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When a company considers a big investment — say, buying a ₹50 lakh machine — the future is uncertain. Sales might be higher or lower, costs might change, the discount rate might shift. Sensitivity Analysis and Scenario Analysis are two techniques that help you stress-test your NPV before committing real money.

Sensitivity Analysis asks: "What if I change just ONE variable — how much does NPV swing?" You keep everything else constant and tweak one input (sales volume, selling price, cost, discount rate) to find two things: (1) the new NPV, and (2) the switching value (also called the break-even value) — the exact level at which NPV hits zero. The variable with the smallest percentage change needed to make NPV zero is the most sensitive — and therefore the riskiest. This is frequently asked as a 5-mark question in exams — they give you a base-case NPV and ask you to find sensitivity % for two or three variables.

Scenario Analysis is a step up — it changes multiple variables together to paint three pictures: Best Case, Base Case (Most Likely), and Worst Case. Think of it like planning a road trip. Base case: normal traffic, arrive on time. Worst case: heavy rain, highway closed, 3 hours late. Best case: empty roads, arrive early. Each scenario has its own NPV. Management looks at the range of outcomes and decides if the risk is acceptable. If even the worst-case NPV is positive, sleep easy. If it is deeply negative, think twice.

The key difference to remember: Sensitivity = one variable changes, others fixed. Scenario = multiple variables change together, giving holistic outcomes. Examiners love asking students to distinguish these two. Also remember — neither technique assigns probability to outcomes. For that, you need Expected NPV (with probability weights), which is a separate but related concept. Sensitivity and Scenario Analysis are qualitative risk tools; they show what can happen, not how likely it is.

📊 Worked example

Example 1 — Sensitivity Analysis

Rajesh & Co. Pvt. Ltd. is evaluating a project:

  • Initial Investment: ₹10,00,000
  • Expected Annual Cash Inflow: ₹3,00,000 for 5 years
  • Discount Rate: 12%
  • PVIFA (12%, 5 years) = 3.6048

Step 1 — Base Case NPV

NPV = (₹3,00,000 × 3.6048) − ₹10,00,000

NPV = ₹10,81,440 − ₹10,00,000 = ₹81,440

Step 2 — Switching Value of Cash Inflow

Set NPV = 0:

Cash Inflow × 3.6048 = ₹10,00,000

Cash Inflow = ₹10,00,000 ÷ 3.6048 = ₹2,77,421

Step 3 — Sensitivity %

Sensitivity = (₹3,00,000 − ₹2,77,421) ÷ ₹3,00,000 × 100

Sensitivity = ₹22,579 ÷ ₹3,00,000 × 100 = 7.53%

Interpretation: If annual cash inflows fall by more than 7.53%, NPV turns negative. The project is quite sensitive to cash flow changes.

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Example 2 — Scenario Analysis

Ms. Iyer is evaluating the same ₹10,00,000 project but considers three scenarios:

| Scenario | Annual Cash Inflow | NPV Calculation | NPV |

|---|---|---|---|

| Best Case | ₹3,50,000 | (₹3,50,000 × 3.6048) − ₹10,00,000 | ₹2,61,680 |

| Base Case | ₹3,00,000 | (₹3,00,000 × 3.6048) − ₹10,00,000 | ₹81,440 |

| Worst Case | ₹2,40,000 | (₹2,40,000 × 3.6048) − ₹10,00,000 | −₹1,34,848 |

Conclusion: Even in the base case, NPV is positive. However, worst case gives a negative NPV of ₹1,34,848. Management must assess whether this downside risk is acceptable before proceeding.

⚠️ Common exam mistakes

  • Confusing Sensitivity and Scenario Analysis in theory questions. Students often describe Scenario Analysis when asked about Sensitivity. Remember: Sensitivity = one variable at a time. Scenario = multiple variables together in a single realistic package.
  • Forgetting to calculate the Switching Value. Many students find the new NPV when a variable changes but stop there. The examiner usually wants the switching value (break-even level) AND the sensitivity percentage — always compute both.
  • Sensitivity % formula errors. Don't use (New Value − Old Value) / New Value. The correct formula is (Base Value − Switching Value) / Base Value × 100. Dividing by the wrong figure is a common slip.
  • Treating lower sensitivity % as 'safer'. A variable with a 5% sensitivity means NPV breaks even with just a 5% change — that is MORE risky, not less. The lower the %, the more fragile that assumption is. Students often interpret this backwards.
  • Ignoring the discount rate as a variable. Questions sometimes ask sensitivity with respect to the discount rate. Don't assume only sales or costs can be the variable — cost of capital is equally testable and requires re-computing PVIFA at the switching discount rate.
📖 Reference: Scenario — Institute of Chartered Accountants of India
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