10.1 Intrinsic Value and Option Pricing Theory


The valuation techniques described in the previous chapters cannot easily answer the following question: why do some stocks with negative shareholder’s equity trade with positive stock prices? This is not an uncommon occurrence; in March of 2010, more than 50 companies with a market value of $500m or more had negative equity, i.e. their debts were larger than their assets.  But their market value was positive.

If you think about it a second, the reason for the positive value of the stock has to be that the shareholders expect the first to become solvent and profitable in the future.  So to value such firms, we cannot do what have been doing, namely projecting current income or free cash flows into the future.  The FCFE model is sometimes extended to a three stage model to handle such companies; in such a model, the company has negative earnings in stage 1, moves from negative to positive in stage 2, and is profitable in stage 3.  The problem of specifying exactly how these earnings will change over time can be difficult because you will have to say what happens to the firm every year until stage 3 (after which it grows in perpetuity).

A particularly elegant solution to this problem is provided by option pricing theory, and in particular a model presented by Merton (1974) which uses option pricing techniques to value a firm.  In Merton’s model, a stock, when viewed from the perspective of the fundamental accounting equation (Total Assets equal Total Liabilities plus Owners Equity) can be thought of as call option on  the assets of the firm.   Think about it this way.  The firm currently has some assets and some debt, with the value of the debt being greater than the value of the assets.  Suppose the debt matures in 5 years.  So even though there is negative equity, what actually matters is whether the firm can pay off the debt when it is due.  So we need to project what happens in five years.  If at that time, the assets are greater than the debt, the firm will be solvent, and the shareholders will own the residual claim, which is the difference between the assets and the debt.  If not, the shareholders will get nothing (since the firm will be insolvent).  But this means that the shareholders have a call option on the assets of the firm, and so the stock can be valued in the same way as we value an option. 

Note that in this chapter, we assume familiarity with option pricing theory. To put the discussion in option pricing terms, the underlying asset is the total assets (!) of the firm, the strike price is the face value of the debt, and the time to expiration is the time to maturity of the debt.  The value of the stock is the value of a European call option. 

Our specific learning objectives in the chapter are:

·         To review Altman’s Z-Score Model for Bankruptcy

·         To become familiar standard credit agency ratings of default risk

·         To become familiar with Merton’s model for a distressed firm

·         To apply this model using Valuation Tutor

We start by reviewing Altman’s Z-Score for predicting bankruptcy and then extend this approach to understanding the information available from the credit agencies that a firm provides in their 10-K report.