IRR Calculation Guide: BA II Plus Step-by-Step
Compute IRR on the BA II Plus in two keystrokes, interpret it against a hurdle rate, and handle the cases that break it: multiple roots, Error 7 and reinvestment.
The short answer
Enter the cash flows in the CF worksheet with the initial outlay negative at CF0, press 2ND QUIT, then press IRR and CPT. The calculator returns the discount rate at which net present value equals zero, expressed as a percentage per period. Accept the project when that rate exceeds your cost of capital, but check the sign pattern first: more than one change of sign means several rates can satisfy the equation and the one displayed may not be the relevant one.
IRR is the most quoted number in project finance and the most easily abused. It compresses a whole schedule of cash flows into a single percentage, which is why people like it, and it throws away scale, timing preferences and any information about what happens to the cash in between, which is why careful analysts never present it alone.
On the BA II Plus it costs two keystrokes once the cash flows are loaded. This guide covers those two keystrokes, then spends most of its length on the part that matters: knowing when the number you just computed is trustworthy.
What IRR is, precisely
The internal rate of return is the discount rate at which a project’s net present value is exactly zero.
-
0 = CF0 + CF1 ÷ (1+IRR) + CF2 ÷ (1+IRR)² + … + CFn ÷ (1+IRR)ⁿ
Note what is unknown. In NPV you supply the rate and solve for a value; in IRR you supply the values and solve for the rate.
There is no closed-form solution for anything past a handful of periods, so the calculator iterates: it guesses a rate, computes NPV, and adjusts. That has two practical consequences. It can be slow on a long series, and it can fail — which is what Error 7 is.
Two keystrokes
The £450,000 machine from the NPV walkthrough: inflows of £120,000, £135,000, £150,000, £160,000 and £175,000 over five years.
-
CF -
2ND -
CLR WORK -
450000 -
+|− -
ENTER -
↓ -
120000 -
ENTER -
↓ -
↓ -
135000 -
ENTER -
↓ -
↓ -
150000 -
ENTER -
↓ -
↓ -
160000 -
ENTER -
↓ -
↓ -
175000 -
ENTER -
2ND -
QUIT -
IRR -
CPT
IRR = 17.9049%.
Against an 11% cost of capital that is a clear accept, and the two measures agree: NPV at 11% was £86,606.78, comfortably positive. They have to agree on a simple accept-or-reject question, because they are reading the same curve — NPV is its height at a given rate, IRR is where it crosses zero.
| Discount rate | NPV | Above hurdle? |
|---|---|---|
| 8% | £132,633.52 | Yes |
| 11% | £86,606.78 | Yes |
| 15% | £33,541.10 | Yes |
| 17.9049% | £0.00 | Break-even — the IRR |
| 18.5% | −£6,415.83 | No |
IRR is a rate per period, not per year
The Cash Flow worksheet has no concept of calendar time. If your flows are monthly, the IRR it returns is a monthly rate, and it needs converting before anyone can compare it to anything.
| Flows | IRR shown | Annual equivalent | Method |
|---|---|---|---|
| Annual | 17.9049% | 17.9049% | Already annual |
| Quarterly | 4.2247% | 18.0000% | 1.042247⁴ − 1 |
| Monthly | 1.3888% | 18.0000% | 1.013888¹² − 1 |
Multiplying instead of compounding — quoting a 1.3888% monthly IRR as 16.67% a year — understates the return and is a common slip in interview case studies. Compounding is the correct conversion because the cash actually arrives monthly and can actually be reinvested monthly.
What IRR throws away
Two projects, both worth doing, and IRR ranks them backwards.
| Project A | Project B | |
|---|---|---|
| Initial outlay | −£100,000 | −£300,000 |
| Annual inflow | £32,000 | £85,000 |
| IRR | 18.0307% | 12.8585% |
| NPV at 8% | £27,766.72 | £39,380.35 |
A has the better rate. B creates £11,613.63 more value. If you can only do one and capital is available, you do B — a higher percentage on a smaller base is not a better outcome, it is a smaller outcome described flatteringly.
The rate at which they tie is 10.1783%, computed as the IRR of the difference between them: −£200,000 at time zero and £53,000 a year. Below that crossover rate B wins on NPV; above it, A does. Knowing that one number tells you exactly how much your choice depends on the cost of capital you assumed.
When there is more than one IRR
Count the sign changes in the cash flow series. One change — money out, then money in — guarantees exactly one IRR. More than one change guarantees nothing.
A film rights deal: pay £4,000 for the option, collect £25,000 on release, pay £25,000 in profit share.
-
CF -
2ND -
CLR WORK -
4000 -
+|− -
ENTER -
↓ -
25000 -
ENTER -
↓ -
↓ -
25000 -
+|− -
ENTER -
2ND -
QUIT -
IRR -
CPT
The calculator reports 25%. That is a correct answer. So is 400% — both rates set NPV to exactly zero, and nothing on the display hints that a second root exists.
| Rate | NPV |
|---|---|
| 0% | −£4,000.00 |
| 25% | £0.00 |
| 100% | £2,250.00 |
| 400% | £0.00 |
| 500% | −£527.78 |
Neither root means “the return on this deal is 25%” or “400%”. The project is only worth doing between those two rates, which is a statement no single percentage can carry. NPV at your actual cost of capital answers the question; IRR does not.
The same trap appears in ordinary industrial projects with a decommissioning cost. Take the £450,000 machine, replace year 3’s £150,000 inflow with an £80,000 overhaul cost, and the calculator returns 3.977% — a plausible-looking rate for a project whose NPV at 11% is −£81,567.24. Anyone who checked only the IRR would see a marginal project rather than a bad one.
Error 7 is not a broken calculator
Error 7 means the solver hit its iteration ceiling without converging. Unlike CPT I/Y in the TVM row,
the IRR worksheet gives you nowhere to seed a guess, so there is no knob to turn — the fix is always in
the cash flows.
Three causes, in the order they actually happen:
- A typing slip. A missing sign or a misplaced digit can produce a series with no root at all. Walk
back through the worksheet with
↑and read every C and F register before you pressCPTagain. The same inputs will fail the same way. - A frequency in the wrong place. An F register holding an amount, or a C register holding a count, changes the shape of the series entirely and is invisible unless you scroll.
- Genuinely no solution. All-positive or all-negative flows have no IRR, because NPV never crosses zero. Two sign changes can also leave the roots complex rather than real.
The diagnostic that works in every case is the NPV profile. Press NPV, try 0%, 10%, 25%, 50%, 100%. If
the sign of NPV never flips across that sweep, there is nothing for IRR to find and the error is the
correct answer.
MIRR: one rate, with the assumptions in the open
MIRR fixes both of IRR’s structural problems at once. You state a reinvestment rate for the cash the project throws off and a finance rate for the cash it consumes, and because those rates are yours rather than the equation’s, the result is unique — no sign-change caveat, no second root.
The BA II Plus Professional has a MOD register in the cash flow worksheet that does this for you. On the
standard BA II Plus you build it from the flows you have already entered, using the CF worksheet once and
the TVM row twice.
The £450,000 machine again, reinvesting and financing at 11%.
-
CF -
2ND -
CLR WORK -
0 -
ENTER -
↓ -
120000 -
ENTER -
↓ -
↓ -
135000 -
ENTER -
↓ -
↓ -
150000 -
ENTER -
↓ -
↓ -
160000 -
ENTER -
↓ -
↓ -
175000 -
ENTER -
2ND -
QUIT -
NPV -
11 -
ENTER -
↓ -
CPT
CF0 = 0 deliberately. With no outlay in the worksheet, NPV is the gross present value of what the project pays you.
PV of inflows = 536,606.78. Compound that forward to year five to get the terminal value, then ask what
rate connects £450,000 to it — both in the same TVM session, because only PV changes between them:
-
2ND -
CLR TVM -
5 -
N -
11 -
I/Y -
536606.78 -
+|− -
PV -
0 -
PMT -
CPT -
FV -
… -
450000 -
+|− -
PV -
CPT -
I/Y
CPT FV returns 904,213.63. Overwrite PV with −450,000, leave N and FV alone, and CPT I/Y gives the MIRR.
MIRR = 14.9772%, against an IRR of 17.9049%. Almost three percentage points of the headline rate were the reinvestment assumption rather than the project.
| Project | IRR | MIRR at 8% | MIRR at 11% |
|---|---|---|---|
| £450,000 machine | 17.9049% | 13.7262% | 14.9772% |
| A (−£100,000, £32,000 × 5) | 18.0307% | 13.4246% | — |
| B (−£300,000, £85,000 × 5) | 12.8585% | 10.6973% | — |
Notice that MIRR compresses the gap between A and B from 5.17 points to 2.73. That is the reinvestment assumption being stripped out: A’s advantage was always partly the flattering arithmetic of a high rate applied to its own interim cash.
And the film deal, which had two IRRs, has exactly one MIRR — 5.5990% at a 10% reinvestment and finance rate. Below the 10% cost of capital, so reject, which agrees with the NPV of −£1,933.88 at that rate. A measure that can only produce one answer is worth the extra keystrokes when the sign pattern is awkward.
Before you quote an IRR
Four checks, none of which takes longer than the calculation itself.
- Count the sign changes. More than one and the number on the display is not “the” IRR.
- Confirm the period. A monthly series returns a monthly rate. Compound it, do not multiply it.
- Name the hurdle rate. An IRR without a cost of capital beside it is a statistic, not a decision.
- Ask what the interim cash actually earns. If it is nowhere near the IRR, quote MIRR too.
IRR is at its best as a summary of a decision you have already made with NPV, and at its worst as the basis for making one. NPV vs IRR works through the cases where the two disagree and which one to put in front of a committee, and the IRR calculator flags the sign changes that tell you a series has more than one root before you trust the single number a keypad returns.