Understand internal rate of return
Interpret IRR as the discount rate that makes a project's NPV equal to zero.
Exam scope and assessment notes
Cambridge International AS & A Level Accounting 9706, 2026–2028 syllabus, Version 2. This topic covers future net cash flows, payback, ARR, NPV, IRR and supported investment decisions. Discounted payback and questions involving a residual value at the end of a project are excluded by Cambridge. Practice is self-checked, not an official Cambridge grade. Full timed Papers 1–4 and human subject-teacher review remain outstanding.
Before you begin
- Use AS Topics 1.5–1.6 for profit, depreciation and financial analysis, and Topic 2.1 for contribution. Keep accounting profit, project cash flow and the time value of money distinct.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
NPV is positive at 6% and negative at 14%. Where is a single IRR likely?
What you will learn
- Define IRR using NPV
- Bracket a likely IRR using NPV signs
- Compare IRR with the required return
Find the rate that sets NPV to zero
IRR is the discount rate at which the present value of project future net cash flows equals the initial investment, so NPV = 0.
If NPV is positive at a lower rate and negative at a higher one, IRR lies between them, assuming a conventional cash-flow pattern with one crossing.
Interpret against the required return
A project with IRR above the stated required rate may pass that criterion. The difference is not a guarantee of actual return.
IRR is easy to communicate as a percentage but may rank mutually exclusive projects differently from NPV when scale, timing or cash-flow patterns differ.
Pause and explain
IRR is 12% and required return is 10%. What does the criterion indicate?
Worked example
NPV is +$6,000 at 8% and −$2,000 at 16%. What can be inferred?
Show the worked solution
- The NPV sign changes between the rates.
- The zero lies between 8% and 16% under a single-crossing assumption.
- More calculation is needed to estimate the rate.
Answer IRR lies between 8% and 16%, assuming one NPV crossing.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
NPV is +$4,000 at 9% and −$3,000 at 15%. State the IRR range.
Give me a hint
Locate the interval containing the sign change.
Compare my reasoning
- At 9%, NPV is positive.
- At 15%, NPV is negative.
- The zero lies between them if there is one crossing.
IRR is between 9% and 15% under the single-crossing assumption.
Look for these in your work
- Signs read
- Interval identified
- Assumption stated
A has IRR 17%, B 13%, and required return is 14%. Which passes, and what caveat remains?
Give me a hint
Compare both rates with 14%, then consider project ranking.
Compare my reasoning
- A is above 14%; B is below.
- A passes this IRR screen.
- For mutually exclusive projects, also compare NPV and feasibility.
A passes the 14% screen; B does not. IRR alone may not rank exclusive projects correctly.
Look for these in your work
- Threshold applied
- Both classified
- Caveat stated
NPV remains positive at two trial rates. What should you do to bracket IRR?
Give me a hint
A sign change has not yet been found.
Compare my reasoning
- Test a higher rate until NPV becomes negative, where appropriate.
- Record each rate with its NPV sign.
- Check the cash-flow pattern before assuming a single IRR.
The rates have not bracketed zero. Try a higher rate and check whether a conventional single IRR applies.
Look for these in your work
- No bracket recognised
- Next test identified
- Assumption checked
Common mistakes
- Calling IRR accounting profit percentage
- Assuming every cash-flow pattern has one IRR
- Comparing with the wrong required rate
What can you explain now?
What defines IRR?
Compare with the explanation
The discount rate at which NPV equals zero
At IRR, discounted future net flows equal the initial outflow.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do NPV signs at two rates help locate IRR?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.