Dynamics of mergers and acquisitions are demonstrated by using an analytical framework which is in the form of a theoretical model. An example to the framework can be the value of a firm given by
V (τ, µ, σ, X, ρ, ...), (1.2)
whereV is firm value, τ is marginal tax rate, µ is cash flows of merging firms, σ is volatility of cash flows,X is unlevered firm value (or expected value of cash flows), ρ is correlation of cash flows. Two firms V1(.) and V2(.) need to be valued including their securities before after the merger. Here a merger operator is also required as
Vmerged(.) = V1(.) ⊗ V2(.), (1.3)
where⊗ defines the merger operator which will map and identify merger synergies.
The task is to construct an applied model considering the trade-off between ab-straction and realistic modelling. An applied model is an explicit, simplified rep-resentation of more general theories which are designed to apply to specific real-world problems or situations (Boland, 1989). The constructed model will be the research tool. The dynamics of the constructed model will measured and analysed to explain the real world phenomena.
The model must be testable for verification purposes. Control variables may be the output of existing literature, or observed data or benchmark models. To test the model’s efficiency and external validity, model parameters/variables will be cal-ibrated to replicate observed values of the variables. The proposed model must be able to value all outstanding securities of merging firms before and after the
merger. The company valuation model employed in this study is contingent claim valuation as applied in Brennan (1979) or in Merton (1973)5. External validity of the model has a key importance. A non-generalizable model cannot be used as an ap-plied model. Internal validity will be provided by following empirical and theoretical literature.
1.4.1 Analytical Framework
The type of modelling needs to be defined before constructing the analytical frame-work. Valuation of the existing securities of the merging firms involves the valuation of contingent claims. These claims can have a positive or negative future value.
Thus, contingency introduces default risk to the model. Black and Scholes (1973) model corporate liabilities as combinations of options. They demonstrate valua-tion of common stocks, warrants and bonds. The framework used in this study is similar to theirs in terms of modelling corporate liabilities as options.
Credit risk models are also employed which handle contingency. There are two classes of credit risk models; reduced form models and structural models. Re-duced form models do not use company specific data and try to model a group of firms’ behaviour. Reduced form models can also be used in merger modelling. In this class of models defaults are caused by exogenous shocks and modelled using hazard functions. For example, merger waves can be analysed under an external economic shock. However structural models use company specific data and try to make company specific valuations for existing securities of firms. The latter of the two modelling frameworks best suits to this study so that the structural class of models is used in this thesis. This will enable to use firms’ default risk, cash flows, volatility of cash flows and other critical parameters for merger modelling.
5Contingent claim is an asset whose payoff depends upon another "underlying" asset (Brennan, 1979).
This framework needs some unobservable data like volatility of cash flows, thus estimation methods will be employed.
The Leland (2007)’s framework is first used and some of the extensions on the model are demonstrated. Consequently, having used the Ammann and Genser (2004) model, a dynamic merger model is constructed. After demonstrating the single period model the next step is to extend the model to run in a multi-period setting. This is not for the sake of a comparison of these two frameworks, rather it is complementary. These models are chosen because of their ability to explain values of existing securities pre- and post-merger with their simple and intuitive designs.
Calibration method will be employed in the modelling phase. Models will be cali-brated to produce observed real world parameters. For example, to model a BBB rated firm in the model, observed values of cashflows, default cost and default risk for a BBB rated firm will be used. This way, models will be available for empiri-cal testing. Model outputs can easily be compared with observed values to test the model. If the model does not fail these tests, then it can be used to make contributions to existing theory by generalisations.
1.5 Contributions
This thesis is the first study to analyse mergers in such detail and also is the first study to model wealth transfer strategies for shareholders. For example, previous studies (Higgins and Schall, 1975; Leland, 2007) pointed out that calling existing bonds may increase shareholders gains in case of a merger however it has never been modeled explicitly.
To our knowledge this thesis is the first study which uses an Arithmetic Brown-ian Motion (ABM) process for earnings before interest and tax (EBIT) of the firm.
This has two advantages. First, ABM process can produce negative realisations for the EBIT. Second, combination of two normal distributions will give a normal distribution therefore creates a mathematical convenience.
Using structural credit risk models, all existing security prices and term structures are modeled with closed form solutions. After using a one period model this thesis also employs a multi period model to analyse interactions of bonds with different maturities in case of a merger.
The main contribution of this thesis is it shows that shareholders can increase their merger returns using various strategies. These strategies include using callable bonds instead of plain bonds, issuing bonds with short maturities or timing of bond reissues. Each method listed here enhances financial synergy gains of sharehold-ers. Increasing shareholder gains is important as it will prevent a conflict between managers and shareholders.
Call provisions on debt increases shareholder gains and firm value after in case of a merger. Even though a risk premium is offered to bond holders firm and shareholders from a synergistic merger.
Debt maturity also affects the gains of shareholders. As debt maturity gets shorter gains of shareholders increase. One extreme case is a merger when merging firms have perpetual bonds outstanding. In this case most of the merger gains are realised by perpetual bond holders.
Firm may also change the merger timing so that it merges before a debt issue and preferably after the maturity of short term debt. This can be used if the firm cannot call the bonds back without any cost. The goal of the firm must be to merge when the outstanding bond portfolio is small with a short maturity.
1.6 Conclusion
Some preliminary models were constructed to investigate the problem further. A merger matrix was used to understand the relation of credit ratings and financial synergies. A CDS contract is modelled to investigate the relations between credit risk and mergers. Callable bonds were used to change the distribution of financial synergies. These showed that there may be a conflict between shareholders and managers as in some cases mergers may decrease the wealth of shareholders. To prevent a wealth decrease shareholders may use callable bonds or CDS contracts.
This thesis investigates the distribution of financial synergies between bondholders and shareholders in a structural credit risk model. While investigating this, strate-gies and instruments were developed to increase the wealth of shareholders.
Rest of this thesis is as follows. Chapter2looks at the existing literature and shows the gap in existing literature. Chapter 3introduces the research methodology and briefly demonstrates some of the methods used in this thesis. Chapter4analyses financial synergies of mergers using a one period model. Chapter 5 introduces a new multi-period model and analyses its dynamics without a merger. Chapter6 introduces mergers to the multi period model introduced in Chapter5and analyses the financial synergies of mergers in a multi-period setting with a complex tax and capital structure. Chapter7concludes.