By Kudret Kutbay, Prof. Dr. Christoph Auckenthaler, 27 December 2000

The thesis of Kudret Kutbay under Professor Christoph Auckenthaler at the Institute of Swiss Banking of the University of Zurich primarily discusses different valuation models. It also provides reasons for and against the use of these products in corporate finance.

Executive Summary

1. Definition of the problem

The asymmetrical information, objectives and interests that prevail among market participants ensure that corporations continue to issue special financing instruments such as hybrid convertible and warrant bonds. This paper examines these two instruments from the perspective of corporate finance.

Hybrid financial instruments contain elements of bonds as well as contingent claims. This involves interest payments and repayment of principle at par value on the one hand and additional rights that promise participation in the equity capital of the issuer on the other hand.

Whereas valuation of the bond component of a warrant bond can be carried out straightforwardly through the discounted cash flow approach (DCF approach), valuation of the warrant requires a more detailed analysis since its exercise would result in dilution of the participation rights held by existing shareholders.

The problem with the valuation of convertibles is that the various conditions stipulated in such contracts represent multiple implicit options that mutually affect each other. Hence, for example, the redemption option (i.e. call feature) that the issuer holds causes the value of the conversion option to immediately drop to zero if the convertible bond is redeemed. For this reason, from the standpoint of an investor, a convertible cannot simply be viewed as a long position in a bond and a call option for the conversion right plus a short call option for the redemption right.

2. Procedure

The first section of this paper looks at similarities and differences as well as reasons for the existence of both instruments, both from the perspective of financial theory and practical financial usage.

From the viewpoint of financial theory, the foundations of Agency Theory are discussed first and then expanded to Signaling Theory and Pecking Order Theory. Together with the explanatory approach of the after-issue risk-shifting problem, these theories are drawn on to explain the existence of hybrid financial instruments.

From the viewpoint of practical financial usage, the primary reasons why issuers and investors make use of convertible and warrant bonds are examined. At the same time, the paper also looks at strategic reasons for their use, such as the financing of long-term projects and the postponement of dilution effects, as well as at real options. Moreover, the tax and demand-side reasons are mentioned. In conclusion, the traditional belief that hybrid financial instruments are a source of cheap capital is analyzed.

The second section of this paper focuses on describing and explaining selected valuation models. First of all, the DCF approach for valuing the bond component of warrant bonds is introduced. Approaches that do not consider dilution effects are illustrated for the warrant - for example, the Black/Scholes Model and the Binomial Model. The paragraph on approaches that explicitly model the dilution effects of the warrant looks at the method of Galai/Schneller (1978) as well as that of Schulz/Trautmann (1994).

Concerning the valuation of convertibles, the approaches of Ingersoll (1977) as well as of Brennan/Schwarz (1977) are explained. Moreover, the Binomial Model is expanded for use in the valuation of convertibles. This extension was implemented by the author in spreadsheet form based on a description by Hull (2000). At the end of the second section of the paper, the outlined models’ suitability for practical use in assessing convertible and warrant bonds is examined.

The third section of the paper puts selected models into practical use in evaluating different convertible and warrant bonds in the Swiss and US markets. In an additional step, an attempt is made to explain any differences between the values calculated by the models and those of the market.

3. Results

The observations from the perspective of financial theory and practical financial usage indicate that hybrid financial instruments are still capable of mitigating certain problems that are attributable to asymmetrically distributed information.

By granting indirect participation rights, the issuers can reduce their regular payment obligations through providing a lower coupon. However, in order to be able to fairly calculate the magnitude of the coupon reduction relative to customary bonds, a valuation procedure that determines the value of the indirect participation rights is needed.

In the valuation of warrant bonds, the focus is on determining the value of the warrant, whereas the value of the bond component can be calculated through the simplified DCF approach.

Schulz/Trautmann (1994) demonstrated with their model that ignoring the dilution effect of at-the-money or in-the-money warrants does not result in any tangible error. With increasing residual maturity, lower out-of-the-money warrants can also increasingly be valued while ignoring dilution without causing any tangible error. Bearing in mind these restrictions, the valuation of the warrant can be carried out with relatively little error based on existing option valuation methods for customary options. In their analysis, Schulz/Trautmann (1994) assume that the option-like warrant valuation is very precise if the potential dilution is already reflected in the current stock price, the warrant is in the money and the sequential exercise of American warrants is not optimal.

The deviations of the model prices relative to the market price range from -0.28% to +0.31%, which is why the practical application can be viewed as a confirmation of the hypothesis of Schulz/Trautmann (1994). In one case, the hypothesis could not be employed because the warrant was deeply out of the money.

The analytical approaches for valuing convertibles start with the Black/Scholes differential equation and solve it after the ancillary conditions of the observed situation have correspondingly been defined. In order to put these approaches into practical usage, a sound understanding of mathematics is required.

The Binomial Model, which is intuitively easy to understand, makes it possible to integrate complicated contract conditions. In this paper, the Binomial Model described by Hull (2000) is implemented by the author in spreadsheet form, taking into account the redemption option of the issuer, the conversion right of the investor, variable redemption prices over time, coupon payments, dividend payments and thus the early exercise of the conversion right.

Practical application has demonstrated that the implemented Binomial Model is certainly capable of valuing the convertible correctly. At the same time, however, the following factors must be taken into consideration:

• The volatility of the underlying stock has the greatest influence on the valuation. The estimation of the volatility therefore may not be carried out independently from the implicit market volatility prevailing on the day of valuation.
• The liquidity of the underlying stock is another important parameter that can materially influence the valuation. Since the applied model does not consider these parameters, in a case in which the underlying stock is very illiquid, an overvaluation of convertible relative to the market price could be seen.

One attribute of the valuation model for convertibles deserves special mention. The special construction of the Binomial Model, which considers the credit risk of the issuer by incorporating both the risk-free interest rate and the risk-adjusted interest rate into the valuation algorithm, makes it possible to calculate the credit spread estimated implicitly for the issuer by market participants. At the same time, the implicit volatility observed in the market is entered into the model. By setting the model price equal to the market price, the credit spread can be calculated in an iterative manner.

4. General assessment

The situation at the moment in the Swiss and US markets suggests that warrant bonds are no longer in demand. This trend appears to be a consequence of the efficient markets, which allow investors to replicate warrant bonds by means of other instruments.

In contrast, convertibles remain in demand because they are less easily replicated in view of the complicated contractual structures.

From the perspective of equity investors, convertibles provide a hedge against falling stock prices because they respond less strongly to the volatility of equities and exhibit a bond floor. For bond investors, convertibles offer participation in rising stock prices without requiring them to forgo the regular coupon payments.

As far as the issuers are concerned, convertibles allow them to mitigate the problems caused by asymmetrically distributed information by granting investors indirect participation rights.

Thanks to the lower interest coupons relative to customary bonds, convertible and warrant bonds make it possible for corporations to finance their projects without excessively increasing their regular payment obligations. In exchange for receiving lower interest payments, investors are granted rights that promise participation in the future success of the issuer.