The Effects of Dilutions and Payout Policy on Equity- and Stock-linked Call Options on a Firm with Leverage

Brill, Nicola

The Effects of Dilutions and Payout Policy on Equity- and Stock-linked Call Options on a Firm with Leverage

Master Thesis

2022

Abstract

Capital-structure models are useful tools for pricing claims on equity. They provide insight into the effects of changing capital-debt structures on the value of options. Backwell et al. (2022) developed a capital structure framework which, in addition to a typical structural model, specifically considers the number of outstanding shares. This allows for the differentiation between options on total firm equity and options on share price. The extension by Backwell et al. (2022) also allows for the effects of dilutions and buyback policy on stock-linked options to be explored. Using the framework developed by Backwell et al. (2022) with asset value dynamics presented by Leland (1994), the capital-debt structure of a firm is modelled. Finitedifference methods utilising a generalised version of the Black-Scholes equation are then used to value and compare call options on total equity and call options on share price. Under the presented model, dilutions have little to no effect on stocklinked call option value in firms with low levels of leverage. However, dilutions clearly decrease the value of call options in firms with higher levels of leverage. Share buybacks significantly improve the value of stock-linked call options, particularly in lower leveraged firms where there is more available cash flow. This indicates that while shareholders are indifferent between cash dividends and share buybacks in a perfect market, holders of options on share price are not indifferent. In fact, option holders prefer payout policies that favour buybacks over dividends. Finally, the leverage effect is demonstrated by calculating implied volatilities under various levels of firm leverage.

Keywords

Mathematical Finance

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