Real Options and Private Equity

Master thesis M.Sc. in Finance &

Strategic Management

Author

Mikael Sahlin Olesen

Advisor

Thomas Einfeldt

Institution

Copenhagen Business School Department of Finance Solbjerg Plads 3, A5.09 DK-2000 Frederiksberg

Date

September 30, 2009

Real Options and Private Equity

Valuation

Executive Summary

The special construction of Private Equity (PE) investments with high leverage and rapidly changing capital structure has meant that a new valuation model was developed – The LBO model – in order to take this onto account. The LBO model is constructed to follow each step of a Private Equity investment by separating that valuation of debt and equity. It is, however, still a static valuation method which does not take managerial flexibility into account. As practitioner and theorists of real option theory states, this results in unrealistic values. The purpose of this thesis it therefore to examine the applicability on real option theory to PE valuation in order to establish weather PE firms are overlooking potential value by not focussing on real options in relation to their exit strategy. Because the main value creation in a PE investment comes from the sale of the portfolio companies, the focus is on the flexibility related to the PE firms exit strategy (PE Exit Option).

Real option theory is the most recognised method for valuing flexibility. It uses the theory from financial options to value real assets. By linking the variables from financial options to characteristics of real assets it can be established that the valuation models for financial models can be used for real options. For the purpose of valuing PE Exit option the binomial model is the most appropriate because it can easily be adjusted for the specific characteristic of the PE Exit Option.

The PE Exit option is divided into two separate options. One for the period where the target is owned by the PE firm (Holding period) – PE Holding option, and another for the period after the expected exit of the target (Post Exit Period) – PE Post Exit option. The most noticeable specifications when applying real option theory to the Exit options is: (1) it is the targets market value which is used as the underlying asset (2) that it is the required return calculated as a enterprise value that is the exercise price, which entails a variable exercise price (3) that the Exit option does not have the choice of not exiting at expiration of the Post Exit option.

Using the theory from real options does add value to the PE firm by incorporating the flexibility of exiting at different times, but this value can only be realised if a potential buyer values the flexibility the same. The value is only as high as a buyer will pay.

Table of contends

1 Introduction ... 6

1.1 Problem Statement ... 7

1.2 Delimitations ... 8

1.3 Methodology ... 9

1.4 Structure... 10

2 Private Equity Business Model ... 11

2.1 Structure of PE firm ... 11

2.2 Strategy of PE firms ... 13

3 Valuation of PE targets – The starting point ... 16

3.1 Discounted Cash Flow model (DCF) ... 16

3.2 Adjusted Present Value (APV) ... 16

3.3 Multiples for Valuation ... 17

3.4 LBO valuation method ... 18

3.5 Inadequacies of LBO model ... 20

4 Real Option Theory ... 21

4.1 Classic Real Options ... 21

4.2 Valuing Real options ... 22

5 Option Pricing Models ... 25

5.1 Binomial Model ... 25

5.1.1 Risk-neutral Probabilities ... 26

5.1.2 Setting up the binomial lattices ... 26

5.2 The Black & Scholes model ... 29

5.3 Model choice ... 30

6 PE Exit options and the general framework ... 31

6.1 PE firms exit option (PE option) ... 31

7 Expanded LBO valuation ... 34

7.1 Expanded LBO ... 34

7.2 Static LBO valuation ... 35

7.2.1 Debt Capacity ... 35

7.2.2 Expected future cash flow for debt repayment ... 35

7.2.3 Expected exit value ... 36

7.2.4 Required rate of return ... 36

7.2.5 Enterprise Value (at time zero) ... 38

7.3 Volatility estimation ... 38

7.3.1 Historic data vs. Forecasts ... 38

7.3.2 Simulating Volatility ... 40

7.4 PE Option valuation (Binomial model) ... 46

7.4.1 The Variables ... 46

7.4.2 Setting up the lattices ... 51

7.5 Total value ... 53

8 TDC A/S valuation using expanded LBO ... 54

8.1 Case Company – TDC A/S ... 54

8.2 Pro Forma Income Statement ... 56

8.3 Static LBO valuation ... 57

8.4 Volatility estimation ... 59

8.5 PE Option valuation (Binomial model) ... 63

8.6 Total value ... 67

9 Criticism of Real options ... 69

9.1 Financial Issues... 69

9.2 Corporate Governance Issues ... 70

10 Discussion ... 72

10.1 The PE Exit options ... 72

10.2 Choice at Exit ... 73

10.3 Interpreting the value ... 73

11 Conclusion ... 75

12 Further research ... 78

13 References ... 79

14 Appendices ... 82

1 Introduction

They have been called everything from Barbarians at the gate to financial pyramid games, and have been thoroughly discussed in the media. But the Private Equity market has been a booming industry for several decades, and up until the credit crunch, the trend suggested an increasing influence in the merger and acquisition market.

In the years leading up to the credit crunch, the financial climate was characterised by low interest rates, global economic boom with little risk of bankruptcy, high liquidity, and increasing competitiveness between banks, resulting in a very favourable debt market. These factors created a very suitable environment for Private Equity firms (PE firms) and their highly levered investments. All this has now dramatically changed, and the PE firms are now challenged by a very difficult debt market and low liquidity, and some experts that many PE firms will default in the coming years (Børsen 2009a).

The credit crunch has also meant the there is a higher uncertainty about the future, and valuation techniques which incorporate this uncertainty is maybe now more than ever a area where potential value can be created.

“Every day, companies “value” projects using a technique that implicitly assumes the world stands still. Markets never change. Consumer demand never rises or falls. New technologies rarely emerge. And lessons are hardly ever learned. Why? Because one of the best ways to value projects—real options analysis—is flying somewhere under the corporate radar.”

AT Kearney (2009)

PE firms’ valuation procedure is no different from the companies’ referred to here. It is tailored completely to the steps in a PE acquisition (Baldwin, 2001A, Baldwin, 2001B and Bonnerup et al 2007). It is, however, based on traditional valuation theory and the discounted cash flow model (DCF model), which in the past decade has been increasingly criticised in modern corporate finance theory for being static and not applicable in real world situations where change and uncertainty is inevitable. The uncertainty can also be beneficial to PE firms. Practitioners of Real Option Theory hypothesize that using real option theory as a complementary valuation tool results in a more realistic valuation which exploit the opportunities of uncertainty and might create a competitive advantage (Copeland and Antikarov, 2001).

There is little literature available on the subject of applying real option theory to the valuation of PE targets, and examinations of the connection between the basics of value creation in PE firms and real options as well as practical implications are virtually nonexistent. This thesis will therefore examine the prospect of applying real options to the valuation of PE targets from a theoretical as well as a practical point of view, in order to determine weather PE firms are overlooking potential value in their exiting valuation prices.

1.1 Problem Statement

The main return from PE investments comes from the selling (exiting) of portfolio companies (targets). The flexibility of exiting when conditions are most favourable could therefore have great undiscovered value to PE firms. The focus of this thesis is thus to examine if and how Real Option Theory can be used as a tool for valuing PE targets by valuing this flexibility. Based on that, the main hypothesis is:

Are PE firms overlooking potential (real) value by not focusing on real options in relation to their exit option?

The overall problem statement will be answered through the following research questions, which provides theoretical as well as practical assessment of real options in PE valuation:

- How is a Private Equity investments valued?

- What is Real Options and how are real options valued?

- What options are available to PE firms?

- How can real option theory be applied to the valuation of PE targets?

- How does the general criticism of Real options apply to PE Exit option?

1.2 Delimitations

The scale and scope of the thesis naturally limits some aspects of the analysis, and I have prioritised the areas which I find most relevant for the analysis. I have chosen to highlight these specific limitations in the sections where they are relevant, as I feel this gives a better overview and a more fluent presentation. There are some general limitations, however, which will be presented next.

The handling of input data has a great influence on the result of the valuation, as the real option analysis is (as any other model) subject to the concept of garbage in – garbage out, meaning that the result is not better than its inputs. Therefore, the main focus of the thesis is a theoretical and technical background combined with a practical analysis and less emphasis on the strategic consideration regarding real option. This should not be interpreted as the strategic considerations are not important, but merely as necessary for the extent of the thesis.

The receivers of the thesis are practicians and theorists of financial theory which can be assumed to have a basic knowledge of theory and method in finance. It is therefore assumed that a presentation of general valuation methods (DCF, multiples and APV) is not necessary, as their application and underlying assumptions a known by the reader, and only a brief description of the main characteristics is presented.

The conclusions in the thesis will be based on theoretical review and a single case study. A large empirical study would of cause give a better foundation for drawing general conclusions. But because of the need for a thorough analysis of the theoretical applicability, the scope of the thesis does not allow a large empirical study.

Even though many real options would be available to PE firms in relation to the target companies, the focus of this thesis will be on the options associated with exiting the target. This is partially because of the scope of the paper and partially because it is a general option which can be applied to most PE targets, while other option will be more specific, such as launching projects or firm specific investments.

1.3 Methodology

The analysis of applying option theory to the valuation of PE targets is first of all a theoretical analysis. That is, since there are no theory that describes this particular combination of real option and private equity theory, it first needs to be established that application is theoretical feasible and can be done in coherence with existing valuation and real option theory. This implies using the most relevant theory from acknowledged text books and articles that can assist in making a modified practice that is consistent with general theory.

After it is established that it is theoretical feasible the next step is to examine the practical feasibility. This is done by developing a practice based on real option and private equity valuation theory, but modified to account for practical implications. Subsequently this practise is challenged by a single case study of a PE target valuation. The aim of the case study is to satisfy the three tenets of the qualitative method: describing, understanding, and explaining (Yin 1994), and I find it reasonable to assume that a single case study is sufficient to fulfil this aim if the three tenets are fulfilled. Yin (1989) supports this by pointing out that generalization of results, from either single or multiple designs, is made to theory and not to populations. Based on that, I find that the similarity of the characteristics of PE acquisitions, the thorough theoretical analysis combined with one qualitative case study is sufficient to make adequate general conclusions.

The case study will be based on NTC’s acquisition of TDC A/S in 2006, and will be build on both qualitative and quantitative data. The qualitative data will primarily consists of articles and market reports of TDC from before the takeover, while the quantitative data is primarily TDC annual reports from 2006 to 2008 and market reports of the telecommunications and internet industry, including projections of future developments in the industries.

Finally, because there is no prior research on this specific use of real options in PE valuation, I find it important to discuss the key findings and implications in order to give a more nuanced view of the applicability. This will be an ongoing process throughout the thesis, meaning that a large part of the thesis is to discuss the different issues in order to determine the best solution.

1.4 Structure

Figure 1 – Structure

Introduction

Problem Statement Method & Limitations

Theoretical review

Private Equity Real Option Theory

Conclusion Applayng Theory

PE Exti Options

Expanded LBO LBO Model

Holding Option Post Exit Option

TDC A/S Case Study

Considerations

General Critique Discussion

2 Private Equity Business Model

Private equity is a broad term, which in general signifies the source of money. As the name suggest the money is private and cannot be reached from public markets, such as stock exchanges. Private equity investments are typically divided into three categories:

Leveraged Buy-Out (LBO) Venture Capital

Other special investments e.g. mezzanine capital

Furthermore they are typically characterised by a group of large investors which, through for example a Private Equity firm (PE firm) or Venture Capital firm (VC firms), invest in different firms in order to get a higher return than they would get by investing in public traded stocks¹. While venture capital firms tend to invest in earlier stage growth companies, PE firms tend to focus on more mature businesses. One of the key differences in the two types of companies is their funding of acquisitions. Where VC firms’ transactions are primarily funded with equity, due to uncertain cash flows, the primary funds for PE firm are usually debt, with up to 75-80 % debt (Vinten & Thomsen 2008a). For this reason the typical PE transaction is called a leveraged buyout (LBO). The focus of this thesis will be PE firms.

2.1 Structure of PE firm

The concept of PE firms can be compared to that of investment- or mutual funds. Instead of each investor invests in separate companies, they invest in a PE firm, which then invest in the different companies (targets). The reason for this structure is that the investors can reap all of the benefits from the excessive expertise, which the PE firm has accumulated through all its transactions. The formal structure of PE firms can be illustrated as follows.

1 Weather PE firm actually perform better than the market is questionable, and will not be discussed in this thesis. But no studies have so far proven that PE firms outperform public traded companies, when looking at a risk-adjusted return (Vinten and Thomsen 2008a).

Figure 2 - Structure of Private Equity Company

Source: Andersen and Frigast 2008 p. 12 and own construction

A PE firm consists of one or more PE funds. Each investor invests in a fund, and not in the PE firm itself. Each fund is usually formed as a limited partnership, with the management company as the general partner (GP), and the investors as limited partners (LP) (Bennedsen et. al. 2008).

The reason for using a limited partnership is that it is easy to make capital increases and decreases, which is what is done each time the investors (LP) deposits into the fund.

Once investors have been found the PE firms get the investors to commit to the funds with a predetermined level of investment. It should be noted that the investors do not actually transfer the money to the fund until financing is needed. The capital can be “called” with short notice, usually within two weeks, when new investments are found. This makes the system very effective and flexible for the PE firm, and ensures instant access to investors’ capital (Bonnerup et al., 2008). Investors, on the other hand, receive the returns when the fund’s portfolio companies (targets) are exited, and it is therefore a relative long term and illiquid investment for the investors (Andersen & Frigast 2008).

The managing of each fund is done by a management company with extensive knowledge in Private Equity takeovers. The management company finds the potential targets, which should be within the characteristics, such as firm size or industry, agreed upon with investors when they committed to the fund, (Bonnerup et al., 2008). When investment in a portfolio company is completed, the management company is also involved in the overall management of the portfolio company. I order to align the interests of the management company and the investors, the partners of the management company is required to invest in the PE fund they are managing.

Private Equity Company (PE firm)

General Partners Pension funds,

Insurence companies, Private inestors etc.

Debt providers Target companies

(portfolio companies) Investors

Debt

Cost of debt Management Company

Wages

Counselling

Sales price/

target return Management

fee

Equity

Carried Interest Marketing

return Capital

This is supplemented with a carried interest, which is a percentage of the return above a given hurdle rate. The hurdle rate is typically 8 % of the total invested capital, and the carried interest in typically around 20 % (Andersen & Frigast 2008). To keep it simple I will in the remainder of the thesis not distinguish between the Management Company and PE firm but see them as one entity.

2.2 Strategy of PE firms

The cornerstone in the strategy of a PE firm is what Andersen and Frigast (2008) calls “active ownership”. This means that the PE firm does not only provide capital, but actively works together with the management of the acquired firms to increase its value over the holding period by making firm specific changes.. Another vital part of the active ownership strategy is optimization of the capital structure, which for practically all PE firms means a high use of leverage. For that reason a PE investment is specified as a leveraged buyout (LBO). This is primarily because of the possibility of a higher return on equity for investors, combined with the tax deductions in the acquired firm (Christensen and Christensen 2007). Furthermore, high leverage entails high debt obligations, which in turn lead to a need for high earnings to fulfil the debt obligations. Because of that, PE firms target mature companies with high cash flow.

The amount of leverage a PE firm uses on its investments is normally determined by the target firm’s ability to service the debt with its operational cash flow, asset liquidity, management’s skills, etc. (Christensen & Christensen 2007). The ability to generate cash allows the investor, in our case the PE firm, to take on more debt. Because of the extensive use of leverage almost all the cash generated must be used to repay the debt obligations. Baldwin (2001) goes as far as calling the net cash flow in an LBO for “cash flow available for debt repayment”. This entails a rapidly changing capital structure which is one of the main characteristics of the LBO, and the main challenge when valuing a PE target (See chapter 3.4).

For these reasons, PE firms are intensely focused on the cash flow of the business, and investors often do not receive a return of their investment until the exit year (when the target is exited), while there is little or even negative return in the early years. This makes an investment in a PE fund very illiquid and the return profile of PE funds will typically follow a j-curve (Andersen &

Frigast 2008).

Figure 3 - Value creation over time in PE Fund (J-curve)

Source: Andersen and Frigast 2008 p. 13 and own construction

Following Miller and Modigliani propositions, the high leverage is not in itself a direct value creating activity, as capital structure has no effect on the return on assets. The higher return is due to higher financial risk. No studies have so far proven that PE firms outperform public traded companies, when looking at a risk-adjusted return (Vinten and Thomsen 2008a).

When a PE firm invest in a company it is typically with the intent to improve the company over a 2-7 years period (holding period) depending on the target (Andersen and Frigast 2008), after which the value of the company will have increased (if successful). In order to realize the gain, PE firms choose one of three possible exit strategies:

An outright sale to a strategic buyer

A public offering (i.e. sell the company through an IPO)

A recapitalization either by the existing PE firm or by a new one

Often PE firms choose to sell to either a strategic buyer or a financial buyer (Andersen and Frigast). However when market conditions are in favour of a public offering the PE firm exits through an IPO. The downside of an IPO is the restrictions of the lock down period, which forces the seller to hold a fraction of the initial shares over a certain period of time. This forces the PE firm to exit over a longer period of time. In the remainder of the thesis I will not distinguish between the different exit strategies, but simply refer to it as the target is exited.

Life of a PE fund

While the PE firm is an ongoing concern, the PE funds are limited life entities, with a lifespan normally of around 10 years, but often with the possibility to extend it with three yeas extra

Value

Time

(Spliid, 2007, p. 34). In order to explain the actions of a PE fund, Cendrowski et. al. (2008) divides the life of a PE fund into four stages: Organising/Fund-raising (0-1.5 years), Investment (1-4 years), Management (2-7 years) and Harvest (4-10 years)

Figure 4 - Stages in the 'life' of a PE Fund

Source: Cendrowski et. al. 2008 p. 11 and own construction

In the organising/Fund-raising stage, the focus of the fund’s investments is determined and investors are recruited. After the investors are found, the management company begin to scout for potential targets, and when suited targets are found, invest in them. This leads to the management stage, where managing of the acquired firms is commencing, which, as mentioned earlier, is one of the key features of the PE business model. Because the returns on the investments are relatively high, the time value of money is crucial to the funds. The funds will therefore try to realize their investments as soon as feasibly possible, which are done in the Harvest stage.

Harvest

+3 years Organizing &

Fund Raising

Investment

Management

Harvest (Exit)

10 Years

3 Valuation of PE targets – The starting point

Before I analyse the applicability of real option to PE valuation, a starting point is needed in order to see where we are coming from. In this chapter I will go through traditional valuation models and relate them to valuing a LBO in order to determine why these are not suitable for valuing a PE target and consequently how they should be valued. This will be followed by an assessment of how this model incorporated the value of the uncertain future and thereby flexibility.

3.1 Discounted Cash Flow model (DCF)

In this section I will examine the Discounted Cash Flow (DCF) model’s applicability to valuing PE investments. The DCF valuation method is the most widely used valuation method in practice because its applicability is perhaps the most profound within the different valuation methods.

The DCF model takes an enterprise approach, where it focuses on the operating cash flows of the company, with both debt and equity holders as residual claimants.

One of the most critical parts in the DCF model is the discount factor. The Weighted Average Cost of Capital (WACC) formula used for discounting the free cash flow (FCF) in DCF valuation assumes the company has a target capital structure, meaning that it keeps debt levels or debt equity ratios constant. Small short-term fluctuations in this ratio are accepted, as long as the company relatively fast returns to the pre-determined level of debt and equity. In addition to this, the WACC formula has fixed the cost of debt and equity given the capital structure chosen by the company (Brealey, Myers & Allen, 2006, p. 518-520). However in relation to valuing a potential PE target some of the models assumptions are challenged. The capital structure is not fixed due to large debt repayments, and the changes cannot be considered as small fluctuation in spite of the company returning to a normal debt-to-equity ratio after the exit of the PE firm. Because of this the DCF will be very cumbersome to use, as many calculations are needed to adjust for the challenged assumptions.

3.2 Adjusted Present Value (APV)

In this section I will examine the Adjusted Present Value model’s (APV) applicability to valuing PE investments. The APV approach takes a different route to the enterprise value than the DCF model. The big difference between the DCF method and the APV method is their way of handling the effects from financial leverage (Koller et al. 2005). APV in contrast to the Enterprise DCF method does not try to account for the leverage by weighing it in the cost of

capital but tries to value it as a separate entity, by dividing the value of the company into an all equity financed part and the value of the tax shield by having debt.

Source: Brealey, Myers & Allen, 2006, p. 521

The basic concept of dividing the value of a company into an all-equity financed part and a part, which captures the value of financial leverage, is, in principal, suitable for valuing a potential PE target. By doing so we get to see how much the leverage creates in value for the LBO. However the model does not actually come up with a direct answer for the market value of debt and equity, which makes it difficult to value the initial investment of the equity holders. Furthermore the model does not have an intuitive explanation for the development in equity value over the lifetime of the LBO, because the value of an all equity-financed company is an arbitrary size.

The final problem, when valuing a LBO using APV is how it addresses the value of the tax shields. The tax shields are definitely not certain and must be weighted by the expected default probability. In relation to this discounting of tax shield should be done with a diminishing rate, which needs to be estimated each year, because required return by debt holders decreases as the firm gets more unlevered.

3.3 Multiples for Valuation

An alternative to the DCF and APV model is using multiples for valuation (MV). This approach uses the intuitive easy-to-understand proposition that similar companies should have similar value. Weston et al., 2001 calls it a “quick and dirty” way to value companies, and because of that it is a widely used approach to valuation.

The basic idea behind MV is to value a firm by comparing it with equivalent firms or transactions (Koller et al., 2005). A multiple is the ratio of a fundamental (enterprise value or equity value) to the value driver (sales or EBITDA etc.). The valuation is done by multiplying a value driver, such as sales, earnings or cash flow, by a multiple from a selected peer group.

If the valuation of a company is related to a potential merger or acquisition (M&A), multiples based on similar transactions might be a better estimator of value than peer group multiples, because they incorporate market premiums and synergies. By averaging many similar transactions it is possible to give a rough estimate of the expected premium of the particular target.

Adjusted Present

Value = Enterprise Value as if company was

all equity financed + Present Value of Tax Shields

The main drawback when using multiples as a valuation tool is the problem of finding suitable peers. This drawback is enhanced when applied to a PE target valuation. Because of the aggressive use of leverage and changing capital structure, it is even harder to find appropriate peers. One way to solve this is by using transaction multiples. But even though this may give a more precise valuation, it still does not eliminate the difficulty of finding appropriate transactions. Furthermore it is problematic to determine, which multiples captures value in the best possible manner.

When this is mentioned MV is an easy to understand measure, which can give a good indication of the value of an LBO, and can be a good support to other valuation models.

3.4 LBO valuation method

As described above, the three most common valuation methods all have different characteristics which are useful for different scenarios. The one thing they have in common though is that they all have shortcomings when applied to a PE target, mainly because of the LBO’s changing capital structure. A different valuation method is therefore needed. In this section I will give an overview of the model used in practise when valuating PE targets The LBO valuation model (Bonnerup et al. 2007).

The purpose of the LBO valuation model is to identify how much equity the PE firm can justify investing in the target company. It is different from valuation methods like the DCF method, which captures all of the enterprise value in one calculation. In the LBO model four steps is needed to calculate the value of a company (Bonnerup et al 2007).

Figure 5 - LBO Valuation method

Source: Own construction

The structure of the LBO valuation can be seen from figure 4. The valuation is divided in two parts. The period where the target is owned by the PE target (Holding Period), and the period after the expected exit where it is owned by the potential buyer/buyers (Post Exit Period). The reason for this division is the characteristics of target in the two periods. In the holding period the PE firm makes firm specific changes (active ownership) and has a dramatically changing capital structure. In the post Exit periods the is assumed to be in a more steady state, as it is the value to potential buyers which is interesting as the target is exited (For elaboration se chapter 7.2 and 7.3).

The reasoning is that first the optimal level of debt is calculated, and the cash flow available for debt repayments is calculated for the holding period in order to get the debt level at exit. Next the total enterprise value at exit is calculated using traditional valuation methods. This is the value the company will to the owners after the PE firms exits (Post Exit Period). The equity is found as the residual of the remaining debt and the total value. Finally the equity is discounted back using an IRR to get the total value by adding the discounted equity value to the debt level estimated at the beginning. The main reason for this approach is the changing capital structure of the company, which make a full enterprise valuation in one step difficult, and furthermore by using this approach, the highest possible price that the PE firm can justify paying for the company is found (Baldwin 2001a).

Debt₀ EQT₀

Step 1 Level of debt

CF₁

CF₂

CF₃

CF₄

CF₅

Debt₅ EQT₅ Step 4

Equity is discounted back using Internal Rate of Return (IRR) to et total value at t=0

t = 0 t = 5

Step 2 - CF lowers debt levels

EV₅ EV₀

Step 3 Total value of the company is estimated using:

- DCF - Multiples etc.

Tota l Enterprice value

The model is bound by some of the same assumptions as the DCF and Multiples valuation because the Enterprise Value in the exit year is determined using these models. However the assumptions are not challenged as much as they are in the holding period, because it is assumed that the company returns to a normal rather steady capital structure at exit and in the following post exit period. In order to determine the equity value in the entry year the LBO models uses an IRR as discount factor. This reflects the changing required return to equity holders during the years of ownership, as well as a liquidity premium and a carried interest for the PE firm.

The LBO valuation model is thus designed to follow every process in an actual Buyout. It therefore has obvious advantages compared to the traditional valuation methods as it captures the risks and value creation of every process in a LBO. Each step of the valuation will be examined in detail in chapter 7.2

3.5 Inadequacies of LBO model

Even though the LBO model is the superior valuation tool for PE targets, it is still a static valuation tool which does not incorporate the value of flexibility. The main problem with the LBO model, as well as all other static valuation models, is that it assumes that the estimated scenario regarding future cash flows will not be revised at a later point in time. Hereby the model implies that a one-off decision is made at t=0 on the basis of the strategy and expected investment plan under the assumption that the decision makers do not have any possibility of future actions.

Because the future is uncertain managers often react in accordance with how the future develops, this assumption is in contrast to reality. For PE firms this could be exiting earlier or later than planned. The flexibility associated with being able to change strategy in the future is not incorporated in the LBO model, and simple sensitivity analysis using different exit points is inadequate for valuating this flexibility. This means that the LBO value only partially captures the total value of the company, and that another valuation tool is needed to assist when valuing PE targets. The focus in the next chapters will be on valuing the flexibility available to PE firms when planning their exit.

4 Real Option Theory

In the previous chapter I stated that the model used by many PE firms (LBO model) has shortcomings when assessing the flexibility of exiting when conditions are most favourable. It is widely recognized in financial literature that Real Option Theory can be useful for analyzing and valuing flexibility. In order to analyze Real Options Theory’s applicability to PE firm’s exit planning, this chapter will give a general description of real option theory and the underlying assumptions.

An option is a concept that has its background in financial theories where it is defined as a right, but not an obligation, to take action at a given time or time period at a predetermined price or price basis. Financial options relate to marketable priced assets, such as stocks, bonds, currencies or other similar assets, with two basic options as the foundation of option theory, call options and put options. A Call Option is the right but not the obligation to buy the underlying asset, while the Put Option is the right but not the obligation to sell the underlying asset (Allan et al., 2006).

Based on the mindset of financial options, the concept of real options was first introduced by Stewart C. Myers in 1977, where he applied it to capital budgeting and allocation of R&D resources. Noting that some investment opportunities give the right, but not the obligation, to use a specific operating action in the future (Leiblein, 2003).

Since then real option theory has been thoroughly discussed in both financial and management literature, with numerous different definitions suggested. Andersen (2000) describes real options as: “the company’s opportunity to use tangible and intangible assets in completely new or alternative ways in the future without having the obligation to do so”, and can be related to “all resource-committing actions in an organization”, and thereby influence the company’s flexibility to react on new opportunities or threats.

4.1 Classic Real Options

Options can be distinguished along different dimensions such as ownership, the source of value, the complexity, and the degree to which options is available. But the most common typology, and the one I will use here, refers to the type of managerial action available (Mun 2006).

Copeland and Antikarov (2001), Trigeorgis (1996), and Mun (2006) have all divided these actions into explicitly defined real options. In the following I will describe the most common Real options:

Option to defer

As the name suggests this option gives the option to defer an investment. Examples of this could be oil companies with license to drill for oil or recover other natural resources or development of real estate. The option is an American call option on the value of the project.

Option to contract/expand

This is an option to either decrease the investment without abandoning it completely or expand the current asset in place, if the asset develops either positive or negative. These are either put or call options on part of a project or investment.

Option to abandon

This is the option to stop a project or shut down a company. Typically this option is used by capital intensive companies, where an option to stop operations and realize some kind of salvage value could have a significant value.

Switching option

Switching option are the right to close down an open operation by paying a fixed shutdown cost and the right to open it again for another fixed cost. This gives a portfolio of puts and calls. An example could be a temporary shutdown of mines due to deceasing mineral prices.

Compound options

These types of options are compounded call options on parts of the combined project, sometimes with an abandoning option at the end. Examples could be R&D projects within medical industry, where product development typically is divided into stages, where each stage is dependent on the previous stages. This option is in some contexts also known as a growth option.

4.2 Valuing Real options

Since real options originates from financial options, the most apparent choice for valuing Real Options must be from existing options pricing models. This chapter will establish that there is a coherence between financial option valuation models and real assets.

Even though Real option theory is based on the concept of financial options, they distinguish themselves in different ways. First of all, financial options are contractually based on financial assets which are commonly traded and priced in markets. Real options are not contractual based, but simply provides the holder with the opportunity to take an action, such as sell an asset or invest in a project. Furthermore, real options refer to the use of real assets which are not always

priced in a market nor have alternate value. The values of such assets are therefore subjective and depended on the utility of its holder and the cash flow it generates to the holder.

Consequently, the underlying variables that determine real option values are less clearly defined and have to be approximated using reasonable assumptions. Therefore, in order to justify using financial models for valuing real options, it is first necessary to demonstrate coherence between the value drivers of financial options and real options. By doing so the characteristics of the real option can be mapped onto the structure of a financial option, and thereby use the option pricing models. Table 6 link the six underlying variables of an option to characteristics of a real option and illustrate how an increase in the variables affects the value of the option. This is done using an option on a common stock as example. Riskiness Timeframe underlying opportunity

Figure 6 – Mapping Option Inputs to Real Asset Characteristics

Source: Luehrman (1998) and Copeland & Antikarov (2001) p. 6

Exercise Price (X): To exploit a business opportunity (exercise option) often costs money. The money spent on doing this can be compared to the price of the stock. This corresponds to the option’s exercise price.

Stock Price (S): The present value of the underlying real asset corresponds to the price of the stock in a traditional financial option on stocks, and is in real option denoted as the options Asset Price.

Risk free rate of return r_f Time value of money

Stock Price S PV underlying asset

Dividends on stock b Dividends on asset

Exercise Price X Cost of exercising option

Time To expiration t Timeframe of opportinity

Stock Volatility σσσσ Riskiness of asset

Variable

Call Option Real option Influence

Time to Expiration (T): The lengths of time the company has before losing the opportunity correspond to the options time to expiration.

Standard deviation (σ): The uncertainty about the future value of underlying asset’s return i.e.

the riskiness of the investment, is equivalent to the standard deviation of the options return.

Risk-free rate of return (rf): Finally, the time value of money for the underlying asset correspond to the risk-free rate of return.

Besides these five general variables (Copeland and Antikarov, 2001) introduces a sixth variable, dividends (b) that may be paid out by the underlying asset or cash flow lost to competitors i.e.

the cash inflows or outflows over the life of the option.

The previous section has made it feasible that real options can be valued using existing option pricing models, which will be examined in the next chapter. I will go more into detail on each parameter when applying real option theory to PE firms exit possibilities in chapter 6.

5 Option Pricing Models

Before I go into the specifics of the PE options, it is necessary to present the different option valuation methods and determine the most appropriate one for valuing a PE option. In this section I will therefore present the two most common option pricing models and compare them in terms of practical applicability to the valuation of a PE option, resulting in a choice of valuation method.

For the purpose of valuing options the two most taught and common valuation methods are The Binomial Model and The Black & Scholes model (Allen et al., 2006). Both models are built on the same underlying principle of the market-replicating portfolio. The main assumptions behind the market-replicating portfolio are that there are no arbitrage opportunities and that there exist a number of traded assets in the market that can be obtained in order to replicate the existing asset’s payout profile. The replicating portfolio must have the same price as the option due to the Law of One Price, which states that two assets having the same future payoffs must have the same price; otherwise, arbitrage opportunities would exist.

The key assumption that differentiates the two methods is the price development of the underlying asset. Binomial model assumes a discrete development of price and can therefore be solved using relative simple algebra, while The Black & Scholes assumes a continuous development which calls for more technical stochastic calculus mathematics (Mun, 2002).

5.1 Binomial Model

Cos, Ross and Rubinstein (1979) was the first to develop a model based on the discrete time approach, where the assumption is that price develops gradually and only at specific points in time. They use discrete mathematics to develop a binomial lattice approach to option pricing.

Lattices are, broadly speaking, more versatile than stochastic calculus when pricing options, and can be used to solve almost all option problems² (Copeland and Antikarov, 2001). No matter what type of real option problem you are trying to solve using the binomial lattice approach, the solution can be found in one of two ways. The market-replicating portfolio, as mentioned above, or the use of risk-neutral probabilities. The results obtained will be identical for both methods.

In this thesis I will use risk-neutral probabilities, as the underlying mathematics are easier to apply. Furthermore, some financial perfectionists will argue that because a market-replicating

2 The reason for this is that the present value of real assets follow a geometric Brownian process as modeled by binomial lattices.

portfolio is based on highly liquid assets, real assets and firm specific projects do not fulfil the assumptions behind the market-replicating portfolio.

5.1.1 Risk-neutral Probabilities

The reasoning behind the risk-neutral probabilities approach is basically simple. Instead of discounting risky cash flows with a risk adjusted discount rate similar to the DCF models, one can easily risk-adjust the probabilities of specific cash flows occurring at specific times.

Consequently, the cash flows are transformed into a certainty equivalent which can be discounted at the risk free rate (Mun, 2002, p. 143-146).

The calculation of the risk-free probability is done using: Time to Expiration (T), Standard deviation (σ), Risk-free rate of return (rf), and Dividends (b). Using the variables the up and down factors are calculated using:

=

=

=

Source: Mun, 2002, p. 144

Where (δt) is the time-steps = . Time-steps are the number of periods that the options time to expiration (T) is divided into. The risk-neutral probability (p) is then calculated as:

= −

−

Source: Mun, 2002, p. 144

Note that these equations assume a continuous development of prices and dividends (b) are therefore also continuous dividend in percentage (Mun, 2002, p 144).

5.1.2 Setting up the binomial lattices

Binomial lattices are used under the assumption that the time intervals are of equal length and that the price in following period can only have two outcomes. The process can be either multiplicative or additive. The main difference of the two is that when the number of periods becomes sufficiently large the multiplicative method tends to follow a log-normal distribution and the additive tends to follow a normal distribution (Copeland and Antikarov, 2001).

In any binomial lattice a minimum of two lattices are needed. One with the price development of the underlying asset (event lattice) and one with the development of the option value (option lattice). A third lattice is often made in order to establish what actions is preferred in each point in time i.e. exercise the option or not. This has no effect on calculating the value of the option, but is used as information on if and when the option should be exercised.

Step 1: Evolution of the underlying asset

The u and d factors described above are used to make the event lattice. The process is multiplicative which entails that the value of the underlying asset at each interval (t_n) is multiplied with the u and d factors, starting with S₀ at t₀ and continuing to t₁, t₂ etc. (from left to right in the lattice) (Copeland and Antikarov, 2001). Figure 7 shows example of underlying asset lattice using the multiplicative process.

Figure 7 – Underlying asset lattice

Source: Own construction

The example in figure 7 is limited to three periods, but the lattice can be extended to include as many periods as required which likewise increases the accuracy of the outcome. Notice that the lattice is recombining meaning that the branches come back to the same point. This simplifies then calculation greatly and non recombining lattices can easily become very chaotic.

Step 2: Option valuation lattice

The second step is to calculate the option value lattice using the evolution of the underlying asset. The procedure for valuing an option using binomial lattice is called backward induction (Mun 2002). This implies that the value of holding the option is derived backward in the lattice (from right to left), starting with the terminal nodes (tn) and then the remaining nodes (tn-1 to t0).

Figure 8 shows an example of an option value lattice.

S₀

u ∙S₀ d∙S₀

u²∙S₀ ud∙S₀ d²∙S₀

u³∙S0

u²d ∙S₀ d²u∙S₀

d³∙S₀

t₁ t₂ t₃

t₀

Figure 8 – Option value lattice

The terminal nodes are calculated through the maximization between exercising the option and letting the option expire, based on the number from the corresponding values in the event lattice.

That is, if the cost of exercising the option exceeds the benefits it is better to let the option expire. The opposite goes for a put option, as this is the right to sell the underlying asset. For a call option the general equation in the terminal node is (Mun, 2002):

=

− !, 0$

Source: Mun, 2002, p. 166

The value at the intermediate nodes is calculated using the risk-neutral probabilities and discounting them with the risk-free interest rate. The general equation for an American option when assuming continuous time, is then the maximum of the two previous values discounted back one period and the difference between asset value and exercise price.

= max () ∙

+ 1 − ∙

/ ∙

, S

− X3

Source: Mun, 2002, p. 166

Using backward induction all the way back to the starting period t0 gives the value of the real option for the firm today.

Step 3: Action lattice

As mentioned above a third lattice is sometimes made in order to determine if and when a option should be exercised. At the final node the decision is only based upon the value of the underlying asset compared to the exercise price. If the value of the underlying asset is higher than the exercise price, the option should be exercised (if call option). In the other nodes the action does not just depend on weather the value of the underlying asset is higher than the exercise price. If the present value of the option value in the next period is higher than the difference between the

C_o= max(p∙C_u+(1-p)∙C_d; S₀-X)∙e^-rf∙δt

C_u= max(p∙Cuu+(1-p)∙Cud ; u∙S0-X)∙e^-rf∙δt Cd= max(p∙Cud+(1-p)∙Cdd ; d∙S0-X)∙e^-rf∙δt

C_uu= max(u²∙S₀-X ; 0)

C_ud= max(ud∙S₀-X ; 0) C_dd = max(d²∙S₀-X ; 0)

t₁ t₂

t0

value of the underlying asset and the exercise price, the option should not be exercised as it has greater value to keep the option for another period.

Notice that the higher the number of time-steps in the lattices, the more accurate the result becomes. At the most extreme, when the number of time-steps approaches infinity, that is the time between steps approaches zero, the discrete binomial lattice approaches that of a continuous model (Closed for solution), such as the Black & Scholes model (Min, 2002, p. 158). In the next section I will take a closer look at the Black & Scholes model.

5.2 The Black & Scholes model

With their article from 1973, Fisher Black, Myron Scholes, and Robert Merton were the first to give a closed form solution for the equilibrium price for a European call option, the Black &

Scholes Model (B&S model). It has since been the basis for numerous studies and papers about the prizing of options and empirical testing hereof. In essence, the model is a special case of the binomial model where the underlying asset is assumed to follow a continuous stochastic process instead of a discrete. Otherwise, it is based on the same underlying assumptions of no arbitrage and market replicating portfolio and that the movement of the underlying asset follows a lognormal distribution (multiplicative binomial model) (Copeland & Antikarov, 2001).

The Black & Scholes model is a so called closed form solution, meaning that a value can be found with an equation using a set of inputs. The inputs in the B&S model are the same as the binomial model, with dividends as the one exception. The value of a call option (C) is calculated as:

=

5

− !

5

Source: Copeland & Antikarov, 2001, p. 106

where N(d1) and N(d2) is the cumulative normal probability of unit normal variable d1 and d2

respectively. d1 and d2 are calculated as:

=

;

=

− =√

Source: Copeland & Antikarov, 2001, p. 107

Other than the assumptions also applying to the binomial model mentioned above, the B&S model has several other restrictive assumptions embedded (Copeland & Antikarov, 2001 and Mun, 2002):

• The option can only be exercised at maturity – it is a European option

• There is only one source of uncertainty

• It can only be used on a single underlying risky asset; ruling out compound options

• No dividends on the underlying asset

• The current market price and stochastic process of the underlying asset is known (observable)

• The variance of the underlying asset is constant over time

• The exercise price is known and constant over time

• No transaction costs

It has to be noted that variants of the B&S model have been made, which relaxes some of these assumptions. Examples are a B&S model for American options and options with dividends (Trigeorgis, 1996). But B&S models are based on calculus of stochastic differential equation, also called Itô calculus, which is highly complex. So unless one can find a modified B&S model that fits one own specific situation, the process of deriving a B&S model that does is very cumbersome and complex.

5.3 Model choice

As stated in the previous sections the Binomial model is more versatile than the B&S model and is therefore more applicable in practice. As the B&S model is a closed form solution and was developed for valuing financial option, many of the underlying assumptions is bound to be violated when dealing with real options. Real options are more specific than financial options and need individual specifications. This is one of the binomial models most distinguished advantages and is therefore easier done using the binomial model and. And as I will highlight later, the options available to PE firms are very specific with distinctive modifications to a general put or call option, and correcting the Black & Scholes model to them would require a very complicated use of algebra, if it is even possible. Moreover, the binomial model can be a close approximation of the Black & Scholes model and the advantages of using continuous time are therefore not decisive. The Binomial model is more intuitive and easier to explain to for example investors, decision makers and potential buyers than a closed form B&S model. So all in all, the binomial model is most appropriate to apply in practice and the model of choice in the further analysis.

6 PE Exit options and the general framework

Now that the appropriate framework has been established, the options available to PE firms in relation to their exit strategy can be determined

6.1 PE firms exit option (PE option)

Basically the option available to PE firms when planning their exit strategy is simple. Exit now or later, meaning that the PE firm can choose to keep the portfolio company until conditions for exit are more favourable.

Similar to financial options, real options can either be exercised at a specific point in time (European option) or merely at any point before expiration (American option). In general there are no restrictions on when a PE firm can exit their investments as they can exit as soon as conditions are favourable of an exit. The PE option can therefore be seen as an American option.

Even though the option to defer exit is the option to divest/sell and not invest, which is normally the characteristics of a put option, the option can still be seen as a call option. The reason for that is that an increase in the value of the underlying asset (Target Company) increases the value of the option. This is the characteristic of a call option, while a put option benefits from a fall in value of the underlying asset. Hence it is not the action (buy vs. sale) that determines the definition but the value creation in relation to the underlying asset. The PE option can therefore, as a starting point, be seen as an American call option with the PE target as the underlying asset.

As described in chapter 3.4, the valuation of a PE target is divided in two parts, the holding period and post exit period. In the holding period the characteristics of the PE target change dramatically because of the PE firm’s active ownership strategy and the rapidly changing capital structure, hence the LBO valuation method. After exit the target is assumed to take on a more steady state with more ‘traditional’ characteristics (Chapter 3.4). Because of these two relatively different stages of a PE targets ‘life’ it is also appropriate to divide the real option available to PE firms into two different options, as the options will also have different characteristics, resulting in, among other things but most important, different volatilities (For elaboration see chap. 7.4). Calculating the value of an option with changing volatility entails changing u and d factors, which, in turn, results in the binomial lattice, no longer beingrecombining. This complicates the valuation a lot, and even a small number of periods results in very cumbersome calculations and chaotic lattices. For example a binomial option valuation using 20 periods would have 21 different possible values at expiration using constant volatility. The same option, but with two volatilities changing in period 10 would end up having 111 different possible values

at expiration instead of 21. This of cause only gets more extreme as the number of periods increases, and it is, in my opinion, not a feasible method to value one option with different volatilities when using binomial lattices as valuation method.

The two options are illustrated in figure 9. The first option is the option to exit before the estimated exit i.e. during the holding period (PE holding option) with maturity at the expected exit. In this option it is the flexibility of being able to exit before the expected exit which is valued. The second is postponing exit to some point after the expected exit (PE post exit option), and is hence the value of the flexibility to postpone exit. In the following I will name these options after their position in the LBO valuation model; the PE Holding option (Holding option) and the PE Post Exit option (Post Exit option) respectively (see figure 8 for illustration).

It has to be noted that ‘now’ in the PE Post Exit option refers to the point in time where exit is expected to be and will have to be discounted back to present (see figure 9). This division into two options also entail that the Post Exit option is only available if the Holding option is not executed. Otherwise it is assumed to be zero.

CFEQTT

Debt0 CF

CF

CF

DebtT

t = 0 Expected Exit

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

PEHolding Option PEPost Exit Option

C

C

C

C

C

C

C

C

C

C

Source: Own construction