Optimal Timing for an IPO with Market Sentiment'

Optimal Timing for an IPO with Market Sentiment Author: Jos´e Diogo Oliveira de Castro Ferreira Master in Finance Dissertation Supervisor: Prof. Paulo Jorge Marques de Oliveira Ribeiro Pereira September 2014 Biographical Note Jos´e Diogo Oliveira Castro Ferreira was born in Coimbra in 1987. Raised in S˜ao Jo˜ao da Madeira, moved to Porto in 2005 to start his Bachelor Degree in Economics, which was finished in 2009 at Faculdade de Economia da Universidade do Porto. After some professional experiences that ranged between auditing, consulting and sales promoter, decided to return to his school to pursue his dream and study Financial Markets more closely. The reading of some books, such as Technical Analysis of Stock Trends from Edwards, Magee and Bassetti (2007) or Futuros e Outros Derivados from Domingos Ferreira (2010), inspired him to give this step forward in order to define a clear path for his career. Since July of 2014 he is working in Lisbon at BNP Paribas Securities Services, dealing with the settlement of trades. i Acknowledgments First of all, I would like to thank Professor Paulo Pereira for his excelent work, dedication and motivation during this last year. It was an honour for me to work with you and to spend some hours in front of a board thinking how would managers react, what they would do and what are the payoffs for each situation. The way that this work evolved was a challenge for both of us and, fortunately, you were there to help guiding me during this path. Secondly, I would like to thank my parents. They helped me in the last few years and for me is an honour to show them this work. It wasn’t always a simple path, but patience paid off. I have to acknowledge the help of all of my friends, specially Alexandra Almeida who supported and listened to me when this Dissertation was in a less solid ground. Finally, to Faculdade de Economia da Universidade do Porto, an honourable school, filled with history and knowledge. The staff from library deserves a special word for being always so kind and gentile. For my Professors during both degrees, I have to say that you helped and inspired me establishing a path in my life. There is only one more name I will quote because of the important role he had during this Master. To Professor Oliveira Marques, who transmitted us his huge knowledge in a relaxed, but always demanding way. I will always remember his quote in my first Master class, in Theoretical Foundations of Finance: ”If any of you ends the semester without doubts, I’ve failed in my mission”. It was an honour to meet you Professor. ii Contents Biographical Note i Acknowledgments ii Abstract vii Sum´ario viii 1 Introduction 1 2 Literature Review 4 3 The Market Sentiment and the Optimal Timing for an IPO 12 3.1 BenchmarkModel......................... 12 3.2 TheModel............................. 14 3.3 Solution of the Model . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Comparative Statics and Numerical Example . . . . . . . . . . 18 3.4.1 Comparative Statics . . . . . . . . . . . . . . . . . . . 18 3.4.2 Numerical Example . . . . . . . . . . . . . . . . . . . . 19 3.5 Studying the Market Sentiment . . . . . . . . . . . . . . . . . 20 3.6 Conclusion of the chapter . . . . . . . . . . . . . . . . . . . . 21 4 IPOs, Market Sentiment and Investment Opportunity 22 4.1 TheSetting ............................ 22 4.2 TheModel............................. 23 4.3 Solution of the Model . . . . . . . . . . . . . . . . . . . . . . . 28 iii 4.4 Numerical Example and Sensitivity Analysis . . . . . . . . . . 29 4.5 Studying the market sentiment . . . . . . . . . . . . . . . . . 37 4.6 Conclusion of the chapter . . . . . . . . . . . . . . . . . . . . 39 5 Conclusion 40 5.1 Contribution to Financial Literature . . . . . . . . . . . . . . 40 5.2 Further Work and Limitations of our Model . . . . . . . . . . 41 Bibliography 43 iv List of Figures 1.1 Variation in the number monthly of IPOs since January 2005 . 2 4.1 Representation of equation (4.5) from Adkins and Paxson (2011). Source: Adkins and Paxson (2011) . . . . . . . . . . . . . . . 26 4.2 Boundary between non-IPO and IPO regions . . . . . . . . . . 31 4.3 Boundary between non-IPO and IPO regions for different θV1’s. The remaining inputs are according to Table 4.1 . . . . . . . . 32 4.4 Boundary between non-IPO and IPO regions for different θV2’s. The remaining inputs are according to Table 4.1 . . . . . . . . 33 4.5 Boundary between non-IPO and IPO regions for different ρ’s. The remaining inputs are according to Table 4.1 . . . . . . . . 33 4.6 Boundary between non-IPO and IPO regions for different σV1’s. The remaining inputs are according to Table 4.1 . . . . . . . . 34 4.7 Boundary between non-IPO and IPO regions for different σV2’s. The remaining inputs are according to Table 4.1 . . . . . . . . 35 4.8 Boundary between non-IPO and IPO regions for different φ’s. The remaining inputs are according to Table 4.1 . . . . . . . . 36 4.9 Boundary between non-IPO and IPO regions for different θV2’s 38 v List of Tables 3.1 Data for the application of the Model . . . . . . . . . . . . . . 19 4.1 Data for the application of the Model . . . . . . . . . . . . . . 29 4.2 Results from variations in V1................... 30 4.3 Results from variations in θV1. The remaining inputs are accordingtoTable4.1........................ 32 4.4 Results from variations in ρ. The remaining inputs are accordingtoTable4.1........................ 34 4.5 Results from variations in σV1. The remaining inputs are accordingtoTable4.1........................ 35 4.6 Results from variations in σV2. The remaining inputs are accordingtoTable4.1........................ 36 4.7 Results from variations in φ. The remaining inputs are accordingtoTable4.1........................ 37 vi Abstract Performing an IPO can be one of the most enthusiastic moments in the life of a company. However, during the last decades a lot of criticism has arisen due to some irrationality that is associated with this sector of Financial Markets. In this work we propose two models that are based on the work of Bustamante (2012). The first is a simpler version of reality in which the owner tries to sell part of his company. In this case it is assumed that the company is wellestablished and without any growth opportunity. The second one includes the idea of an IPO to expand the companies activities and, therefore, its cash flows. As a result, we conclude that the market sentiment plays a very interesting role in the definition of the moment of the IPO. This role is diminished when we are considering the second case. vii Sum´ario Realizar uma OPV pode ser um dos momentos mais entuasmantes na vida de uma empresa. No entanto, nas ´ultimas d´ecadas tˆem existido muitas cr´ıticas relacionadas com a irracionalidade associada a este setor dos Mercados Financeiros. Neste trabalho propomos dois modelos que tˆem por base o trabalho de Bustamante (2012). O primeiro ´e uma vers˜ao simplista da realidade em que o dono da empresa tenta vender parte da mesma, estando esta bem estabelecida e n˜ao tendo oportunidades de crescimento. O segundo modelo inclui a ideia de a OPV ser feita para expandir as atividades da empresa e, assim, os seus cash flows. Como resultado, conclu´ımos que o sentimento do mercado tem um papel bastante interessante na defini¸c˜ao do momento da OPV. Este papel ´e diminu´ıdo quando consideramos o segundo caso. viii distraction of directors from their main activities to concentrate in the process. According to these authors, this may lead to an increase in operational costs or to the loss of some investment opportunities. In another article, Dalziel et al. (2011) explore the heterogeneity among principals. This heterogeneity leads to a suboptimal performance of the firm, where one of the shareholders may redirect governance devices according to its own interests. Usually it is also referred that companies perform IPOs in order to finance new investments or to deleverage the company after the execution of any expansion project. Pagano et al. (1998) observe that the investment of companies after the IPO actually decrease, suggesting that companies use this process to rebalance their balance sheet, decreasing the weight of debt and, consequently, the costs of debt financing. A contrasting finding was made by Albornoz and Pope (2004) and Kim and Weisbach (2008), concluding that IPOs are actually motivated by large investments that occur after the process. In the survey of Brau and Fawcett (2006), the answers of the CFOs allowed to conclude that the timing of the IPO is strongly influenced by the “need for capital to support growth”. In a study of privately-held companies, Boehmer and Ljunqvist (2004) and Bharath and Dittmar (2006) supported the idea that investment opportunities increase the probability of an IPO. The last motive massively studied is the acquisition motive. The IPO allows the company to issue stock and later in their lifetime, they may aim to buy other companies. Instead of offering money to the shareholders of the target company, they may offer shares. Thus, the IPO gives the chance to create a new coin of exchange for further acquisitions. Theoretically, in periods of high valuation of the stocks, the company could use them to finance these acquisitions, reducing the need for capital in these operations. Albornoz and Pope (2004) concluded that companies that were acquired after the IPO had as their basic incentive the promotion of that takeover. On the contrary, Brau and Fawcett (2006) rejected the idea that companies go public to be acquired in the future, showing that in the majority of the cases, IPO companies were acquirers in the future, concluding that “IPOs facilitate 7 acquisition activity”. Also, they found no statistical significant difference between IPO firms and private firms regarding their positioning to become targets of takeovers. Finally, they concluded that IPOs were used to allow the creation of a new way of payment (using stocks as currency), reinforcing the answers given by the CFOs. The idea of IPO as a way to facilitate acquisition activity and to create “currency” for those acquisitions is also supported by Celikyurt et al. (2010) which study the US IPOs from January 1994 until December 2004, with proceeds higher than $100 million. As stated in the beginning of this chapter, an IPO involves certain economic costs. A firm has to comply with several standards, causing it to spend money and time to prove its compliance. According to the PwC Roadmap for an IPO, before the IPO the company incurs in expenses related to legal and accounting advisors, the filing fee, the exchange listing fee and underwriting fees. These are around 7% of the total proceeds from the IPO in US, according to a study by Abrahamson et al. (2011). Although, for European IPOs, underwriting fees are consistently lower than those paid in US. Draho (2000) simply divides these costs as direct costs, including filing fees, legal expenses and administrative costs and indirect costs, which are the underwriting fees. Dalziel et al. (2010) shed some light over costs sometimes omitted in literature, such as the board monitoring and the distraction of directors from their main activities to concentrate in the process. This may lead to an increase in operational costs or to the loss of some investment opportunities. From the literature referred above, we can understand that an IPO is an option that the owner of the company has, allowing us to model the optimal timing of an IPO as a Real Option. This field of study in finance allows to model several business and management decisions the same way financial options are treated. The first to contribute to this field of study was Myers (1977) that, building on the work of Black and Scholes (1973), identified the importance of distinguishing between assets in place and opportunities to grow, which value is computed by the use of Real Options. Soon, this 8 new field was adapted to many applications, most of them concentrated in the valuation of investment opportunities. This kind of approach allows to overcome the main limitations of the Net Present Value (NPV) approach. One of the main works in this field is the one Dixit and Pindyck (1994).1 Despite the huge amount of work regarding Real Options, such as McDonald and Siegel (1986), Luerhman (1998) and Bowman and Moskowitz (2001), there are not many authors that aimed to study IPOs with Real Options. One of the first models that times IPOs was created by Zingales (1995). The author looks at the IPO as a way of transferring control in the company. Starting with a separation between cash flow and control rights, Zingales suggests that the owner must sell the former first, retaining the control of the company. After that, the owner must sell the rest of the company in a direct negotiation. As the author assumes, this model is suitable for subsidiaries. In a different approach, Draho (2000) considers the dynamics of going public using relative valuation techniques. This way, the author values the waiting option and considers its exercise as a cost of the IPO. In this model, private companies are valued in accordance to market indexes. The author conclusions help to explain the hot markets subject, being these a consequence of the optimal exercise of waiting options. Using a binomial model, Benninga et al. (2005) model the decision to go public considering that at the beginning of each period, the owner of the company can take the company public or keep it private (or turn it into a privately held company or not, in the case of being public in the previous period). If the company is private, the owner will receive the value of its cash flows and the private benefits of control. If it is public, its shareholders will receive the cash flows, besides the gains of diversification. When the cash flows are sufficiently high, the gains from diversification outweigh the private benefits of control and the company goes public. Casassus and Villalon (2010) propose a framework where the IPO company (or group of companies) may have an impact in the market condi1If you’re interested in this field of study and want to know more, see also Trigeorgis, Lenos (1996), Real Options – Managerial Flexibility and Strategy in Resource Allocation, The MIT Press or Copeland, Tom and Antikarov, Vladimir (2003), Real Options: A Practitioner’s Guide, New York, Cengage Learning 9 tion, being this impact known by the entrepreneur before the decision. With a general-equilibrium model and studying only the diversification motive to perform an IPO, the author concludes that bigger companies will perform the IPO first, because of greater gains from diversification. Bustamante (2012) uses signaling game theory to model the time of IPOs. It is assumed that companies time their decision in order to provide private information to outsiders. This way, Bustamante demonstrates that in cold markets, the best companies start the IPO process earlier, in order to signal their quality. On the contrary, in hot markets, all companies go public at the same time. We will build our model on top of the basic model of Bustamante. We change it in several ways, in an effort to make it more realistic. Bustamante’s model is a signaling one, in which asymmetry appears in the difference between good and bad companies. However, her basic model considers perfect information. Also, it is considered that the company performs the IPO to fund the expansion of its current business. We relax the inexistence of asymmetric information, considering that there is a variable reflecting the market sentiment. This variable reflects the premium investors are willing to pay to acquire the company, reflecting the lower amount of liquidity that the owner of the company obtains, when compared to a sale of the totality of the company. We consider likewise that the company performs the IPO to allow the owner to exit from its initial investment. This assumption is only considered in our first model which aims to construct a basic model for the next analysis. Later on in our work we will introduce another approach, differentiated from the one of Bustamante. We consider that an investment will be taken after the IPO but, unlike Bustamante, in our case the investment will allow the company to enter a new segment in the market. Another aspect that is lacking in the basic model of Bustamante is the costs of the IPO. As we have seen before, these can be divided between direct and indirect costs. We consider both of them in our analysis. 10 Notice that we have constructed over the basic model of Bustamante. In fact, the author corrects some of the aspects referred above, such as the absence of costs in the operations and the inexistence of asymmetries of information. However, the author conducts her work to construct a signaling model, having a very different objective, when compared to our analysis that ignores differences in companies and focuses on the market sentiment and its impact in their valuation. In the next section we will design our first and basic model, considering that the company has no opportunities to grow and only seeks the listing to allow its owners to exit. We will show that the company will only undertake the IPO if the market is overvalued. Further in our work, we will improve the basic model, with the objective of incorporating the investment motive to perform the IPO. 11 Chapter 3 The Market Sentiment and the Optimal Timing for an IPO 3.1 Benchmark Model The starting point of our work was the basic model developed by Bustamante (2012). In the first section of this article, the author considers the optimal timing for an IPO with perfect information. This is the model that we use as the basis of our work. The company makes the IPO to finance a project which allows to expand the current cash flows, which is implemented simultaneously with the IPO. Despite the fact that the author develops in further sections of her article a model that considers asymmetric information, mainly considering the difference between good and bad companies, we believe that there are some critics that must be referred to this model. The first one is the concept of information asymmetry in the model. This model is a signaling model aiming to time the IPO decision of different companies. This difference between companies is present a factor that measures the growth capacity of a firm, with that factor being bigger for good companies than for bad companies. We introduce a different idea, consistent with Pastor and Veronesi (2003) where companies go public due to changes in the variations observed in the 12 market. Our factor of market sentiment, θ, can be seen as a premium that investors are willing to pay to have part of that company. This implies that all companies, independently of their type, may have incentives to go public when the market is overvalued. The other aspect that we believe to be important is the inclusion of the costs of the IPO. In the simplest model, Bustamante (2012) does not consider these costs. These costs can either be fixed or variable. We have first designed a model in which a well established company, without any growth opportunity, aims to perform an IPO. Thus, the owner (or perfectly aligned owners) performs this IPO in order to exit from the initial investment, consistent with the literature presented above (R¨oell (1996), Rydqvist and H¨ogholm (1995), Pagano et al. (1998) and Albornoz and Pope (2004)). This way, we do not condition our model to the case of companies that have an investment opportunity. In a first model, we consider companies aiming to explore the market overvaluation, considering that the owners will behave in a opportunistic way (Ritter (1991), Lee et al. (1991), Lerner (1994) and Ibbotson and Ritter (1995)). This rationality of the owner is based on the idea that the owner does not have any financial restriction. This way, he won’t have any urge to turn the company publicly traded because he has no need to exchange part of his stake for money. If there were any restrictions, the owner could have the temptation to sell, even if it wasn’t for an amount that compensated the loss of that stake plus the IPO costs. The inclusion of the investment opportunity will be conceived in the next chapter. Finally, it is important to notice that we have included a variable for the market sentiment. The reasoning behind this variable is that the owner knows the true value of the company and knows when the market is overvaluing it or not. However, this valuation bias on the market side is not necessarily a sign of market inefficiency. The market can overvalue the company because it sees a possibility of expanding it if the company turns to be publicly listed. 13 3.2 The Model We will use the Contingent Claims Approach, as defined by Dixit and Pyndick (1994). The present value of future cash flows, Vt, follows a Geometric Brownian Motion (gBm) process, represented by: dVt=µVtdt +σVtdz (3.1) where dz is the increment of a Wiener process, µis the risk-neutral instantaneous conditional expected relative change in V (or drift) and σis the instantaneous conditional standard deviation. Note that µ=r−δ, being rthe risk-free rate and δthe opportunity cost from deferring the process. Also, it is important to state that V0>0. Virtually, every private company has the option to go public. This option, as any financial option, has a cost associated with it. According to financial literature, according to the literature presented above, can be divided in two types. First, a fixed amount, that we denote by C > 0, that covers all the expenses such as auditing, monitoring and legal fees, between others. Second, a variable amount, hereafter λ > 0, which is the amount paid to the underwriters. Also, the owner will sell a fraction φ∈(0,1] of its stake in the company. We consider that this value is exogenously chosen (similar to the basic model of Bustamante (2012)). To sell this stake, the owner will consider market conditions, trying to exploit any mispricing. This is coherent with the assumption that there are no financial constraints. Consequently, the owner will only sell if the market is overvalued, paying a higher premium, captured by θ. We assume that this factor already includes the IPO premium reported by Brau et al. (2003) due to the inexistence of a liquidity discount for the company insiders. 14 Finally, we have considered an all equity company, meaning that the company has not incurred in any kind of debt to leverage its activity. Thus, the owner is the only one entitled to receive the cash flows of the company. The IPO option value for the owner, F(V), must satisfy the following ordinary differential equation (ODE): σ2 2V2∂2F(V) ∂V 2+µV ∂F (V) ∂V −rF = 0 (3.2) The general solution for this ODE is given by F(V) = A1Vβ1+A2Vβ2. Where: β1=1 2−µ σ2+sµ σ2−1 22 +2r σ2(3.3) and β2=1 2−µ σ2−sµ σ2−1 22 +2r σ2(3.4) With β1>1 and β2<0. To compute the optimal moment to perform the IPO we have to impose some boundary conditions. The first one is the absorbing barrier and is stated as: F(0) = 0 (3.5) This condition means that if the company does not generate cash flows, the value of the option must be zero. The second condition is the value matching condition and is as follows: F(V∗) = P∗(φ, θ, λ, V ∗, C)−φV ∗(3.6) 15 where P∗(φ, θ, λ, V ∗, C) = φ(1 −θ)V∗(1 −λ)−Crepresents the proceeds from the IPO. The value matching condition states that at the moment of the exercise of the option, the value of that option is given by the difference between what he receives, P∗(φ, θ, λ, V ∗, C) and what he loses, −φV ∗. Notice that the costs are incurred by the owner because those are taken prior to the IPO, per se. Also, have in mind that the owner bears the costs of underwriting. Finally, we have the smooth-pasting condition that ensures that the option value is equal in V∗for both branches and that the transition between branches is smooth. It is given by: ∂F (V∗) ∂V ∗=∂P ∗(φ, θ, λ, V ∗, C) ∂V ∗−φ(3.7) These three conditions allow us to discover the values for A1,A2and the optimal moment V∗. 3.3 Solution of the Model The boundary conditions consist on the restrictions that allow us to define the model. Hereafter, we will develop them in order to obtain the value of the option to perform an IPO. From the absorbing barrier, we have: lim V→0F(V) = ∞(3.8) Given that β1>1 and β2<0, we must set A2= 0, otherwise the absorbing barrier condition would not be satisfied. Using the smooth-pasting condition 16 pany. The second corresponds to the premium related with the new segment. This model is based on the investment opportunity idea that can be found in Boehmer and Ljunqvist (2004), Kim and Weisbach (2008) and Brau and Fawcett (2006), among others. This means that immediately after the IPO the company will invest in order to expand its cash flows. While these authors do not differentiate between an investment in the existing segment and a new segment of business, we consider that it concentrates in a new line of business. This implies that companies have a business that is well developed, trying to find a new source to increase their growth rate and, consequently, their value. Thus, we consider that the company is investing in a segment that is strategically important for its future, leading to a higher premium. As we will see below, we won’t use a factor of growth as Bustamante (2012) did. We will consider that this factor is already reflected in the premium that investors are willing to pay when investing in the company. To develop this model we need to distinguish between the old cash flows of the company and the ones that arise from the new investment. This implies the utilization of two stochastic processes. The basis for this work is the one of Adkins and Paxson (2011). In this article, the authors solved a model with two stochastic variables without homogeneity of degree one. The methodology followed here is similar to the one presented in that article. This section is divided as follows: first we will present the pillars of our model; second, we will present its solution, followed by the comparative statics and the numerical example. Finally, we conclude and synthesize the main ideas. 4.2 The Model Using the Contingent Claim Approach, as defined by Dixit and Pyndick (1994), we will have two stochastic processes that follow distinct Geometric 23 Brownian Motions (gBm) that are represented as follows: dX =µXXdt +σXXdz, (4.1) where X={V1, V2},µXis the instantaneous conditional expected relative change in X,σXis the instantaneous conditional standard deviation and dz is the increment of a Wiener process. Notice that µV1=r−δ1and µV2=r−δ2. The covariance between the two variables is given by: Cov[dV1, dV2] = ρσV1σV2V1V2dt (4.2) In this model we aim to build a boundary as a function of V1and V2in order to define, for each level of each of the variables, when it is optimal to perform an IPO. This implies that both variables must attain their threshold levels in order to the company turn itself publicly-traded. As before, we assume that the company has to pay a fixed amount to perform the IPO. This amount, represented by C > 0, is supported by the owner of the company pre-IPO. The underwriting fees, λ∈(0,1], are also supported by the owner of the company. As stated above, the company will perform an investment in a new segment. Similarly to Bustamante (2012), this investment occurs at the same time (or right after) of the IPO. This investment cost is represented by Iand is included in the same way as in Bustamante’s model. Furthermore, this investment has associated a cash flow stream that will be presented by V2(being V1the cash flow stream of the old business). Both these segments will have associated a premium investors are willing to pay. Thus, θ1represents the premium for the old business and θ2the premium for the new business. As stated before, the new segment where the company is investing is expected to have a higher growth rate that the old one (θ2> θ1). The value of the option to perform an IPO, F(V1, V2), must satisfy the fol24 lowing partial differential equation (PDE): 1 2σ2 V1V2 1 ∂2F(V1, V2) ∂V 2 1 +1 2σ2 V2V2 2 ∂2F(V1, V2) ∂V 2 2 +ρσV1σV2V1V2 ∂2F(V1, V2) ∂V1∂V2 + + (r−δ1)V1 ∂F (V1, V2) ∂V1 + (r−δ2)V2 ∂F (V1, V2) ∂V2 −rF (V1, V2) = 0 (4.3) The general solution for this PDE has the form: F(V1, V2) = AV β 1Vη 2(4.4) Replacing F(V1, V2) in equation (4.3) we obtain the following elliptical equation: Q(β, η) = 1 2σ2 V1(β−1)β+1 2σ2 V2(η−1)η+ρσV1σV2βη+ + (r−δ1)β+ (r−δ2)η−r= 0 (4.5) The equation above describes an ellipse. For β= 0, the equation becomes: Q(0, η) = 1 2σ2 V2(η−1)η+ (r−δ2)η−r= 0 (4.6) Solving equation (4.6) in order to ηwe find two roots, a positive and a negative. The same applies for the case of η= 0. In that case, the equation becomes: Q(β, 0) = 1 2σ2 V1(β−1)β+ (r−δ1)β−r= 0 (4.7) As Adkins and Paxson (2011) argue: ”(.. . ) the ellipse passes through all 4 axes and has a presence in each of the 4 quadrants. When we impose the line β+η= 1 on the graph Q= 0, represented by the line LL’ in Figure 1, it clearly intersects the function at 2 distinct points, A and B. If homogeneity degree 1 holds, the values of β and ηare uniquely specified by points A and B. When homogeneity degree 1 does not hold, the values of βand ηwill lie somewhere along the arc ADB or ACB, depending on whether β+ηis greater than or less than 1. Thus, 25 we require additional information from the boundary conditions in order to solve βand ηwhen β+η6= 1.” Figure 4.1: Representation of equation (4.5) from Adkins and Paxson (2011). Source: Adkins and Paxson (2011) The figure above illustrates the statement from Adkins and Paxson referred above. Following Adkins and Paxson (2011) methodology, we will develop a function that arises from the value matching and from the smooth-pasting condition. This function will intersect the function Q(β, η) = 0, generating the values for βand η. From figure 4.1 we can infer the possible values for these variables. S1:{β1, η1} → β1≥0, η1≥0; (4.8) S2:{β2, η2} → β2≥0, η2≤0; (4.9) S3:{β3, η3} → β3≤0, η3≤0; (4.10) S4:{β4, η4} → β4≤0, η4≥0; (4.11) Thus, we can rewrite the solution of equation (4.3) as being: F(V1, V2)H=A1Vβ1 1Vη1 2+A2Vβ2 1Vη2 2+A3Vβ3 1Vη3 2+A4Vβ4 1Vη4 2(4.12) 26 As in the previous model, we need to establish the boundary conditions that will allow us to find the solution. The first boundary condition is the absorbing barrier. It is expressed below. It is similar to the one in the previous chapter. However, in this case we are stating that if the cash flows of both investments tend to zero, the value of the company to the owner is zero and so does the option. F(0,0) = 0 (4.13) The second boundary condition is the value matching condition. This one says that the value of the option for the owner in the moment of exercise equals the stake of th new segment that he retains, plus the proceeds from the IPO, deducted by the stake that he has lost and the investment cost. The proceeds from the IPO can be expressed as follows: P∗(φ, θ1, θ2, V ∗ 1, V ∗ 2, λ, C) = φ[(1 + θ1)V∗ 1+ (1 + θ2)V∗ 2](1 −λ)−C(4.14) The value matching condition is given by: F(V∗ 1, V ∗ 2) = (1 −φ)V∗ 2+P∗(φ, θ1, θ2, V ∗ 1, V ∗ 2, λ, C)−φV ∗ 1−I(4.15) Contrary to the previous model, in which we had a smooth-pasting condition, we now have two. This happens because there are two stochastic variables. Thus, the following two equations define the smooth-pasting conditions. ∂F (V∗ 1, V ∗ 2) ∂V ∗ 1 =φ(1 + θ1)(1 −λ)−φ(4.16) ∂F (V∗ 1, V ∗ 2) ∂V ∗ 2 = (1 −φ) + φ(1 + θ2)(1 −λ) (4.17) With these boundary conditions we can determine the IPO boundary. Contrary to the previous model, we cannot provide a closed-form solution, as we will explain in the following section. 27 4.3 Solution of the Model From the absorbing barrier we can easily conclude that A2,A3and A4are equal to zero. Thus, the solution for F(V1, V2) can be reduced to: F(V1, V2) = A1Vβ1 1Vη1 2≡AV β 1Vη 2(4.18) Consequently our function regarding the value for the shareholder is given by: F(V1, V2) = AV β 1Vη 2(4.19) We now have three equations (equation (4.15)-(4.17)) for four variables to be determined. Since the number of unknows is bigger than the number of equations, we cannot provide a unique solution for our model, meaning that there is no closed-form solution. Thus, we are going to determine a boundary of countless pairs of {V1, V2}. While in the previous model there was a threshold after which the IPO should be undertaken, now we have a region where the IPO should occur and other where it should not. Thus, every company after having computed the value of the new segment can simply calculate the value of the current business after which it should turn publicly-traded. In the next section we will explore a practical example. The procedure adopted was to consider a fixed value for the company that is considering the IPO. This allows us eliminate a variable that needs to be determined and remain with four variables (A1,β,η,V2) for four equations, the ellipse (equation (4.5)) and equations (4.15) to (4.17). 28 4.4 Numerical Example and Sensitivity Analysis Numerical Example As explained at the end of the previous section, there is no close-form solution for our model. However, Adkins & Paxson (2011) developed a method that allowed to define a discriminatory boundary between the IPO decision and the non-IPO decision, being indifferent to do it or not in that boundary. We have used Mathematica software to compute several values of the boundary. Using those values, we have created a graphic representing these points and, finally, we have regressed those values in order to obtain that boundary. This is a very simple analysis with a very powerful output. We will construct over the case of the previous model. However, it is necessary to consider some new variables. Let us imagine that Houghton Mifflin Harcourt Company has the possibility to enter in a new and fast-growing business, such as the Apps market. The table below represents a summary of the variables used. Variable Value Description r0.03 Risk-free interest rate δV10.02 Discount rate of the old segment δV20.025 Discount rate of the new segment σV10.25 Volatility associated to the old segment σV20.35 Volatility associated to the new segment ρ0.2 Correlation between the two segments φ0.15 Stake to be sold λ0.06 Underwriting fees C$4.5M Cost of the IPO θV10.133 Market sentiment for the old segment θV20.25 Market sentiment for the new segment I$40M Investment needed to enter the new segment Table 4.1: Data for the application of the Model We are considering here that an investment of $40 million is necessary to 29 construct an infrastructure to develop this business. As it is a relatively new business, the volatility associated with it is higher than the volatility of the old segment of the company. Also, the premium is considered to be higher because of the appetite of the investors for companies in this new segment (similarly to what happened in the dotcom bubble). We assume that the owner(s) is(are) trying to sell 15% of the company and that the underwriting fees and the fixed costs of the process are the same. We will start by computing the value of V2for which is optimal to perform the IPO, considering the actual value of the company (V1= $1,614.19 million). We could also perform this exercise on the opposite direction, i.e. having the actual value of the new segment, we could compute the optimal value of the company after which we should perform the IPO. Using the FindRoot function in Mathematica, we determine that the value of V∗ 2is $125.71 million, with a β= 0.1571 and η= 1.2867. After this, we must induce some changes in V1and execute the FindRoot function again. The following table illustrates some of the results obtained: V10.00 695.29 1,177.47 1,615.19 2,149.82 2,861.41 3,462.3 β0.00 0.05 0.10 0.16 0.25 0.41 0.59 η1.30 1.29 1.29 1.29 1.28 1.24 1.19 V2189.74 161.49 142.45 125.71 106.28 82.97 66.48 Table 4.2: Results from variations in V1 With these results we are now in a position of creating the boundary that will help in the decision making. The figure below demonstrates this relation between V1and V2. As we can see from figure 4.2, there is a ”negative relation” between the value of the current business and the value of the new business, meaning that an increase in the value of the new business demands a lower value of the current business, leading to an earlier IPO. On the contrary, if the value of the new 30 Figure 4.2: Boundary between non-IPO and IPO regions business is relatively small, the IPO must be made later, demanding a bigger initial business. Below we will study the impact of variations in several variables, aiming to understand its impact on the trigger values. Sensitivity Analysis In this section we will impose some changes in the variables of the model. The objective is to study the impact of those variations mainly in the trigger of the second segment. Variations in θV1In the previous chapter, when analyzing the impacts of variations in the market sentiment we have concluded that higher levels of market sentiment lead to lower trigger values. Now, there is a new segment in which the company is going to enter after the IPO. We tested for three levels of market sentiment: the original one, of 0.133, a lower one of 0.09975 and a larger one of 0.16625. The graphic below depicts the differences between the three levels. As it can be seen, the level triggers for the new sector tend to diminish with increases in the market sentiment of the old sector. This happens because, as before, the owner tends to take advantage of this market premium to take the company public. This way, a higher market sentiment anticipates the 31 Figure 4.3: Boundary between non-IPO and IPO regions for different θV1’s. The remaining inputs are according to Table 4.1 IPO process. Table (4.3) shows the variations in the trigger value of the new segment to our current value of the business: θV10.09975 0.133 0.16625 V2155.77 125.71 97.98 Table 4.3: Results from variations in θV1. The remaining inputs are according to Table 4.1 As in the previous model, there is a tendency to anticipate the IPO given market conditions. Variations in θV2Regarding θV2, this factor has less impact in the determination of the trigger of the new segment. This is so because in our setting the new segment is much smaller than old segment, being not so relevant as the old segment. Just to illustrate, the graphic below shows the conclusions for three different values of θV2: 0.1875, 0.25 and 0.3125. As we can see, there are small moves of the boundary for the right or left, depending on a decrease or increase in the market sentiment for the new segment, respectively. The below figure could have been different if the new segment was more relevant. 32 the decrease of importance of the old segment. 4.6 Conclusion of the chapter During this chapter we tried to give a step further in order to provide a framework for real life IPO’s. This is a very demanding process for the owner/management team and we aimed to focus on the main decisions. We considered a case where the company performs the IPO to allow not only the exiting of the owner but also the entering in a new segment. This implied the inclusion of some factors, such as the volatility and the market sentiment of the new segment, the investment cost to ensure the new line of business and the correlation between the two segments. It is important to notice that this entry in a new segment can be done in very different ways. We considered here an entry with an investment from the ground, however this can be made by acquiring an existing company, for example. It is important to notice the impact of both the volatility of the new segment and the correlation between segments in the decision making process. Both these factors play a very important role in the determination of the trigger for the investment. Also, the percentage of the company to be sold has a very interesting role considering the behavioral hindsights. Finally, in the study of the market sentiment we concluded that the sentiment in the old segment played a similar rolen when compared to the previous chapter. The sentiment in the new segment also presented a negative relation to the market timing, meaning that a higher sentiment represented a lower trigger to perform the IPO. 39 Chapter 5 Conclusion 5.1 Contribution to Financial Literature During this work we have developed two models that aim to support the decision for an IPO in different settings. Our main goal was to create a model that did not concentrate in the market sentiment but, at the same time, allowed to study it. We have focused on the managerial decision, bearing in mind that this decision is taken considering a given framework for the owner. This is the logic undedrlying the inclusion of a variable for the market sentiment. And it is this way that we have given a step forward on IPO literature. As presented in Chapter 2, the main works regarding the IPO process with a Real Options perspective are the ones from Draho (2000), Benninga (2005) and Bustamante (2012). These works build over different perspectives but with a similar objective, to time the IPO. Our distinctive approach allowed us to differentiate from these works. While the basic model clearly lies on the market sentiment parameter, showing us that the manager/owner would only perform the IPO if the market was paying more for the company than the value he attributes to her, the second model does not depend exclusively on this parameter. This capacity to focus in the management decision allows to determine, in 40 the second model, the timing of the investment and of the IPO. Also, the inclusion of some behavioral insights allows to approximate our model to reality, trying to overcome the typical critics that appear to financial models. As defined before, there is plenty of space to develop from now on, being important to build models that help the decision making process of the owners of these companies. Thus, we think our model provide a solid ground to build on in the future. Being this such an important aspect of the strength of an economy, any model that helps entrepreneurs to better decide are welcome. We differentiated from the work of Bustamante, the model that we’ve used as a basis for ours, by ignoring the signalling game idea. In her article, Bustamante builds over this idea, creating a dynamic between private firms. In our model, we define the moment as a sole decision. This way, our model applies also to companies that are the first in their sector to perform IPOs. Obviously, in this case, the market sentiment would have to be adapted, given that we had no benchmark to evaluate the market. In conclusion, we tried to build a solid model, based in a very well-established theoretical environment. We reconciled evidence from many authors identified in the literature review with the objective of providing an intuitive, but realistic, model. 5.2 Further Work and Limitations of our Model The path until this final point allowed us to find several aspects we would like to include but, because of time constraints and the objectives of a Master Dissertation, were not developed, yet. We believe to be in a position to address some possible paths for further studies. First, we were considering the inclusion of agency issues. As Dalziel et al. (2011) shows there are some costs of an IPO that arise from principalprincipal conflicts. These can have a great impact in the IPO decision. 41 Second, we omit here the presence of debt. As it can be seen from our examples, we do not consider the existence of debt, ignoring a factor that can promote the IPO, anticipating it. On the other hand it could be a factor of deferral of the IPO because the owner could leverage the company first and only after that promote the going public process, receiving more funds in the meanwhile. Also, R¨oell (1996) demonstrates that the IPO allows to reduce the leverage of the company, being this one of the motivations for the process. It would be interesting to include this factor here. Third, the computation of the θparameters should be based on behavioral methods. This would allow to reconcile two very innovative and interesting fields of finance: Real Options and Behavioral Finance. Considering the contributions of both these fields, they would probably provide a bigger contribute if they could be developed together. However, Considering that this is not the main goal of this work, we believe that the measure proposed suffices to demonstrate the model. Finally, the consideration of two separate models with the objective of building an equilibrium model. One of the models would represent the perspective of the owner (or owners) of the company. The other would represent the market perception and willingness to enter in this process. The idea of equilibrium model is directly related to Traditional Finance. This ”doubleheaded” model would allow to join Traditional and Behavioral Finance along with the Real Options perspective. It is possible that the model would be so complex that it was almost inoperable, however it would allow to understand better the market for IPOs. 42 Bibliography •Abrahamson, M., Jenkinson, T. and Howard, J. (2011), Why Don’t U.S. Issuers Demand European Fees for IPOs?, The Journal of Finance, Vol. LXVI, No. 6, December 2011, 2055-2082; •Adkins, R. and Paxson, D (2011), Renewing Assets with Uncertain Revenues and Operating Costs, Journal of Financial and Quantitative Analysis, Vol. 46, No. 3, June 2011, 785-813; •Albornoz, B. G. and Pope, P. F. (2004), The Determinants of Going Public Decision: Evidence from the U.K., Working Papers, Serie AD, Instituto Valenciano de Investigaciones Econ´omicas, S.A.; •Baker, M. and Wurgler, J. (2007), Investor Sentiment in the Stock Market, Journal of Economic Perspectives, Volume 21, Number 2, Spring 2007, 129-151; •Benninga, S. and Helmantel, M. and Sarig, O. (2005), The Timing of Initial Public Offerings, Journal of Financial Economics, 75, 115-132; •Bharath, S. and Dittmar, A (2006), To Be or Not to Be (Public), University of Michigan Ross School of Business Research Paper, December 2006; •Black, F. and Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, The Journal of Political Economy, Vol. 81, No. 3: 637-654; •Blum, Rachel (2011), IPO Timing Determinants, Undergraduate Honors Thesis, Duke University; 43 •Ljungqvist, A. and Boehmer, E. (2004), On the Decision to Go Public: Evidence from Privately-held Firms, February 12, 2004; •Bolton, P. and Von Thadden, E.-L. (1998), Blocks, Liquidity, and Corporate Control, The Journal of Finance, Vol. 53, No. 1, February 1998, 1–25; •Bowman, E. H. and Moskowitz, G. T. (2001), Real Options Analysis and Strategic Decision Making, Organization Science, Vol. 12, No. 6 (Nov. - Dec., 2001), 772-777; •Brau, J., Francis, B. and Kohers, N. (2003), The Choice of IPO versus Takeover: Empirical Evidence, Journal of Business, Vol. 76, No. 4, 583-612; •Brau, J. and Fawcett S. (2006), Initial Public Offerings: An Analysis of Theory and Practice, The Journal of Finance, Vol. LXI, No. 1, February 2006, 399-436; •Bustamante, M. C. (2012), The Dynamics of Going Public, Review of Finance, Vol. 16, No. 2, 577-618; •Casassus, J. and Villalon, M. (2010), Optimal IPO Timing in an Exchange Economy, Working Paper, PUC-Chile; •Celikyurt, U., Sevilir, M. and Shivdasani, A. (2010), Going Public to Acquire: The Acquisition Motive for IPOs, Journal of Financial Economics, Vol. 96, No. 3, June 2010, 345-363; •Dalziel, T., White, R. E., Arthurs, J. D. and Hoskisson, R. E. (2010), Initially Distracted: The Influence of Boards on Agency Costs in Initial Public Offering (IPO) firms, published in Audretsch, David B., Dagnino, Giovanni B., Faraci, Rosario and Hoskisson, Robert E. (2010), New Frontiers in Entrepreneurship: Recognizing, Seizing, and Executing Opportunities, New York, NY: Springer; 44 •Dalziel, T., White, R. E. and Arthurs, J. D. (2011), Principal Costs in Initial Public Offerings, Journal of Management Studies, Vol. 48, 1346–1364; •Dixit, A. and Pindyck, R. (1994), Investment Under Uncertainty, Princeton University Press, New Jersey; •Draho, Jason (2000), The Timing of Initial Public Offerings: A Real Option Approach, December 2000, Working Paper; •Holmstrom, B. and Tirole, J. (1993), Market Liquidity and Performance Monitoring, The Journal of Political Economy, Vol. 101, No. 4, August 1993, 678–709; •Ibbotson, R. and Ritter, J. (1995), Initial Public Offerings, published in Jarrow, R., Maksimovic, V. and Ziemba, W. (1995), Handbooks of Operations Research and Management Science: Finance, Amsterdam: North-Holland; •Jensen, Michael and Meckling, William (1976), Theory of the firm: Managerial Behavior, agency costs and ownership structure, Journal of Financial Economics, Vol. 3, No.4, 305-360; •Kim, W. and Weisbach, M. (2008), Motivations for Public Equity Offers: An International Perspective, Journal of Financial Economics, Vol. 87, February 2008, 281-307; •Lee, C. M. C., Shleifer, A. and Thaler, R. (1991), Investor sentiment and the closed-end fund puzzle. The Journal of Finance, Vol. 46, 75-109; •Lerner, J. (1994), Venture Capitalists and the Decision to Go Public, emphJournal of Financial Economics, Vol. 35, 293-316; •Luehrman, T. A. (1998), Strategy as a Portfolio of Real Options, Harvard Business Review, pp. 89-99; 45 •Markowitz, H. (1952), Portfolio Selection, The Journal of Finance, Vol. 7, No. 1, 77-91; •McDonald, R. and Siegel, D. (1986), The Value of Waiting to Invest, The Quarterly Journal of Economics, Vol. 101, No. 4, 707-728; •Mello, A. S. and Parsons, J. E. (1998), Going Public and the Ownership Structure of the Firm, Journal of Financial Economics, Vol. 49, 79-109; •Myers, S. C. (1977), Determinants of Corporate Borrowing, Journal of Financial Economics, Vol. 5, 147-175; •Pagano, M., Panetta, F. and Zingales, L. (1998), Why Do Companies Go Public? An Empirical Analysis, The Journal of Finance, American Finance Association, Vol. 53, No. 1, 27-64; •P´astor, L. and Veronesi, P. (2003), Stock Valuation and Learning about Profitability, Journal of Finance, American Finance Association, Vol. 58, No. 5, 1749-1790; •Rajan, R. and Servaes, H. (2002), The Effect of Market Conditions on Initial Public Offerings, January 2002; •Ritter, J. (1991), The Long-Run Performance of Initial Public Offerings, Journal of Finance, Vol. 46, No. 1, 3-27; •R¨oell, A. (1996), The Decision to Go Public: An Overview, European Economic Review, Vol. 40, 1071-1081; •Rydqvist, K. and H¨ogholm, K. (1995), Going Public in the 1980s: Evidence from Sweden, European Financial Management, Vol. 1, No. 3, 287-315; •Zingales, L. (1995), Insider Ownership and the Decision to Go Public, Review of Economic Studies, Vol. 62, No. 3, 425-448. 46