Application of option pricing theory in investment decisions

Welcome to the World of Real Options!

Hi there! If you’ve made it this far in your AFM journey, you already know how to calculate Net Present Value (NPV). But here’s a secret: NPV has a flaw. It assumes that once we start a project, we follow a rigid path without ever changing our minds.

In the real world, managers are flexible. They can wait for better market conditions, expand if things go well, or quit if things go badly. This managerial flexibility has value, and that’s exactly what "Real Options" help us measure. Don't worry if this seems tricky at first—we're going to break it down step-by-step!

1. Why NPV Isn't Always Enough

Traditional NPV is static. It’s like a "now or never" decision. However, real-life projects are dynamic.

The Limitation: NPV often ignores the value of being able to change a decision later. This means a project with a slightly negative NPV might actually be worth doing if it gives us the "option" to do something profitable in the future.

The Solution: Total Value = Traditional NPV + Value of Real Options.

2. The Three Big Types of Real Options

In the ACCA AFM syllabus, you mainly need to understand three types of options. Think of these as "financial insurance" for your projects.

A. The Option to Delay (Wait)

Imagine you own a piece of land. You could build an office block today, but the market is uncertain. If you wait a year, you’ll know if rents are going up or down.
- What it is: A Call Option.
- Why: You have the right, but not the obligation, to invest (buy the project) later.

B. The Option to Expand

You launch a new product in a small test market. If it's a hit, you have the right to build a massive factory and go global.
- What it is: A Call Option.
- Why: The initial small project is like a "ticket" that lets you make a bigger investment later if things look good.

C. The Option to Abandon

You start a project, but you include a clause in your contracts that allows you to sell the equipment and exit if losses get too high.
- What it is: A Put Option.
- Why: You have the right to "sell" or get rid of the project at a fixed price (the salvage value) to stop further losses.

Quick Review: Delay and Expand are Call options (the right to buy/start). Abandon is a Put option (the right to sell/quit).

3. Mapping Project Variables to Black-Scholes

To calculate the value of these options, we use the Black-Scholes Option Pricing Model (BSOPM). The hardest part for most students is knowing which number from the exam scenario goes into which variable. Let’s make it simple:

\(P_a\) (Current Price of the Asset): This is the Present Value (PV) of the future cash flows the project will generate.
\(P_e\) (Exercise Price): This is the cost to invest in the project (for Call options) or the salvage value (for Put options).
\(r\) (Risk-free rate): Usually given in the question as a percentage.
\(t\) (Time to expiry): How long you can wait before you have to make the decision.
\(s\) (Volatility/Standard Deviation): This represents the risk or uncertainty of the project’s cash flows.

Memory Trick! Think of \(P_a\) as what you GET and \(P_e\) as what you PAY.

4. Using the Black-Scholes Formula

You don't need to memorize the big formula (it's in the exam formula sheet!), but you must know the steps to solve it.

Step 1: Calculate \(d_1\)

\( d_1 = \frac{\ln(P_a/P_e) + (r + 0.5s^2)t}{s\sqrt{t}} \)

Step 2: Calculate \(d_2\)

\( d_2 = d_1 - s\sqrt{t} \)

Step 3: Find \(N(d_1)\) and \(N(d_2)\)

Use the normal distribution tables provided in the exam to find these probabilities. Hint: These represent how likely the option is to finish "in the money."

Step 4: Plug into the Call Option formula

\( Value = (P_a \times N(d_1)) - (P_e \times e^{-rt} \times N(d_2)) \)

Common Mistake: Forgetting that \(P_e\) needs to be discounted using the risk-free rate (\(e^{-rt}\)) in the formula! Always double-check your calculator work here.

5. Real-World Example: The "Phased" Project

Scenario: A pharma company is considering a new drug.
Phase 1: Costs \$10m today. NPV is -\$2m (Negative!).
Phase 2: If Phase 1 works, they can spend \$100m in 3 years to launch globally. The PV of those future global cash flows is \$80m.

In a normal NPV exam, you'd say "Don't do it!" because NPV is negative.
But in AFM, we see Phase 1 as the cost of a Call Option to expand. If the Option Value is \$5m, then:
\nTotal Value = -\$2m (NPV) + \$5m (Option) = +\$3m.
Decision: Accept the project!

6. Assumptions and Limitations

Examiners love asking you to critique the model. If you're stuck, remember these points:

• Standard Deviation (\(s\)): In real life, it’s very hard to estimate the volatility of a unique project (unlike a stock price).
• Risk-free rate (\(r\)): The model assumes this stays constant, but interest rates change.
• Exercise: BSOPM assumes the option can only be exercised at the very end (European style), but real-life managers can often exercise options at any time (American style).
• Cost: Using the model is complex and might cost more in management time than it's worth.

7. Key Takeaways for the Exam

1. Identify the option: Is it a right to wait (Delay), grow (Expand), or quit (Abandon)?
2. Label your variables: Clearly state what your \(P_a, P_e, r, s,\) and \(t\) are before calculating.
3. Interpret the result: If the "Total Value" (NPV + Option) is positive, the project is worth it.
4. Use your "Common Sense" check: If uncertainty (\(s\)) or time (\(t\)) increases, the value of a real option usually increases. This is because you have more time for things to turn out great, but you are protected from the downside!

Did you know? High risk is usually bad for traditional NPV (it increases the discount rate), but high risk increases the value of a Real Option. This is because options give you the "upside" of risk without the "downside."

You've got this! Practice mapping the variables in past exam questions, and you'll find that the math becomes second nature.