ModelRisk example · Corporate finance

Real Options: Expand or Abandon

Build big now, or start small and decide later? The value of flexibility when demand is uncertain.

Complexity: ★★★★★
Free Excel workbook (CF-08)
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From the model’s saved run

Which strategy?

NPV (US$m) on the business-case demand and over the simulated futures.

Strategy	Business case	Mean simulated	10th pct	90th pct	Chance of a loss
Build big now	63.7	16.1	−55.0	74.3	36.4%
Build small, stay small	28.4	20.4	0.2	28.4	9.9%
Build small, decide later	28.4	24.5	−5.8	58.1	13.3%

NPV of each strategy — cumulative probability

S-curve (cumulative probability) of Build big now, Build small, Build small, decide later from the saved simulation.

The business question

A manufacturer is entering a new market where demand is about 100,000 units a year, growing about 3% a year but very uncertain. It can build a plant for 120,000 units now for US$90 million, or a 60,000-unit plant for US$55 million.

The small plant can be doubled at the start of year 3 for US$40 million, once two years of sales have shown whether demand is strong. If demand collapses, it can be sold for US$35 million instead. On the expected demand, the large plant has much the higher NPV, and the business case recommends it.

But the large plant's capacity is only valuable if demand grows, and its cost is sunk if it does not. The model simulates ten years of demand and values the three strategies on the same paths, with the decision rule of the staged strategy applied in every iteration.

Who it is for: Strategy and corporate development teams, capital allocation committees, project sponsors.
Main outputs: NPV of each strategy: the business case against the simulation, its range and the chance of a loss · the value of the options to expand and abandon · how often each decision is taken · the range of demand.

How the model works

Three sheets after this one, read from left to right. Each one feeds the next.

Inputs sheet
Today's demand, its growth and volatility; contribution per unit; each plant's capacity, cost and fixed costs. The expansion cost and the sale value; the demand levels at which to expand or to sell; the discount rate.
Strategies sheet
VoseTimeGBM draws ten years of demand. Each strategy sells what demand and its capacity allow. The staged strategy looks at year-2 demand: above the expansion level it doubles capacity from year 3, below the abandonment level it sells the plant at the end of year 2, otherwise it carries on.
Results sheet
Each strategy's NPV on the business-case demand and in the simulation, its range and chance of a loss; the value of the options; how often the plant is expanded or sold.

ModelRisk techniques

Demand as GBM VoseTimeGBM
Common random numbers
Real-option decision rules
NPV S-curves, demand fan chart

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The results in detail

The value of flexibility

What the options to expand and to sell add, and how often they are used.

Demand by year — 10th to 90th percentile

Line chart: 90th percentile, Median, Mean, 10th percentile, Expand at or above, Sell at or below.

Measure	Unit	Value
Mean NPV, build small and decide later	US$m	24.5
Mean NPV, build small and stay small	US$m	20.4
Mean NPV, build big now	US$m	16.1
Value of the options (decide later − stay small)	US$m	4.1
Value of waiting (decide later − build big now)	US$m	8.4
Chance the plant is expanded	probability	31.6%
Chance the plant is sold	probability	1.8%

How to read these results

On the business case, demand grows steadily and the large plant fills up: its NPV is far ahead. But demand is uncertain, and the large plant's extra capacity only pays when demand grows. Averaged over the possible futures its NPV is much lower, and the chance of losing money is high.
Starting small keeps the decision open. If demand is strong after two years, the company expands; if it collapses, it sells. The options turn part of the downside into upside: the staged strategy has the highest mean NPV.
The value of waiting is not free: expanding later costs more in total than building big at once, and two years of strong demand are lost to the small plant's capacity. The simulation weighs these costs against the protection.
The decision rules matter. Expanding at too low a demand level, or selling too readily, destroys the options' value: try other levels on the Inputs sheet and run again. The fan chart shows the two levels against the spread of demand.
On the business case, demand in year 2 is about 106 thousand units: between the two levels, so the plant carries on and neither option is used. The options exist only because demand is uncertain, which is why the business case cannot see their value.

See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.

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Inputs and assumptions

Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.

Market 4 inputs

Demand for the product and what each unit earns.

Assumption	Unit	Value
Demand todayMarket study.	thousand units / year	100
Expected demand growth	per year	3.0%
Volatility of demandA new market: demand could double or halve within a few years.	per year	30%
Contribution per unitPrice less variable cost.	US$ per unit	300

Plants 8 inputs

The two plant sizes, the expansion and the sale.

Assumption	Unit	Value
Large plant: capacity	thousand units / year	120
Large plant: investment	US$m	90
Large plant: fixed costs	US$m / year	10.0
Small plant: capacity	thousand units / year	60
Small plant: investment	US$m	55
Small plant: fixed costs	US$m / year	5.0
Expansion to the large plant's capacityPaid the year after the decision; the doubled plant has the large plant's fixed costs.	US$m	40
Sale of the small plantReceived at the end of the decision year.	US$m	35

Decision rules 3 inputs

Applied to the staged strategy at the end of the decision year.

Assumption	Unit	Value
Decide at the end of yearAfter two years of sales; an expansion is ready the year after.	year	2
Expand if demand in the decision year is at least	thousand units	120
Sell the plant if demand in the decision year is at most	thousand units	40

Finance 1 input

Assumption	Unit	Value
Discount rateCost of capital, real.	per year	9.0%

Units and conventions

Money: US$ million (US$m), today's prices; contribution in US$ per unit.
Demand: Thousand units a year.
Years: Year 0 is the investment; cash flows at the end of years 1 to 10.
Business case: The same calculation with demand growing exactly at its expected rate.

Key assumptions and limitations

Demand: Geometric Brownian motion: growth is persistent and the range widens every year.
Decisions: Taken once, at the end of year 2, on year-2 demand; the expansion is ready for year 3.
Plants: No residual value after year 10; fixed costs stop when the plant is sold.
Data: The company and all figures are invented for this example.

How to use it

Enter your market, plant options and costs on the Inputs sheet.
Press F9 on the Strategies sheet to watch the three strategies play out on the same demand.
Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
Change the decision rules (the expansion and abandonment levels) and run again to find the best ones.

ModelRisk functions used

VoseTimeGBM: Ten years of demand: a growing, uncertain, persistent series.
VoseOutput: The NPV of each strategy, the decisions and the demand of every year as outputs.
VoseSimMean, VoseSimPercentile, VoseSimProbability: Statistics of the simulation for the tables and charts on the Results sheet.

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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.