Valuation of the Liability Structure by Real Options

2The New Allocation of Company Value Using the Optional Approach

2.1. Introduction

The review of financial literature dedicated to optional valuation of equity is first reserved for Black and Scholes (1973)¹. Their article presents a company financed by shares and investors whose assets are only made up of ordinary shares coming from another company. The bonds are zero-coupons and have a maturity of 10 years.

Moreover, the company plans to sell all of the shares it owns at the end of these 10 years, pay back the bond holders if possible and repay the remaining money to shareholders in the form of dividends. Under such conditions, the shareholders have an option over the company’s assets that are financed by the bond holders. At the end of the 10 years, the value of equity, w(x,t), is the value of assets, x, reduced by the face value of bonds if the latter is positive or zero. Thus, the economic value of bonds is x – w(x,t). If the company holds company assets rather than financial assets and if, at the end of the period of 10 years, it creates new shares to reimburse the bond holders (and repay the remaining money to the initial shareholders so they can part with their shares), the economic value of bonds remains x – w(x,t), where x is the value of the company.

Black and Scholes underscore that a rise in the company debt, with a constant company value, augments the risk of default and thus reduces the market value of bonds. This has repercussions that are negative for bond ...