Decision Trees and Project Flexibility
A standard NPV assumes the firm sets a plan at the outset and never deviates. Real projects carry flexibility, the ability to expand, delay or abandon as new information arrives. Decision trees map that flexibility step by step. Decision nodes, drawn as squares, are points where management chooses an action. Event nodes, drawn as circles, are points where chance resolves an uncertainty. Terminal nodes end each branch with a payoff. The tree is solved by folding back, taking expected values at chance nodes and the best action at decision nodes, which prices the option that flexibility creates.
Why it matters
Without flexibility a firm is locked onto one road no matter the weather. With flexibility it can change route once the fog clears. The decision tree draws every road, attaches probabilities where nature decides and choices where management decides, then works backwards from the destinations to today. The value of the abandonment option is simply the difference between the expected NPV when you can walk away and the expected NPV when you are forced to continue. Flexibility is worth something precisely because it caps the losses in the bad branch.
Formulas
Worked examples
CSM faces a 20 percent chance an EPA ruling adds A$80,000 a year to Earthilizer’s costs. Without an exit, the bad branch has NPV near minus A$236,608 and the expected NPV is 0.80 times A$43,062 plus 0.20 times minus A$236,608, about minus A$12,872. With an abandonment option the firm stops after year one in the bad branch, cutting that loss to about minus A$167,108. What is the option worth?
With the right to abandon, the expected NPV becomes 0.80 times A$43,062 plus 0.20 times minus A$167,108, which is roughly plus A$1,028. The flexibility flips the project from an expected loss of about minus A$12,872 to a small expected gain, so the abandonment option is worth around A$13,900 of expected NPV. The option matters only in the unfavourable branch, where walking away caps the loss rather than absorbing the full A$80,000 annual hit. These figures are from the Earthilizer decision-tree example.
Common mistakes
- ✗A decision node and an event node are interchangeable. Squares are management choices and circles are chance outcomes, and the tree is solved differently at each kind of node.
- ✗An unfavourable outcome always means abandon. You compare continuing against abandoning and pick the less bad option, and exit costs or a possible recovery can make continuing better.
- ✗Flexibility has no value because the bad branch is still negative. The option caps the downside, so its value is the loss it avoids relative to being forced to continue, even if that branch stays negative.
- ✗Decision trees replace NPV. They extend NPV by valuing managerial choices that a static NPV ignores, and each branch still ends in a discounted cash-flow payoff.
Revision bullets
- •Map flexibility to expand, delay or abandon as information arrives
- •Squares are decision nodes, circles are event nodes, vertical lines are terminal nodes
- •Solve by folding back, expected value at chance nodes, best action at decision nodes
- •The abandonment option caps losses in the unfavourable branch
- •Earthilizer EPA case improves expected NPV from about minus A$12,872 to plus A$1,028
- •Compare continue versus abandon, do not assume bad news forces an exit
Quick check
In a decision tree, a square node represents a point where
The value of an abandonment option in a decision tree comes from the fact that it
Connected topics
Sources
- Titman & Martin, Ch. 3Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.Uses decision trees to value project flexibility, including the abandonment-option example.