Capital Investments and Capital Allocation

Corporate Issuers. Worth 6 to 9 percent of the exam. One session: the lesson, the rules, the method, then the questions.

Corporate IssuersCapital Investments and Capital Allocation
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The lesson

The video lesson for this unit is recorded and waiting to be published. Until it is, the rules and the method below carry everything this session needs; watching is a way of hearing it, not the only way of getting it.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to calculate net present value and internal rate of return, decide which one governs when the two methods disagree, describe why IRR's reinvestment assumption is less realistic than NPV's, and identify which cash flows belong in the analysis in the first place, excluding sunk costs and including opportunity costs.

Net present value discounts every cash flow a project produces at the firm's required rate of return, sums those present values, and nets out the initial cost. A positive NPV means the project is expected to return more than its cost of capital, and that surplus, expressed in today's dollars, is exactly how much value the project adds to the firm. Accept when NPV is positive; that single rule is the whole decision.

Internal rate of return asks a related but different question: at what discount rate does this project's NPV fall to exactly zero. For an independent project with a conventional cash flow pattern, one initial outflow followed only by inflows, NPV and IRR always agree on accept or reject. They can disagree sharply once two projects are compared against each other, because IRR is a rate and NPV is a dollar amount, and a smaller project can carry a higher rate while creating less total wealth. When mutually exclusive projects conflict, only one of which can be undertaken, NPV governs the choice every time, regardless of how the two IRRs compare. A project creating $200,000 of value at 14 percent is worth more to owners than one creating $100,000 at 18 percent, because NPV measures wealth and IRR only measures a rate.

The disagreement traces back to a hidden assumption each method makes about reinvestment. IRR implicitly assumes every interim cash flow can be reinvested at the IRR itself, an assumption that grows less realistic the higher that IRR climbs. NPV assumes reinvestment at the firm's own required return, the more defensible assumption, which is exactly why NPV is the theoretically preferred method for ranking competing projects.

Only cash flows the decision actually changes belong in the analysis. A sunk cost, money already spent regardless of what is decided now, never enters the calculation, because no choice available today can recover it or change it. An opportunity cost, the value given up by using an asset the firm already owns for this project instead of its next best use, must be included even though no new cash physically changes hands. Financing costs, interest and dividends among them, stay out of the cash flow stream entirely, because they are already captured inside the discount rate itself; including them there and again in the cash flows double-counts the cost of financing.

When a firm cannot fund every positive-NPV project because its capital budget is limited, the profitability index, the present value of future cash flows divided by the initial investment, ranks independent projects to maximize total value created within that constraint. Raw NPV cannot do this job on its own, since it favors larger projects regardless of how efficiently they use scarce capital. The profitability index has no role, however, in ranking mutually exclusive projects of different sizes; NPV still governs that decision, exactly as it does when no capital constraint exists at all.

The NPV profile, crossing zero at the IRR NPV discount rate IRR NPV positive, accept NPV negative, reject
NPV falls as the discount rate rises. Where the curve crosses zero is the IRR; to the left of that point NPV is positive and the project is worth taking.

Worked in full

A project costs $250,000 today and is expected to generate $80,000 per year for 4 years. The firm's required return is 9 percent. What is the project's NPV, and should the firm accept it? PV of the annuity = $80,000 x [1 - (1.09)^-4] / 0.09 = $80,000 x 3.2397 = $259,177.59. NPV = $259,177.59 - $250,000 = $9,177.59. Because NPV is positive, the firm should accept the project: it is expected to return more than the 9 percent required return and adds about $9,178 of value.

The same problem, one step removed

Same project: $250,000 initial cost, $80,000 per year for 4 years, required return 9 percent. Set up the present value of the annuity yourself, then net out the initial cost to find NPV.

The trap

A higher IRR only means a higher rate, never automatically more value; whenever two mutually exclusive projects disagree on NPV and IRR, NPV wins the decision every time, because it measures wealth in dollars and IRR does not.

What this unit turns on

Read these before the questions, not after them. Everything here traces to this module's own lesson and to the 2026 outline.

NPV discounts every cash flow at the required return and sums the present values; accept when NPV is positive

Net present value equals the sum of each period's cash flow discounted at the firm's required rate of return, netted against the initial outlay; a positive NPV means the project is expected to return more than its cost of capital and adds that amount of value to the firm. For independent projects with conventional cash flow patterns, the NPV and IRR accept-or-reject decisions agree; they can disagree only when projects are compared against each other for a single choice, or when cash flows are non-conventional.

IRR assumes reinvestment at the IRR itself; NPV assumes reinvestment at the required return

Internal rate of return is the discount rate that sets a project's NPV to zero, and it implicitly assumes every interim cash flow can be reinvested at that same rate, an assumption that grows less realistic as the IRR itself grows large. NPV's reinvestment assumption, the firm's own required return, is the more defensible one, which is why NPV, not IRR, is the theoretically preferred ranking method whenever the two disagree.

For mutually exclusive projects, choose the higher NPV, never the higher IRR

When only one of two or more competing projects can be undertaken, ranking by IRR can select the project that creates less total value, because IRR is a rate and NPV is a dollar amount; the CFA curriculum's position is unambiguous that NPV governs the ranking decision whenever mutually exclusive projects are involved, regardless of how the IRRs compare.

Return on invested capital measures realized return on capital already deployed, a different question from NPV or IRR

Return on invested capital compares a company's after-tax operating profit to the capital invested to generate it, evaluating how efficiently capital already committed is being used, rather than whether a specific future project should be undertaken. NPV and IRR are forward-looking project-selection tools; ROIC is a backward-looking measure of how well past capital allocation decisions are performing, and the two families of measures answer different questions even though both are part of the capital allocation toolkit.

Only incremental cash flows belong in the analysis: exclude sunk costs, include opportunity costs, exclude financing costs

A sunk cost, money already spent regardless of the decision at hand, never belongs in a capital budgeting cash flow, because it cannot be changed by the decision being made now. An opportunity cost, the value given up by using an asset the firm already owns for this project instead of its next-best alternative use, must be included even though no new cash changes hands. Financing costs, such as interest expense, are captured in the discount rate itself and must not also be subtracted from the cash flows, which would double-count the cost of debt.

The profitability index exists specifically for capital rationing among independent projects, not for ranking mutually exclusive ones

When a firm cannot fund every positive-NPV project because its capital budget is limited, ranking independent projects by profitability index, the present value of future cash flows divided by the initial investment, maximizes total value created within that constraint, something raw NPV cannot do on its own because it favors larger projects regardless of capital efficiency. Profitability index still fails as a ranking tool for mutually exclusive projects of different scale, where NPV remains the correct criterion.

The trick

NPV is wealth; IRR is a rate

A project creating $200,000 of value at 14% is worth more to owners than one creating $100,000 at 18%. When NPV and IRR disagree on a mutually exclusive choice, the dollar figure wins every time.

The Concorde test for sunk costs

Money already spent does not belong in the decision no matter how large it was or how tempting it feels to justify past spending. Continuing a project purely because of what has already been spent on it is the sunk cost trap in its purest form.

PI is the capital-rationing tool, not the mutually-exclusive tool

Profitability index ranks independent projects competing for a limited budget. It does not fix the scale problem when two mutually exclusive projects of different sizes are compared; NPV still governs that decision.

The method

The order to work a question of this type in, every time, before you touch the numbers.

  1. Identify whether the projects under comparison are independent (evaluate each on its own NPV or IRR against the hurdle rate) or mutually exclusive (rank by NPV only).
  2. List every cash flow the decision actually changes; strip out sunk costs, add in opportunity costs, and leave financing costs out of the cash flow stream since they already live in the discount rate.
  3. Compute NPV by discounting each period's incremental cash flow at the required rate of return and summing, netting the initial outlay.
  4. If IRR is requested or the question turns on a reinvestment-assumption trap, remember IRR assumes reinvestment at the IRR itself, not at WACC.
  5. If the scenario describes a limited capital budget across several independent projects, rank by profitability index rather than raw NPV to maximize value created per dollar available.
  6. [BA II Plus: enter CF0 as the negative initial outlay, then C01 through Cnn for each period's incremental cash flow, set I to the required rate, then NPV, CPT for net present value, or IRR, CPT for internal rate of return]

Two worked examples, then you are on your own

The first is worked in full. The second gives you the setup and stops. After that the questions give you nothing, which is the point: the help fades on purpose, so the last thing you practise is the thing the exam actually asks of you.

Worked in full

An analyst is evaluating two mutually exclusive projects. Project Alpha has an NPV of $120,000 and an IRR of 14%. Project Beta has an NPV of $95,000 and an IRR of 18%. The firm's required rate of return is 10%. Which project should the firm select, and which method should most likely guide the decision?

Answer A. The correct answer is Project Alpha. NPV is the preferred method for mutually exclusive projects because it directly measures value added to the firm. Project Beta's higher IRR does not mean it adds more wealth. It means it earns a higher percentage return on a potentially smaller or differently-timed cash flow base. NPV of $120,000 exceeds NPV of $95,000, so Alpha creates more shareholder value..

Your turn, setup given

A project has the following cash flows: Year 0: -$50,000; Year 1: $30,000; Year 2: $20,000; Year 3: $15,000. The firm's WACC is 12%. What is the project's NPV (nearest dollar), and should it be accepted, most likely?

Identify whether the projects under comparison are independent (evaluate each on its own NPV or IRR against the hurdle rate) or mutually exclusive (rank by NPV only).

The practice run

Pick an answer, say how sure you are, then reveal. Being sure and wrong is the most useful thing that can happen in a session, so answer honestly: it sends the unit back to learning and puts it at the front of your revision queue.

Question 1Exam level

The IRR of a project is 15%. The firm's WACC is 12%. A key assumption embedded in the IRR calculation is that interim cash flows are most likely reinvested at:

How sure are you?

Correct: A. The correct answer is 15% (the IRR itself). IRR implicitly assumes all interim cash flows can be reinvested at the IRR. This is the reinvestment rate assumption and it is the primary theoretical weakness of IRR. Because in practice, the marginal reinvestment opportunity is closer to WACC, not IRR..
B. WACC is the firm's cost of capital and feels like the natural reinvestment rate. WACC is the correct reinvestment assumption for NPV, not IRR. IRR mathematically assumes reinvestment at the IRR itself. This distinction is precisely why NPV is theoretically superior.
C. The risk-free rate is conservative and might seem prudent. Neither IRR nor NPV assumes risk-free reinvestment. This answer conflates capital budgeting with modified duration formulas.

Unit: capital-investments-and-capital-allocation

Question 2Exam level

A project costs $100,000 today. It generates cash inflows of -$30,000 in Year 1, +$200,000 in Year 2, and -$50,000 in Year 3. How many IRRs might this project most likely have?

How sure are you?

Correct: A. The correct answer is Up to 2 IRRs. Descartes' rule of signs states the number of possible IRRs equals the number of sign changes in the cash flow stream (or fewer). The cash flows are: -100,000 (Year 0), -30,000 (Year 1), +200,000 (Year 2), -50,000 (Year 3). Sign changes: negative to negative (no change), negative to positive (change 1), positive to negative (change 2). Two sign changes = up to 2 IRRs. When multiple IRRs exist, the IRR method cannot be used. NPV must be used instead..
B. Most textbook examples show one IRR. Projects with non-conventional cash flows (multiple sign changes) can have zero, one, or multiple IRRs. A unique IRR only exists for conventional cash flows (one sign change).
C. Mixed flows seem problematic. Mixed flows don't prevent an IRR from existing. They create the possibility of multiple IRRs. The number of IRRs is bounded by the number of sign changes.

Unit: capital-investments-and-capital-allocation

Question 3Exam level

A project has an initial cost of $80,000 and generates annual cash inflows of $25,000 for 5 years. What is most likely the payback period?

How sure are you?

Correct: A. The correct answer is 3.2 years. After Year 3, cumulative cash flows = $75,000. Remaining unrecovered investment = $80,000 - $75,000 = $5,000. Fraction of Year 4 needed = $5,000 / $25,000 = 0.2. Payback period = 3.2 years..
B. Rounding to the nearest year. The payback period requires fractional year precision. Year 3 cumulative cash flows are $75,000, not $80,000. The investment is not yet recovered.
C. Rounding up to next whole year. The payback period is expressed as a fractional year. Rounding up to 4 years overstates the time to recovery.

Unit: capital-investments-and-capital-allocation

Question 4Exam level

Which of the following is LEAST likely a limitation of the payback period method?

How sure are you?

Correct: A. The correct answer is It is difficult to calculate. The payback period is actually one of the simplest capital budgeting methods to calculate. The actual limitations are: it ignores cash flows after the payback cutoff (A), it ignores the time value of money (B), and it lacks an objectively derived acceptance criterion (D). 'Difficult to calculate' is not a limitation..
B. You might focus on TVM as the 'main' limitation. This IS a real limitation. A project could have enormous cash flows in later years that the payback period completely ignores, leading to rejection of a highly profitable project.
C. You might might think 'discounted payback fixes this, so maybe it's not a limitation of payback itself'. TVM ignorance is THE primary limitation of standard (undiscounted) payback period. Discounted payback is a separate method.

Unit: capital-investments-and-capital-allocation

Question 5Exam level

Project X has an initial investment of $500,000 and an NPV of $60,000. Project Y has an initial investment of $100,000 and an NPV of $30,000. The projects are mutually exclusive. Using the profitability index, which project ranks higher. And does the CFA curriculum support this ranking, most likely?

How sure are you?

Correct: A. The correct answer is Project Y ranks higher by PI. PI(X) = (500,000 + 60,000) / 500,000 = 1.12. PI(Y) = (100,000 + 30,000) / 100,000 = 1.30. Project Y has the higher PI. However, the CFA curriculum does NOT support using PI to rank mutually exclusive projects when project scales differ. NPV is the correct decision tool: Project X creates $60,000 of value vs Project Y's $30,000. If the projects are mutually exclusive, choose Project X based on NPV..
B. Higher absolute NPV sounds like the right answer. For PI ranking specifically, Project Y has the higher PI (1.30 vs 1.12). This question asks who ranks higher by PI, then separately evaluates whether PI should be used. So this answer confuses the two sub-questions.
C. PI's per-dollar framing sounds efficient and rigorous. PI is useful for capital rationing (limited budget, must rank independent projects), but fails for mutually exclusive projects with different scales. The CFA curriculum is explicit: use NPV for mutually exclusive decisions.

Unit: capital-investments-and-capital-allocation

Question 6Exam level

When evaluating a proposed plant expansion, which of the following costs should most likely be included in the project's incremental cash flows?

How sure are you?

Correct: A. The correct answer is Opportunity costs. The correct principle: include all incremental cash flows that change because the project exists. Including opportunity costs (foregone value from the next-best alternative use of an asset). Exclude: sunk costs (already spent, cannot be recovered), financing costs (captured in WACC/discount rate), and allocated overhead (not truly incremental)..
B. Sunk costs feel relevant because money was already spent on preliminary work. Sunk costs are the most important exclusion in capital budgeting. They are irrelevant to the go/no-go decision because they cannot be recovered regardless of what happens next.
C. Borrowing money to fund a project seems like a project-specific cost. Financing costs are captured in the discount rate (WACC), not in the cash flow stream. Including interest expense in cash flows double-counts the cost of debt.

Unit: capital-investments-and-capital-allocation

Question 7Exam level

Two projects have equal NPVs at the firm's WACC of 9%. Project A generates large cash flows early; Project B generates large cash flows late. At which discount rate would most likely Project B's NPV be higher than Project A's?

How sure are you?

Correct: A. The correct answer is At discount rates below 9% (the crossover rate / Fisher rate). When the discount rate decreases, the present value of distant cash flows rises disproportionately compared to near-term cash flows. Project B (back-loaded) benefits more from lower discount rates. The NPV profiles of Projects A and B cross at 9%. Below that rate, Project B dominates; above it, Project A dominates. The Fisher rate is the discount rate at which the two NPV profiles intersect (here, 9%)..
B. Higher rates seem to penalize cash flows, so candidates flip the logic. Higher discount rates penalize LATER cash flows more severely (because of compounding over more periods). Project B (back-loaded) is hurt more by high rates, not Project A.
C. The word 'equal' in the question stem seems absolute. NPVs are equal at one specific discount rate (9%). As the rate changes, the NPV profiles diverge. This is the entire point of the NPV profile graph. NPV is a function of discount rate, not a fixed number.

Unit: capital-investments-and-capital-allocation

Question 8Exam level

According to the CFA curriculum, which capital budgeting method is MOST appropriate when a firm faces capital rationing and must choose among several independent projects?

How sure are you?

Correct: A. The correct answer is Profitability Index (PI). Under capital rationing. Where the firm cannot fund all positive-NPV projects. PI ranks projects by value created per dollar invested. This helps maximize total NPV within the budget constraint. PI = (PV of future cash flows) / Initial investment, or equivalently, 1 + (NPV / Initial investment). It is only appropriate for ranking independent projects under a budget constraint..
B. NPV is almost always the 'best' answer in capital budgeting questions. Under capital rationing, raw NPV cannot be used for ranking because it favors larger projects. A $1M project with NPV $100K would rank above a $50K project with NPV $80K using NPV. But the latter is far more capital-efficient. PI is the correct tool here.
C. Scale-independence sounds ideal for capital rationing. IRR has the reinvestment rate assumption problem and can conflict with NPV. PI is the correct capital rationing tool in the CFA curriculum.

Unit: capital-investments-and-capital-allocation

Question 9Above the exam

A company evaluates a project with an initial cost of $1,000,000, WACC of 10%, and cash inflows of $300,000, $400,000, and $600,000 in years 1 through 3. Combining the NPV and IRR decision rules, an analyst who finds IRR is approximately 19% but incorrectly concludes the project should be rejected because '19% seems low compared to some of the firm's other opportunities earning 25%' has most likely made an error because:

How sure are you?

Correct: A. For an independent project, the standard decision rule is to accept if IRR exceeds the project's own cost of capital (here, 10%); an IRR of approximately 19% clears that hurdle comfortably and the project should be ACCEPTED (also confirmed by computing a positive NPV at 10%). Comparing this project's IRR to an unrelated 25% opportunity elsewhere conflates the accept/reject decision for THIS project with a separate capital RATIONING or opportunity-ranking decision, which is a different question requiring different analysis (such as comparing NPVs or profitability indexes under a capital constraint).
B. IRR is a standard, widely used capital budgeting tool (alongside NPV); the LOS does not reject IRR altogether, it teaches candidates to apply the correct comparison benchmark (the project's own cost of capital) and to be aware of IRR's specific limitations (such as with non-conventional cash flows), not to discard it entirely.
C. Rejecting a project because a DIFFERENT, unrelated opportunity offers a higher return confuses an independent accept/reject decision with a capital-rationing comparison; unless the two projects are mutually exclusive or capital is explicitly constrained, a project with a positive NPV at the firm's cost of capital should be accepted on its own merits.

Unit: capital-investments-and-capital-allocation

Question 10Above the exam

A firm has two mutually exclusive projects of different scale: Project Small costs $100,000 with an IRR of 40%, and Project Large costs $1,000,000 with an IRR of 18%, both using the firm's 10% WACC. Project Small's NPV is $15,000; Project Large's NPV is $120,000. Combining the NPV and IRR decision rules for mutually exclusive projects, the firm should most likely:

How sure are you?

Correct: B. When NPV and IRR rank mutually exclusive projects DIFFERENTLY (as they do here, IRR favors Small, NPV favors Large), NPV is the theoretically preferred criterion because it directly measures the dollar amount of value added to the firm, using a realistic reinvestment assumption (at the cost of capital). IRR's percentage return can favor a much smaller project simply because of its smaller scale, even though the larger project creates far more total value; NPV correctly captures that scale effect.
A. A higher IRR on a much SMALLER project does not mean it creates more value; IRR is a percentage return that ignores project scale, which is exactly why it can conflict with NPV (which correctly reflects the larger dollar value created by Project Large) when comparing projects of very different sizes.
C. Payback period is not the standard rule for resolving NPV/IRR ranking conflicts; it ignores the time value of money and any cash flows beyond the payback point entirely, and is not the theoretically preferred tiebreaker taught for mutually exclusive project comparisons, NPV is.

Unit: capital-investments-and-capital-allocation