How to Calculate NPV on the BA II Plus Calculator

The TVM keys only work when every payment is the same size. Real projects are not like that: you spend a lot at the start, earn a little in year one, more in year two, and something different every year after. That is what the Cash Flow worksheet is for, and NPV is the number it exists to produce.

The worksheet holds a time-zero amount plus up to 24 groups of flows, and it feeds two dedicated keys: NPV and IRR. This guide walks a full project through it with every keystroke, then covers the two features that separate people who are fast at this from people who are not — the frequency register and the NPV profile.

What NPV actually measures

Net present value takes every cash flow a project produces, discounts each one back to today at a rate that represents what your money could otherwise earn, and subtracts what you have to spend.

1. NPV = CF0 + CF1 ÷ (1+r) + CF2 ÷ (1+r)² + … + CFn ÷ (1+r)ⁿ

CF0 is negative for an investment. r is the discount rate per period, not per year, unless the periods happen to be years.

The result is money, in today’s terms. An NPV of £86,606.78 means the project is worth £86,606.78 more than putting the same money into whatever the discount rate represents. That is the whole decision rule: positive, take it; negative, do not.

How the Cash Flow worksheet is laid out

Press CF and you land on CF0. Arrow down and the worksheet alternates between two kinds of register:

• C01, C02 … C24 — the amount of a cash flow.
• F01, F02 … F24 — how many consecutive periods that same amount occurs.

So the worksheet does not store 24 cash flows. It stores 24 groups, which is why a 30-year project with a level annual flow fits comfortably.

A worked project: £450,000 in, five years of returns

A manufacturer buys equipment for £450,000. It expects net cash inflows of £120,000, £135,000, £150,000, £160,000 and £175,000 over the next five years, then scraps the machine for nothing. The cost of capital is 11%.

1. CF
2. · 2ND
3. · CLR WORK
4. · 450000
5. · +|−
6. · ENTER
7. · ↓
8. · 120000
9. · ENTER
10. · ↓
11. · ↓
12. · 135000
13. · ENTER
14. · ↓
15. · ↓
16. · 150000
17. · ENTER
18. · ↓
19. · ↓
20. · 160000
21. · ENTER
22. · ↓
23. · ↓
24. · 175000
25. · ENTER

The double arrow-down skips past each F register, leaving it at its default of 1.

Now discount them:

1. 2ND
2. · QUIT
3. · NPV
4. · 11
5. · ENTER
6. · ↓
7. · CPT

NPV = 86,606.78.

The project is worth taking. It returns £450,000 of capital, covers an 11% required return on that capital for five years, and leaves £86,606.78 of value on top.

Where that number comes from

Discounting each flow individually shows which years are carrying the project:

Year	Cash flow	Discount factor	Present value
0	−450,000.00	1.000000	−450,000.00
1	120,000.00	0.900901	108,108.11
2	135,000.00	0.811622	109,569.03
3	150,000.00	0.731191	109,678.71
4	160,000.00	0.658731	105,396.96
5	175,000.00	0.593451	103,853.98

Years 2 and 3 contribute almost the same present value despite year 3 being £15,000 larger in cash terms, because the extra year of discounting eats the difference. By year 5 the £175,000 has shrunk to £103,854 — a 41% haircut for waiting.

The F register: repeated flows without the typing

A software licence costs £60,000 up front and saves £15,000 a year for three years, then £22,000 a year for two years as usage grows, then £9,000 in a final wind-down year.

Typed one flow at a time that is six entries. Using the frequency registers it is three:

1. CF
2. · 2ND
3. · CLR WORK
4. · 60000
5. · +|−
6. · ENTER
7. · ↓
8. · 15000
9. · ENTER
10. · ↓
11. · 3
12. · ENTER
13. · ↓
14. · 22000
15. · ENTER
16. · ↓
17. · 2
18. · ENTER
19. · ↓
20. · 9000
21. · ENTER

C01 = 15,000 with F01 = 3, C02 = 22,000 with F02 = 2, C03 = 9,000 with F03 left at 1.

1. 2ND
2. · QUIT
3. · NPV
4. · 10
5. · ENTER
6. · ↓
7. · CPT

NPV = 11,069.61.

Two rules for the F register. It must be a whole number, and it counts consecutive periods — a flow that skips a year needs a group of zeros in between, not a gap. If years 3 and 4 produce nothing, enter 0 with a frequency of 2, because the calculator counts periods by position, not by label.

The discount rate is the entire argument

NPV looks objective because it produces one number, but that number depends completely on a rate that somebody chose. Change the rate and watch:

Discount rate	NPV	Decision
0%	£290,000.00	Trivially yes — no cost of capital
8%	£132,633.52	Yes
11%	£86,606.78	Yes
15%	£33,541.10	Yes, but thinner
17.9049%	£0.00	Indifferent — this is the IRR
18.5%	−£6,415.83	No

That table is the project’s NPV profile, and building it is the fastest way to stress-test a decision. The rate at which NPV crosses zero is the internal rate of return, so the two measures are two readings of the same curve. How to compute IRR directly takes one keystroke once the flows are in.

Producing the whole table takes seconds, because the cash flows stay loaded: press NPV, type a new rate, ENTER, ↓, CPT. Repeat.

Monthly cash flows need a monthly rate

The worksheet has no idea how long a period is. It discounts by one period per position, so the rate you type has to be the rate for that period.

Cash flows arrive	Annual rate	Enter at I
Yearly	11%	11
Quarterly	11%	2.75
Monthly	11%	0.916667

Dividing the annual rate by the number of periods is the convention almost every textbook uses and the one exam answers are keyed to. If a question specifies an effective annual rate and monthly flows, the correct monthly rate is 1.11^(1/12) − 1 = 0.873459% rather than 0.916667% — a small difference that compounds into a visible one over a long project.

Net future value, in one extra step

The same surplus can be stated at the end of the project rather than today. It answers a slightly different question: not “how much value does this create now” but “how much better off am I when it finishes” — useful when the comparison is a savings account rather than a share price.

On the BA II Plus Professional there is an NFV register sitting directly below NPV in the same worksheet, so it costs two keystrokes:

1. NPV
2. · 11
3. · ENTER
4. · ↓
5. · CPT
6. · ↓
7. · CPT

On the standard BA II Plus there is no NFV register, and you compound the NPV forward yourself:

1. NFV = NPV × (1 + i)ⁿ = 86,606.78 × 1.11⁵ = 145,937.46

Or use the TVM row: 5 N, 11 I/Y, 86606.78 +|− PV, 0 PMT, CPT FV.

NFV = 145,937.46. NPV and NFV never disagree about whether a project is worth doing — they are the same number read from opposite ends of the timeline, so they share a sign.

Cross-checking against the TVM keys

When the flows happen to be level, the same problem can be solved twice — and doing it both ways once is the cheapest way to convince yourself you are using the worksheet correctly.

A project costs £380,000 and returns £100,000 a year for five years. Cost of capital 9%.

Route	Keys	Result
TVM	5 N, 9 I/Y, 100000 PMT, 0 FV, CPT PV	−388,965.13
Cash flow	CF0 = −380,000, C01 = 100,000, F01 = 5, NPV at 9	8,965.13

The TVM route gives the present value of the inflows, £388,965.13. Subtract the £380,000 you spend and you have the £8,965.13 the Cash Flow worksheet reported directly. Same arithmetic, different bookkeeping.

Once the flows stop being level, only the Cash Flow worksheet can do it, which is why it is worth learning even though the TVM row feels faster.

Salvage values and mid-life costs

Two things routinely appear in the last column of a project and get entered wrongly.

A salvage value is not a separate flow. It happens in the same period as that year’s operating cash, so it is added to it. Give the £450,000 machine a £90,000 resale value in year 5 and C05 becomes £175,000 + £90,000 = £265,000, which lifts NPV from £86,606.78 to £140,017.40. The £53,410.62 of improvement is the £90,000 discounted five years at 11%.

A mid-life overhaul is a negative flow in the middle of the series, and it is entered exactly like that. Replace year 3’s £150,000 inflow with an £80,000 outflow and NPV falls to −£81,567.24. The project dies, and it is worth noticing why: that year was carrying £109,678.71 of present value, and losing it costs more than the overhaul itself.

Four ways an NPV goes wrong

1. The worksheet was not cleared. Everything else on this list is rarer than this.
2. A missing zero. Cash flows are positional. A year with no flow needs a 0 entered, or every subsequent flow arrives one year too early and NPV comes out too high.
3. The initial outlay entered as positive. CF0 has to be negative for an investment, otherwise you have modelled a windfall.
4. An annual rate on monthly flows. Twelve times too much discounting, which usually turns a good project negative and is obvious once you look for it.

If you are deciding which measure to actually present, NPV vs IRR covers where the two disagree and why NPV wins the argument.