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Performance Management · Dealing with risk and uncertainty in decision-making

How to Do Sensitivity Analysis in ACCA PM

Updated 11 October 2026 · Fact-checked

Sensitivity analysis shows how far one variable can change before a decision changes, usually before NPV or profit hits zero. You calculate sensitivity as the NPV (or profit) ÷ the present value (or amount) of the variable × 100%. The smaller the percentage, the more critical the variable.

Understand Sensitivity Analysis

Every decision rests on estimates: sales volume, selling price, costs, discount rate. Any of them can turn out wrong. Sensitivity analysis asks one simple question: how wrong can this estimate be before I would change my decision?

In PM the usual decision test is NPV. A project is acceptable if NPV is positive. Sensitivity analysis finds the change in one variable that makes NPV exactly zero. That is the break-even point for that variable. You express it as a percentage of the original estimate.

You change one variable at a time and hold all others at their original values. A small percentage means a small error in the forecast would reverse the decision. That variable is critical or key. A large percentage means the decision is safe against errors in that variable.

Sensitivity analysis deals with uncertainty, not probability. It does not tell you how likely a change is. It tells you where management should focus attention, for example by checking the forecast more carefully or negotiating fixed prices with suppliers.

It differs from expected value. Expected value uses probabilities to produce a single average outcome. Sensitivity analysis uses no probabilities and shows how much room for error exists in each estimate.

Key rules to remember

Sensitivity (NPV approach)
Sensitivity % = NPV of project ÷ PV of the cash flows affected by the variable × 100%
Use the present value of the specific cash flow, after tax if tax applies. This is the percentage fall in that variable that makes NPV zero.
Sensitivity (profit or contribution approach)
Sensitivity % = Profit ÷ the total amount of the item flexed × 100%
Use when there is no discounting, for example a one-period decision. The item flexed is the total contribution for volume, total revenue for price, total variable costs for variable costs and total fixed costs for fixed costs.
Discount rate sensitivity
Break-even discount rate = IRR
The IRR is the discount rate at which NPV is zero. Compare it with the cost of capital; the gap shows how much the rate can rise.
Reading the result
Smaller percentage = more sensitive = more critical variable
Rank the variables by percentage to see which matter most.

How to solve Sensitivity Analysis questions

Use this method for any sensitivity question on NPV or profit. Work one variable at a time.

  1. 1Calculate the base-case NPV (or profit) using the original estimates. Check it is positive; if it is negative the project is already rejected.
  2. 2List the variables asked for: sales volume, price, variable cost, fixed cost, investment, discount rate.
  3. 3For each variable, work out the present value of its cash flows over the project life, using the same tax and discount factors as in the base NPV.
  4. 4Divide the base NPV by that present value and multiply by 100% to get the break-even percentage change.
  5. 5State the direction. For revenue items, it is a fall. For costs and investment, it is a rise.
  6. 6Compare the percentages. The smallest is the most sensitive variable.
  7. 7Comment: say what management should do, such as verify the key forecast, and note that the method changes one variable at a time and has no probabilities.

Quickest way: Quick table method

When to use it: Use when the question gives the base NPV and asks for several sensitivities under time pressure.

  1. Write the base NPV once at the top.
  2. Build a mini table: variable, PV of its cash flows, then NPV ÷ PV.
  3. For sales volume, use PV of contribution (PV of revenue minus PV of variable costs), because a volume change moves both. For price, use PV of total revenue. For variable costs, use PV of total variable costs.
  4. For investment, use the initial outlay at time 0, since its PV is its own value.
  5. Tax-affected items must be taken after tax. Do not mix pre-tax and post-tax figures.
  6. Circle the smallest percentage and write one sentence of comment.

Common mistakes in Sensitivity Analysis

  • Dividing NPV by the undiscounted total of the variable.

    Students forget that the NPV is in present-value terms.

    Fix: Always use the present value of the variable's cash flows, using the same discount factors as the NPV.

  • Using contribution instead of sales revenue when flexing selling price.

    Volume sensitivity uses contribution, so students copy it across.

    Fix: A price change flows straight to profit with no change in variable cost, so use the full PV of revenue.

  • Giving the wrong direction of change.

    Students quote the number without saying whether it is a rise or a fall.

    Fix: Write 'a fall of x% in sales' or 'a rise of x% in costs'. Costs and investment break even when they rise.

  • Changing several variables at once.

    Students try to model a realistic downside.

    Fix: Standard sensitivity flexes one variable at a time. Mention as a limitation that variables may move together.

  • Ignoring tax or working capital in the PV of the variable.

    Students take figures from the question without checking the NPV workings.

    Fix: Use the same post-tax figures that went into the NPV. If the NPV is after tax, the variable must be too.

  • Treating sensitivity analysis as giving a probability of success.

    It sounds similar to expected value.

    Fix: Remember it gives no likelihood. It only shows how much a variable can change before the decision reverses.

Worked examples

Example 1

A project needs an initial outlay of ₹10,00,000 now. The present value of after-tax sales revenue is ₹30,00,000, the PV of after-tax variable costs is ₹15,00,000 and the PV of after-tax fixed costs is ₹3,00,000. Calculate the sensitivity of the NPV to changes in (a) selling price, (b) variable costs, (c) the initial investment and (d) sales volume.

Show the solution
  1. Base NPV = 30,00,000 − 15,00,000 − 3,00,000 − 10,00,000 = ₹2,00,000. It is positive.
  2. (a) Selling price: 2,00,000 ÷ 30,00,000 × 100% = 6.67%.
  3. (b) Variable costs: 2,00,000 ÷ 15,00,000 × 100% = 13.33%.
  4. (c) Initial investment: 2,00,000 ÷ 10,00,000 × 100% = 20%.
  5. (d) Sales volume: PV of contribution = 30,00,000 − 15,00,000 = ₹15,00,000. Sensitivity = 2,00,000 ÷ 15,00,000 × 100% = 13.33%.
  6. Rank: selling price is the most sensitive (6.67%), then sales volume and variable costs (both 13.33%), then investment (20%). Volume and variable costs are equal only because the PV of contribution happens to equal the PV of variable costs (both ₹15,00,000) in these figures. This is a coincidence and will not usually happen.

Answer: NPV is ₹2,00,000. Selling price can fall by 6.67%, sales volume can fall by 13.33%, variable costs can rise by 13.33% and investment can rise by 20% before NPV is zero. Selling price is the key variable.

Example 2

A company can sell 10,000 units in a year at ₹50 each. Variable cost is ₹30 per unit and fixed costs are ₹1,50,000. There is no discounting. Calculate the percentage change in (a) sales volume and (b) fixed costs that makes profit zero, and comment.

Show the solution
  1. Contribution per unit = 50 − 30 = ₹20. Total contribution = 10,000 × 20 = ₹2,00,000.
  2. Profit = 2,00,000 − 1,50,000 = ₹50,000.
  3. (a) Volume: profit ÷ total contribution = 50,000 ÷ 2,00,000 × 100% = 25% fall. Check: 7,500 units × 20 = 1,50,000, which equals fixed costs, so profit is zero.
  4. (b) Fixed costs: 50,000 ÷ 1,50,000 × 100% = 33.33% rise. Check: 1,50,000 × 1.3333 = 2,00,000, which equals contribution.
  5. Comment: volume is the more sensitive variable, so management should check demand forecasts first.

Answer: Profit is ₹50,000. Volume can fall by 25% and fixed costs can rise by 33.33% before profit is zero. Sales volume is more critical.

Exam tips

  • In OT questions, read whether the answer is a fall or a rise and pick the option with the right direction and size.
  • Show the formula and the PV figures in Section C. Method marks are given even if one figure is wrong.
  • Always add a comment. Say which variable is most sensitive and what management should do.
  • When asked for advantages and disadvantages, give both sides: it is simple and highlights key variables, but it ignores probability and changes one variable at a time.
  • When asked about the difference from expected value, say that sensitivity uses no probabilities and expected value gives a weighted average outcome.

Practice questions from Dealing with risk and uncertainty in decision-making

Sensitivity Analysis in other exams

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

Sensitivity Analysis: frequently asked questions

What is the formula for sensitivity analysis in ACCA PM?

Sensitivity % = NPV ÷ PV of the variable's cash flows × 100%. This gives the percentage change in that variable that makes NPV zero. For costs it is a rise and for revenue it is a fall.

What are the advantages and disadvantages of sensitivity analysis?

Advantages: it is simple, it identifies critical variables and it needs no probabilities. Disadvantages: it changes one variable at a time, gives no likelihood of change and does not give a decision on its own.

What is the difference between sensitivity analysis and expected value?

Expected value weights outcomes by probabilities to give one average figure. Sensitivity analysis uses no probabilities and shows how much a single estimate can change before the decision reverses.

Which variable is the most critical?

The one with the smallest sensitivity percentage. A small error in that variable is enough to make NPV zero.