Financial Management · Adjusting for risk and uncertainty in investment appraisal

Sensitivity Analysis in Investment Appraisal for ACCA FM

Updated 11 October 2026 · Fact-checked

Sensitivity analysis shows how far one input can move before a project's NPV falls to zero. Calculate the sensitivity margin as NPV ÷ PV of the cash flow affected × 100%. The smaller the margin, the more critical the variable. Rank the margins to find the key variables management must monitor.

Understand Sensitivity Analysis

An NPV is built from estimates: sales volume, selling price, costs, the investment and the discount rate. Any of them can be wrong. Sensitivity analysis asks: how wrong can one estimate be before the project stops being worthwhile?

You change one variable at a time and hold the rest at their expected values. You find the change that makes NPV exactly zero. That change is the sensitivity margin, usually shown as a percentage of the original estimate.

Why does the formula work? A change in one variable changes the NPV by the PV of that cash flow multiplied by the percentage change. NPV falls to zero when the percentage change multiplied by the PV of that cash flow equals the current NPV. So margin = NPV ÷ PV of the cash flow.

A small margin means a small error wipes out the NPV. That variable is critical or key. Management should check those estimates carefully and monitor them if the project goes ahead.

Advantages: it is simple to do and understand. It identifies the variables that need most attention. It shows how much room for error there is. It needs no probabilities.

Disadvantages: it changes only one variable at a time, but in real life variables move together. It gives no probability of the change happening. It does not give a decision rule, so judgement is needed on what margin is acceptable. It is only as good as the original estimates. It does not show the best or worst outcomes.

Key rules to remember

Sensitivity margin (general): Sensitivity margin = NPV ÷ PV of the cash flow affected × 100%; Use the PV of the specific cash flow being flexed, over its whole life. Use a positive NPV.
Initial investment: Margin = NPV ÷ initial investment × 100%; The investment is already at time 0, so its PV is the amount itself.
Selling price: Margin = NPV ÷ PV of sales revenue × 100%; Price changes flow straight to profit, so use revenue (not contribution).
Sales volume: Margin = NPV ÷ PV of contribution × 100%; Volume changes revenue and variable costs together, so use contribution.
Variable or fixed costs: Margin = NPV ÷ PV of that cost × 100%; Use the PV of the cost line only. A rise in cost lowers NPV.
Discount rate: Margin = IRR − cost of capital (in percentage points); This is usually measured as an absolute difference, not a percentage of NPV.

How to solve Sensitivity Analysis questions

Use this method for any sensitivity question. It works whether the exam asks for one variable or several.

1Calculate the base-case NPV. Confirm it is positive. Sensitivity margins are measured from this NPV.
2List the variables to be tested, such as investment, selling price, volume, variable costs, fixed costs and the discount rate.
3For each variable, find the PV of its cash flows. Use the same discount factors, inflation and tax treatment as the base NPV. Show your workings.
4Divide the NPV by each PV and multiply by 100% to get the margin.
5State the direction. Revenue and volume can fall by the margin. Costs and investment can rise by the margin.
6Rank the margins. The smallest margin is the most sensitive, or key, variable.
7Comment: say which variables need careful forecasting or monitoring, and mention one or two limitations if the question asks for evaluation.

Quickest way: One-line margin per variable

When to use it: Use this in Section A and Section B objective questions, where you need a single margin quickly and there is no time for a full table.

Write the NPV.
Identify the one cash flow in the question that changes. Ask whether it is revenue, contribution, a cost or the investment.
Find its PV: annual amount × annuity factor, or the sum of the discounted yearly figures if they vary.
Compute NPV ÷ PV × 100%.
Sense-check: the margin for revenue is normally small, because the PV of revenue is large relative to NPV. A margin over 100% means the PV of that item is smaller than the NPV. Check the direction in the answer options.

Common mistakes in Sensitivity Analysis

Dividing NPV by the undiscounted cash flow.
Students use the annual figure and forget that NPV is a present value.
Fix: Always divide by the PV of that cash flow, using the same discount factor as in the NPV.
Using revenue for a volume margin, or contribution for a price margin.
Both relate to sales, so they seem interchangeable.
Fix: Price changes affect revenue only, so use PV of revenue. Volume changes affect revenue and variable costs, so use PV of contribution.
Changing several variables at once.
Students try to model a realistic downturn.
Fix: Sensitivity analysis flexes one variable at a time. Combined changes are scenario analysis.
Choosing the key variable as the one with the largest margin.
Students think a larger number means more important.
Fix: The smallest margin is the most critical, because the NPV is least tolerant of an error there.
Leaving out tax, inflation or working capital effects in the PV.
Students rush and use a simplified line from the cash flow table.
Fix: Use the PV exactly as it appears in the NPV, after the same tax and inflation adjustments.
Stating the discount rate margin as a percentage of NPV.
Students apply the general formula by habit.
Fix: For the discount rate, compare the IRR with the cost of capital. The margin is the gap in percentage points.

Worked examples

Example 1

A project needs an investment of $150,000 now. For four years it gives annual sales revenue of $120,000, variable costs of $50,000 and fixed cash costs of $20,000. The cost of capital is 10% and the four-year annuity factor is 3.170. Ignore tax. Calculate the base NPV and the sensitivity margin for each of the investment, revenue, variable costs and fixed costs. Identify the key variable.

Show the solution

Annual net cash flow = 120,000 − 50,000 − 20,000 = $50,000.
PV of net cash flows = 50,000 × 3.170 = $158,500.
NPV = 158,500 − 150,000 = $8,500.
Investment: 8,500 ÷ 150,000 = 5.7%. The investment can rise by 5.7%.
Revenue (selling price): PV = 120,000 × 3.170 = $380,400. 8,500 ÷ 380,400 = 2.2%. Selling price can fall by 2.2%.
Sales volume (for comparison): PV of contribution = (120,000 − 50,000) × 3.170 = $221,900. 8,500 ÷ 221,900 = 3.8%. Volume can fall by 3.8%.
Variable costs: PV = 50,000 × 3.170 = $158,500. 8,500 ÷ 158,500 = 5.4%. Variable costs can rise by 5.4%.
Fixed costs: PV = 20,000 × 3.170 = $63,400. 8,500 ÷ 63,400 = 13.4%. Fixed costs can rise by 13.4%.
The smallest margin is 2.2%, for selling price (revenue).

Answer: NPV = $8,500. Margins: investment 5.7%, selling price (sales revenue) 2.2%, variable costs 5.4%, fixed costs 13.4%. Selling price is the key variable at 2.2%, so forecasts of price need the most careful checking. If sales volume is flexed instead, its margin is 3.8%, using the PV of contribution.

Example 2

A project has an NPV of $36,000. The PV of its sales revenue is $900,000, the PV of its variable costs is $540,000 and the initial investment is $400,000. What is the sensitivity margin for selling price? A 4.0% B 10.0% C 9.0% D 6.7%

Show the solution

Selling price changes revenue only, so the relevant PV is the PV of sales revenue: $900,000.
Margin = 36,000 ÷ 900,000 = 0.04 = 4.0%.
Check the other options: 10.0% is 36,000 ÷ 360,000, the PV of contribution (900,000 − 540,000), which is the base for sales volume. 9.0% is 36,000 ÷ 400,000 (investment). 6.7% is 36,000 ÷ 540,000 (variable costs).

Answer: A. Selling price can fall by 4.0% before the NPV reaches zero.

Exam tips

Show the PV of each cash flow as a separate line before dividing. Method marks in Section C depend on clear workings.
In objective questions, read which variable is flexed. The wrong base (revenue vs contribution) is the usual trap, because each distractor is the margin for a different base.
State the direction of change with each margin: revenue falls, costs rise.
When asked to evaluate, name the key variable, give the advantages and limitations in a sentence or two each, and link them to the project in the scenario.
Keep the same rounding as the question. Margins to one decimal place are normally enough.

Practice questions from Adjusting for risk and uncertainty in investment appraisal

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 sensitivity analysis formula in ACCA FM?

Sensitivity margin = NPV ÷ PV of the cash flow affected × 100%. It gives the percentage change in that variable that reduces NPV to zero. For the discount rate, the margin is the IRR minus the cost of capital.

Which variable is the most sensitive?

The one with the smallest sensitivity margin. A small margin means a small forecasting error can make the NPV zero or negative. That variable deserves the most attention.

What are the advantages and disadvantages of sensitivity analysis?

It is simple, shows which variables are critical and needs no probabilities. But it flexes one variable at a time, gives no likelihood of change and offers no decision rule. It also relies on the accuracy of the base estimates.

Do I use contribution or revenue for the sales margin?

Use revenue for selling price, because price changes do not affect variable costs per unit. Use contribution for sales volume, because volume changes both revenue and variable costs.

Is sensitivity analysis the same as scenario analysis?

No. Sensitivity analysis changes one variable at a time to find the break-even change. Scenario analysis changes several variables together to model a set outcome such as best case or worst case.