HP 12C Learn

NPV for Uneven Cash Flows

Enter CF0, CFj, and the discount rate correctly to evaluate a non-uniform investment.

8 min

What this solves

This tutorial shows how to evaluate an investment when cash flows do not arrive in equal amounts each period.

Before you start

  • Clear cash flow memory before entering a new CF0 and CFj sequence.
  • Decide which cash flow is the initial investment and assign its sign correctly.
  • Use a discount rate that matches the same period spacing as the cash flows.

Key ideas

CF0 is usually the initial outlay

In many project examples CF0 should be negative.

NPV is a discounted comparison

It tells you whether future inflows justify the initial investment at the chosen rate.

Worked example 1

Example: evaluate a project with uneven inflows

An investment requires an upfront outlay and produces different inflows over the next three periods.

Setup

  • Assume one cash flow per year.
  • Use an annual discount rate.

Inputs

CF0
-10,000
Initial investment
CF1
4,000
CF2
4,200
CF3
4,500
Discount rate
8%

Keystrokes and checkpoints

1
f CLEAR REG
Remove the prior project and its stored cash flows.
Display: 0.00
2
10000 CHS g CF0
Store the initial outlay as a negative cash flow.
Display: -10,000.00
3
4000 g CFj
Store the first future 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
8 i
Set the annual discount rate.
Display: 8.00
7
f NPV
Compute the present-value result.
Display: 876.77

Result

NPV = -10,000 + 4,000/1.08 + 4,200/1.08² + 4,500/1.08³ ≈ +876.77.

Interpretation

The positive result means the discounted inflows exceed the initial outlay by about 876.77 at an 8% annual discount rate.

Sanity checks

  • If the sign of CF0 is wrong, the meaning of the result flips.
  • If old cash flows were not cleared, the answer is unusable.
  • If cash flows are monthly, the discount rate must also be monthly or consistently converted.

Why it works

  • NPV discounts each future cash flow back to present value.
  • The HP 12C cash flow memory stores uneven streams cleanly.
  • Correct sign convention is critical because NPV compares inflows against the initial outlay.

Common mistakes

  • Forgetting to clear old cash flow memory.
  • Entering the initial investment with the wrong sign.
  • Using a discount rate that does not match the cash flow period.

Practice prompt

Run the same project again with a higher discount rate and watch how the NPV changes.

Try it in the HP 12C emulator

Follow the steps above, then test the sequence live.

Related guides

IRR for Uneven Cash Flows
8 min