DISCUSSION OF OPTIMAL DEBT SERVICE: STRAIGHT

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1 Gunther Friedl * DISCUSSION OF OPTIMAL DEBT SERVICE: STRAIGHT VS. CONVERTIBLE DEBT 1 MOTIVATION AND OBJECTIVE OF THE PAPER Corporate bond default plays a significant role in today s business environment. According to Moody s, a leading provider of credit ratings, corporate bond issuers that it rated as of January 1, 2004, defaulted on a total of US $16 billion in Credit default not only affects the equity investors of a firm, but also the debt holders, who may loose part of their credit. Default can also have dramatic consequences for a firm s future operations. Therefore, the decision of if and when to default is important for both the firm and its stakeholders. There is a substantial body of literature on the determination of optimal default points as a strategic decision by the owners of a firm 1. According to this view, optimal default occurs when the continuation value of the firm, less the discounted value of all future taxadjusted coupon payments, falls below zero. However, some studies on optimal default points are limited, since these studies usually assume a simple capital structure with only equity and straight debt. Christian Koziol extends this literature by relaxing the assumption of a simple capital structure and by allowing for convertible debt. The main objectives of his paper are (i) to determine optimal default and conversion strategies, when debt is convertible; and (ii) to highlight the differences between this strategy and the strategy for straight debt. Since convertible debt plays a significant role in corporate finance decisions, Koziol s approach seems to be both important and of wide interest. To analyze these problems, the author uses a widely accepted time-independent model with a perpetual bond that pays a continual coupon in the presence of both bankruptcy costs and tax deductibility. My discussion is organized as follows. In section 2, I relate Koziol s paper to previous literature and provide an intuitive explanation for the results. Section 3 discusses an application in the area of real option games. * Gunther Friedl, University Professor, Universität Mainz, Professur für Betriebswirtschaftslehre, insbesondere Controlling, D Mainz, 1 A standard model is Leland (1994). 152 SBR 58 APRIL

2 2 RELATION TO THE LITERATURE AND CONTRIBUTION For traditional financial options, firms usually derive their optimal exercise strategies and the option values without considering the strategic interactions across option holders. Firms base this simplification on the assumption that the option s exercise does not influence the characteristics of the underlying or other options on this underlying. For example, the standard model of the determination of a firm s optimal default strategy uses this assumption (e.g., Leland (1994)). The firm s equity holders have the option to default on debt payments, which can be viewed as an option to sell the firm at an exercise price of zero. In the standard model there are no additional options of other parties, so there is no room for strategic interactions. This assumption can be justified if firms have a simple capital structure with only equity and straight debt. However, if we assume a richer capital structure by including, for instance, convertible debt, this simple view no longer holds. Not only do the equity holders have the option to default, but so do the holders of convertible debt, who have the option to exchange their debt for a fraction of the equity of the firm. In this case, the optimal exercise of the debt holders call option influences the value and the optimal exercise of the equity holder s put option, and vice versa. Now there are strategic interactions across option holders, and a game-theoretic approach must be used to derive the optimal exercise strategies. Two lines of research in the area of strategic option exercise games relate to the paper and are relevant to my discussion. First, there is a substantial body of literature on the strategic exercise of convertible debt and warrants. Examples include Constantinides (1984), who analyzes the equilibrium exercise strategies of a continuum of competitive warrant holders, and Spatt and Sterbenz (1988), who demonstrate that depending on the firm s policy on the use of the exercise proceeds, optimal warrant exercise strategies can be either sequential or simultaneous. Both studies show that strategic interactions across option holders change the results of traditional option pricing theory. While these studies analyze financial options, a second line of literature examines the strategic exercise of real options. Examples include Grenadier (1996), who develops an equilibrium framework for strategic option exercise games. Grenadier uses this framework to analyze the timing of real estate development and provides insights into the forces that shape market behavior. Huisman and Kort (2003) examine the optimal timing of a technology investment of a single firm in a duopoly framework, which they interpret as the exercise of call options on the investment s cash flows. In both cases, the option values and the exercise strategies have properties that strongly differ from the case of a simple option without strategic effects. All these papers analyze the strategic exercise of symmetric call options. Koziol s paper differs from this work in that it considers two different options. Koziol assumes that convertible debt holders can convert their bonds into a fraction γ of total equity. This option is available in perpetuity, which is clearly a simplification of reality. Until conversion, the fi rm continuously pays a coupon C per instant of time. After conversion, SBR 58 APRIL

3 G. FRIEDL convertible debt holders receive γ V, where V represents the asset value of the firm after conversion. Before conversion, Koziol interprets V as the value of an otherwise identical, but purely equity financed, firm after taxes. Obviously, V cannot be observed, so an empirical examination of the model would be difficult, if not impossible. Equity owners hold a put option, which they exercise when the firm stops paying the coupon payment to the debt holders. In this case, the firm is liquidated, equity holders are left with nothing, and debt holders receive the asset value V less bankruptcy costs α V. The asset value V is assumed to follow a geometric Brownian motion, which is a standard assumption in these types of models. As an extension to the standard model, Koziol allows for a non-negative payout ratio β, which indicates the instantaneous payments to equity holders as a percentage of the asset value V. The basic trade-offs for equity holders that determines the optimal default strategy are keeping the firm alive, and keeping the claim on instantaneous payments of the payout ratio times the asset value less the tax-adjusted coupon payment or declaring default with a payoff of zero. The valuation functions of both equity and convertible-debt holders depend on the exercise strategies of both parties and the asset value. The optimal exercise strategies of equity and debt holders form a Nash equilibrium. Given the optimal conversion strategy of convertible debt holders, equity holders have no incentives to deviate from their default strategy, and vice versa. Koziol can derive these optimal exercise strategies numerically from the smooth-pasting conditions for the equity and debt value functions. In the special case in which there is no net payout to equity holders, Koziol obtains a closed-form solution for the optimal default strategy. Koziol derives his main results by comparing the modelled firm financed with equity and convertible debt with a fictitious firm financed with only equity and straight debt. Koziol resorts to this fictitious benchmark case, because in practice, convertible securities are frequently decomposed into a straight bond and an option component. The reason for decomposing convertibles is that single components are easier to price. Pricing the straight bond component requires the knowledge of the firm s default strategy. In practice, this default strategy is obtained by considering the fictitious benchmark firm that has only equity and straight debt. This default strategy makes a strong argument for Koziol s benchmark case. Using this firm s strategy for the valuation of the single components instead of the equilibrium strategy of the modelled firm might lead to a different value and different exercise strategies for convertible debt. Koziol s results confirm this deviation. The optimal default for a firm with convertible debt occurs earlier than would a default if the firm were financed with straight debt only. In terms of asset value, the default barrier is higher for the firm with convertible debt than it is for the firm with straight debt. This result has consequences for the optimal conversion strategy. When the firm optimally defaults, the conversion barrier is below the conversion barrier when the firm follows the false strategy. Under the false strategy, the firm acts as if there was no convertible, but only straight, debt. Moreover, the value of convertible debt is higher when firms follow the false straight debt default strategy than when they follow the optimal strategy. 154 SBR 58 APRIL

4 These results are explained by considering the basic trade-offs for equity holders under the optimal default strategy. On the one hand, if the equity holders keep the firm alive, they keep the claim on instantaneous net payments of the payout ratio times the asset value (uncertain) less the tax adjusted coupon payment (certain). On the other hand, if the equity holders declare default, they get a payoff of zero. Equity holders are worse off if debt holders have a conversion right. The possibility of conversion leads to an additional claim on the firm. Therefore, the claim on the payout ratio times the asset value is worth less than with straight debt only. As described above the basic trade-off shifts to higher asset values. Hence, optimal default occurs earlier for convertible debt than for straight debt. This result has important implications for credit-rating agencies. Firms that use convertible securities in their capital structure should be downgraded relative to otherwise identical firms that are straight-debt financed. Koziol analyzes a number of influencing factors for these results. In particular, he finds that the deviation between the optimal default strategy and the false default strategy is high if the payout rate is low, and if the fraction of total equity obtained by the convertible bond holders upon conversion is high. 3 APPLICATION IN THE AREA OF REAL OPTION GAMES An important application of financial option pricing theory is in the area of real investments. These applications are frequently referred to as real options. Despite concerns on the suitability of option valuation techniques for the valuation of real investments (e.g., Ballwieser (2002)), the literature on real options has grown substantially during the last two decades. Since investment opportunities are often not exclusive to a single firm, strategic interactions across firms must be taken into account. Despite this fact, most of the real options work has been done in the area of exclusive options. Strategic interactions between the investment opportunities of different firms have been mostly neglected. I demonstrate the applicability of Koziol s results in the area of real options. For example, the results explain some licensing behavior characteristics of small firms that acquire the right to use the brand name of a large corporation in a small market segment. Suppose that the value of the brand in this specific market segment follows a geometric Brownian motion, and that existing assets can span the stochastic changes in that value. Assume that the licensee must make continuous payments to the licenser for the right to use the brand name. The difference between the payout from the brand value in this market segment as a fraction of brand value, and the license fee is the licensee s profit. If the brand value decreases, the licensee has the option to stop payments to the licenser by canceling the agreement. In this sense, he possesses a put option. On the other hand the licenser receives the license fees. If the value of his brand name in the specific market increases, he might be tempted to enter this particular market. If he does, the licenser would cancel the agreement with the licensee. In exchange for the forgone future license fees, he receives a fraction of the market value of his brand in this specific market segment. It is reasonable to assume that he only receives a fraction, not the SBR 58 APRIL

5 G. FRIEDL full amount, of the brand value, because he has to cope with difficulties of a new entrant. For example, the licenser s access to distribution channels in this specific market segment might not be as good as the licensee s. Canceling the agreement and entering the new market could be viewed as the exercise of a call option on a fraction of the brand value. Interpreting the equity holder in Koziol s model as the licensee and the convertible-debt holder as the licenser provides some interesting insights into the behavior of firms that enter into licensing agreements. This interpretation can help to value single components of licensing agreements. If the licenser has the option to cancel the licensing agreement and to enter the market, the licensee s market exit occurs earlier than in the case when the licenser must stick to the agreement and cannot enter the market. From the licensee s perspective, a licenser s long-term commitment would be quite valuable. Koziol s model allows for a quantification of this value. Moreover, using the comparative statics results, the model shows the main influencing factors for a high value long-term commitment. For example, the value of this long-term commitment is high if the payment rate for the licensee is relatively low, or if the fraction of the brand value, the licenser receives upon conversion is relatively high. This stylized discussion can serve as a first step in developing new application areas for this model. Of course, the model must be adjusted for different applications. The conditions under which the model can be applied must be carefully analyzed. Most importantly, the spanning condition must hold, i.e., capital markets must be sufficiently complete, so that one could construct a dynamic portfolio of assets, the price of which is perfectly correlated with the asset value V. However, in my view, strategic option games are a way to better understand empirically observable behavior not only in financial, but also in real investment markets. REFERENCES Ballwieser, Wolfgang (2002), Unternehmensbewertung und Optionspreistheorie, Die Betriebswirtschaft 62, Constantinides, George M. (1984), Warrant exercise and bond conversion in competitive markets, Journal of Financial Economics 13, Grenadier, Steven R. (1996), The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets, Journal of Finance 51, Huisman, Kuno J. M. and Peter M. Kort (2003), Strategic investment in technological innovations, European Journal of Operational Research 144, Koziol, Christian (2006), Optimal Debt Service: Straight vs. Convertible Debt, sbr 58, Leland, Hayne E. (1994), Corporate Debt Value, Bond Covenants, and Optimal Capital Structure, Journal of Finance 49, Spatt, Chester S. and Frederic P. Sterbenz (1988), Warrant exercise, dividends, and reinvestment policy, Journal of Finance 43, SBR 58 APRIL

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