Capital Budgeting: NPV, IRR and Payback, and Why NPV Wins When They Disagree

Give three appraisal methods the same cash flows and you can get three different answers, and only one of them is a number of riyals. That is why the AICPA Blueprint never asks for one of them alone: its representative task is to compare investment alternatives using financial metrics and modeling, and it names payback period, net present value, economic value added, cash flow analysis and internal rate of return in a single line.

NPV and IRR are built from the same discounted cash flows and can still rank two projects in opposite orders. Payback is built from the same cash flows and answers a different question: not what the project is worth, but how long the money is exposed.

What follows is the relevant cash flow rule, one project carried through all five measures, where NPV and IRR part company, ranking under a capital ceiling, and the depreciation tax shield a Saudi company paying Zakat does not have. Every figure is illustrative and was recomputed for this article.

Relevant cash flows

ACCA compresses the first step into one line: to be a relevant cash flow an item must be a future, incremental cash flow. Three tests, and an item is out if it fails any one. Most lost marks here violate that sentence rather than the discounting.

Item	In or out	Why
Feasibility study already paid for	Out	Sunk. No decision now can change it.
Apportioned head office overhead	Out	Notional. Only a genuine increase is incremental.
Depreciation	Out	Not cash. The asset's cost is already in, in full, at time zero.
Interest on the loan that buys the machine	Out	The cost of finance sits in the discount rate; charging it again counts it twice.
Contribution lost on the product this one displaces	In	An opportunity cost, and incremental.
Increase in working capital	In	The change, not the balance. Released at the end.
Tax on incremental profit, and tax saved by tax depreciation	In	Where the entity is taxed at all. See below.

Net present value, and what the discount rate is doing

NPV discounts every relevant flow at the cost of capital and adds them. The rate is not a hurdle invented for the project; it is what the company pays for money, and BAR carries a separate representative task for calculating it. One project, in riyals: equipment of 1,000,000 and working capital of 150,000 now, operating inflows over four years, then the working capital released and a residual value of 100,000.

Year	Cash flow	Factor at 10%	Present value	Cumulative
0	(1,150,000)	1.0000	(1,150,000)	(1,150,000)
1	350,000	0.9091	318,182	(831,818)
2	450,000	0.8264	371,901	(459,917)
3	500,000	0.7513	375,657	(84,260)
4	650,000	0.6830	443,959	359,699

359,699 is not a score. It is how much better off the owners are in today's money, and NPVs measured at the same rate add across projects, which no percentage does. The rate also carries the risk, shrinking the later years fastest: at 15% this NPV falls to 195,010, and at 20% to 56,983.

Internal rate of return, and where it parts company with NPV

ACCA defines the IRR as the discount rate which, when applied to the cash flows of a project, produces a net present value of nil. Here it is 22.3%, reached in an exam by linear interpolation between one rate with a positive NPV and one with a negative: extrapolating from 10% and 20%, where both NPVs are still positive, gives 21.9%, and interpolating between 20% and 25% gives 22.4%, because interpolation runs a straight line across a curve. On a single conventional project with no capital constraint the IRR always agrees with NPV, since NPV falls as the rate rises and so is positive exactly when the cost of capital sits below the rate at which it reaches zero.

Scale, and timing

The method is blind to size: 400,000 that returns 600,000 in a year has an IRR of 50% and adds 145,455 at a 10% cost of capital, while 1,000,000 that returns 1,300,000 has an IRR of 30% and adds 181,818. Timing is subtler, and it is where the exam lives. Two mutually exclusive projects, same outlay, A taking its money early and B taking more of it later.

	Project A	Project B
Outlay at time zero	(1,000,000)	(1,000,000)
Year 1	600,000	200,000
Year 2	400,000	400,000
Year 3	300,000	800,000
NPV at 10%	101,427	113,449
NPV at 12%	68,126	66,873
IRR	16.5%	15.1%

Below 11.8% NPV prefers B while IRR prefers A; above it both prefer A. That crossover rate is also the IRR of the difference between them: subtract A's flows from B's and an outflow of 400,000 in year one buys an inflow of 500,000 in year three, which breaks even at 11.8% exactly. Choosing B is lending 400,000 for two years at 11.8%, worth doing when money costs 10% and not when it costs 12%. The two therefore disagree only when the profiles cross inside the range of plausible rates, and the projects' own IRRs never say where.

Two IRRs, or none

The IRR is a root of a polynomial, so cash flows that change sign more than once can produce more than one. A two year extraction that costs 1,000,000 now, returns 2,450,000 at the end of year one and needs 1,500,000 of site restoration at the end of year two has an NPV of nil at 20% and nil again at 25%, and negative on either side. At a 10% cost of capital it is negative 12,397 and should be rejected, yet both IRRs clear the target and the rule accepts it twice over. Raise the restoration cost and there is no IRR at all. The rate at which NPV is nil describes a curve, and a curve can cross an axis any number of times.

The last limitation is invisible. ACCA states it plainly: the method assumes that the net cash inflows generated through the project life will be reinvested to earn the same return as the IRR, which may not be possible in real life. NPV re-employs them at a rate the company can observe instead, and the modified internal rate of return, an ACCA advanced topic rather than a BAR task, exists to force the assumption back to it. None of this makes IRR useless. A percentage travels, and a board that will not read a schedule will read 22%. Use it to communicate and NPV to decide.

Payback and discounted payback

Payback is the point at which cumulative cash flow turns positive. Undiscounted, the balance runs (1,150,000), (800,000), (350,000) and then positive 150,000, so it falls 350,000 into year three: 2.7 years. On present values, in the last column above, it is still negative 84,260 at the end of year three and turns during year four, at 3.2 years. That half year is the cost of the money during the wait, the only defect discounting repairs.

Both still ignore everything after the cut-off, so a project that pays back in two years and then collapses outscores one that pays back in three and runs for fifteen. Neither is useless: payback says how long capital is exposed to a forecast, and forecasts decay, which is why ACCA keeps adjusted payback among its risk techniques. Treat it as a screen, never as the ranking.

The profitability index, and capital rationing

Accepting everything positive assumes the money is there. Cap one year's capital and the question becomes which combination extracts the most value per riyal available. The answer is the profitability index: the present value of the future cash flows divided by the outlay, here 1,509,699 over 1,150,000, or 1.31. Above 1.00 is the same decision as a positive NPV, and the definition some texts use, NPV per riyal invested, is that figure less one and ranks identically.

ACCA's examiner's report is unusually blunt: where a divisible approach is required, project profitability indices should be calculated and displayed, as should the ranking of projects, and the ranking of projects based upon the size of their NPVs is incorrect and will not lead to the optimum allocation of limited capital investment funds. Four divisible projects and a ceiling of 1,000,000 show why.

Project	Outlay	NPV	Index	Rank by index	Rank by NPV
P1	400,000	120,000	1.30	2	3
P2	500,000	130,000	1.26	3	2
P3	300,000	105,000	1.35	1	4
P4	600,000	138,000	1.23	4	1

Spend the ceiling by index and you take P3 whole, P1 whole and 60% of P2, for 303,000 of NPV. Spend it by the size of the NPVs and you take P4 whole and 80% of P2, for 242,000. The ranking that looks like it is maximising value destroys 61,000 of it, and the two orders are exact reverses, because here the largest projects are the least efficient. Both conditions matter: the ceiling binds one period only, and the projects are divisible. Where they are not, the index ranks nothing and you price every feasible combination of whole projects instead.

The depreciation tax shield, and the company that does not have one

Depreciation is not a cash flow and the relevant cash flow rule throws it out. Then it returns, because where profit is taxed a depreciation deduction lowers the tax bill, and tax is cash. The shield is the deduction multiplied by the tax rate, and nothing else. If the 1,000,000 machine above were written off for tax at 250,000 a year and the rate were 20%, each deduction would save 50,000, worth 158,493 in present value at 10% over four years: more than 40% of the project's NPV, out of a line that is not a cash flow.

Which depreciation matters, because it is the deduction the tax authority allows and not the charge in the accounts. Article 17 of the Saudi Income Tax Law sets it by asset group, at 25% for factories, machines, hardware, software and equipment including vehicles and 5% for stationary buildings, applied to the balance of the whole group rather than a single asset, with only half the cost of an addition entering the group in its first year. A BAR item supplies the tax depreciation inside the question; a real appraisal does not.

Then there is whether a tax exists to shield. Saudi Arabia runs two levies and ownership decides which applies: the Saudi and GCC share of a resident company pays Zakat, the non-Saudi share pays 20% income tax on its share of taxable profit. The Zakat base is built from funding rather than from earnings, so a depreciation deduction does not reduce it and the shield line is not there at all. In a mixed company it attaches to the taxed share only, so at 40% foreign ownership the 158,493 becomes roughly 63,000. Which levy falls on whom is set out in Zakat or Income Tax? Who Pays What in Saudi Arabia.

How BAR and the Fellowship ask it

In the Blueprint effective January 2026, capital budgeting sits in BAR Area I, Business Analysis, weighted 40 to 50% of the section, under investment alternatives using financial valuation decision models. Its three representative tasks are to calculate the present value of future cash flows or the net present value of an investment, to determine the impact of changes to the assumptions used to value it, and to compare investment alternatives using financial metrics and modeling. The Blueprint says in terms that the number of tasks attached to a topic is not indicative of how much it is assessed, so no honest percentage can be put on capital budgeting itself. The section profile does say that BAR allocates no Evaluation at all: 45 to 55% Application, 30 to 40% Analysis, 10 to 20% Remembering and Understanding.

The middle task is the under-practised one. A change in assumption is sensitivity analysis, and the answer is the NPV divided by the present value of the item flexed: here the operating inflows, worth 1,338,945, can fall 26.9% before the project breaks even, and the outlay can rise 31.3%. Flex the discount rate and the answer is the IRR itself, which is a sensitivity measure wearing a decision rule's clothes.

The SOCPA Fellowship asks the same material inside the Cost, Managerial and Governmental Accounting paper, in the decision-making part beside relevant costing, special orders and transfer pricing, which is where Prepito's course outline places it. SOCPA's Fellowship topic list weights only the paper's four main topics: capital budgeting is one item under Managerial Accounting, which carries 26 to 45% of the exam questions, so confirm the current list before budgeting hours. Its habit is a longer computation than BAR's, in Arabic or English, and the Zakat point above is the part no imported textbook supplies. The single period version of the same arithmetic, where nothing is discounted because everything happens inside one year, is cost-volume-profit analysis, and this is the article it hands off to.

Where to practise this

The skill is laying the flows out until the layout stops being a decision, which comes from repetition rather than reading. Prepito's BAR course covers Area I, including cost of capital, decision models and the sensitivity questions built on them, and the SOCPA Cost, Managerial and Governmental Accounting course covers the same material for the Fellowship in Arabic and English. For where it sits in each syllabus, see the CPA BAR study guide and the SOCPA Cost and Managerial study guide, and for the qualifications the CPA programme and the SOCPA Fellowship programme.

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Every project, rate and figure here is illustrative and was computed for this article; none is a market rate, a published cost of capital or tax advice. Sources: AICPA Uniform CPA Examination Blueprints effective 1 January 2026, ACCA Financial Management syllabus, section D, ACCA on relevant cash flows, ACCA on the internal rate of return, the ACCA Financial Management examiner's report, and ZATCA on the Income Tax Law. Blueprint weights are ranges and are revised periodically, ACCA reissues its syllabus yearly, and Saudi rates, depreciation groups and the Zakat base are set by ZATCA and change, with a replacement Income Tax Law issued in draft. Confirm any rule before relying on it.