IRR Exam Training
Exam IRR questions usually give you uneven cash flows and no Excel. The trick is to bracket the answer: find one rate where NPV is positive and one where it is negative, then interpolate. Finally, compare the IRR with the hurdle rate and state a clear accept or reject decision.
What you will learn
- How to set up an IRR exam question quickly
- How to choose sensible trial rates for uneven cash flows
- How to interpolate between a positive and a negative NPV
- How to compare IRR with the hurdle rate and decide
- Common IRR mistakes that cost exam marks
The formulas
- C₀
- initial investment
- CFₜ
- cash flow in year t
- r₁, NPV₁
- lower rate and its positive NPV
- r₂, NPV₂
- higher rate and its negative NPV
Worked example
A project costs $5,000 and returns $2,000, $2,500 and $1,500 at the end of years 1 to 3. The hurdle rate is 12%. Find the IRR and decide.
- NPV at 12%: 2,000 ÷ 1.12 + 2,500 ÷ 1.12² + 1,500 ÷ 1.12³ − 5,000 = −153.63
- Negative, so try lower. NPV at 10% = 11.27
- NPV at 11% = −72.36, so IRR is between 10% and 11%
- Interpolate: 10% + [11.27 ÷ (11.27 + 72.36)] × 1% ≈ 10.13%
- Compare: 10.13% is below the 12% hurdle rate
Answer: IRR ≈ 10.1% (exact ≈ 10.13%). It is below the 12% hurdle rate, so reject the project. The negative NPV at 12% confirms it.
Common questions
How do you find IRR in an exam without Excel?
Calculate NPV at a guessed rate, then move the rate up or down until you have one positive and one negative NPV. Interpolate between them. The closer the two rates are, the more accurate your estimate will be.
How do you calculate IRR with uneven cash flows?
Discount each cash flow separately at a trial rate, since you cannot use an annuity factor. Add the present values, subtract the cost, and check the sign of the NPV. Repeat at another rate and interpolate between the two results.
When should you accept a project using IRR?
Accept an independent project when its IRR is higher than the hurdle rate or cost of capital, and reject it when the IRR is lower. For mutually exclusive projects, rank them by NPV instead, because IRR can give the wrong ranking.
Why is my interpolated IRR slightly different from the calculator?
Interpolation draws a straight line between two points on a curved NPV profile, so it is only an estimate. The wider the gap between your two trial rates, the bigger the error. Examiners normally accept a reasonable interpolated answer.