HP 12C Learn
IRR for Uneven Cash Flows
Use the same cash flow setup as NPV, then solve for the internal rate of return.
8 min
What this solves
This tutorial helps users calculate the internal rate of return after entering an uneven cash flow series.
Before you start
- Clear cash flow memory first.
- Verify that the cash flow signs make economic sense.
- Remember that some cash flow patterns make IRR misleading or unstable.
Key ideas
IRR is the rate that makes NPV equal zero
Think of IRR as the break-even discount rate for the stored project.
Worked example 1
Example: solve IRR after entering the project cash flows
Use the same uneven project structure as an NPV example, but now solve for the implied return rate.
Setup
- Use one initial outflow followed by inflows.
- Keep the time spacing consistent across the project.
Inputs
- CF0
- -10,000
- CF1
- 4,000
- CF2
- 4,200
- CF3
- 4,500
Keystrokes and checkpoints
1
f CLEAR REG
Reset the previous project and its stored cash flows.
Display: 0.00
2
10000 CHS g CF0
Store the initial outflow.
Display: -10,000.00
3
4000 g CFj
Store the first inflow.
Display: 4,000.00
4
4200 g CFj
Store the second inflow.
Display: 4,200.00
5
4500 g CFj
Store the third inflow.
Display: 4,500.00
6
f IRR
Solve for the periodic internal rate of return.
Display: 12.70
Result
The IRR is approximately 12.70% per period for these cash flows.
Interpretation
Because the cash flows are one year apart, this is an annual rate. At this rate, the project NPV is approximately zero.
Sanity checks
- If the result is strange, recheck the sign of CF0 first.
- If IRR feels ambiguous, compare the project with NPV at realistic discount rates.
Why it works
- IRR is the discount rate that drives the project NPV to zero.
- The HP 12C solves IRR from the same stored cash flow set used for NPV.
- Interpretation matters as much as keystrokes when cash flow patterns are non-standard.
Common mistakes
- Trying to solve IRR without clearing the previous cash flow series.
- Ignoring sign changes that produce unstable IRR outputs.
- Assuming the returned rate is annual when the periods are monthly or quarterly.
Practice prompt
After solving IRR, run the same cash flows through NPV at a discount rate just below and just above the returned value.
Try it in the HP 12C emulator
Follow the steps above, then test the sequence live.