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Financial Management · Adjusting for risk and uncertainty in investment appraisal

Simulation, Scenario and Worst-Case Analysis in Investment Appraisal

Updated 11 October 2026 · Fact-checked

Scenario, worst-case and simulation analysis test how an investment's NPV behaves when several variables change together. Scenario analysis uses a few defined sets of values, such as worst, base and best. Simulation uses random numbers and probability distributions to generate many outcomes and a spread of possible NPVs.

Understand Simulation, Scenario and Worst-Case Analysis

Sensitivity analysis changes one variable at a time. That is a weakness, because in real projects variables move together. If selling price falls, volume may rise or fall, and costs may move as well. Scenario analysis and simulation fix this by changing several variables at once.

Scenario analysis builds a small number of coherent stories, usually a worst case, a base (most likely) case and a best case. For each story you set values for all the key variables and calculate one NPV. You can then see the range of outcomes. If you assign probabilities to the scenarios, you can also calculate an expected NPV.

Worst-case analysis is the pessimistic end of scenario analysis. You ask: if everything goes badly, what is the NPV, and can the company survive it? It shows the downside but says nothing about how likely it is. A project that is acceptable even in the worst case is very safe.

Simulation (often called Monte Carlo simulation) gives each uncertain variable a probability distribution, such as sales volume 10,000 with probability 0.3. A computer draws random values for every variable, calculates the NPV, and repeats this hundreds or thousands of times. The result is a distribution of NPVs. From it you can read the expected NPV, the spread, and the probability that NPV is negative.

Simulation is the most informative of the three, but it needs the most work. You must estimate distributions and any links between variables. The output is only as good as those inputs. None of these methods tells you what to decide. They give the decision maker information about risk.

Key rules to remember

Expected NPV from scenarios
E(NPV) = Σ (probability of scenario × NPV of scenario)
Probabilities across all scenarios must total 1. Use only if probabilities have been given or estimated.
Probability of a negative NPV (scenarios)
P(NPV < 0) = sum of probabilities of scenarios with negative NPV
Only meaningful with a few discrete scenarios. With three scenarios it is a rough guide.
Random number allocation
Allocate two-digit random numbers 00–99 in proportion to probability: probability 0.3 = 30 numbers
Ranges must be cumulative, must not overlap and must cover 00–99.
NPV in each trial
NPV = Σ (cash flow in year t × discount factor in year t) − initial investment
Simulation repeats this calculation many times with different random inputs.

How to solve Simulation, Scenario and Worst-Case Analysis questions

Use this method for both calculation and discussion questions on scenario analysis, worst-case analysis and simulation.

  1. 1Read the requirement. Decide whether you must calculate, discuss, or both.
  2. 2List the variables that change in each scenario or in the simulation. Note which ones may move together.
  3. 3For scenario questions, calculate the NPV for each scenario using the values given. Keep a neat layout so each scenario is easy to mark.
  4. 4If probabilities are given, calculate the expected NPV and the probability of a negative NPV. Check that the probabilities total 1.
  5. 5For simulation questions, allocate random number ranges to each outcome. Read off each variable from the random numbers given and calculate the NPV for the trial.
  6. 6State what the result tells the decision maker: range, downside, expected value. Compare it with the base-case NPV.
  7. 7Add limitations that fit the case: subjective inputs, no decision rule, cost and complexity, and correlations between variables.
  8. 8Finish with a short recommendation or comment. Say clearly that the technique informs the decision but does not make it.

Quickest way: Three-line exam approach

When to use it: Use this in Section A or Section B objective test questions, and for quick written comments in Section C.

  1. For a "which technique" question: one variable at a time means sensitivity; a few set combinations means scenario; random numbers and distributions mean simulation.
  2. For a calculation: multiply each scenario NPV by its probability and add. Check the probabilities add up to 1 before you start.
  3. For a simulation question: build cumulative ranges from 00 to 99 first, then match each random number to a range. Never read off a value before the ranges are written down.

Common mistakes in Simulation, Scenario and Worst-Case Analysis

  • Describing scenario analysis as changing one variable at a time.

    It is confused with sensitivity analysis, which also looks at "what if".

    Fix: Remember the contrast: sensitivity changes one variable and holds the rest constant; scenario and simulation change several together.

  • Saying simulation gives the correct decision or the best project.

    The output looks precise, so students assume it is a decision rule.

    Fix: Say it shows a range and the probability of outcomes. The decision still depends on management's attitude to risk.

  • Setting up random number ranges that overlap or do not use all of 00–99.

    Students allocate ranges quickly without working cumulatively.

    Fix: Write cumulative probabilities first. For 0.3, 0.5 and 0.2 use 00–29, 30–79 and 80–99. Check the ranges end at 99.

  • Treating the worst case as the expected outcome or as certain to happen.

    Pessimistic figures are mistaken for a forecast.

    Fix: The worst case is a lower limit that may be very unlikely. It shows the downside, not the probability.

  • Listing only advantages of simulation in a discussion answer.

    Students remember that it is more realistic and stop there.

    Fix: Give balanced points: it handles several variables and gives a probability distribution, but it needs good input estimates, is costly and does not give a decision rule.

  • Calculating expected NPV with probabilities that do not add to 1.

    Students rush and do not check the data.

    Fix: Add the probabilities first. If they do not total 1, re-read the question for a missing scenario.

Worked examples

Example 1

A company is appraising a project. Three scenarios have been prepared, each with all key variables changed together. Worst case: probability 0.25, NPV −$120,000. Base case: probability 0.55, NPV $150,000. Best case: probability 0.20, NPV $400,000. Calculate the expected NPV and the probability that the NPV is negative, and comment.

Show the solution
  1. Check the probabilities: 0.25 + 0.55 + 0.20 = 1.00. Good.
  2. Worst case: 0.25 × (−120,000) = −30,000.
  3. Base case: 0.55 × 150,000 = 82,500.
  4. Best case: 0.20 × 400,000 = 80,000.
  5. Expected NPV = −30,000 + 82,500 + 80,000 = $132,500.
  6. Probability of a negative NPV: only the worst case is negative, so it is 0.25, or 25%.
  7. Comment: the expected NPV is positive, which supports acceptance. The expected value is below the best case and also below the base case of $150,000, because the worst case pulls it down. There is a one in four chance of losing $120,000, so the board's attitude to risk matters. The probabilities are subjective and only three scenarios are used, so the analysis is a guide only.

Answer: Expected NPV = $132,500. The probability of a negative NPV is 25% (worst case only). The project looks worthwhile on expected value, but the downside should be weighed against the company's risk appetite.

Example 2

A three-year project costs $60,000 now. The cost of capital is 10%. Annual contribution is $8 per unit and annual fixed cash costs are $70,000. Annual sales volume is uncertain: 10,000 units (probability 0.3), 12,000 units (0.5), 15,000 units (0.2). Volumes in each year are independent. Use the two-digit random numbers 47, 85 and 12 for years 1, 2 and 3 to run one simulation trial. Discount factors at 10%: year 1 0.909, year 2 0.826, year 3 0.751.

Show the solution
  1. Allocate random numbers by cumulative probability: 10,000 units = 00–29; 12,000 units = 30–79; 15,000 units = 80–99.
  2. Year 1: 47 is in 30–79, so volume = 12,000 units. Year 2: 85 is in 80–99, so 15,000 units. Year 3: 12 is in 00–29, so 10,000 units.
  3. Net cash flow year 1 = 12,000 × 8 − 70,000 = 96,000 − 70,000 = $26,000.
  4. Year 2 = 15,000 × 8 − 70,000 = 120,000 − 70,000 = $50,000.
  5. Year 3 = 10,000 × 8 − 70,000 = 80,000 − 70,000 = $10,000.
  6. Present values: 26,000 × 0.909 = 23,634; 50,000 × 0.826 = 41,300; 10,000 × 0.751 = 7,510. Total = $72,444.
  7. NPV for this trial = 72,444 − 60,000 = $12,444.
  8. One trial is only one possible outcome. A real simulation repeats this many times and records every NPV to build a distribution.

Answer: This trial gives an NPV of $12,444. A full simulation needs many trials before you can estimate the expected NPV or the probability of a negative NPV.

Exam tips

  • Know the three-way contrast cold: sensitivity changes one variable, scenario changes several together in a few set cases, simulation uses random numbers to produce many outcomes.
  • In discussion questions, give both strengths and weaknesses. Link each point to the case given rather than writing general theory.
  • In objective tests, watch for "probability of a negative NPV" wording. Add the probabilities of all scenarios or trials with negative NPV.
  • For simulation allocation, write out the cumulative ranges before reading any random numbers. It is easy to lose marks for a small slip.
  • Always end with what the result means for the decision. Examiners reward a comment on risk attitude, not just a number.

Practice questions from Adjusting for risk and uncertainty in investment appraisal

Simulation, Scenario and Worst-Case Analysis in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Simulation, Scenario and Worst-Case Analysis: frequently asked questions

What is the difference between sensitivity analysis and simulation?

Sensitivity analysis changes one variable at a time and shows how much it can move before NPV becomes zero. Simulation changes all uncertain variables together using random numbers and probability distributions. It gives a spread of NPVs and the probability of a loss.

How is scenario analysis different from sensitivity analysis?

Scenario analysis changes several variables together to build coherent cases such as worst, base and best. Sensitivity analysis changes one variable while holding the others constant. Scenario analysis is more realistic when variables are linked, but it only covers a few cases.

What are the advantages and disadvantages of simulation for ACCA FM?

Advantages: it models several variables at once, uses probability distributions, and shows the range and probability of outcomes. Disadvantages: it is costly and complex, depends on estimated inputs and correlations, and gives no decision rule. It can also seem more accurate than it really is.

What is worst-case analysis in investment appraisal?

It is the NPV when all key variables take their most pessimistic values. It shows the maximum likely loss and whether the company could survive it. It does not show how likely that outcome is.