IRR - Three Year Project

Find the IRR for a three-year project and compare to the hurdle rate.

Problem Scenario

Invest $5,000 today. Cash inflows: Year 1 = $2,000, Year 2 = $2,500, Year 3 = $1,500. Hurdle rate = 10%.

Given Data

Initial$5,000

Year 1$2,000

Year 2$2,500

Year 3$1,500

Requirements

Estimate IRR
Accept or reject at 10% hurdle

Solution

Step 1:

At 10%: NPV = 2000/1.1 + 2500/1.21 + 1500/1.331 - 5000 = 1818.18 + 2066.12 + 1126.97 - 5000 = 11.27.

Step 2:

At 11%: NPV = 2000/1.11 + 2500/1.2321 + 1500/1.3676 - 5000 = 1801.80 + 2028.24 + 1096.82 - 5000 = -73.14.

Step 3:

IRR is between 10% and 11%. Linear interpolation: IRR ≈ 10% + 11.27/(11.27+73.14) × 1% ≈ 10.13%.

Final Answer

IRR ≈ 10.13%. Accept since IRR > 10% hurdle rate (barely).

Key Takeaways

✓Trial-and-error narrows the IRR range
✓Small NPV means IRR is close to the tested rate

Common Errors to Avoid

✗Rounding too early in interpolation
✗Forgetting that negative NPV means rate is too high

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FAQs

Common questions about this problem type

Yes. Small margin suggests sensitivity to assumptions—run a sensitivity analysis.

Only for simple cases with 1-2 cash flows. For 3+ periods, use trial and error, linear interpolation, or a financial calculator's IRR function. Most exam problems expect the interpolation method.