BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Initial investment
- What it is
- The up-front cash spent at the start of the project, at year zero, before any benefits arrive.
- Units and format
- Enter a number in AUD: Australian dollars. The form accepts 0.000001 AUD or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger investment lowers IRR and NPV and lengthens payback.
- Get it right
- Enter it as a positive amount; the tool treats it as an outflow.
What this means: Hurdle (discount) rate
- What it is
- The lowest rate of return your organisation accepts for an investment, used to discount the cash flows for NPV.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher hurdle lowers NPV; IRR does not change.
- Get it right
- Type the percentage itself; your finance team usually sets it.
What this means: Net cash flow, year 1
- What it is
- The net cash the project brings in during year 1: savings or extra income minus running costs, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a net figure; a negative value means the project costs money that year.
What this means: Net cash flow, year 2
- What it is
- The net cash the project brings in during year 2, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a net figure: benefits minus running costs for that year.
What this means: Net cash flow, year 3
- What it is
- The net cash the project brings in during year 3, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a net figure: benefits minus running costs for that year.
What this means: Net cash flow, year 4
- What it is
- The net cash the project brings in during year 4, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a net figure: benefits minus running costs for that year.
What this means: Net cash flow, year 5
- What it is
- The net cash the project brings in during year 5, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If this is the last year, include any salvage or resale value here.
What this means: Net cash flow, year 6
- What it is
- The net cash the project brings in during year 6, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 if the project ends earlier; trailing zero years are ignored.
What this means: Net cash flow, year 7
- What it is
- The net cash the project brings in during year 7, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 if the project ends earlier; trailing zero years are ignored.
What this means: Net cash flow, year 8
- What it is
- The net cash the project brings in during year 8, counted at the end of the year.
- Units and format
- Enter a number in AUD: Australian dollars. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 if the project ends earlier; include salvage in the final year.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · Library collection
NPV, IRR and payback answer different questions: reading investment measures when they disagree
In Investment Appraisal and Business Cases
What it covers: One option has the higher return percentage and faster payback; another creates more value. How to read NPV, IRR and payback together, spot when IRR misleads and make the trade-off visible.
Method explained here · BIZOMAT original book
Self-consumption, tariffs and the business case
In Rooftop Solar for Factories by the Numbers
What it covers: How to value a factory array's energy by self-consumption and export, build the business case with NPV, IRR and payback, test it at a P90 yield and a shorter stay, and plan the loan.
BIZOMAT 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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