Real options
Real options give a company the right, not the obligation, to act later: wait, expand, shrink or abandon, change prices or output, or proceed only if an outside price is right. Flexibility can turn a project with a negative net present value (NPV) positive. Project NPV = NPV without options − option cost + option value.
Before this: The capital allocation process, NPV and IRR, Probability Trees and Conditional Expectations
On the exam
- Describe types of real options relevant to capital investments
Describe the types of real options relevant to capital investments. Expect to name the option from a scenario, apply the project NPV equation, and read a small decision tree to value an abandonment option.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
What is a real option?
The NPV method in the earlier lessons assumes a company decides everything on day one and then sticks with it. In practice, many investments are a series of decisions: some taken today and others postponed until the company has learned more. A real option is the right, but not the obligation, to take such an action in the future, on a real investment rather than a financial asset. The company should exercise it only if doing so adds value.
Just as a financial option derives its value from an underlying asset, a real option depends on future events for the company: demand, a commodity price, a regulatory decision. This flexibility can add a great deal to a project’s NPV.
What types of real option are there?
- Timing option Memorize delay or stage the investment to learn more
- Sizing option Memorize change the scale after the investment
- Abandonment option stop and recover value if results disappoint
- Growth (expansion) option invest more if results are strong
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- Flexibility option Memorize operating choices once the project runs
- Price-setting option raise prices when demand exceeds capacity
- Production flexibility option change output: overtime, shifts, inputs
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- Fundamental option Memorize the whole value rides on an outside variable
- Examples a mine or a gas field depends on the commodity price; many R&D projects
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| Option | What it lets you do | Example |
|---|---|---|
| Timing | delay or stage the investment to learn more | wait a year for a subsidy decision before building |
| Sizing: abandonment | stop and recover value if results disappoint | sell specialized equipment if demand flops |
| Sizing: growth / expansion | invest more if results are strong | add floors to a warehouse if leasing runs ahead of plan |
| Flexibility: price-setting | raise prices when demand exceeds capacity | a ski resort lifts weekend ticket prices when queues form |
| Flexibility: production | change output: overtime, extra shifts, input switching | a power plant switching between gas and oil |
| Fundamental | the whole value depends on an outside variable | a lithium deposit developed only if lithium prices are high |
Try this 0 of 3
- Switch on the abandonment option and watch the decision flip
- Cut the sale value to 20 or less
- Raise strong demand until the plant is worth building without any option
Build for 200: strong demand (60%) pays 330, weak demand (40%) pays 20. NPV without flexibility is −12.73. The right to sell for 110 if demand is weak is worth 32.73.
- Decision today, NPV −12.73, (warning)
- Build: Build for 200, −12.73, NPV
- p = 0.6: Strong demand, +330, year 1 cash flow
- p = 0.4: Weak demand, +20, year 1 cash flow, (warning)
- Skip: Don't build, 0, NPV
- Build: Build for 200, −12.73, NPV
Hover over or tap a box to follow its path.
Show working
NPV without the option = −200 + (0.6 × 330 + 0.4 × 20) ÷ 1.1 = −12.73
With the option, the weak branch pays max(keep 20, sell 110) = 110: NPV = −200 + (0.6 × 330 + 0.4 × 110) ÷ 1.1 = +20.00
Value of the option = p(weak) × max(0, 110 − 20) ÷ 1.1 = 0.4 × 90 ÷ 1.1 = 32.73
Project NPV = NPV without − cost of the option + value of the option = −12.73 − 0.00 + 0 (option off) = −12.73
- 0.6×330=STO1
- 0.4×20+RCL1=÷1.1−200=−12.73
STO store · RCL recall a stored number
- 0.6ENTER330×0.4ENTER20×+1.1÷200−−12.73
ENTER enter (on the HP, puts the number on the stack)
Display: −12.73
- 110−20×0.4÷1.1=32.73
- 110ENTER20−0.4×1.1÷32.73
ENTER enter (on the HP, puts the number on the stack)
Display: 32.73
A timing option gives up near-term returns in the hope of better information; investments can also be sequenced so that one project creates the option for the next. A sizing option changes the scale after the investment. The abandonment option lets the company walk away: if the cash from abandoning exceeds the present value of continuing, it should. The growth option (also called an expansion option) is the mirror image, investing more when results are strong.
A flexibility option concerns how the project is run. With a price-setting option , a firm facing demand beyond its capacity raises prices instead of output. With a production flexibility option , it changes output when demand differs from the forecast, for instance by adding overtime or extra shifts.
A fundamental option is different: the entire value of the investment depends on factors outside the firm’s control. A lithium deposit is worth developing only if lithium prices are high enough; a natural gas field depends on the gas price. Many research and development (R&D) projects behave in the same way.
How do you value flexibility?
There are three approaches.
- Ignore the options Use it if NPV is already positive, invest
- Options are a bonus the NPV is a minimum
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- Project NPV equation Memorize NPV without − option cost + option value
- Decision trees or option pricing models Use it for more complex cases
- Decision tree probability-weight the branches
- Option pricing model needs inputs that are hard to observe
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- Ignore the options if NPV is already positive. If the NPV is positive without options and the project carries options that could add to it, the NPV is a minimum, so invest.
- Use the project NPV equation. Start from the NPV on expected cash flows, subtract what the option costs and add what it is worth.
- Use decision trees or option pricing models for more complex projects.
A project has an NPV of -6.00 without options. A real option costs 1.50 and is worth 9.00. The project's NPV including the option is closest to:
-6.00 − 1.50 + 9.00 = 1.50
Project NPV with the option1.50
- 6+|-−1.5+9=1.5
+|- change sign
- 6CHSENTER1.5−9+1.5
CHS change sign · ENTER enter (on the HP, puts the number on the stack)
How does a decision tree value an abandonment option?
A decision tree lays out the outcomes in each branch with their probabilities and values the project as a probability-weighted average. The abandonment option shows up as the better of two payoffs on the weak branch.
Go deeper Why option pricing models are hard to use, and what real options are not
Option pricing models need inputs that are hard to observe for a real project: the volatility of the project’s value, the timing of decisions, the probability of each outcome. That is why decision trees, which make the assumptions visible, are common. Sequential investments such as the stages of R&D can be thought of as options on options, which makes valuation harder still.
A real option is not a hedge. It adds flexibility inside a project. An airline that wants to lock in the cost of next year’s jet fuel uses financial derivatives for that, not real options.
Exam tip The cost of an option is subtracted, its value is added. Forget the cost and you overstate the project.
Memorize this
MemorizeTypes of real option
| Option | What it lets you do | Example |
|---|---|---|
| Timing | delay or stage the investment | wait for a subsidy decision |
| Sizing: abandonment | stop and recover value | sell specialized equipment if demand fails |
| Sizing: growth / expansion | invest more when results are strong | add a second production line |
| Flexibility: price-setting | raise prices when demand beats capacity | a ferry lifts peak fares |
| Flexibility: production | change output | overtime, extra shifts, input switching |
| Fundamental | value depends on an outside variable | a mine opened only if the metal price is high |
Memory hook T-S-F-F: Timing, Sizing, Flexibility, Fundamental. Sizing has two ends (shrink or grow); flexibility has two levers (price or output).
Know it cold Project NPV = NPV without options − option cost + option value. An option is a right, never an obligation: exercise only if it adds value.
MemorizeAbandonment test
| Compare | Action |
|---|---|
| cash from abandoning > value of continuing | exercise: abandon |
| cash from abandoning < value of continuing | keep going |
Memory hook You walk away only if the sale price beats what the project is still worth to you.
Know it cold In a decision tree, use the better of the two payoffs on each branch.
- Timing option Memorize delay or stage the investment to learn more
- Sizing option Memorize change the scale after the investment
- Abandonment option stop and recover value if results disappoint
- Growth (expansion) option invest more if results are strong
-
- Flexibility option Memorize operating choices once the project runs
- Price-setting option raise prices when demand exceeds capacity
- Production flexibility option change output: overtime, shifts, inputs
-
- Fundamental option Memorize the whole value rides on an outside variable
- Examples a mine or a gas field depends on the commodity price; many R&D projects
-
- Ignore the options Use it if NPV is already positive, invest
- Options are a bonus the NPV is a minimum
-
- Project NPV equation Memorize NPV without − option cost + option value
- Decision trees or option pricing models Use it for more complex cases
- Decision tree probability-weight the branches
- Option pricing model needs inputs that are hard to observe
-
Quick example
NPV without options is 8.0, the option costs 1.0 to hold and is worth 3.5. Project NPV = 8.0 − 1.0 + 3.5 = 10.5.
- 8−1+3.5= 10.5
- 8ENTER1−3.5+ 10.5
ENTER enter (on the HP, puts the number on the stack)
How it is asked
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Name the option
A retailer signs a store lease that lets it hand back the premises after two years for a small fee. What is the option?
An abandonment option, a sizing option. Trap: growth (that is the opposite end).
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Option value from the equation
NPV without options 7.0; option cost 1.8; project NPV with the option 9.2. Option value?
9.2 = 7.0 − 1.8 + V, so V = 4.0. Traps: 2.2 (ignores the cost) and 11.0.
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Decision tree
Strong demand 60%, weak 40%. Abandon in the weak branch for more than the weak cash flow. What is the option worth?
Probability of the weak branch × (sale price − weak cash flow), discounted one period.
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Fundamental option
A drug company funds early trials, and the whole project pays off only if the compound proves effective.
Fundamental option. The value depends on an outcome outside the firm's control, as in many R&D projects. Trap: timing option (nothing is being postponed).
Exam traps
- Confusing real options with financial hedges. A real option adds flexibility to a project; commodity price risk is hedged with financial derivatives.
- Forgetting to subtract the cost of the option in the project NPV equation.
- Treating an option as an obligation. The company exercises only when it adds value.
- Calling an expansion option an abandonment option (or the reverse). Both are sizing options, at opposite ends.
Checkpoint
6 exam-style questions. About 90 seconds each.
1A company can add a second production line if early sales beat expectations. This is a(n):
2A project's NPV without flexibility is EUR 12.0 million. Waiting a year for better information costs EUR 2.5 million, and the project's NPV including the timing option is EUR 14.0 million. The value of the timing option is closest to:
3A mining company owns a nickel deposit that it will develop only if the nickel price rises above a set level. The deposit most likely contains a:
4A company can invest 150 now. Next year, with a probability of 55%, demand is strong and the cash flow is 260. With a probability of 45%, demand is weak and the cash flow is 30, but the company could instead sell the assets for 100. The required return is 8%. The value of the abandonment option is closest to:
5A bakery adds extra shifts when orders exceed its planned production. This is best described as a:
6A project has a positive NPV when its real options are ignored, and it also carries valuable real options. The firm should most likely:
Key takeaways
- A real option is the right, not the obligation, to take an action later.
- Types: timing, sizing (abandon or expand), flexibility (price or production), fundamental.
- Project NPV = NPV without options − option cost + option value.
- Flexibility can turn a rejected project into an accepted one.
Quick example
NPV without options is 8.0, the option costs 1.0 to hold and is worth 3.5. Project NPV = 8.0 − 1.0 + 3.5 = 10.5.
- 8−1+3.5= 10.5
- 8ENTER1−3.5+ 10.5
ENTER enter (on the HP, puts the number on the stack)
All Corporate Finance formulas, every lesson
Practice exam-style questions on Capital Investments and Capital Allocation
Questions about this lesson?
Where this comes back
- Pricing and Valuing Options Derivatives
- Private Capital: Private Equity and Private Debt Alternative Investments
Questions candidates ask
What are real options in capital budgeting?
A real option gives a company the right, but not the obligation, to take an action later on a real investment, such as waiting, expanding, abandoning, changing prices or output. It adds flexibility, and that flexibility has value that a plain NPV leaves out.
How do you value an abandonment option?
Use a decision tree. In each branch, compare the cash from abandoning with the value of continuing and take the better. The option is worth the probability-weighted extra cash from abandoning in the branches where it is used, discounted to today.
What is the difference between a real option and a financial option?
Both give a right, not an obligation. A financial option is on a financial asset such as a share. A real option is on a real investment decision, such as expanding a plant, and cannot be traded. Real options add flexibility to a project; they are not hedges against price risk.
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