QF5213 Chap.7 Decision Trees and Real Options
Decision Trees and Real Options
Why a single NPV can undersell a project
Ordinary discounted cash flow analysis quietly assumes that management commits on day one and then watches. In practice, capital projects unfold in stages, and each stage reveals something new: a trial succeeds or fails, demand comes in strong or weak, input prices drift.
A manager who can respond to that news holds something valuable, and this chapter is about putting a number on it.
The course treats the topic as the last step in project analysis, after the appraisal rules, unequal lives and sensitivity work. Its message is practical.
Flexibility does not replace NPV; it changes which cash flows belong in the calculation, because a sensible manager will not keep pouring money into a branch that has already turned bad.
Decision trees as the working tool
A decision tree draws the sequence of choices and uncertain events as branches.
Choice points and chance points are drawn differently so the reader can see where the firm acts and where it simply learns. The tree is solved from the far right: value each end point at the date its cash flows begin, choose the best branch wherever management decides, take probability weighted averages wherever nature decides, and discount back one period for every step toward the present.
Two mistakes dominate.
The first is mixing dates, for example adding a payoff valued at year 1 to a cost paid at year 0 without discounting. The second is forgetting that a bad branch is usually optional: if the firm would never invest after a failed trial, the large negative payoff from investing anyway should not be averaged into the answer.
Getting that one choice right can turn a rejected project into an accepted one.
Three families of real options
The timing option asks when to start rather than whether. If costs are falling or information is improving, a later launch can carry a larger present value even though it postpones the cash flows, so each candidate start date has to be restated to today before the dates are compared.
The abandonment option lets the firm sell equipment or close an operation once results disappoint, which raises the floor under the worst outcomes; it is often valued by finding the sales level at which resale beats continuing.
The expansion option lets a successful pilot be replicated, magnifying the good outcome without multiplying the bad one.
In every case the value of the option is measured the same way: the project value when the flexibility is recognised minus the value when it is ignored.
The class slides also show a strategic variant, where a costly facility produces no cash of its own but preserves an operating right whose loss would wipe out a much larger stream of inflows.
Seen alone the facility looks wasteful; seen with what it protects, it becomes one of the most valuable things the firm could build.
For the tests, expect to draw or read a two stage tree, compute expected values at chance nodes, and find an option value as a difference of two NPVs. Neat diagrams with dated values make these questions much quicker to check under time pressure.
What this chapter covers
- 01
Decision and chance nodes in a decision tree
- 02
Solving a tree backward from the final payoffs
- 03
The option to delay and choosing a launch date
- 04
The option to abandon and salvage values
- 05
Abandonment thresholds in units of sales
- 06
The option to expand a successful project
- 07
Strategic investments that protect other cash flows
Worked example · free
Valuing the option to wait one year
- 1Find the three-year annuity factor at 9% and the NPV of starting today.
- 1Find the NPV of the delayed project, dated at year 1 when it starts.
- 1Discount the delayed NPV back to year 0 and compare the two start dates.
- 1Compute the option value as the difference between the two NPVs today.
Key terms
- Decision Tree
- A diagram that sets out the choices open to a firm in each period together with the uncertain outcomes that may follow each choice.
- Decision Node
- A point in a tree where management chooses among alternatives, solved by keeping whichever branch carries the highest value.
- Chance Node
- A point in a tree where information arrives and an outcome is revealed, solved by taking the probability weighted average of its branches.
- Real Option
- A right, not an obligation, to change a real investment later, such as delaying, abandoning or expanding it as conditions become clearer.
- Option to Delay
- Flexibility to postpone the start of a project, valuable when costs fall or information improves faster than discounting erodes the payoff.
- Option to Abandon
- Flexibility to exit a project and recover a salvage value, valuable when demand proves weaker than expected and losses would otherwise continue.
- Option to Expand
- Flexibility to scale up or replicate a successful project, valuable when demand proves stronger than expected at the first site.
- Value of Option
- The amount flexibility adds, measured as project value with the option recognised minus project value when the option is ignored.
Decision Trees and Real Options FAQ
How do you solve a decision tree in capital budgeting?
Start at the right-hand end and value each final branch at the date its cash flows begin. At every choice square keep the best branch, at every chance circle take the probability weighted average, then discount back one period at a time until you reach year 0 and subtract any first-stage cost.
Why can a project with negative NPV still be worth undertaking?
A plain NPV assumes the firm cannot react once uncertainty resolves. If management can sell assets after bad news, delay until conditions improve, or copy a winning pilot, the payoffs on some branches improve. Adding that flexibility can push the total above zero even when the static estimate was negative.
How do you calculate the value of an abandonment option?
Value the project twice: once assuming the firm must continue after a poor outcome, and once allowing it to take the salvage value instead. The difference is the option value. In a one-period problem it equals the probability of the poor outcome times the salvage, discounted one period.
How do I find the best time to launch a project?
List the cost and benefits for each possible start year, compute the NPV at that start year, then discount each of those figures to today. Choose the year with the highest present value. Picking the largest undiscounted launch-date NPV usually points to a start that is too late.
What is the difference between a decision node and a chance node?
A decision node is controlled by the firm, so you select the single best branch there. A chance node is controlled by events outside the firm, so you weight each branch by its probability. Mixing these up, for example averaging over a choice, is a frequent source of wrong answers.
Exam move
Take one two-stage tree from the course materials and redraw it from memory, writing the date beside every payoff. Solve it backward twice: first letting the firm stop after bad news, then forcing it to continue. The gap between the two answers is the option value, so state it in one line. Repeat with a timing table, restating each launch-year NPV to today before choosing, until you can do both in under ten minutes.
Working through Decision Trees and Real Options in QF5213? Sia is AskSia’s AI Finance tutor — ask any QF5213 Decision Trees and Real Options question and get a clear, step-by-step explanation grounded in how QF5213 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
