Practice: Capital Investments and Capital Allocation

Corporate Issuers. 12 question(s) in this unit's pool (2 above the exam). Free up to ten a day; the coach picks which ones based on what you have already answered and when each is next due.

Corporate IssuersCapital Investments and Capital Allocation

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Today's practice

Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own explanation. Questions you have already answered correctly and confidently stay out of the way until they are due for review again.

Question 1Exam level

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?

A. Project Alpha, because NPV is the correct decision criterion for mutually exclusive projects B. Project Beta because its IRR of 18% exceeds Project Alpha's IRR of 14% C. Either project, since both have IRR above the required rate of 10%

How sure are you?

Sure Fairly sure Guessing

Correct: 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..

B. A higher percentage return intuitively feels like a better investment. IRR is a rate, not a value measure. For mutually exclusive projects, the project with the higher IRR can create less total value. CFA Institute explicitly states NPV is superior for ranking mutually exclusive projects.

C. Both projects pass the IRR accept/reject screen. Passing the accept/reject screen means both are acceptable independently, but only one can be chosen. The ranking decision requires NPV.

Unit: capital-investments-and-capital-allocation

Question 2Exam level

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?

A. NPV = -50,000 + 30,000/1.12 + 20,000/1.12^2 + 15,000/1.12^3 = -50,000 + 26,786 + 15,944 + 10,677 = $3,407. Since NPV > 0, accept the project. On BA II Plus: CF0=-50000, C01=30000, C02=20000, C03=15000, I=12, NPV=CPT. B. NPV = $15,000 (sum of undiscounted cash flows minus initial investment: 65,000 - 50,000). Adding up raw cash flows is the payback period instinct. C. Reject because the total undiscounted cash inflows ($65,000) barely exceed the outflow. Small margin feels risky.

How sure are you?

Sure Fairly sure Guessing

Correct: A. The correct answer is NPV = -50,000 + 30,000/1.12 + 20,000/1.12^2 + 15,000/1.12^3 = -50,000 + 26,786 + 15,944 + 10,677 = $3,407. Since NPV > 0, accept the project. On BA II Plus: CF0=-50000, C01=30000, C02=20000, C03=15000, I=12, NPV=CPT..

B. Adding up raw cash flows is the payback period instinct. NPV requires discounting each cash flow to present value. Ignoring the time value of money gives a meaningless number for decision-making.

C. Small margin feels risky. NPV > 0 is the correct accept criterion. The positive NPV of $3,407 means the project returns the WACC plus creates $3,407 of additional value.

Unit: capital-investments-and-capital-allocation

Question 3Exam 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:

A. 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. 12% (the WACC). 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. C. The risk-free rate. The risk-free rate is conservative and might seem prudent.

How sure are you?

Sure Fairly sure Guessing

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 4Exam 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?

A. 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. Exactly one IRR, as every project has a unique IRR. Most textbook examples show one IRR, since a single upfront outflow followed only by positive inflows changes sign exactly once and always converges to one solution. Projects with non-conventional cash flows, meaning more than one sign change, can have zero, one, or multiple IRRs depending on how many times the cash flow stream crosses from positive to negative or back. Here the stream runs negative, negative, positive, negative, which is two sign changes, not one, so the uniqueness rule for a conventional project does not apply. C. No IRR, because the project has mixed positive and negative cash flows. Mixed sign patterns can look alarming, but mixed flows do not by themselves prevent an IRR from existing at all. What they create is the possibility of more than one IRR satisfying the NPV-equals-zero equation, not the absence of any solution. The number of IRRs a project can have is bounded above by the number of times the cash flow stream changes sign, which here is two, giving up to two IRRs, not zero.

How sure are you?

Sure Fairly sure Guessing

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 5Exam 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?

A. 3.2 years B. 3 years, because cash flows cover the investment by Year 3 C. 4 years

How sure are you?

Sure Fairly sure Guessing

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 6Exam level

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

A. 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. It ignores cash flows that occur after the payback period. Focusing 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. It does not account for the time value of money. Mighting think 'discounted payback fixes this, so maybe it's not a limitation of payback itself'.

How sure are you?

Sure Fairly sure Guessing

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 7Exam 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?

A. 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. Project X because it has the higher absolute NPV ($60,000 vs $30,000). 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. C. Project Y should be selected because PI measures return per dollar invested, which is the most relevant metric. PI's per-dollar framing sounds efficient and rigorous.

How sure are you?

Sure Fairly sure Guessing

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 8Exam level

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

A. 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, because they represent committed resources already allocated to the project. 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. Interest expense on project debt, to capture the true cost of financing. Borrowing money to fund a project seems like a project-specific cost.

How sure are you?

Sure Fairly sure Guessing

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 9Exam 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?

A. 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. At discount rates above 9%, because higher rates penalize Project A's early cash flows more. 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. NPVs are always equal regardless of the discount rate, since the two projects were stated to have equal NPVs. The word 'equal' in the question stem seems absolute.

How sure are you?

Sure Fairly sure Guessing

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 10Exam 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?

A. 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, because it always gives the correct accept/reject decision. 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. C. IRR, because it measures percentage return and is scale-independent. Scale-independence sounds ideal for capital rationing.

How sure are you?

Sure Fairly sure Guessing

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 11Above 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:

A. The NPV/IRR accept-reject decision for a single independent project depends on whether IRR exceeds the project's OWN cost of capital (WACC), not on comparison to unrelated opportunities elsewhere in the firm B. IRR should never be used for capital budgeting decisions under any circumstances. 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. The analyst's conclusion is correct, since any project below the firm's best available return should be rejected. 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.

How sure are you?

Sure Fairly sure Guessing

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 12Above 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:

A. Choose Project Small, since it has the much higher IRR. 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. B. Choose Project Large, because for mutually exclusive projects NPV is the theoretically superior decision criterion, and Project Large's higher NPV means it adds more total value even though its IRR is lower C. Choose whichever project has the shorter payback period, since payback always resolves conflicts between mutually exclusive projects. 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.

How sure are you?

Sure Fairly sure Guessing

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