the other hand, improvements in terms of efficiency often lead to initial layoffs. On average the number of employees is down 1% after 2 years of PE­ownership [16], this takes into account initial layoffs and newly hired employees for new venues.

In the post­crisis years, the companies that were backed by Private Equity firms did

1Bank of England, Quarterly Bulletin 2013 Q1

2.3. How do Private Equity Firms create Value? 11

not decrease their spending as much as their non­PE­backed counterparts and were able to seize market opportunities [4]. These companies experienced growth of their assets, market shares and profitability. PE­backed firms also reported employment growth in the years following the crisis, again in contrast to companies that were not backed by PE­firms [15]. This illustrates the advantages of access to capital for companies.

2.3. How do Private Equity Firms create Value?

Investors acquire their portfolio companies to improve their performance and with that, increase their value. The target company is expected to be worth more after the holding period than at the moment of acquisition. So the question arises: how do these investors achieve an increased company value?

2.3.1. Improve company performance

Previous research mentions three leading strategies to improve performance in target companies, resulting in increased returns for Private Equity investors [17, 18]:

• Financial Engineering.

• Governance Engineering.

• Operational Engineering.

Financial Engineering involves the financial structure of the deal and the financial con­

struction of the company post­transaction. For example, a higher proportion of debt de­

creases the risk for the investor and increases the value of the tax shield due to the lower profits that remains after everything is paid [19]. The latter is an advantage for the investor and the bank receiving interest payments, but a clear disadvantage for the government that receives less taxes.

Governance Engineering concerns the way the company is managed. As Private Equity investors are more involved with day­to­day business in comparison to public in­

vestors, this is an important aspect to increase their returns. This results in different man­

agement structures in PE­backed firms when compared to their non­PE­backed counter­

parts. PE­firms are not afraid to replace managers: one in three CEOs is replaced within 100 days after the acquisition, while two in three are replaced within four years [8].

Operational Engineering is structured around adding (sector) expertise. Using the

industry and operational experience they have, Private Equity investors can streamline

companies. This is easier done for companies that are acquired by a financial sponsor for

the first time, as the ’low­hanging fruit’ is still present, in contrast to companies acquired

in a secondary or tertiary buyout.

2.4. Leverage used in Private Equity deals 12

2.3.2. Buy & Build

An important strategy used by PE­investors is the buy­and­build (B&B) strategy. Here the investor first acquires a firm that will act as a ”platform” for future acquisitions, often in a market new to the investors. The ”add­on” acquisitions, focused on companies aligned with the initial investment, are combined with the platform company to create a single entity. The platform company often offers a quality such as a good reputation or brand­

name, while the add­on acquisitions offer specific knowledge or assets [20].

The value­adding activities in Subsection 2.3.1, are also relevant for this new combina­

tion of firms. Next to these advantages, there are also the typical merger and acquisition (M&A) effects: efficiency and synergy advantages are relatively easily realized when the companies operate in the same industry.

2.4. Leverage used in Private Equity deals

Private Equity deals are in general financed using only a small portion of equity from the Private Equity firm, while financing the rest with a bank loan. This enables the GP to leverage the investments and maximize the return on their invested capital. Imagine, for example, that you acquire Company X for €100 and after some years you can sell it for

€200. Figure 2.5a illustrates the impact on your equity.

However, you could have taken a loan from the bank for €90 and only used €10 of your own equity. When you then sell the company for €200, you use €90 to pay off the bank (assuming 0% interest) and keep €110 for yourself. You then realize a multiplier of

= 11 on your investment, much higher than the unleveraged alternative. This is illustrated in Figure 2.5b. Private Equity funds are eager to use these kinds of leverage, as it enables them to invest in multiple companies with their fund. In our example, using loans you would be able to use your €100 to invest in 10 companies, instead of only one.

(a) Unleveraged: turning €100 into

€200 (100% return)

(b) Leveraged: Turning €10 into €110 (1000% return)

Figure 2.5: An illustration of the increased returns for leveraged investments. This is a simplified example with 0% interest and no tax shield.

2.4. Leverage used in Private Equity deals 13

The proportion of the deal financed by debt depends significantly on market conditions [21]. It is easily argued that in times of low interest rates, capital is readily available for Private Equity firms. The past decade, full of quantitative easing and low interest rates, enabled Private Equity investors to obtain an abundance of capital at low cost. The low interest rates also simulated Private Equity firms in another way: (institutional) investors looking for yield are eager to invest in Private Equity funds [22]. These factors contribute to the abundance of capital and the record­high dry­powder capital available [7].

2.4.1. Negative leverage aspects

An important characteristic of the leverage, and therefore the loan, is that it ends up on the balance sheet of the target company. This exposes the company to increased risks, for example the possibility of bankruptcy due to the high interest payments that have to be made. Examples of these are the acquisition of Mervyn by a consortium including Cerberus Capital and Sun Capital Partners in the US

and the aquisiton of V&D by KRR and Alpinvest in the Netherlands

.

2.4.2. Too much leverage

Leveraged deals are not without risk, the debt attracted by the Private Equity firm, and therefore the target company, requires the company to make interest payments. This can lead to situations where a company with a positive EBITDA pre­transaction (a ’healthy’

company), finds itself unable to pay the high interest and debt payments. This is illus­

trated in the case described below in Exhibit 2.1.

Case Example ­ Toys ”R” Us

Based on articles in the Wall Street Journal

and The Atlantic

In 2005, a consortium of 3 financial parties acquired the company Toys ”R” Us.

KKR, Bain Capital, and Vornado Realty Trust paid a total of $ 6.6 billion for the chain of toy stores, of which $5.2 billion was debt that was added to the balance sheet of Toys ”R” Us. In the following years, the debt was not paid down, and 97% of the operating profit was used to pay the $400 million interest expenses.

This led to a net loss of $36 million in 2007, on a revenue of $11.5 billion. The next decade would continue in this way, revenues staying at $11.5 to $13.5 billion and paying $425 to $517 million in interest each year. Due to the debt, the company had no room to innovate or invest. This resulted in a bankruptcy filing in 2017.

aWall Street Journal: ”Who Killed Toys ‘R’ Us? Hint: It Wasn’t Only Amazon”.

bThe Atlantic: ”The Toys ”R” Us Bankruptcy and Private Equity”.

Exhibit 2.1 : An example of the negative effects of a leveraged buyout.

2Bloomberg: ”How Private Equity Strangled Mervyns”.

3Volkskrant: ”The demise of the Vendex­empire”.

2.5. Multiple Arbitrage 14

2.5. Multiple Arbitrage

When assessing the value of a company, often so­called ’multiples’ are used. These give the ratio between the company value and a key metric, e.g. EBITDA, EBIT or revenue.

These multiples enable investors to compare investment in different­sized companies.

In general, we can say that larger, more stable businesses are worth a higher multiple of their financial metrics than smaller businesses with a more uncertain outlook. An im­

portant value driver for PE investors is the opportunity for multiple arbitrage. This occurs often within a buy­and­build strategy when the large and stable platform company buys one or more smaller companies as add­on acquisitions. The values of these smaller com­

panies increase when they become part of the large company; they are deemed to be part of a stable business. To illustrate how these acquisitions create value, an example situation, where we use a multiple on the EBITDA to determine the company value, is shown in Table 2.1. Here we have a large company, with a 10x multiplier on its EBITDA, and 2 smaller companies, with multipliers of 3x and 6x.

Company 1 Company 2 Company 3

EBITDA (€m) 60 5 20

multiple 10x 3x 6x

Company Value (€m) 600 15 120

Table 2.1: An example situation where multiple arbitrage occurs.

When Company 1 acquires the other two companies, it has to pay €15 million for Company 2 and €120 million for Company 3. With a total investment of €135 million, the EBITDA of the new company increases with €25 million. Company 1 now has a total EBITDA of €85 million and still has a 10x multiplier. Table 2.2 gives the new situation.

New EBITDA €85m

New company multiple 10x New Company Value €850m

Table 2.2: Situation after the takeover (simplified example).

Here we can see that the multiple associated with the large and stable Company 1 also applies to the EBITDA previously generated by Companies 2 and 3. Therefore, the new company value is €250 million higher than the initial value of Company 1, while it only used

€135 million to acquire the other companies. Neglecting costs associated with integrating

the companies and benefits from synergies, €115 million is created out of thin air, hence

the term arbitrage. It is important to note that this new company value is only relevant

when there is a possibility for a sale; since we are considering Private Equity investments,

we assume that they are always planning an exit and look to sell their investment within

some years.

3

Leveraged Buyout Model

Contents

3.1 Introduction to the Model . . . 15 3.2 Goal of the Model. . . 16 3.3 Assumptions & Parameters . . . 17 3.4 Model Output . . . 23 3.5 Parameter Summary . . . 24

3.1. Introduction to the Model

Determining the optimal parameters for a leveraged buyout is not easy: future cash flows are uncertain and no set of equations can precisely calculate the impact of all factors during the lifetime T of an investment.

A solution to this is the LBO­model, where for each year of the investment the asso­

ciated cash flows, equity and debt positions are simulated. This model is often used in Private Equity to determine the expected IRR of an investment [23]. By using varying input parameters and simulating the cash flows, we obtain indications regarding the ex­

pected performance. We do this for all years up to t = T , the final investment year. By incorporating parameters that are random, within certain given bandwidths, we can use the model to simulate a large number of outcomes and draw conclusions from the results.

We will specify these parameters in this chapter.

15

3.2. Goal of the Model 16

Figure 3.1 gives a schematic representation of the mechanism of an LBO model. Step 2 in this figure is the most simulation­heavy part of the simulation, as the different cash flows for each year will be calculated based on the parameters.

Figure 3.1: Illustration of an LBO model, adapted from Olesen & Einfelt [24].

Step 1: The Company is acquired for the Enterprise Value at time 0 (EV0).

Step 2: For each year t, the model results in a cash flow CFtthat is used to pay down the debt.

Step 3: At time T the company is valued and the final debt and equity positions are determined.

Step 4: The final equity position is compared with the initial equity and the ex­post IRR is determined.

3.2. Goal of the Model

We want to determine the impact of various parameters on investment performance to determine the optimal deal structure. The performance metric most used in the sector is the Internal Rate of Return (IRR): this metric takes into account the cash flows of all years of the investment, from the initial negative cash flow at the moment of acquisition, through the final cash inflow at the moment of sale. Since the IRR is the most widely used performance metric in private equity investments, we use it in this report as well. As we will be determining the IRR after we have simulated the cash flows, we are not using the IRR as a forward looking metric, but we calculate the ex­post IRR after the simulation.

When we refer to IRR in this report, this will concern the realized or ex­post IRR.

We evaluate the IRR for different scenarios, where we vary the parameters of interest.

Variables as leverage ratio and multiple are important, as these can be directly influenced

by the investor. This in contrast to variables as interest rates, tax rates and, to some

degree, the rate and volatility of growth. Our final goal is to obtain the optimal combination

of the multiple and leverage ratio used in the deal. As investors can influence these

parameters, the results of our research enable them to optimise their deal structure in

terms of leverage and multiple.

3.3. Assumptions & Parameters 17

3.3. Assumptions & Parameters

One important characteristic of an LBO­model is that it assumes that at the end of the holding period, year T , all debt is paid off. This means that a significant part of the free cash flows must be used to pay off debts.

Certain assumptions are essential within the model. These govern the growth rates, default conditions and equity value. This section outlines the assumptions made and also specifies the required input parameters for this LBO­model.

3.3.1. Revenue

The core of the performance for any company, revenue during each modelled year (R

) also plays a major role in our LBO­model. While we have assumptions and expectations on the (average) growth of the revenue, we are not certain of the exact revenue in any year t.

Demand, the most important driver for revenues, is often modeled using Geometric Brownian Motion (GBM) [25–28], which we use to model the revenue in our model. The Geometric Brownian Motion consists of a Wiener process combined with a drift rate. We use Itô’s lemma [29] to derive a function for our model.

Wiener Process

A Wiener process is a stochastic process {W

}

with the following characteristics [30]:

• The value at time t+1 is only dependent on the value at time t, not any value before.

• The process has stationary and independent increments.

• The increments W

− W

are N (0, 1) distributed.

With ! as random N (0, 1) distributed variable and timesteps of dt to find the following discrete formulas:

W

− W

∼ !

(t + s) − t! (3.1)

dW ∼ √

dt! (3.2)

With ! ∼ N (0, 1)

3.3. Assumptions & Parameters 18

Geometric Brownian Motion

The Geometric Brownian Motion, a stochastic process that combines an expected growth rate, volatility and the Wiener process, defines the increase in revenue dR

as follows:

dR

= µR

dt + σR

dW (3.3)

Where:

R

= Revenue at time t.

µ = Expected growth rate.

σ = Expected volatility.

W

= Wiener process.

Itô’s Lemma

Itô’s lemma [29] states how we can derive the formula for the revenue at time t using Equation 3.3. This function is a stochastic differential equation (SDE), a type of differential equation that includes stochastic processes, in this case the Wiener process. Itô Lemma states that for a variable x that follows the process as in Equation 3.4, then for the function f (x, t) the SDE is given by Equation 3.5.

dx = a(x, t)dt + b(x, t)dz (3.4)

df =

" ∂f

∂t + ∂f

∂x a + 1 2

∂

f

∂x

b

#

dt + ∂f

∂x bdz (3.5)

Using these equations with f(R) = ln(R) and a = µR

and b = σR

, we find (by using

∂ ln(R)

∂t

= 0):

d(ln(R

)) = ∂ ln(R

)

∂R

µR

dt + 1 2

∂

ln(R

)

∂R

σ

R

dt + ∂ ln(R

)

∂R

σR

dz (3.6) Using the properties of the logarithmic functions,

=

,

= −

, and rewrit­

ing we find:

d(ln(R

) = 1 R

µR

dt − 1 2

1

R

σ

R

dt + 1 R

σR

dz (3.7)

d(ln(R

) =

"

µ − σ

2

#

dt + σdz (3.8)

Which is integrated from 0 to t to find the formula we use in our model to define the revenue at time t as a function of time and the initial revenue.

R

= R

exp

"

(µ − σ

2 )dt + σ! √ dt

#

(3.9)

In this final formula, we need µ, σ, R

and the number of intervals per unit of time dt

as inputs and generate random numbers for !.

3.3. Assumptions & Parameters 19

3.3.2. EBITDA

To arrive at the EBITDA from the revenue, we need the ratio

. To find this EBITDA margin, we use a database containing data on 46,580 companies across 94 industries [31].

We incorporate the possibility to increase the EBITDA­margin with some basis points linearly over the investment horizon. This can be used to provide resemblance to in­

creased efficiencies and economies of scale that are experienced by growing companies.

Using EM

and EM

as inputs for the margin at the start and end, we determine the EBITDA of each period in the following way:

EB

= EM

∗ R

(3.10)

Where:

EB

= EBITDA at time t EM

= EBITDA Margin at time t EM

= EM

+ t ∗

" EM

− EM

T

#

for 0 ≤ t ≤ T T = final year of holding period; year of sale

3.3.3. Leverage Ratio

We found the importance of leverage in Chapter 2, being one of the defining parameters for the return of the portfolio. The model uses the leverage ratio to determine how much of the company is financed using debt at time t = 0. We set L to be the fraction of the total enterprise value at the time of acquisition, EV

, that is financed with debt. We assume that the remaining part (1 − L) is financed by equity of the PE sponsor. For leverage ratio L, between 0 and 1, we can determine the amount of debt and equity in the target company after the acquisition at t = 0:

D

= EV

∗ L (3.11)

E

= EV

∗ (1 − L) (3.12)

Where:

D

= Debt at time t E

= Equity at time t

EV

= Enterprise Value at time t

L = Leverage ratio, with L ∈ [0, 1]

3.3. Assumptions & Parameters 20

3.3.4. EBITDA to Free Cash Flow

To arrive at the free cash flow to the investor, we need to add and subtract some factors to the EBITDA we determined for each period t. Table 3.1 on the next page shows the required steps. Both deprecation and amortization are not costs that are associated with cash flow going out, however they are still needed to calculate the amount of taxes to be paid. Therefore, these costs are subtracted before calculating the taxes and added back to find the free cash flow.

EBITDA

Depreciation & Amortization ­ EBIT

Interest payments ­

EBT

Taxes ­

Net Income

Depreciation & Amortization + Capital Expenditures ­

∆ Net Working Capital ­ Free Cash Flow

Table 3.1: How to arrive at the Free Cash Flow from the EBITDA.

Depreciation and Amortization

We use a percentage of revenues to determine the deprecation and amortization (D&A) per year. While this does not influence the free cash flow (it is added back later, since it is no expense), it does impact the taxable income and therefore the amount of tax to be paid. We model the D&A­costs as a percentage of the revenue, an input parameter for our model. The percentage is given by r

, that has a value between 0 and 1. The amount of depreciation & amortization costs in year t (DA

) are given by:

DA

= r

∗ R

(3.13)

Interest & Debt payments

We can calculate the costs associated to interest and debt redemption as soon as we know the debt position at time t

. We use the interest rate on debt, i

, as an input parameter for our model. Each period t, the required interest payment IP equals:

IP

= i

∗ D

(3.14)

Where:

IP

= Interest payments at time t

i

= interest rate on debt

3.3. Assumptions & Parameters 21

As the LBO­model assumes a debt of 0 at time T , each period has debt repayments, DR

:

DR

=

" 1 T

#

∗ D

(3.15)

Where:

DR

= Debt repayment at time t

This results in the total obligations in period t of T O

:

T O

= IP

+ DR

(3.16)

Taxes

To calculate the amount of taxes that are due, we use the corporate tax rate τ

as input for our model. The corporate tax rate is applied to the earnings after the interest has been paid, this is a tax advantage known as an interest tax shield. Interest payments are non­taxable and lead to a reduction in the required tax payments. The amount of taxes to be paid in year t is given by:

T ax

= τ

∗ Earning Before Tax

(3.17) T ax

= τ

∗ (EB

− DA

− IP

)

Where:

T ax

= Tax payments at time t τ

= Corporate tax rate Capital Expenditures & Net Working Capital

Both Capital Expenditures (CapEx) and Net Working Capital (NWC) are linked to the revenue. While CapEx entails cost that are made in the business, the NWC indicated the required capital within a company to do business (e.g. paying suppliers and personnel while waiting for creditors). Within our model, we will look at the CapEx per year, and the

∆N W C, since the increase of this capital should be subtracted.

CapEx

= r

∗ R

(3.18)

∆N W C = r

∗ (R

− R

) (3.19) Where:

r

= ratio CapEx Revenue r

= ratio N W C

Revenue

3.3. Assumptions & Parameters 22

Based on Table 3.1, we then find the following formula for the FCF:

F CF

= EB

− IP

− T ax

− CapEx

− ∆NW C (3.20)

3.3.5. Multiple

To determine the company value, we multiply the EBITDA of the company with a certain factor to obtain the company value, a method commonly used in Private Equity. We call this factor the multiple. The model uses the multiple at the time of purchase as input and expects the multiple at the time of sale to be the same. The multiple at t = 0, m

is one of the parameters that we expect will impact the investment performance significantly.

Therefore we will simulate a variety of different values in our model. This multiple enables us to calculate the company value EV

at every moment t by using the following formula:

EV

= EB

∗ m

(3.21)

Where:

m

= EBITDA multiple at time t

3.3.6. Default

Every simulated period, the formulas defined in the previous subsections lead to a cash obligation and new debt and equity positions. We now define when we consider a com­

pany to default and what the consequences for the investment are. We use the Free Cash Flow after Debt Repayments as a criterion to determine when a company defaults.

The metric ratio

, used in the contracts of 97% of PE­sponsored loans [32], is not used to simulate defaults. The report of Achleitner et al. [32] shows the mean of the maximum

ratio specified in the contracts was 5.48. Using this value would lead to certain combinations of leverage ratio and multiple to immediately lead to a default in our simulation. This is illustrated by the following formulas:

multiple ∗ leverage = Debt

EBIT DA (3.22)

EV

EBIT DA ∗ Debt

EV = Debt

EBIT DA (3.23)

We want to test high multiples (up to 20) with high leverage (up to 1), only a small amount would be below the mean ratio of the contracts at 5.48. We use this ratio to validate our outcomes later in this report.

Free Cash Flow after Debt Repayments

If we arrive at the Free Cash Flow (FCF) as outlined in Section 3.3.4, the only payment

left to make concerns the debt repayment. Depending on the chosen debt repayment

strategy, this can be a fixed amount or a percentage of the FCF. If the FCF after this

payment is negative for pd consecutive periods, this triggers a default. We define the

3.4. Model Output 23

default condition as a Boolean variable that is True (1) when the default condition is met, and False (0) otherwise.

Def ault

=

 



 

1 if max

i∈[t−pd:t]

F CF aD

< 0 0 else

(3.24)

Where:

Def ault

= Boolean variable specifying the default condition based on the FCF pd = Period of negative FCFs that lead to default

F CF aD = Free cash flow after Debt repayments

3.4. Model Output

This section outlines the outputs of the model that we find after we have simulated the cash flows. Most important are the cash flows to the investor and the associated IRR.

3.4.1. Investor’s cash flow

When provided with all required inputs, the model calculates the cash flows, debt and equity positions, and payments for every period t up to time T . It then determines the associated cash flow to the investor for each year, ICf

. The cash flow paid by the investor in year t = 0 is easily determined, it is the part of the company value that is not financed by debt:

ICf

= − ((1 − L) ∗ EV

) (3.25)

Where:

ICf

= Investor cash flow at time t

The cash flows for the other periods depend on the F CF aD, if this is positive this can be paid out to the investor. However, if it is negative the investor has to invest extra money into the company to ensure it can fulfill its payment obligations. In this case, the PE sponsor generally start to negotiate with the bank to determine who will pay what of the deficit. Both have a stake in keeping the company operational, so in general both will pay some of the debt (or write off some of the debt in case of the bank).

The cash flows to the investor for each period t will be modelled as:

ICf

=

 



F CF aD if F CF aD ≥ 0 α ∗ F CF aD if F CF aD < 0

(3.26)

Where:

α = Portion of the deficit to be paid by PE sponsor

3.5. Parameter Summary 24

3.4.2. Internal Rate of Return

When all cash flows up to t = T are calculated, we determine the Internal Rate of Return (IRR).

The IRR is defined as the discount rate that ensures a Net Present Value (NPV) of zero if all cash flows are discounted using that rate, satisfying the following formula:

0 = (

CF

(1 + IRR)

(3.27)

Where:

IRR = Internal Rate of Return

3.5. Parameter Summary

Summarising the previous sections, Table 3.2 gives an overview of all parameters.

Parameter Specification General

T Lifetime of investment

dt Simulated time steps per year Revenue

R

Revenue at time t = 0 µ Growth rate of the revenue σ Volatility of the revenue growth EBITDA

EM

EBITDA margin at t = 0 EM

EBITDA margin at t = T Multiple

m

EBITDA multiple at time t = 0

m

EBITDA multiple estimate at time t = T Debt

L Leverage ratio i

Interest on debt Expenses

r

ratio

(Depreciation & Amortization) r

ratio

(Capital Expenditures) r

ratio

(Net Working Capital)

Tax

τ

Corporate tax rate Default

DE

Debt/EBITDA­ratio

pd Consecutive years of negative F CF aD leading to bankruptcy α Portion of the deficit to be paid by PE sponsor

Table 3.2: Input parameters for the LBO­model grouped per section.

4

Simulation

Contents

4.1 Introduction . . . 25 4.2 Scenarios . . . 26 4.3 IIR: the performance indicator . . . 27 4.4 Main input variables . . . 28 4.5 Simulation Results . . . 29

4.1. Introduction

Where the previous chapter covered the assumptions and formulas that form the core of the Leveraged Buyout (LBO) simulation model, this chapter outlines the input variables we use and their outcomes of the simulation. As our goal is to determine the optimal financial structure of an LBO deal, we analyze different scenarios, each with different configurations for the input parameters. Using the outcomes of these simulated scenarios, we are able to determine the financial structure that leads to the highest returns for each scenario.

Our simulation will take the input variables and generate a random T ­year revenue path accordingly. For every year we find cash flows according to the formulas and rela­

tionships outlined in the previous chapter. Each year the remaining free cash flow is paid to the investor, and together with the final sale of the company this leads to a realized IRR. For each combination of multiple and leverage ratio, we do this 1,000 times, take the median IRR of these trials and move on to the next combination.

25

4.2. Scenarios 26

4.2. Scenarios

This section outlines the different scenarios that we simulate and the corresponding pa­

rameter values. Different parameter­sets, representing different types of companies, are introduced after the general parameters for all simulations are outlined.

4.2.1. General Parameters

Table 4.1 shows the general parameters we use in our simulations. These parameters are not scenario­dependent and will be the same in all simulations. These values are based on industry standards, real­world observations and expert opinions.

Parameter Source Value

Investment holding time T Industry standard 5

Tax rate τ

Real world 20%

Liquidation Parameter Expert 0.9

Deficit Proportion Expert 0.5

Default Condition (Years) Expert 3 years

Table 4.1: General parameters.

4.2.2. Scenario parameters

The business sectors are determined based on relevant recent transactions, expert opin­

ions within the company and whether sectors have proven to be fit for private equity over time. Table 4.2 contains the list of sectors and the corresponding parameters for the model. These values are found in the databases [31].

A B C D E

Sector EM

& EM

r

r

r

i

Business & Consumer Services 11% ­ 15% 1.3% 0.9% 11.2% 4.1%

Consumer Electronics 7% ­ 11% 1.5% 3.8% 9.8% 2.1%

Drugs (Pharmaceutical) 24% ­ 28% 8.6% 5.1% 26.1% 3.3%

Food Processing 10% ­ 14% 1.8% 3.1% 11.4% 3.8%

Healthcare Info. & Tech. 17% ­ 21% 3.2% 2.8% 23.2% 3.9%

Retail (General) 6% ­ 10% 0.2% 0.2% 2.8% 4.0%

Semiconductor 27% ­ 31% 8.6% 14.8% 20.7% 3.1%

Software (System & applications) 24% ­ 28% 6.0% 6.0% 13.6% 3.8%

Table 4.2: Selected sectors and corresponding values for the parameters.

A: EBITDA Margin, B: Depreciation & Amortization, C: Capital Expenditures, D: Working Capital, E: Interest.

Next to the parameters regarding the financial structure within different sectors, there

4.3. IIR: the performance indicator 27

are also differences in expected growth rates [31]. These growth rates, and the associ­

ated volatilities are listed in Table 4.3. These volatilities are based on the realized volatility over 6 months for the respective Global Industry Classification Standard (GICS) sector [33]. We are interested in the optimal financial structure for an LBO deal for each sector, not in finding the sector that leads to the highest overall IRR. If the latter would be the case, Table 4.3 would provide us with an easy answer, looking at the highest growth rate and relatively low volatility of the third sector, Drugs (Pharmaceutical).

Growth rate Volatility GICS volatility sector

Sector µ σ

Business & Consumer Services 3.8% 18.8% Consumer Discretionary

Consumer Electronics 5% 21.1% Information Technology

Drugs (Pharmaceutical) 34.3% 12.1 % Health Care

Food Processing 4.9% 11.3% Consumer Staples

Healthcare Info. & Tech. 15.1% 12.1 % Health Care

Retail (General) 0.6% 11.3% Consumer Staples

Semiconductor 9.3% 21.1% Information Technology

Software (System & applications) 10.9% 21.1% Information Technology

Table 4.3: Growth rates and volatility per sector as defined by the Global Industry Classification Standard.

4.3. IIR: the performance indicator

We have now determined all input parameters and the values for the probability distribu­

tion. For every set of input parameters, i.e. every simulated sector, we use our model to simulate revenue paths, cash flows and debt positions. This allows us to find an IRR for each simulation. As each simulation of a set of parameters is executed 1,000 times, we set the IRR to be the median of the 1,000 simulated IRRs. Taking the mean would lead to an IRR heavily influenced by extremes. Figure 4.1 gives an example of this.

Figure 4.1: Example of an IRR Histogram.

4.4. Main input variables 28

4.4. Main input variables

Each simulation consists of multiple iterations of 1,000 simulated revenue paths. Each it­

eration, the value of the variable(s) for which we want to find the optimal value will change, which allows us to compare performance across the range of values for the target value.

This section outlines the variables for which we will maximize the IRR.

4.4.1. Input variable: Leverage ratio

The amount of debt used to acquire a target company is one of the variables that has the most impact and is the easiest to influence for the Private Equity firm. In our simulation we will look at performance in situations ranging from wholly equity­funded deals (leverage ratio of 0) to transactions almost completely funded by debt (leverage ratio approaching 1). As debt providers require at least some equity investment by the PE­company, we use a maximum leverage ratio of 0.95.

4.4.2. Input variable: Multiple

The valuation of the company dependents on different factors, where the valuation multi­

ple, the company value divided by the EBITDA, is of major importance. A higher multiple amplifies increased and decreased revenues and heavily impacts the final IRR. A multi­

ple of 10 for example, amplifies an increase or decrease in EBITDA of €1, resulting in an increase in company value of €10 or a decrease of (­)€10. Sectors with different charac­

teristics (Table 4.2) are expected to require different multiples in their optimal financing scenario. Again this is simulated during multiple iterations, where we analyse the impact of the parameters on the performance of the investment and determine the optimal value.

Since multiples in the range of 0­4x only occur in less than 4% of the deals

, we start at a minimum multiple of 4, increasing with 0.2 every iteration up to a multiple of 21. This is done to ensure we will not encounter unrealistic outcomes with a multiple below 4.

4.4.3. Optimization order

To determine the order in which we optimize the leverage ratio and the multiple, we first look how these variables relate in a real world transaction. However, there is no clear order in which the multiple paid for the company and the leverage are determined in the process. It is a continuous process in which multiples are determined based on the debt (leverage) a private equity firm can get at a bank, and the amount of debt a bank is willing to lend depends on the valuation (multiple) of a company.

We first analyze the impact of these factors on optimization outcomes. If the amount of leverage has little effect on the outcomes of the multiple optimization or the other way around, we can first determine the optimal value for one and then for the other.

1Visual Capitalist: Ballooning Valuations In Private Equity Deals

4.5. Simulation Results 29

Figure 4.2 shows the impact of the initial leverage ratio on the outcome of the optimiza­

tion with respect to the multiple. Different values lead to significantly different outcomes, so optimizing the multiple without knowing the ideal leverage ratio leads to meaningless outcomes.

(a) Leverage ratio = 0.4 (b) Leverage ratio = 0.6 (c) Leverage ratio = 0.8

Figure 4.2: Testing simulation order: 3 simulations for Sector 1 with different leverage ratios leading to different optimal multiples (9.4x, 6.6x, 3.2x respectively). Optimal is defined as the combination that gives the

highest IRR.

A similar outcome is observed in Figure 4.3 where we see the results of three sim­

ulations with different initial values of the multiple variable. Here again it can be stated that optimizing the leverage ratio before knowing the right multiple renders meaningless outcomes that provide us no insight in optimal combination between the two variables.

(a) Multiple = 5 (b) Multiple = 7.5 (c) Multiple = 10

Figure 4.3: Testing simulation order: 3 simulations for Sector 1 with different multiples leading to different optimal leverage ratios (0.86, 0.54, 0.35 respectively). Optimal is defined as the combination that gives the

highest IRR.

From these results we can conclude that it is required to optimize the leverage ratio and the multiple at the same time. In our simulation we will test all combinations of leverage ratio and multiple to find the optimal combination in terms of IRR and the number of defaults. This will result in a 3D­graph of which the previous figures are a cross section.

4.5. Simulation Results

In this section we look into the outcomes of the simulations and the observations that can

be made using the data. We look at a general overview, the relationship between the

multiple and leverage ratio and the optimal financial structure per sector.