Option Pricing and Its Application in Corporate Valuation

Before applying option pricing to corporate valuation, we need a refresher. The Black-Scholes model is used for European-style options (exercised only at expiration). It's driven by several inputs: current stock price (S), strike price (K), time to expiration (T), risk-free interest rate (r), volatility (σ), and dividends (D). The formula is complex, but its core logic is the present value of the expected payoff.

Example: A company's stock currently trades at $50 (S). A one-year call option has a strike price of $55 (K), the risk-free rate is 5% (r), and the volatility is 30% (σ). We can use a Black-Scholes calculator (readily available online) to determine the option's value.

Binomial option pricing, on the other hand, is a more flexible, discrete-time model. It assumes the stock price can move up or down over a series of time steps. It's especially useful for valuing American-style options (exercisable anytime before expiration). The model creates a tree of possible stock prices and calculates option values at each node, working backward from the expiration date.

Example: Consider a simple two-period binomial tree. The stock is currently at $100. In each period, it can go up 10% or down 10%. With a strike price of $105, we can calculate the option's value at each step and then discount back to the present. The binomial model allows us to easily incorporate the possibility of early exercise. We will use this model for more complex case studies.

Real options are the application of option pricing theory to capital budgeting decisions. They represent management's flexibility to make decisions in response to future events. Key real options include:

• Option to Expand: The right, but not the obligation, to expand a project if market conditions are favorable. This is similar to a call option.
• Option to Abandon: The right, but not the obligation, to abandon a project if market conditions are unfavorable. This is similar to a put option.
• Option to Delay: The right, but not the obligation, to postpone an investment. This can be viewed as an option to wait and learn more about the project's prospects.
• Option to Switch: The flexibility to change the output or the input of a project. Think of a power plant that can switch between different types of fuel.

Example: Option to Expand. A pharmaceutical company is considering a new drug development project. The initial investment is $100 million. The present value of the expected cash flows is estimated at $110 million, yielding a positive NPV. However, the company believes that if the drug is successful, it can significantly expand its production capacity, doubling the expected cash flows. This expansion opportunity is a real option. If the expansion requires an additional investment of $50 million in three years, and the present value of the increased cash flow is $150 million, we can use option pricing models (or decision tree analysis) to calculate the value of the expansion option. This increases the total value of the project.

Note: Real option valuation often uses the binomial model due to its ability to handle multiple periods and the complexities of management's flexibility.

ESOs and warrants create a dilution effect. ESO's grant employees the right to purchase the company's stock at a predetermined price. Warrants are similar, but issued to other investors. Both dilute the existing shareholder's equity. To accurately value a company, we must consider this dilution.

Valuation Implications:

• Decrease in value per share: As more shares are outstanding, the value of each existing share decreases.
• Exercise Price and Dilution: The exercise price of ESOs/warrants is crucial. The higher the exercise price relative to the current market price, the less the dilutive effect.
• Black-Scholes Application: The Black-Scholes model (or a variation) can be used to estimate the value of ESOs and warrants as if they were traded options. This allows you to estimate their impact on equity value. This value is then deducted from the equity value before dividing by the new share count.

Example: ESOs. A company has 10 million shares outstanding, and 1 million unexercised ESOs. The current stock price is $20, and the exercise price of the ESOs is $15. The Black-Scholes model estimates the value of each ESO at $6. Therefore, the total value of the ESOs is $6 million. If the dilution is not adjusted for, then the company's equity is overvalued.

Distressed companies often face complex capital structures, including debt, equity, and potentially warrants and convertible securities. Option pricing can be particularly valuable in these situations.

Debt as a Put Option: The equity of a distressed company can be viewed as a call option on the firm's assets, while the debt can be viewed as a short put option. If the company's asset value falls below the face value of the debt, the debt holders effectively take control of the firm's assets.

Valuation of Bankruptcy Options: The option to abandon or the option to file for bankruptcy is also a critical real option, effectively a put option. Option pricing models can provide insights into the likelihood of default, helping in negotiations with creditors and restructuring efforts.

Example: A company has assets worth $50 million and debt of $60 million due in one year. The volatility of the company's assets is 40%. The equity holders effectively have a call option on the company's assets with a strike price of $60 million. The value of this call option represents the equity value. Conversely, creditors have a put option on the assets to protect their interests, in the event the company's assets are valued at less than their debt.