Strategic Financial Management · Evaluation of Risky Proposals for Investment Decisions

Sensitivity Analysis and Scenario Analysis in Capital Budgeting

Updated 11 October 2026 · Fact-checked

Sensitivity analysis changes one input at a time, such as sales, cost or discount rate, and shows how much project NPV moves. Scenario analysis changes several inputs together into worst, expected and best cases and gives an NPV for each. To solve: compute base NPV, find break-even values, then compare scenario NPVs.

Understand Sensitivity Analysis and Scenario Analysis

Capital budgeting rests on forecasts of sales, costs, life and discount rate. All of them can be wrong. Sensitivity and scenario analysis show how much a wrong forecast would hurt, without needing a full probability model.

Sensitivity analysis asks: if one variable changes and everything else stays the same, what happens to NPV? You pick a variable, change it by a set percentage (say -10%), and recompute NPV. The variable that moves NPV the most is the critical variable. Management then spends its effort forecasting and controlling that variable.

A useful form is the break-even (NPV = 0) value of each variable. It tells you how far a variable can fall before the project stops adding value. The smaller the percentage change needed to bring NPV to zero, the more sensitive the project is to that variable.

Scenario analysis fixes the main weakness of sensitivity analysis: in real life, variables move together. A weak economy lowers volume and price and raises costs at the same time. So you build a worst case, an expected (base) case and a best case, each with a consistent set of inputs, and compute NPV for each. If you assign probabilities to the cases, you can also compute an expected NPV and the chance of a negative NPV.

Both methods are simple and decision-friendly, but neither gives a full probability distribution. Sensitivity ignores links between variables. Scenario analysis uses only a few cases and the choice of cases is subjective. For a fuller picture you move on to decision trees and simulation.

Key rules to remember

NPV: NPV = Σ [CFt ÷ (1 + k)^t] − Initial investment; Base-case NPV is the starting point for every sensitivity or scenario question.
Break-even annual cash flow (level inflows): Break-even cash flow = Initial investment ÷ Annuity factor (k, n); Valid when inflows are equal each year and there is no salvage value. Otherwise equate PV of inflows to the outflow.
Sensitivity of NPV to cash inflows: % fall in inflows that makes NPV zero = NPV ÷ PV of inflows × 100; Applies when the whole inflow stream changes by the same percentage.
Sensitivity of NPV to initial investment: % rise in investment that makes NPV zero = NPV ÷ PV of investment × 100; Use PV of the outflow; if the investment is all at time 0, this is the investment itself.
Scenario NPV and expected NPV: Expected NPV = Σ (Probability of scenario × NPV of scenario); Probabilities must add to 1. Use only if probabilities are given.
Range of NPV: Range = Best-case NPV − Worst-case NPV; A simple measure of how widely the outcome can vary.

How to solve Sensitivity Analysis and Scenario Analysis questions

Use this order for any sensitivity or scenario question. It keeps the working clean and earns method marks even if one number slips.

1Read the question and list every input: investment, life, annual cash flows, salvage, working capital, tax and discount rate. Note which are changed and whether they change singly or together.
2Compute the base-case NPV with proper discount factors. Show the PV of inflows and PV of outflows separately.
3For sensitivity analysis, change one variable at a time by the stated percentage and recompute NPV. Or find the break-even change that makes NPV zero.
4Rank the variables by how little change is needed to turn NPV negative. The one needing the smallest change is the most critical.
5For scenario analysis, build each scenario with all its inputs together. Compute the NPV of the worst, expected and best case.
6If probabilities are given, compute the expected NPV and the probability of NPV below zero. Give the range as well.
7Write a recommendation: accept, reject or accept with conditions. Name the critical variable and say what management should monitor.
8State the limitations briefly if the question asks for comments.

Quickest way: Break-even shortcut for NPV sensitivity

When to use it: Use when inflows are level, the investment is at time 0 and the question asks which variable is most sensitive or how far a variable can move.

Compute PV of inflows once using the annuity factor.
Compute NPV = PV of inflows − investment.
Divide NPV by PV of inflows to get the % fall in cash flow that makes NPV zero. Divide NPV by the investment to get the % rise in investment that does the same.
Compare the percentages. The smallest is the most sensitive variable.
For scenarios, reuse the same annuity factor: multiply each scenario's annual cash flow by it and subtract the investment.

Common mistakes in Sensitivity Analysis and Scenario Analysis

Changing several variables at once and calling it sensitivity analysis.
Students mix up the two methods because both test 'what if' changes.
Fix: In sensitivity analysis change one variable and hold the rest at base values. Changing a combined set of inputs is scenario analysis.
Dividing the NPV by the wrong base, for example by the annual cash flow instead of the PV of inflows.
Students forget that NPV is a present-value figure and must be compared with a present-value base.
Fix: Use NPV ÷ PV of inflows for cash-flow sensitivity and NPV ÷ PV of the investment for investment sensitivity.
Applying a percentage change to the discount rate as if it were a cash flow.
Discount-rate changes do not move NPV in a straight line.
Fix: Recompute NPV at the new rate, or use IRR. The IRR is the break-even discount rate.
Treating the expected NPV as the answer and ignoring the downside.
Students stop once they see a positive weighted figure.
Fix: Also state the worst-case NPV and the probability of a negative NPV, then link the recommendation to the firm's capacity to bear loss.
Forgetting that scenarios must be internally consistent, such as a best-case price with worst-case volume.
Students pick extreme values for each input independently.
Fix: Choose inputs that would plausibly occur together in each economic situation, and say so in your answer.
Ending without a recommendation or without naming the critical variable.
Students treat it as a pure calculation.
Fix: Close every answer with an accept or reject decision and the variable management should watch most closely.

Worked examples

Example 1

Sundaram Auto Components Ltd is evaluating a machine costing ₹10,00,000 with a 5-year life and no salvage value. Net annual cash inflow after tax is ₹3,00,000. The cost of capital is 10%. The 5-year annuity factor at 10% is 3.7908. (a) Compute NPV. (b) Find the percentage fall in annual cash inflow and the percentage rise in investment that would make NPV zero. (c) Which variable is more critical?

Show the solution

PV of inflows = ₹3,00,000 × 3.7908 = ₹11,37,240.
NPV = ₹11,37,240 − ₹10,00,000 = ₹1,37,240.
Cash-inflow sensitivity: 1,37,240 ÷ 11,37,240 × 100 = 12.07%. Check: break-even inflow = 10,00,000 ÷ 3.7908 = about ₹2,63,800, which is a fall of ₹36,200 on ₹3,00,000, or 12.07%.
Investment sensitivity: investment can rise until it equals PV of inflows, ₹11,37,240. Rise = 1,37,240 ÷ 10,00,000 × 100 = 13.72%.
Comparison: a smaller change (12.07%) in annual inflow turns NPV negative than in investment (13.72%). So annual cash inflow is the more critical variable.
Further check on the discount rate: at 15% the annuity factor is 3.3522 and at 16% it is 3.2743. The required factor for zero NPV is 10,00,000 ÷ 3,00,000 = 3.3333, so IRR is about 15.2%. The cost of capital can rise from 10% to about 15.2% before NPV turns negative.

Answer: Base NPV is ₹1,37,240. NPV becomes zero if annual inflow falls 12.07% or investment rises 13.72%. Annual cash inflow is the more critical variable, so management should focus on securing the inflow forecast. The project is acceptable on the base case.

Example 2

Kaveri Foods Ltd is considering a project costing ₹8,00,000 with a 4-year life and no salvage value. The cost of capital is 12%; the 4-year annuity factor is 3.0373. Management prepares three scenarios. Worst: annual cash inflow ₹2,00,000, probability 0.25. Expected: ₹3,00,000, probability 0.50. Best: ₹4,00,000, probability 0.25. Compute the NPV in each scenario, the expected NPV, the range and the probability of a negative NPV, and advise.

Show the solution

Worst case: PV of inflows = 2,00,000 × 3.0373 = ₹6,07,460. NPV = 6,07,460 − 8,00,000 = −₹1,92,540.
Expected case: PV = 3,00,000 × 3.0373 = ₹9,11,190. NPV = 9,11,190 − 8,00,000 = ₹1,11,190.
Best case: PV = 4,00,000 × 3.0373 = ₹12,14,920. NPV = 12,14,920 − 8,00,000 = ₹4,14,920.
Expected NPV = (0.25 × −1,92,540) + (0.50 × 1,11,190) + (0.25 × 4,14,920) = −48,135 + 55,595 + 1,03,730 = ₹1,11,190.
Range = 4,14,920 − (−1,92,540) = ₹6,07,460.
Only the worst case gives a negative NPV, so the probability of a negative NPV is 0.25, or 25%.
Decision: expected NPV is positive, but there is a one-in-four chance of losing ₹1,92,540 in present-value terms.

Answer: Scenario NPVs are −₹1,92,540 (worst), ₹1,11,190 (expected) and ₹4,14,920 (best). Expected NPV is ₹1,11,190 and the range is ₹6,07,460. There is a 25% chance of negative NPV. Accept the project if the company can absorb the worst-case loss; otherwise look at ways to reduce the downside, such as firm offtake contracts.

Exam tips

Read the verb. 'Test the effect of a change in one variable' means sensitivity analysis. 'Best, worst and expected cases' means scenario analysis.
Always show the base-case NPV first, even if the question does not ask for it. Every later figure depends on it.
Show the discount factors you use. Examiners give marks for method when a rounding difference changes the final figure.
End with a recommendation that names the critical variable. Case-based questions reward the decision and its reasoning.
In MCQs, remember the key contrast: sensitivity changes one variable at a time, scenario analysis changes a set of variables together.

Practice questions from Evaluation of Risky Proposals for Investment Decisions

Sensitivity Analysis and Scenario 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 and Scenario Analysis: frequently asked questions

What is the difference between sensitivity analysis and scenario analysis?

Sensitivity analysis changes one input at a time and holds the others constant. Scenario analysis changes several inputs together to form a worst, expected and best case. Sensitivity finds the critical variable, while scenario analysis shows the range of outcomes.

How do I do sensitivity analysis of NPV in the exam?

Compute the base NPV, then recompute it after changing one variable by the stated percentage. Or find the percentage change in that variable that makes NPV zero, using NPV divided by the present value of that variable. Rank the variables and recommend.

How is break-even analysis used in project appraisal?

Here break-even means the value of a variable at which NPV is zero. For level inflows, break-even cash flow equals the investment divided by the annuity factor. It tells you the margin of safety in the forecast.

What are the limitations of these methods?

Sensitivity analysis ignores links between variables and gives no probabilities. Scenario analysis uses only a few cases and the choice of cases is subjective. Both are simple, so for a full probability picture you use decision trees or simulation.