## **Learning Outcomes**

After reading this article, you will understand how to extend traditional Net Present Value (NPV) analysis by including real options to obtain a more strategic view of project value. You will be able to identify and classify key types of real options, apply fundamental option valuation techniques (including Black-Scholes), and assess their practical impact on investment decisions in the ACCA Advanced Financial Management (AFM) context.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand the limitations of standard NPV and how real options expand appraisal techniques. In particular, you should focus your revision on:

- Identifying the main types of real options embedded in projects (delay, expand, abandon, switch)
- Classifying and explaining the value of flexibility within investment appraisal
- Applying the Black-Scholes Option Pricing model to real (non-financial) options in projects
- Evaluating how to calculate and interpret strategic NPV by including real options
- Advising on situations where a real options approach is appropriate compared to conventional NPV

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which of the following is NOT a common real option in a capital investment project?
   a) Option to expand
   b) Option to delay
   c) Option to short-sell shares
   d) Option to abandon

2. True or false? The inclusion of real options can only increase the calculated NPV of a project, never reduce it.

3. Briefly describe the main limitation of standard NPV analysis when applied to projects involving strategic uncertainty.

4. What are the five variables required to apply the Black-Scholes formula to value a real option in project appraisal?

## **Introduction**

Traditional NPV analysis assumes that managers commit today to a project's cash flows as initially forecast. However, real investment projects usually carry significant uncertainty and allow managers to respond as new information emerges. By recognising the value of flexibility—specifically, the right but not the obligation to take certain actions—real options theory provides a structured way to account for these managerial choices within investment appraisal. This article explains how real options transform NPV into strategic NPV, reviews key types of real options, and demonstrates practical valuation techniques relevant for the ACCA AFM exam.

> **Key Term: real option**
> A right, but not an obligation, embedded within a real (non-financial) investment project, allowing managers to make future choices—such as delaying, expanding, contracting, switching use, or abandoning a project—in response to changing circumstances.
>
> **Key Term: strategic NPV**
> The value of a project calculated by combining the conventional NPV with the additional value generated by real options, reflecting a more complete estimate of project worth under uncertainty.
>
> **Key Term: Black-Scholes Option Pricing model**
> A mathematical model for valuing European-style options, requiring five key inputs: current asset value, exercise price, time to expiry, volatility, and risk-free rate. Used in investment appraisal to value project-related real options.

## **STANDARD NPV VS. STRATEGIC NPV**

NPV quantifies the financial return of a project based on fixed expected cash flows. It does not account for the future choices managers may exercise as conditions change. This can undervalue projects where management flexibility adds significant value, particularly in uncertain or innovative contexts.

By identifying, quantifying, and valuing real options (such as the right to defer, expand, contract, or abandon a project), you can supplement the base NPV to obtain a _strategic NPV_. This more comprehensive approach often makes projects with high uncertainty and flexible response mechanisms appear more attractive.

### Types of Real Options

Projects may contain several forms of embedded flexibility. Key real option types include:

- **Option to delay**: The right to postpone project commencement until more information becomes available, reducing downside risk.
- **Option to expand**: The right to increase the scale if initial results are favourable.
- **Option to abandon**: The right to halt a project part-way and recover some value, limiting losses.
- **Option to switch/redeploy**: The ability to alter use between outputs, technologies, or markets if market conditions shift.

Each of these options creates value by allowing managers to respond optimally as uncertainty resolves.

> **Key Term: option to abandon**
> The real option giving management the right to cease a project before completion and recover some value, typically viewed as a put option on the project's future cash flows.
>
> **Key Term: option to expand**
> The real option to increase project capacity or commit extra resources if market or operational developments are favourable, similar to a call option.

### How Real Options Add Value

Including real options does not simply add an arbitrary premium to NPV. Each option is separately valued (often using adapted financial option models) and then added to the base case NPV calculation to yield strategic NPV. Real options are especially important in industries with volatile, uncertain, or rapidly changing conditions, where flexibility can impact investment timing and scale decisions.

### **Worked Example 1.1**

**A company is considering a new retail site that shows a base NPV of –£500,000. However, if successful, it could open a second, larger facility in two years. The option to expand will require a £2.5m investment at year 2 and could yield an additional NPV (excluding expansion cost) with present value £2.1m. The expansion decision is affected by high uncertainty, and the standard deviation of projected returns is 35%. Risk-free rate is 4%. Should management re-evaluate the project using a real options approach?**

> **Answer:**
> The base NPV is negative, but management holds a real option to expand, akin to a call option on future cash flows. By applying the Black-Scholes model (inputs: baseline asset value £2.1m, exercise price £2.5m, time 2 years, volatility 35%, risk-free 4%), the option may have significant value. If the calculated value of the expansion option exceeds the negative NPV, strategic NPV can become positive, making the project attractive on a flexible, options-aware basis.

## **VALUING REAL OPTIONS: THE BLACK-SCHOLES APPROACH**

To quantify the value of real options, the Black-Scholes model (originally for financial options) can be adapted to investment appraisal. The key challenge is to map project features to model inputs:

- **Baseline asset value (Pa):** Present value of project cash flows excluding the option exercise cost
- **Exercise price (Pe):** Investment outlay required if exercising the option
- **Time to expiry (t):** Period over which the option can be exercised
- **Volatility (s):** Annual standard deviation of the asset’s value (can be estimated from historical cash flows or industry data)
- **Risk-free rate (r):** Current yield on government securities

Using these, the Black-Scholes formula gives the value of the call or put option representing the project's flexibility.

### **Worked Example 1.2**

**A pharmaceutical company can delay launch of a new product for up to three years. The present value of future expected sales (excluding launch cost) is £10m. The cost to launch and produce is £8m. Volatility of project PV is estimated at 30% per year, and risk-free rate is 3%. What is the value of the option to delay?**

> **Answer:**
> Map the project elements to Black-Scholes variables: Pa = £10m, Pe = £8m, t = 3, s = 0.3, r = 0.03. Applying the model (often using a spreadsheet), management can derive the value of the option to delay. If, for example, the option is worth £2m, the strategic NPV = base NPV + real option value = £2m + (£10m – £8m) = £4m, confirming that flexibility is highly valuable in this context.

### **Exam Warning**

> When using Black-Scholes for real options, the inputs must be justified. If volatility data is unavailable, document your assumption. Marks are often lost for failing to state basis for key variable estimates.

## **STRATEGIC NPV IN PRACTICE**

Combining real option values with the base NPV allows a more informed investment decision. Strategic NPV = conventional NPV + sum of real option values.

However, not every project justifies the complexity of real option analysis. The approach is most useful when flexibility is significant, uncertainty is high, and managers have real choices they can exercise.

### **Worked Example 1.3**

**A mining project has a base NPV of £5m, but also an option to abandon after two years for a resale value of £7m if commodity prices fall. The PV of remaining cash flows if the project continues is calculated at £6m at that point. Volatility is 25%, risk-free rate is 3.5%, and two years are available before the decision must be made. What is the impact of the abandonment option?**

> **Answer:**
> Here, the option to abandon is similar to a put option. Using Black-Scholes with the baseline asset value (£6m), exercise price (£7m), time (2 years), volatility (25%), and risk-free rate (3.5%), the value of the abandonment option is calculated. This value should be added to the base NPV for a more complete (strategic) project valuation.

### **Revision Tip**

> In exam scenarios, clearly identify which real options are present before attempting valuation. State your reasoning for classifying the option as a call or a put, and show each input used in the Black-Scholes formula.

## **Summary**

Real options analysis supplements traditional NPV by valuing managerial flexibility. Tools like the Black-Scholes model make it possible—when reasonable estimates are available—to attach a monetary value to options to delay, expand, contract, abandon, or switch use. Strategic NPV therefore reflects both committed and contingent project value, supporting more robust investment decisions in uncertain environments.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- The limitations of conventional NPV when flexibility and uncertainty are present
- The main types of real options: delay, expand, abandon, switch
- How real options provide additional value in project appraisal
- Applying the Black-Scholes model to real options in investment decisions
- The calculation and interpretation of strategic NPV
- Practical steps for using real options valuation in ACCA AFM scenarios

## **Key Terms and Concepts**

- real option
- strategic NPV
- Black-Scholes Option Pricing model
- option to abandon
- option to expand

Integrating real options into appraisal - Expanding NPV to strategic NPV