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Internal Rate of Return (IRR) answers a simple question: at what discount rate does a project exactly break even on a present-value basis? It is the rate that makes the Net Present Value (NPV) equal to zero. If this rate exceeds your cost of capital (hurdle rate), the project creates value — accept it. If it falls below, reject it.

Think of it this way: Mr. Sharma's factory project promises ₹50,000 cash inflows every year for 5 years on an investment of ₹1,50,000 today. The bank charges 12% on funds. If the project's IRR works out to 18%, the project earns more than it costs — green light. If IRR is 9%, the project doesn't even cover borrowing costs — red light. This is why IRR is so popular with CFOs: it gives a single percentage you can compare directly to a borrowing rate or a benchmark return.

Because IRR has no closed-form formula, you calculate it by interpolation (trial and error). The exam-standard method: pick two discount rates — one giving a positive NPV (rate too low) and one giving a negative NPV (rate too high). Then use the formula: IRR = Lower Rate + [NPV at Lower Rate ÷ (NPV at Lower Rate − NPV at Higher Rate)] × (Higher Rate − Lower Rate). The closer your two trial rates bracket the true IRR, the more accurate your answer. ICAI typically awards marks even for a slightly off answer if the working is correct, so always show both trial NPVs.

Key limitations the examiner loves to test: (1) IRR assumes cash inflows are reinvested at the IRR itself — which is often unrealistic; NPV's reinvestment assumption (at cost of capital) is more conservative and reliable. (2) With non-conventional cash flows (sign changes mid-project), you can get multiple IRRs — the method breaks down. (3) For mutually exclusive projects, IRR can mislead if project sizes differ; always cross-check with NPV. This is asked frequently as a 4–6 mark theory or numerical question, especially in combination with NPV comparison.

📊 Worked example

Example 1 — Standard IRR by Interpolation

Rajesh & Co. Pvt. Ltd. is evaluating a machine costing ₹1,00,000 that generates ₹40,000 per year for 4 years. Cost of capital = 15%. Should they invest?

Step 1 — Trial at 20%

Annuity PV factor (20%, 4 yrs) = 2.589

PV of inflows = ₹40,000 × 2.589 = ₹1,03,560

NPV at 20% = ₹1,03,560 − ₹1,00,000 = +₹3,560

Step 2 — Trial at 22%

Annuity PV factor (22%, 4 yrs) = 2.494

PV of inflows = ₹40,000 × 2.494 = ₹99,760

NPV at 22% = ₹99,760 − ₹1,00,000 = −₹240

Step 3 — Interpolate

IRR = 20% + [3,560 ÷ (3,560 + 240)] × (22% − 20%)

IRR = 20% + [3,560 ÷ 3,800] × 2%

IRR = 20% + 0.937 × 2% = 20% + 1.87%

IRR ≈ 21.87%

Decision: IRR (21.87%) > Cost of Capital (15%) → Accept the project.

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Example 2 — IRR vs NPV conflict in mutually exclusive projects

Ms. Iyer must choose between Project A (cost ₹50,000, IRR = 25%) and Project B (cost ₹2,00,000, IRR = 20%). Cost of capital = 12%.

Both IRRs exceed 12%, but Project B has a much larger base. Suppose:

  • NPV of Project A = ₹18,000
  • NPV of Project B = ₹55,000

Decision: IRR ranks A first; NPV ranks B first. Since NPV measures absolute wealth creation, choose Project B (NPV rule prevails for mutually exclusive decisions).

Lesson: Never rely on IRR alone for mutually exclusive projects.

⚠️ Common exam mistakes

  • Students confuse IRR with the discount rate used in NPV. IRR is not an input — it is the output (the rate that zeroes out NPV). The cost of capital is the input you compare IRR against.
  • Choosing trial rates that are too far apart (e.g., 10% and 30%) introduces large interpolation error. Keep your two trial rates within 3–5 percentage points of each other for exam accuracy.
  • Forgetting to show both trial NPVs. ICAI awards method marks for the two NPV calculations. Jumping straight to the formula without showing working loses marks even if the final answer is correct.
  • Using IRR to rank mutually exclusive projects without cross-checking NPV. The project with the higher IRR is not always the better choice — size matters. Always confirm with NPV when projects differ in scale or life.
  • Misapplying the interpolation formula sign. The denominator is (NPV at lower rate minus NPV at higher rate) — both treated as absolute values added together when one is positive and one negative. Writing it as (positive NPV + |negative NPV|) avoids sign errors.
📖 Reference: IRR — Institute of Chartered Accountants of India
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