NPV and IRR on the HP 12C

The HP 12C financial calculator (including Platinum versions) has built-in functions for calculating Net Present Value (NPV) and Internal Rate of Return (IRR) based on a series of cash flows. These are useful for investment analysis:

• NPV: Discounts future cash flows to the present using a specified interest rate (i). A positive NPV indicates a profitable investment at that rate.
• IRR: The discount rate that makes NPV equal to zero. If IRR exceeds your required rate of return, the investment is attractive.

Cash flows are entered sequentially, with the initial investment (outflow) as CF₀ (typically negative). Subsequent inflows/outflows are CF₁, CF₂, etc. The calculator supports up to 20 unique cash flows (plus CF₀) and handles grouped (repeated) flows with Nⱼ.

Key Notes Before Starting:

• The HP 12C uses Reverse Polish Notation (RPN)—enter numbers first, then operators.
• Always clear previous data to avoid errors.
• Enter outflows as negative (e.g., -800) and inflows as positive.
• Interest rate (i) is entered as a percentage (e.g., 10 for 10%).
• For NPV, set i before computing. For IRR, the calculator iterates to find the rate.

Step-by-Step: Preparing the Calculator

• Turn on the calculator: Press ON.
• Clear financial registers: Press f CLEAR FIN (this zeros TVM keys like n, i, PV, PMT, FV).
• Clear storage registers: Press f CLEAR REG (this clears all registers, including cash flows). This is crucial—do it every time!
• Set decimal places (optional): Press f 4 (for 4 decimals) or adjust as needed.

Calculating NPV

• Enter the initial cash flow (CF₀): Key in the value (e.g., -800 for outflow), then press g CF0.
• For each subsequent cash flow (CFⱼ, j=1 to 20):
  • Key in the value, press g CFj (e.g., g CFj).
  • If the cash flow repeats n times consecutively, key in n, then press g Nj (e.g., for 3 identical years: 3 g Nj).
• Set the discount rate: Key in the annual rate (e.g., 10), press i.
• Compute NPV: Press f NPV.

The result is the NPV (positive = good). It is also stored in PV.

Example: NPV Calculation (Ungrouped Cash Flows)

Project: Initial investment $400 (outflow), then inflows: $150 (Yr1), $80 (Yr2), $90 (Yr3), $100 (Yr4), $110 (Yr5). Discount rate: 10%.

Interpretation: Positive NPV means the project adds value at 10% discount rate.

Handling Repeated (Grouped) Cash Flows

If a cash flow repeats (e.g., $100 for 3 years):

• Enter the cash flow: 100 g CFj (for the period j).
• Enter frequency: 3 g Nj.

Example Adjustment: If Years 3–5 are $100 each (repeating 3 times at CF3):

• After CF2: 100 g CFj (3 g Nj).

Calculating IRR

• Follow the same steps as NPV to enter cash flows (1–2 above). No need to set i—the calculator solves for it.
• After entering all cash flows, compute IRR: Press f IRR.
• Result is the IRR as a percentage. It may take a few seconds to compute (displays "running") on old HP12c models - instantaneous on newer models using the Atmel processors

Example: IRR for the Same Project

Using the cash flows above (no i needed):

• (Cash flows as in NPV example)......
• Compute: f IRR 10.49 (IRR ≈ 10.49%)
• Interpretation: IRR > 10% hurdle rate, so accept the project.

Reviewing and Changing Cash Flow Entries

• Review a single cash flow: Press RCL then the register number (e.g., RCL 1 for CF1). Or store j in n, then RCL g CFj.
• Review all cash flows: Press RCL g CFj repeatedly (starts from last).
• Review a group size (Nⱼ): Store j in n, then RCL g Nj.
• Review all with groups: Press RCL g Nj RCL g CFj repeatedly.
• Change a cash flow: Key in new value, press STO, key in register number.
• Change a group size: Key in new Nⱼ, store j in n, press g Nj.
• Insert or delete: Re-enter all flows from scratch, as there's no direct insert/delete.

After reviewing, reset n to the total number of cash flows entered (excluding CF₀) by pressing RCL n or manually if changed.

Tips and Troubleshooting

Error? If "Error 5" appears (no solution for IRR), cash flows may not change signs enough (e.g., all positive). Ensure at least one sign change.

Multiple IRRs? Rare, but if cash flows change signs more than once, IRR may not be unique—use NPV for decisions.

Annual vs. other periods: i and IRR are annual rates. For monthly, divide by 12 (e.g., 10 g 12÷ i).