Vose SoftwareModelRisk example · Corporate finance
Investment Appraisal of a New Production Line
The business case says invest. What does the risk say? NPV, IRR and payback of a new production line.
From the model’s saved run
Should the company invest?
The business case (most likely values) against the simulation.
| Measure | Unit | Value |
|---|---|---|
| NPV with most likely values (the business case) | US$m | 4.5 |
| Mean NPV (simulated) | US$m | 1.5 |
| Chance of a negative NPV | probability | 38.5% |
| Chance that the NPV falls short of the business case | probability | 71.0% |
| IRR with most likely values | 11.2% | |
| Mean IRR (simulated) | 9.7% | |
| Verdict | Invest, but negative in 38% of futures |
S-curve (cumulative probability) of NPV from the saved simulation.
Histogram of NPV from the saved simulation.
The business question
A manufacturer of industrial components is considering a new production line. Engineering puts the investment at about US$40 million. Marketing expects to sell about 60,000 units a year at full production, at about US$520 each; operations expects a variable cost of about US$300 a unit and fixed costs of about US$4 million a year.
Production ramps up over two years and the line runs for ten. With these most likely values the line earns 11% a year against a 9% cost of capital: a positive NPV of about US$4.5 million.
But every estimate is uncertain, and most are more likely to turn out worse than better: volume and price have more room to fall than to rise, and costs more room to rise. The model replaces each single value with a three-point estimate and simulates the cash flow.
- Who it is for
- Finance and strategy teams, project sponsors and investment committees; a first ModelRisk model.
- Main outputs
- NPV and IRR: the most-likely-values case against the simulation, the chance of a negative NPV, the ranges of NPV, IRR and payback · what drives the NPV.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
Five uncertain inputs as three-point estimates: the investment, the sales volume at full production, the price, the variable cost per unit and the fixed costs. The ramp-up, the tax rate and the cost of capital are fixed.
Cash flow sheet
Year 0 is the investment. In each operating year, revenue = volume × price; EBITDA = revenue − variable and fixed costs. Tax is charged on EBITDA less straight-line depreciation; free cash flow = EBITDA − tax.
The NPV discounts the free cash flows at the cost of capital, the IRR is the rate at which the NPV is zero, and the payback year is the first in which the cumulative cash flow turns positive.
Results sheet
The NPV and IRR with most likely values against the simulation, the chance of a negative NPV, the ranges of NPV, IRR and payback, and the drivers of the NPV.
ModelRisk techniques
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The results in detail
NPV, IRR and payback
10th percentile, median and 90th percentile.
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| NPV | US$m | −5.2 | 1.6 | 8.0 | 1.5 |
| IRR | 6.3% | 9.8% | 13.0% | 9.7% | |
| Payback year | year | 6 | 7 | 8 | 7 |
What drives the NPV
Lowest and highest mean NPV over ten equal groups of each input (VoseSimSensitivityMean), drawn from the overall mean.
Tornado chart: the inputs ranked by how far the mean output moves across each input’s range.
The ranking as a table 5 inputs
| Input (ranked by influence) | Lowest mean | Highest mean | Rank |
|---|---|---|---|
| Sales volume | −4.4 | 6.3 | 1 |
| Price | −3.8 | 5.9 | 2 |
| Variable cost | −2.3 | 4.6 | 3 |
| Investment | −1.6 | 4.0 | 4 |
| Fixed costs | −0.7 | 3.2 | 5 |
How to read these results
- With every estimate at its most likely value the line earns more than its cost of capital. The simulation tells a weaker story: the average NPV is lower, and the NPV is negative in a large share of the possible futures.
- The gap comes from the shape of the estimates, not from bad luck: volume and price can fall further than they can rise, and costs can rise further than they can fall, so the average of each estimate is worse than its most likely value.
- The IRR and the NPV tell the same story: when the cash flow turns positive once and stays positive, the IRR is below the cost of capital exactly when the NPV is negative — so the chance of a negative NPV is also the chance that the IRR falls short.
- The tornado chart shows where to work before committing: a supply agreement with a first customer firms up volume and price, and a fixed-price contract for the equipment firms up the investment.
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.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Investment and finance 4 inputs
What the line costs, and what the money costs.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Investment in the lineEngineering estimate; quotes for the main equipment. | US$m | PERT | 36.0 | 40.0 | 46.0 |
| Tax rateOn EBITDA less depreciation. | Fixed | 25% | |||
| Depreciation lifeStraight line from year 1, within the 10 years of the cash flow. | years | Fixed | 10 | ||
| Cost of capitalReal, after tax: the discount rate for the NPV. | per year | Fixed | 9.0% | ||
Market 2 inputs
How many units the line sells, and at what price.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Sales volume at full productionMarketing forecast; the line can make 66,000 units a year. | thousand units / year | PERT | 48.0 | 60.0 | 66.0 |
| PriceCompetitors may cut prices; little room to raise them. | US$ per unit | PERT | 480 | 520 | 540 |
Ramp-up 2 inputs
How fast the line reaches full volume.
| Assumption | Unit | Uncertainty | Step 1 | Step 2 | Step 3 |
|---|---|---|---|---|---|
| Operating yearCommissioning and first customers; the last share holds from its year on. | year | Fixed · profile | 1 | 2 | 3 |
| production, share of full volume | share | Fixed | 50% | 80% | 100% |
Operations 2 inputs
What it costs to make and sell the units.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Variable costMaterials and energy; supplier quotes. | US$ per unit | PERT | 285 | 300 | 330 |
| Fixed costsStaff, maintenance and overheads. | US$m / year | PERT | 3.60 | 4.00 | 4.80 |
Units and conventions
- Money
- US$ million (US$m) in today's prices; prices and unit costs in US$ per unit.
- Volumes
- Thousand units a year.
- Years
- Year 0 is the investment; years 1 to 10 are the operating years; cash flows at the end of each year.
- NPV and IRR
- NPV at the cost of capital; the IRR is the discount rate at which the NPV is zero.
Key assumptions and limitations
- Cash flows
- In today's prices; no working capital, inflation or residual value.
- Tax
- 25% of EBITDA less depreciation; a loss in an early year reduces the group's tax bill (negative tax).
- Estimates
- The five uncertain inputs are independent of each other and hold for all ten years (CF-02 forecasts sales that change over time).
- Data
- The project and all figures are invented for this example.
How to use it
- Enter your project's estimates on the Inputs sheet: the minimum, most likely and maximum of each uncertain value.
- Press F9 on the Cash flow sheet to see other possible cash flows.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Compare the simulation with the single-value business case, and firm up the top drivers before committing.
The tornado chart fills in after a simulation with ModelRisk’s classic engine.
ModelRisk functions used
- VosePERT
- The five uncertain inputs, from their minimum, most likely and maximum.
- VoseInput, VoseOutput
- Name the uncertain inputs for the tornado chart, and the NPV, IRR and payback as outputs.
- LOOKUP, COUNTIF (Excel)
- The production in each year from the ramp-up profile; the payback year as the years with a negative cumulative cash flow.
- NPV, IRR (Excel)
- The IRR of each simulated cash flow, and the NPV of the most-likely-values case.
- VoseSimMean, VoseSimPercentile, VoseSimProbability
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: every VoseInput ranked by how far the mean NPV moves across its range.
Further reading
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Brealey, R. A., Myers, S. C. & Allen, F. (2020). Principles of Corporate Finance, 13th edition. McGraw-Hill.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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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.