HP 12C Learn

NPV for Uneven Cash Flows

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

8 min| Draft

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
Clear cash flow registers
Remove the prior project.
Display: 0
2
10000 CHS CF0
Store the initial outlay as a negative cash flow.
Display: -10000
3
4000 CFj
Store the first future inflow.
Display: 4000
4
4200 CFj
Store the second inflow.
Display: 4200
5
4500 CFj
Store the third inflow.
Display: 4500
6
8 i
Set the annual discount rate.
Display: 8
7
NPV
Compute the present-value result.
Display: NPV value

Result

The displayed NPV shows whether the discounted inflows beat the initial investment.

Interpretation

A positive NPV means value is added at the chosen 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.

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