**
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.