Merton's Distressed Firm Valuation Model

Contents - Index

Merton's Distressed Firm Valuation Model
©2009 OS Financial Trading System

If a firm is not a going concern then it is expected to have some much shorter finite life left. Under these circumstances the firm's stock is more accurately assessed as an option.
Aside: If the time to maturity for an option approaches infinity then the stock and option values coincide which is why this model does not add value for a going concern whose life is assessed to be very long.
Merton's option model then views the equity holders as having a call option claim on the underlying assets of the firm. The strike price for this option equals the Face Value of the Debt. This follows because bondholders must be paid in full before stockholders receive a payoff.
Summary of Inputs are:
Value of the underlying asset = Value of the Firm as a whole (V)
Exercise Price = Face Amount of Outstanding Debt (F)
Life of the Option = this is equated to the average duration of the outstanding debt (T)
Volatility of the underlying firm value = This is an important estimate for the option value (s). This can be estimated from the stock price volatility as indicated below.
Riskless rate of interest = the Treasury rate corresponding to the life of the option
The value of equity then follows from Black Scholes:

and the implied relation from equity volatility to firm volatility is:

This model can be further applied to estimating the distance to default which can be converted into an expected default probability (Bharath and Schumway 2004 RFS 2008).