Vose SoftwareModelRisk example · Corporate finance
Company Valuation with Terminal-Value Uncertainty
Is the price right? A discounted cash flow valuation with its range, and how much of it is the terminal value.
From the model’s saved run
Is the price right?
Enterprise value against the price and the bank's case.
| Measure | Unit | Value |
|---|---|---|
| Price agreed | US$m | 600 |
| Value in the bank's case (most likely values) | US$m | 639 |
| Mean value (simulated) | US$m | 616 |
| Chance that the company is worth less than the price | probability | 44.4% |
| Chance that it is worth less than the bank's case | probability | 61.7% |
| Mean value by exit multiple | US$m | 635 |
| Walk-away price: worth at least this 80% of the time | US$m | 539 |
S-curve (cumulative probability) of DCF (Gordon growth), Exit multiple from the saved simulation.
Histogram of Enterprise value from the saved simulation.
The business question
A buyer has agreed to pay US$600 million, debt included, for a logistics-software company with revenue of US$310 million and an EBITDA margin of 17%. The company expects to grow about 6% a year and to raise its margin to about 20% within three years.
The buyer's bank has valued it at about US$640 million by discounting five years of free cash flow at an 8.5% cost of capital, with a terminal value that grows at 2% a year after that — a comfortable margin over the price.
But each of those inputs is an estimate, growth and margin tend to rise and fall together, and three quarters of the value comes from the terminal value, which rests on the cost of capital and long-term growth. The model simulates the valuation and compares it with the price.
- Who it is for
- Corporate development and M&A teams, valuation analysts, investment committees.
- Main outputs
- Enterprise value: the bank's case against the simulation, its range, and the chance that it is below the price · value by an exit multiple · the terminal value's share of the value and the multiple it implies · drivers.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The agreed price, revenue and margin in the last year. Growth, the steady-state margin, capex, the cost of capital, long-term growth and the exit multiple as three-point estimates (PERT); growth and margin are correlated through a copula.
Valuation sheet
Revenue grows at the drawn rate. The margin moves to its steady state over three years. Free cash flow = after-tax operating profit + depreciation − capex − the increase in working capital. The terminal value is the year-5 cash flow growing for ever (Gordon), or year-5 EBITDA times the exit multiple. Both are discounted at the cost of capital.
Results sheet
Enterprise value against the price and the bank's case, the range by both methods, the share of value in the terminal value and the multiple it implies, and the drivers.
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The results in detail
The range of values
10th percentile, median and 90th percentile.
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| Enterprise value (DCF) | US$m | 504 | 612 | 732 | 616 |
| Enterprise value (exit multiple) | US$m | 538 | 633 | 736 | 635 |
| Terminal value's share of the value | 73% | 75% | 78% | 75% | |
| Exit multiple implied by the DCF | × EBITDA | 7.5 | 8.6 | 9.8 | 8.6 |
What drives the value
Lowest and highest mean value (DCF) 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 |
|---|---|---|---|
| EBITDA margin | 509.3 | 715.8 | 1 |
| Revenue growth | 524.0 | 707.1 | 2 |
| Cost of capital | 542.1 | 694.0 | 3 |
| Capex | 567.7 | 664.4 | 4 |
| Long-term growth | 570.2 | 666.8 | 5 |
How to read these results
- The bank's case uses the most likely value of every input. Growth and margins have more room to disappoint than to surprise, so the simulation's average is lower, and the chance that the company is worth less than the price is close to one half: the price leaves little margin of safety.
- About three quarters of the value is the terminal value — the years beyond the forecast. The cost of capital and long-term growth, which set it, rank close behind the margin and growth among the drivers.
- Growth and margin are correlated, because a strong market lifts both. Their bars in the tornado chart are both long for the same reason. Treating them as independent would narrow the range of values.
- The exit-multiple method gives a similar range. The multiple implied by the DCF's terminal value is a useful check: if it falls far outside the multiples paid for similar companies, the long-term assumptions need another look.
- The walk-away price answers the committee's question directly: the value the company is worth at least as often as the confidence on the Inputs sheet asks. Paying more than it means accepting a larger chance of overpaying.
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.
The deal 4 inputs
The price agreed, and where the company stands today.
| Assumption | Unit | Value |
|---|---|---|
| Price (enterprise value)Agreed, debt included. | US$m | 600 |
| Revenue in the last year | US$m | 310 |
| EBITDA margin in the last year | 17.0% | |
| Confidence the committee requiresThe Results sheet gives the walk-away price: the value the company is worth at least this often. | probability | 80% |
Forecast 10 inputs
Five years of growth and margins; investment and working capital.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Revenue growthManagement plan 6%; new contracts are not yet signed. | per year | PERT · correlated | 2.0% | 6.0% | 9.0% |
| EBITDA margin, steady stateScale economies and the price increase in the plan. | PERT · correlated | 16.0% | 20.0% | 22.0% | |
| Years for the margin to reach itA straight line from the last year's margin. | years | Fixed | 3 | ||
| Correlation: growth vs marginA strong market lifts both volumes and prices: growth and margin tend to move together. | Normal copula | Fixed · copula | 0.60 | ||
| Copula draw for growth (U)Generated by VoseCopulaBiNormal and passed to the U argument of the distribution it correlates. Do not edit. | 0 – 1 | Calculated | 0.201 | ||
| Copula draw for margin (U)Both draws come from one copula, so the two inputs move together as specified. | 0 – 1 | Calculated | 0.775 | ||
| Capital expenditurePlatform investment may rise. | of revenue | PERT | 3.0% | 4.0% | 5.5% |
| Depreciation and amortisation | of revenue | Fixed | 3.0% | ||
| Working capital | of the revenue increase | Fixed | 10% | ||
| Tax rate | Fixed | 25% | |||
Valuation 3 inputs
How the cash flows are turned into a value.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Cost of capital (WACC)Beta and the equity risk premium are debated. | per year | PERT | 7.5% | 8.5% | 10.0% |
| Growth after year 5Long-term inflation plus a little real growth. | per year | PERT | 1.0% | 2.0% | 3.0% |
| Exit multiple, for the checkRecent sales of similar companies. | × EBITDA | PERT | 7.0 | 9.0 | 11.0 |
Units and conventions
- Money
- US$ million (US$m); enterprise value, before net debt.
- Years
- Year 0 is the last full year; cash flows at the end of years 1 to 5.
- Terminal value
- The value at the end of year 5 of all later cash flows.
- Bank's case
- The same valuation with every input at its most likely value.
Key assumptions and limitations
- Growth
- One growth rate for the five years; the margin moves linearly to its steady state by year 3.
- Cash flow
- Depreciation 3% of revenue; working capital 10% of the revenue increase; tax 25% of operating profit.
- Dependence
- Growth and margin are correlated (0.6); the cost of capital and long-term growth are independent.
- Data
- The company and all figures are invented for this example.
How to use it
- Enter the price and the target's last-year figures, and your ranges for the forecast and valuation inputs.
- Press F9 on the Valuation sheet to see other possible valuations.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Set a walk-away price at the confidence the committee requires, and probe the terminal value before signing.
The tornado chart fills in after a simulation with ModelRisk’s classic engine.
ModelRisk functions used
- VosePERT
- Growth, margin, capex, cost of capital, long-term growth and the exit multiple.
- VoseCopulaBiNormal
- Correlates growth and margin: its two U values feed the U argument of the two VosePERTs.
- VoseInput, VoseOutput
- Name the inputs for the tornado chart, and the values as outputs.
- VoseSimMean, VoseSimPercentile, VoseSimProbability
- Statistics of the simulation for the tables and charts on the Results sheet.
- VoseSimSensitivityMean
- The tornado chart: the five VoseInputs that move the mean value (DCF) most across their range, ranked. The exit multiple does not enter the DCF value.
Further reading
- Sensitivity analysis in Excel: a tornado chart step by step (Vose guide)
- Koller, T., Goedhart, M. & Wessels, D. (2020). Valuation: Measuring and Managing the Value of Companies, 7th edition. Wiley.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — correlation and copulas.
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.