In this analysis we look at one of the more unique methods to value the equity of a business that is loss making and is highly leveraged, i.e. a distressed business. In this instance we will be looking at Alliance Healthcare Services, Inc. (NYSE:AIQ).

Valuing a loss making, highly leveraged business can be very difficult. One of the traditional valuation methods is the discount cash flow (DCF) method. In situations where a firm has a substantial amount of debt there is a very real possibility that the business will default on this debt and a DCF will often be very inadequate for valuations in such situations. In distressed cases we can say that the equity of the business is the equivalent of a call option, as the business has the option to either liquidate the firm or pay off the debt. So as the value of the assets in a distressed firm has significant doubt, this and the option to liquidate add value to the equity. We therefore use a real options valuation model to value the equity of AIQ as the equivalent of a call option on the company.

Firstly, lets look at a simple example. If we have a distressed firm that's assets are currently valued at say $100 and they have debt with a value of $150 with an average maturity of 5 years, in a sense, we can say the equity of the firm is a call option. This is because in that 5 years they may climb above the debt amount and be in a better position to pay it off, or they are under and,liquidate and the call holder gets nothing. The future asset price is usually very hard to predict in a distressed firm and so its volatility has value. So as mentioned, because of these option characteristics of equity, the equity in a distressed firm can have substantial value and be valued as a call option.

Keeping this in mind, we use the Black-Scholes model to price the value the equity in AIQ as a call option. We will also run a Monte Carlo Simulation to price the call option. If the value derived is higher than that of the market value, it shows that investment in AIQ could result in a substantial gain, for those willing to take the risk. Note, that an investment in this situation is similar to making a gamble, but one where the cards you are holding tell you to take that bet as you are in a mathematically advantaged position.

The inputs for the Black-Scholes model are as follows:

Now we shall determine the above inputs for AIQ. AIQ is a business in financial distress and highly leveraged with a negative net asset value of nearly $160 million. Further, they have been loss making for nearly 3 years.

**Value of Underlying Assets**

As per the latest balance sheet figures of AIQ, their total asset value is $635 million. We will therefore use this as our asset value for this input.

**Strike Price**

This is the value at which the firm has risen above their debt and now has, in a sense, the ability to pay off their debt, that is excess book value. In this case it is the value of debt that must be climbed over. We use the conservative full balance sheet liability figure of AIQ as per there latest statements for this input, $795 million

**Volatility**

For this we use the standard deviation of the AIQ stock. The monthly volatility of AIQ over the previous 4 years has been 30.76%.

**Time of Expiration**

We used the latest annual report available of AIQ to determine the average life of their outstanding debt. Based on the figures the weighted average of their long term debt was 4.27 years, and we assumed their outstanding current liabilities have an average 0.5 years to maturity. We then determined a weighted average of long term debt and current liabilities and this resulted in a weighted average maturity of 3.89 years. Finally, we need to account for the year that has passed, since this information is old. This results in a period of 2.89 years.

**Risk Free Rate**

We used the yield for 5 year US treasuries as of today, which is 0.88%.

**Real Option Black-Scholes Valuation**

To conduct the valuation we placed the above inputs into the Black-Scholes option valuation model to determine the value of a call option as below.

The resulting value is $85.6 million for the equity of AIQ.

**Monte Carlo Simulation**

After this, we then ran the real option valuation with the same variables, but in a Monte Carlo simulation. A Monte Carlo simulation relies on a risk neutral valuation. As explained by Wikipedia "the technique applied then, is (1) to generate several thousand possible (but random) price paths for the underlying (or underlyings) via simulation, and (2) to then calculate the associated exercise value (i.e. "payoff") of the option for each path. (3) These payoffs are then averaged and (4) discounted to today. This result is the value of the option.

This resulted in a value of $70.8 million for AIQ's equity.

**Conclusion**

Our analysis determined that a highly leveraged, somewhat distressed firm's equity behaves like that of a call option, and can therefore be valued in a similar manner.

We ran this analysis on AIQ and it resulted in a value of $85.6 million and $70.8 million using the Black-Scholes and Monte Carlo option pricing models, respectively.

This tells us that the equity value of AIQ is potentially somewhere between $70.8 and $85.6 million. AIQ currently has a market value of $68.6 million. As such, it appears the Monte Carlo model is pricing the value of AIQ's equity very similarly to the market. However, the Black-Scholes model prices it at a premium of up to 25% to market value. This indicates that AIQ could be a good buy. However, those who invest should only be investors who are willing to take on the considerable risk of investing in a distressed company.

This strategy in a sense mimics investing in deep out of the money options at a discount to their intrinsic value and having hope that there will be a large pay off.

In the near future we hope to conduct this same analysis, with deeper insight into the selections and inputs, in several companies in similar situations. Depending on the results we will then construct a portfolio and track its performance.

Finally, please note that just as with many valuations this requires the input of many assumptions and these significantly affect the value. There can be much disagreement around these, but these are our opinion of the best estimates at the time.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.