Hypothetical worked example and primary educational references; not observed market data.
Make the uncertain inputs explicit
Sensitivity analysis changes selected inputs while holding others constant to show how a model responds. In a DCF, common inputs include cash-flow amount, timing, discount rate, growth, and investment needs. A table of results is not a probability distribution unless probabilities have been independently justified. IFRS 13 provides context for valuation assumptions including risk; company disclosures provide business evidence, but neither makes this hypothetical grid a market forecast. Start by stating which uncertainties the table isolates and which it leaves untouched. The purpose is to reveal dependence on assumptions, not to make uncertainty disappear behind a set of neatly formatted values.
Supporting references: 1. IFRS Foundation: IFRS 13 · 2. SEC: How to Read a 10-K
Build a small hypothetical grid
Assume three equal year-end cash flows with no terminal value. At USD 100 per year and an 8% hypothetical discount rate, present value is 257.71. At the same cash amount and 12%, it is 240.18. If each annual cash flow is 80 instead, the corresponding values are 206.17 and 192.15. The cash stream is already net of all costs and investments under the stipulated example. Both rates and cash amounts are illustrative. The grid demonstrates that lowering cash and increasing the rate reduce value through separate mechanisms, while making the arithmetic simple enough to reconstruct.
Supporting references: 1. IFRS Foundation: IFRS 13
Hypothetical worked example
Hypothetical two-input finite DCF grid
Model setup
Read these assumptions before comparing the scenarios.
- All monetary amounts in this example are hypothetical U.S. dollars (USD), not current prices, quoted account terms or observed market data. Percentages, counts, time periods and index levels retain their stated units.
- Three equal annual net cash flows occur at year-end; no terminal value.
- Cash alternatives are 100 and USD 80; discount-rate alternatives are 8% and 12%.
Present value (USD): annual cash × discount rate
Darker cells mean larger present values, not higher likelihood. Four conditional cases; no probabilities assigned.
Hypothetical model, not observed market data or a forecast. Assumptions above; original values and calculations below.
| Annual cash (USD) | Discount rate | Present value (USD) |
|---|---|---|
| 100 | 8% | 257.71 |
| 100 | 12% | 240.18 |
| 80 | 8% | 206.17 |
| 80 | 12% | 192.15 |
Calculation details
- 100 cash at eight percent
- 257.71 USD
(((100 / 1.0800000000000001) + (100 / (1.0800000000000001 ^ 2))) + (100 / (1.0800000000000001 ^ 3))) - 80 cash at twelve percent
- 192.15 USD
(((80 / 1.1200000000000001) + (80 / (1.1200000000000001 ^ 2))) + (80 / (1.1200000000000001 ^ 3)))
Do not treat the midpoint as expected value
A midpoint or average of the four cells is not automatically an expected value. Expected value requires a reasoned probability model and a relevant set of outcomes. The cells may not be equally likely, independent, or exhaustive. Labeling the central case base case does not make it observed truth. A useful sensitivity can still be informative without probabilities: it tells the reader which assumptions deserve the most attention and how much error matters. Avoid converting that information into a confidence claim. If evidence does not support probabilities, present the range as conditional model outputs and explain the commercial reasons for selecting the tested bounds.
Supporting references: 1. IFRS Foundation: IFRS 13
Use coherent combinations when drivers interact
Cash-flow amount and risk can move together. A severe demand shortfall may reduce cash and change financing exposure, while an expansion can require more capital. Holding every other input constant is useful for isolating one effect, but it may not describe a realistic full scenario. Build additional scenarios where revenue, margin, working capital, investment, and financing assumptions fit together. Then distinguish those coherent scenarios from one-variable sensitivities. A model that raises growth while eliminating investment might create an attractive cell with no business logic. Numerical consistency is necessary, but commercial consistency determines whether the scenario teaches anything meaningful about the firm's economics.
Supporting references: 2. SEC: How to Read a 10-K · 3. IFRS Foundation: IAS 7
Identify where precision is misleading
Present values rounded to cents reflect arithmetic precision, not certainty in the inputs. If annual cash flow is a broad estimate, a final value of 257.71 should not suggest that the analyst knows value within a few cents. Show the detailed calculation for auditability while describing the range of uncertainty in plain language. Likewise, a dense grid of tiny rate increments can look rigorous without improving evidence about risk. Choose variations that correspond to meaningful business questions. The worked example uses two cash levels and two rates because those four cells clearly reveal the directional effect without implying a finely measured valuation interval.
Supporting references: 1. IFRS Foundation: IFRS 13
Turn the sensitivity into an evidence plan
After reading the grid, ask which missing evidence would most improve the model. If value changes mostly with cash flow, investigate margins, collections, and capital requirements. If long-duration value depends strongly on the rate, examine risk assumptions and horizon consistency. If a threshold decision changes within plausible cases, report that fragility rather than selecting the favorable cell. The hypothetical finite model intentionally excludes terminal value, financing claims, and actual market data. A good conclusion identifies the model's dependencies and the evidence needed to narrow them. Sensitivity analysis supports disciplined judgment; it does not supply a guarantee or a substitute for understanding the business.
Supporting references: 2. SEC: How to Read a 10-K
Test another situationCalculate the receipt required to justify the commitment
A separate hypothetical case. Its inputs differ from the main worked example above.
Calculate the receipt required to justify the commitment
Consider a hypothetical project costing USD 800 today and producing a single receipt at the end of year two. At a chosen 10% annual discount rate, the receipt must be USD 968 for NPV to equal zero. A USD 900 receipt gives approximately negative USD 56.20 NPV. These results convert the valuation question into a commercial threshold: can the project credibly generate the required net collection at the specified date? No other receipts, payments, or terminal value are included. A threshold can focus investigation without supplying evidence about demand. The rate is illustrative and does not represent an available yield.
Supporting references: 1. IFRS Foundation: IFRS 13
Use a threshold as an evidence request
IFRS 13 emphasizes valuation assumptions, including risk. For this model, work backward from the required receipt into the order quantity, customer price, and unavoidable costs needed to produce it, while retaining uncertainty in those inputs. A reverse calculation can reveal an implausible requirement even when a favorable scenario looks attractive. Do not interpret the zero-NPV receipt as an expected outcome or select a probability merely because the threshold is known. If the project has several cash dates, solve against those dates rather than comparing an undiscounted total with this single-receipt boundary. The operational question is which assumption must change for the decision to reverse.
Supporting references: 1. IFRS Foundation: IFRS 13
Check this case’s calculations
- Year-two break-even receipt
- 968.00 USD
(800 * (1.1000000000000001 ^ 2)) - NPV with smaller receipt
- -56.20 USD
((900 / (1.1000000000000001 ^ 2)) - 800)
Limits of this additional case
- The receipt threshold applies only to this single-date finite stream; multiple payments and correlated cost changes require a different model.
Limits of this analysis
- The tested cells are not an exhaustive or probability-weighted outcome set.
- Correlated operating and financing changes require coherent scenarios beyond isolated sensitivities.
- The finite model excludes terminal value and enterprise-to-equity claims.
Sources and scope
- IFRS Foundation: IFRS 13
Fair value uses market-participant assumptions including risk.
Scope: IFRS measurement context; does not prescribe investment models or market prices.. Reference accessed 2026-10-06.
- SEC: How to Read a 10-K
Notes and management discussion provide context for reported results.
Scope: Historical US educational bulletin; used for reading principles, not current filing requirements.. Reference accessed 2026-10-06.
- IFRS Foundation: IAS 7
Cash flow presentation and the operating, investing and financing categories.
Scope: IFRS overview; classification details and US GAAP may differ.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
