KEVOS® MAKEOS · Money
Internal Rate of Return (Uneven Cash Flows)
What rate of return does this investment earn with these yearly cash flows?
Internal rate of return, NPV at a hurdle rate and payback for an investment with up to eight uneven yearly cash flows, solved by bisection.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Initial investment | AUD | Up-front cost at year 0. |
| Hurdle (discount) rate | % | Your organisation’s required rate of return. |
| Net cash flow, year 1 | AUD | Net cash inflow (savings minus costs) in year 1. |
| Net cash flow, year 2 | AUD | Net cash flow in year 2. |
| Net cash flow, year 3 | AUD | Net cash flow in year 3. |
| Net cash flow, year 4 | AUD | Net cash flow in year 4. |
| Net cash flow, year 5 | AUD | Net cash flow in year 5 (include salvage in the final year). |
| Net cash flow, year 6 | AUD | Net cash flow in year 6 (0 if none). |
| Net cash flow, year 7 | AUD | Net cash flow in year 7. |
| Net cash flow, year 8 | AUD | Net cash flow in year 8. |
Method and formulas
- NPV(i) = −P + Σ CFₜ ÷ (1 + i)ᵗ.
- IRR is the rate where NPV = 0, found by bisection between −99% and 1000%.
- Payback = year in which cumulative cash flow turns positive (interpolated).
- Example: the default project has an IRR of 10.946% and an NPV of $3,108 at 10%.
Limitations
- Cash flows with several sign changes can have more than one IRR; check the NPV instead.
- Year-end cash flows; tax and inflation only as built into the inputs.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Evaluate an equipment or improvement project with uneven savings
- Compare a project with the hurdle rate
- Check a supplier’s ROI claims
Who it is for
- Engineering managers
- Project engineers
- Finance and business analysts
What you get
- Internal rate of return
- NPV at the hurdle rate
- Simple payback
Interpreting the result
- Accept when IRR exceeds the hurdle rate (equivalently, NPV > 0) and the risks are acceptable.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 140–144. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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