Introductory Corporate Finance: Capital Budgeting - Real Options, Abandonment Expansion Timing Flexibility Strategic Valuing with Decision Trees or BlackScholes

What This Is

Real options are a financial concept that helps investors and corporate finance professionals value investments with uncertain outcomes. It's essential in corporate finance because it allows us to incorporate managerial flexibility and strategic decisions into our valuation models. For example, consider Tesla's decision to expand its electric vehicle production capacity. By using real options, we can value this investment by considering the potential to abandon or delay the project if market conditions change.

Key Formulas & Models

• Real Option Value (ROV) = PV of expected cash flows + PV of option value – measures the value of a real option, which is the present value of expected cash flows plus the present value of the option value.
  • PV: present value
  • ROV: real option value
• Black-Scholes Model: d1 = (ln(S/K) + (r + ?^2/2)T) / (T) – calculates the probability of exercising an option.
  • S: stock price
  • K: strike price
  • r: risk-free rate
  • ?: volatility
  • T: time to expiration
• Decision Tree: Expected Value = ?(probability × outcome) – calculates the expected value of a decision tree.
  • probability: probability of each outcome
  • outcome: value of each outcome
• Abandonment Option Value (AOV) = PV of expected cash flows - PV of expected abandonment costs – measures the value of an abandonment option.
  • PV: present value
  • AOV: abandonment option value
• Expansion Option Value (EOV) = PV of expected cash flows - PV of expected expansion costs – measures the value of an expansion option.
  • PV: present value
  • EOV: expansion option value
• Timing Option Value (TOV) = PV of expected cash flows - PV of expected timing costs – measures the value of a timing option.
  • PV: present value
  • TOV: timing option value
• Flexibility Option Value (FOV) = PV of expected cash flows - PV of expected flexibility costs – measures the value of a flexibility option.
  • PV: present value
  • FOV: flexibility option value
• Strategic Option Value (SOV) = PV of expected cash flows - PV of expected strategic costs – measures the value of a strategic option.
  • PV: present value
  • SOV: strategic option value

Step-by-Step Calculation

1. Identify the type of real option (abandonment, expansion, timing, flexibility, or strategic).
2. Estimate the expected cash flows and costs associated with the option.
3. Calculate the present value of the expected cash flows and costs.
4. Calculate the option value using the relevant formula (e.g., Black-Scholes Model for a call option).
5. Add the option value to the present value of the expected cash flows to get the real option value.
6. Consider the impact of managerial flexibility and strategic decisions on the option value.

Common Mistakes

• Mistake: Ignoring the impact of managerial flexibility on the option value.
  • Correction: Consider the impact of managerial flexibility on the option value by using decision trees or real options models.
• Mistake: Using the wrong discount rate for the option value.
  • Correction: Use the risk-free rate or the cost of capital for the option value, depending on the type of option.
• Mistake: Failing to consider the impact of uncertainty on the option value.
  • Correction: Use probability distributions or sensitivity analysis to consider the impact of uncertainty on the option value.

Exam / CFA Tips

• Tip: Be able to distinguish between different types of real options (abandonment, expansion, timing, flexibility, and strategic).
• Tip: Understand how to calculate the option value using decision trees or real options models.
• Tip: Be able to identify the key assumptions and limitations of real options models.

Quick Practice Problem

A company has EBIT of $10M, interest $2M, tax 25% – compute DFL (Degree of Financial Leverage).

Answer: DFL = 5 (EBIT/Interest) = 5.

Explanation: DFL measures the sensitivity of EBIT to changes in sales.

Last-Minute Cram Sheet

• Real options are a financial concept that helps investors and corporate finance professionals value investments with uncertain outcomes.
• The Black-Scholes Model is used to calculate the probability of exercising an option.
• Decision trees are used to calculate the expected value of a decision tree.
• Abandonment option value (AOV) measures the value of an abandonment option.
• Expansion option value (EOV) measures the value of an expansion option.
• Timing option value (TOV) measures the value of a timing option.
• Flexibility option value (FOV) measures the value of a flexibility option.
• Strategic option value (SOV) measures the value of a strategic option.
• In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.
• Real options are not the same as financial options.
• The risk-free rate is used as the discount rate for the option value.
• The cost of capital is used as the discount rate for the option value.