Last reviewed: 2026-05-19

NPV and IRR on the BA II Plus

For most uneven cash-flow problems on the Chartered Financial Analyst (CFA) exam, the Net Present Value (NPV) and Internal Rate of Return (IRR) live behind the BA II Plus Cash Flow (CF) worksheet. The keystroke path is short, but four things trip candidates up: forgetting to clear the prior CF list, fumbling the frequency key when a flow repeats, picking the wrong discount-rate input order, and missing that IRR can have multiple roots on a flow with sign changes.

This page is the calm worked-example guide. Four problems are walked end to end with the exact keystrokes and the expected answer to four decimals. The free Charterly BA II Plus calculator replays each example so you can watch the values land in real time.

If you use an HP 12C, the HP 12C version of this page covers the same four problems with HP keystrokes.

Open the BA II Plus calculator

Contents

  1. The CF worksheet, in plain language
  2. Worked example 1: simple uneven cash flows
  3. Worked example 2: a repeated cash flow with the frequency key
  4. Worked example 3: a non-standard discount rate
  5. Worked example 4: IRR with a sign change
  6. The four mistakes that cost candidates marks
  7. Frequently asked questions

1. The CF worksheet, in plain language

The CF worksheet stores up to 24 cash flows. Slot zero is the initial outlay, written CF0. The next slots, CF1 through CF23, hold subsequent cash flows. Each non-zero slot can have a frequency, written F01 through F23, which is the count of consecutive periods that share the same value.

Once the flows are entered, two functions live alongside the worksheet:

  • NPV asks for a periodic discount rate and computes the present value of the cash flows at that rate.
  • IRR solves for the discount rate that sets NPV to zero.

Three rules apply to every problem:

  1. Clear before entering. Press CF, then 2nd then CLR WORK. The home-screen CE/C does not clear the CF list.
  2. Sign convention. Money the candidate parts with is negative. Money received is positive.
  3. Periodic rate, not annual. The discount rate you type into NPV must be the periodic rate. For an annual cash flow, that is the annual rate. For a quarterly cash flow, divide the annual rate by four first.

2. Worked example 1: simple uneven cash flows

Problem. A project requires a 10,000 outlay today and is expected to produce 4,000 in year 1, 5,000 in year 2, and 6,000 in year 3. At a 10 percent annual discount rate, compute NPV and IRR.

Keystrokes:

  1. CF
  2. 2nd then CLR WORK
  3. 10000 then +/- then ENTER (CF0 is -10,000)
  4. Arrow down. 4000 then ENTER (CF1). Arrow down. (F01 stays at 1; arrow past it.)
  5. Arrow down. 5000 then ENTER (CF2). Arrow down. (F02 stays at 1.)
  6. Arrow down. 6000 then ENTER (CF3). Arrow down. (F03 stays at 1.)
  7. NPV. 10 then ENTER. Arrow down. CPT.

Expected NPV: 2,276.4838.

Continuing from the same CF list, press IRR then CPT.

Expected IRR: 21.6478 percent.

Replay this example in Charterly

3. Worked example 2: a repeated cash flow with the frequency key

Problem. A project requires a 50,000 outlay today and produces 8,000 in each of the next five years, followed by a 25,000 terminal cash flow in year 6. Compute NPV at 9 percent and IRR.

A naive candidate enters 8,000 six times. The frequency key lets you enter 8,000 once with F01 set to 5, saving keystrokes and reducing the chance of a typo.

Keystrokes:

  1. CF
  2. 2nd then CLR WORK
  3. 50000 then +/- then ENTER (CF0 is -50,000)
  4. Arrow down. 8000 then ENTER (CF1).
  5. Arrow down. 5 then ENTER (F01 is 5; this means CF1 of 8,000 repeats for periods 1 through 5).
  6. Arrow down. 25000 then ENTER (CF2 lands in period 6 because F01 covered periods 1 through 5).
  7. Arrow down. (F02 stays at 1.)
  8. NPV. 9 then ENTER. Arrow down. CPT.

Expected NPV: -3,976.1067.

IRR then CPT gives expected IRR: 6.7045 percent.

Why the frequency key matters on the exam. Time pressure. A repeated flow of 8,000 for five years entered six times is six chances to mistype 8,000 as 80,000. F01 = 5 is one ENTER.

Replay this example in Charterly

4. Worked example 3: a non-standard discount rate

Problem. A project requires a 20,000 outlay today and produces 6,000 quarterly for the next eight quarters. The annual discount rate is 12 percent, compounded quarterly. Compute NPV.

The CF worksheet does not know whether each slot represents a year, a quarter, or a month. The candidate must convert the annual rate to the periodic rate before typing it into NPV.

The periodic rate is 12 / 4 = 3 percent per quarter.

Keystrokes:

  1. CF
  2. 2nd then CLR WORK
  3. 20000 then +/- then ENTER (CF0).
  4. Arrow down. 6000 then ENTER (CF1). Arrow down. 8 then ENTER (F01 = 8 for eight quarters).
  5. NPV. 3 then ENTER (periodic quarterly rate). Arrow down. CPT.

Expected NPV (project value including the -20,000 outlay): 22,118.1531. The gross present value of the eight 6,000 flows in isolation is 42,118.1531.

Replay this example in Charterly

5. Worked example 4: IRR with a sign change

Problem. A project has cash flows -1,000, 5,000, -6,000. Compute IRR.

Two sign changes mean IRR can have two real roots. The BA II Plus returns one. Which one depends on the engine's seed.

Keystrokes:

  1. CF
  2. 2nd then CLR WORK
  3. 1000 then +/- then ENTER (CF0 = -1,000).
  4. Arrow down. 5000 then ENTER (CF1). Arrow down.
  5. Arrow down. 6000 then +/- then ENTER (CF2 = -6,000). Arrow down.
  6. IRR then CPT.

Expected IRR returned by the BA II Plus: 100 percent. The other real root is 200 percent. The mid-flow 5,000 is large enough that the project's value is positive at any discount rate between the two roots and negative outside that band.

What this means for the exam. When a CFA problem includes a project with non-conventional cash flows (more than one sign change in the flow sequence), the BA II Plus IRR alone is not enough. Either the question gives you a discount rate and asks for NPV, or it expects you to know that multiple IRRs exist and that NPV is the safer decision rule. Modified IRR (MIRR) is the formal fix; it is not a built-in key on the standard BA II Plus and is computed by hand on the rare exam question that requires it.

Replay this example in Charterly

6. The four mistakes that cost candidates marks

This is the cash-flow subset of the twelve calculator mistakes Charterly tracks.

  1. CF list has leftover entries (mistake M5). Your NPV and IRR are off by the amount of a stale flow. Fix: inside CF, press 2nd then CLR WORK before entering the new list.
  2. Annual rate typed into NPV on a non-annual flow. Your project looks much better than it is because the discount is too aggressive. Fix: convert the annual rate to the periodic rate before pressing NPV.
  3. Frequency key left at 1 on a repeated flow. You entered the value once and never typed the count. Your flows are now treated as one occurrence each, and the schedule is wrong. Fix: arrow into F0n after each CF and set the count explicitly.
  4. IRR with multiple roots. The BA II Plus returns one root; you do not see the second. Fix: count the sign changes in the flow sequence. If there is more than one, do not use IRR alone as the decision rule.

Charterly's BA II Plus calculator catches mistake M5 in real time and surfaces a non-blocking warning while the result is still on screen. The other three are workflow habits this page teaches; they are not currently tagged as named device-state warnings because the calculator alone cannot infer the candidate's intent.

See all twelve calculator mistakes

7. Frequently asked questions

Can the BA II Plus compute Modified IRR (MIRR)? The standard BA II Plus does not have a dedicated MIRR key. The BA II Plus Professional model adds one. For the standard model, MIRR is computed by hand on the rare exam question that requires it.

What is the maximum number of cash flows the CF worksheet holds? Twenty-four, indexed CF0 through CF23. The frequency key compresses repeated flows into a single slot, so a real schedule of more than 24 periods can still fit if the flows repeat.

Does NPV expect the periodic rate or the annual rate? The periodic rate. If your cash flows are quarterly and the question gives an annual rate, divide by 4 before pressing NPV. If monthly, divide by 12.

The BA II Plus returned an IRR I did not expect on a project with mixed signs. Why? A project with more than one sign change in its cash flow sequence can have more than one real IRR root. The BA II Plus returns one of them. Worked example 4 above walks through a case with two roots.

Does Charterly auto-fix the CF list for me? No. Charterly surfaces a warning if the CF list has leftover entries from a prior problem. It never silently changes your inputs. You always press the keys.

Where do I practice problems like these? Charterly's question library is tagged by Learning Outcome Statement (LOS), including cash-flow-specific LOSs. Browse the LOS tagged drills.