Managerial Accounting Quiz: Comparing Capital Projects
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Comparing Capital ProjectsQuestion 1 of 20

A firm is evaluating two mutually exclusive investment projects, Alpha and Beta. Project Alpha has a higher Net Present Value (NPV) but a lower Internal Rate of Return (IRR) than Project Beta. The firm's weighted average cost of capital (WACC) is 10%, which is lower than the IRR of both projects and lower than the crossover rate. A manager advocates for Project Beta, arguing its higher IRR represents a superior return.

The manager is correct because IRR is a more intuitive measure of a project's financial efficiency and percentage return.
The manager is incorrect; the conflict is due to different project scales, and the incremental NPV of Alpha over Beta is positive.
The manager's choice depends on the firm's ability to reinvest cash flows; if it can reinvest at Beta's IRR, Beta is the better choice.
The manager is incorrect because the NPV method's assumption of reinvesting cash flows at the WACC is more realistic than the IRR's assumption.
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Managerial Accounting Quiz

Managerial Accounting Quiz: Comparing Capital Projects

Practice Comparing Capital Projects in Managerial Accounting with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Comparing Capital Projects, giving you a quick way to practice the rules, question types, and explanations that matter most for Managerial Accounting.

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Question 1

A firm is evaluating two mutually exclusive investment projects, Alpha and Beta. Project Alpha has a higher Net Present Value (NPV) but a lower Internal Rate of Return (IRR) than Project Beta. The firm's weighted average cost of capital (WACC) is 10%, which is lower than the IRR of both projects and lower than the crossover rate. A manager advocates for Project Beta, arguing its higher IRR represents a superior return.

  1. The manager is correct because IRR is a more intuitive measure of a project's financial efficiency and percentage return.
  2. The manager is incorrect; the conflict is due to different project scales, and the incremental NPV of Alpha over Beta is positive.
  3. The manager's choice depends on the firm's ability to reinvest cash flows; if it can reinvest at Beta's IRR, Beta is the better choice.
  4. The manager is incorrect because the NPV method's assumption of reinvesting cash flows at the WACC is more realistic than the IRR's assumption. (correct answer)
Explanation: The core of the NPV vs. IRR conflict for mutually exclusive projects lies in their implicit reinvestment rate assumptions. NPV assumes that cash flows generated by the project can be reinvested at the company's cost of capital (WACC). IRR assumes cash flows can be reinvested at the project's own IRR. Since it is more reasonable to assume the firm can find other projects that earn its cost of capital rather than the high IRR of one specific project, the NPV assumption is considered more realistic and reliable. Therefore, when NPV and IRR conflict, the project with the higher NPV should be chosen.

Question 2

Two mutually exclusive projects have NPV profiles that intersect at a discount rate of 14%, known as the crossover rate. Project A has a higher NPV at discount rates below 14%, while Project B has a higher NPV at rates above 14%. The company's weighted average cost of capital (WACC) is currently 11%. Which of the following conclusions is most accurate?

  1. Project B has a higher IRR, and if the company's WACC increases to 15%, Project B would be the preferred investment.
  2. Project A has a higher IRR, and it should be selected regardless of the company's WACC.
  3. The crossover rate of 14% represents the IRR of the incremental project (B - A), and Project A is currently the preferred investment. (correct answer)
  4. Both projects have an IRR of 14%, and the choice depends on which project has a shorter payback period.
Explanation: The crossover rate is the discount rate at which the NPVs of two projects are equal. It is also the IRR of the incremental cash flows between the two projects. Since the company's WACC (11%) is below the crossover rate (14%), the project with the higher NPV at lower discount rates should be chosen, which is Project A. Statement C correctly identifies the meaning of the crossover rate and that Project A is currently preferred. Statement A is plausible but C is more complete; we can infer B has a higher IRR because its NPV is less sensitive to discount rate changes (it becomes preferred at higher rates), but C's statement about the current preference is the key decision point.

Question 3

A company is three years into a seven-year project. The project's equipment has a current salvage value of $250,000. A new analysis estimates that the present value of the project's future operational cash flows over the remaining four years is $220,000. The original investment in the project was $1,000,000, and initial projections for the remaining four years' cash flows had a present value of $400,000.

  1. Continue the project, because the initial $1,000,000 investment is a sunk cost and should not influence the decision.
  2. Abandon the project, because its performance is significantly below the initial projections for this stage.
  3. Abandon the project, because its current salvage value of $250,000 is greater than the present value of its expected future cash flows. (correct answer)
  4. Continue the project, because the present value of its remaining cash flows is positive.
Explanation: The decision to continue or abandon a project should be based on a comparison of the value of continuing versus the value of abandoning at the time the decision is made. Sunk costs (the original $1,000,000 investment) and original projections are irrelevant to the current decision. The relevant comparison is between the value of abandoning now (the salvage value of $250,000) and the value of continuing (the PV of future cash flows, $220,000). Since the abandonment value is greater than the value of continuing, the firm should abandon the project to maximize value.

Question 4

A firm is comparing Project X, a conventional factory with a calculated NPV of $2.0 million, and Project Y, a flexible manufacturing system with a calculated NPV of $1.8 million. The analysis of Project Y did not formally value the fact that its flexible design would allow for a low-cost switch to producing a different product if the original product's market declines. This option to switch production is not possible with Project X.

  1. Project X should be selected because it has a demonstrably higher NPV based on the quantitative analysis performed.
  2. Project Y may be the superior choice if the value of the embedded real option to switch production is greater than $200,000. (correct answer)
  3. The projects are incomparable because real options cannot be valued and added to a traditional NPV analysis.
  4. The discount rate for Project Y should be lowered to reflect its reduced risk, which will increase its NPV above that of Project X.
Explanation: Traditional NPV analysis often fails to capture the value of managerial flexibility, such as the option to abandon, expand, or, in this case, switch use. This flexibility is a 'real option.' The calculated NPV of Project Y is $200,000 less than that of Project X. However, if the value of the option to switch production (which is a valuable form of risk mitigation) is greater than this $200,000 difference, then the total value of Project Y (NPV + Option Value) would exceed the value of Project X. Therefore, the decision hinges on whether the option's value exceeds this threshold.

Question 5

A firm is comparing two projects using a nominal discount rate of 11%, which includes a 4% expected inflation component. Project A's cash flow forecasts were prepared in nominal terms, including inflationary effects. Project B's cash flow forecasts were prepared in real terms (i.e., in today's purchasing power) and do not include inflationary adjustments.

  1. The NPV of Project A will be correctly stated, but the NPV of Project B will be understated. (correct answer)
  2. The NPV of Project B will be correctly stated, but the NPV of Project A will be overstated.
  3. The NPVs of both projects will be correctly stated because the discount rate is applied consistently.
  4. The NPV of both projects will be understated due to the high nominal discount rate.
Explanation: The consistency principle in capital budgeting requires that nominal cash flows be discounted with a nominal rate, and real cash flows be discounted with a real rate. The firm is using a nominal rate of 11%. This is appropriate for Project A's nominal cash flows. However, applying this nominal rate to Project B's real cash flows is incorrect. The real cash flows should be discounted at the real rate (approx. 1.11/1.04 - 1 ≈ 6.7%). By using the higher nominal rate on real cash flows, the firm is essentially penalizing Project B twice for inflation, which will lead to an understatement of its NPV.

Question 6

A company is comparing two mutually exclusive projects. Project M requires an asset that will be depreciated using the straight-line method over 5 years. Project N requires an asset of identical cost and life, but it qualifies for an accelerated depreciation method (e.g., MACRS). Both projects are expected to generate the same operating revenues and cash operating expenses. The tax rate and discount rate are constant.

  1. The projects will have the same NPV because total depreciation expense over the 5-year life is identical for both.
  2. Project M will have a higher NPV because its reported net income will be higher in the project's early years.
  3. Project N will have a higher NPV because the depreciation tax shields occur earlier in the project's life. (correct answer)
  4. The choice of depreciation method is an accounting decision and has no impact on project cash flows or NPV.
Explanation: Depreciation is a non-cash expense, but it affects cash flow through its impact on taxes (the depreciation tax shield, which is Depreciation * Tax Rate). An accelerated depreciation method, like MACRS, allows the firm to take larger depreciation expenses in the early years of a project's life compared to the straight-line method. This results in larger tax shields (i.e., greater tax savings) in the early years. Due to the time value of money, receiving these cash savings earlier makes them more valuable, thus increasing the project's NPV. Therefore, Project N will have a higher NPV.

Question 7

A firm is analyzing two mutually exclusive projects with the following expected cash flows:

  • Project Fast: Investment: $200,000. Cash Inflows: $120,000 (Year 1), $80,000 (Year 2), $20,000 (Year 3).
  • Project Slow: Investment: $200,000. Cash Inflows: $40,000 (Year 1), $60,000 (Year 2), $200,000 (Year 3).

The company's cost of capital is 11%.

Which of the following statements correctly compares the two projects?

  1. Project Slow has a higher Net Present Value (NPV) than Project Fast, making it the better financial choice. (correct answer)
  2. Project Slow is superior because its total undiscounted cash inflows are greater than Project Fast's.
  3. Project Fast is superior because it has a shorter payback period and thus returns the initial investment more quickly.
  4. Both projects are financially equivalent because their initial investments are identical.
Explanation: A full comparison requires calculating the NPV for both projects at the 11% cost of capital. NPV_Fast = -$200,000 + $120,000/(1.11) + $80,000/(1.11)^2 + 20,000/(1.11)3=−20,000/(1.11)^3 = -200,000 + $108,108 + $64,960 + 14,625=−14,625 = -12,307. NPV_Slow = -$200,000 + $40,000/(1.11) + $60,000/(1.11)^2 + 200,000/(1.11)3=−200,000/(1.11)^3 = -200,000 + $36,036 + $48,720 + $146,252 = $31,008. Even though Project Fast has a shorter payback period (2 years), it has a negative NPV. Project Slow has a positive NPV and is therefore the superior investment. Total undiscounted cash flows are $220k for Fast and $300k for Slow, so B is also incorrect in its premise and conclusion.

Question 8

A city must purchase a new street-sweeping machine and must choose between two models. The city's discount rate for capital projects is 8%. The machines provide an essential service, and the chosen model will be replaced indefinitely. The costs are as follows:

  • Model A: Initial Cost: $90,000; Annual Operating Costs: $20,000; Life: 4 years
  • Model B: Initial Cost: $120,000; Annual Operating Costs: $15,000; Life: 6 years

Based on the Equivalent Annual Cost (EAC) method, which model is the more economical choice?

  1. Model A, because its total undiscounted costs over its life are lower.
  2. Model B, because its EAC is approximately $39,150.
  3. Model A, because its EAC is approximately $47,155.
  4. Model B, because its EAC is approximately $41,232. (correct answer)
Explanation: This is a comparison of two cost-only projects with unequal lives, requiring the EAC method. First, find the NPV of the costs for each model. PVIFA(8%, 4) = 3.3121; PVIFA(8%, 6) = 4.6229. NPV_A = -90,000−(90,000 - (20,000 * 3.3121) = -$90,000 - 66,242=−66,242 = -156,242. NPV_B = -120,000−(120,000 - (15,000 * 4.6229) = -$120,000 - 69,344=−69,344 = -189,344. Next, convert the NPV of costs to an EAC. EAC_A = NPV_A / PVIFA(8%, 4) = -156,242/3.3121=−156,242 / 3.3121 = -47,172. EAC_B = NPV_B / PVIFA(8%, 6) = -189,344/4.6229=−189,344 / 4.6229 = -41,232. The goal is to choose the option with the lowest annual cost. Since the EAC of Model B (-41,232)islessnegative(i.e.,alowerannualcost)thantheEACofModelA(−41,232) is less negative (i.e., a lower annual cost) than the EAC of Model A (-47,172), Model B is the more economical choice.

Question 9

Project A requires an initial investment of $200 and generates a single cash inflow of $280 at the end of year 1. Project B requires an initial investment of $300 and generates a single cash inflow of $405 at the end of year 1. What is the crossover rate at which the NPV of these two mutually exclusive projects would be equal?

  1. 35.0%
  2. 37.5%
  3. 40.0%
  4. 25.0% (correct answer)
Explanation: The crossover rate is the IRR of the incremental cash flows between the two projects. Let's analyze the incremental project (B - A):
  • Incremental Investment (Year 0): $300 - $200 = $100
  • Incremental Cash Inflow (Year 1): $405 - $280 = $125
The IRR is the rate 'r' that makes the NPV of this incremental project equal to zero: NPV = 0 = -100 + [125 / (1 + r)] 100 = 125 / (1 + r) 1 + r = 125 / 100 1 + r = 1.25 r = 0.25 or 25.0% At a discount rate of 25%, both projects will have the same NPV.

Question 10

A manager is comparing two mutually exclusive projects, Early Harvest and Late Yield. Both require a $5,000 investment and have a 4-year life. Early Harvest generates cash flows of $2,500, $2,000, $1,500, and $1,000 in years 1-4. Late Yield generates cash flows of $1,000, $1,500, $2,000, and $2,500 in years 1-4. The firm's cost of capital is positive.

  1. Early Harvest will have a higher NPV due to the time value of money. (correct answer)
  2. Late Yield will have a higher IRR because its largest cash flows occur at the end of the project's life.
  3. Both projects will have the same NPV because their total cash inflows of $7,000 are identical.
  4. The projects will have the same payback period since the investments and total cash flows are equal.
Explanation: This question tests the conceptual understanding of the time value of money. Both projects have the same initial investment and the same total undiscounted cash inflows ($7,000). However, the timing of these cash flows is different. Project Early Harvest receives larger cash flows in the earlier years. Because money received sooner is more valuable than money received later (it can be reinvested earlier), the present value of Early Harvest's cash flows will be higher than the present value of Late Yield's cash flows when discounted at any positive rate. Therefore, Early Harvest will have a higher NPV.

Question 11

A company is considering two mutually exclusive projects, Project Alpha and Project Beta. Standard discounted cash flow analysis indicates that NPV(Alpha) = $150,000 and NPV(Beta) = $125,000. However, management ultimately selects Project Beta. The justification provided is that Project Beta involves a proprietary technology that could open up future investment opportunities, a strategic benefit not captured in the cash flow projections.

  1. The decision is flawed because projects should always be selected based on the highest calculated NPV.
  2. This decision implies that management has placed a minimum value of $125,000 on the strategic benefit.
  3. This decision implies that management has placed a minimum value of more than $25,000 on the strategic benefit. (correct answer)
  4. The value of the strategic benefit is equal to the difference in the initial investments of the two projects.
Explanation: For management to rationally choose the project with the lower quantitative NPV, the unquantified (qualitative or strategic) benefits must be valuable enough to overcome the calculated NPV disadvantage. The NPV disadvantage of Project Beta is $150,000 (NPV of Alpha) - $125,000 (NPV of Beta) = $25,000. Therefore, management must implicitly believe the strategic value of the future opportunities associated with Project Beta is worth at least this difference. To tip the scales in favor of Beta, the value must be more than $25,000.

Question 12

A company is considering replacing an old asset. The new asset costs $500,000. The old asset has a book value of $120,000 and can be sold today for $80,000. The company's marginal tax rate is 25%. What is the relevant initial cash outflow for the purpose of an NPV analysis of the replacement decision?

  1. $500,000
  2. $420,000
  3. $380,000
  4. $410,000 (correct answer)
Explanation: The initial cash outflow is the cost of the new asset minus the after-tax proceeds from the sale of the old asset.
  1. Cost of new asset = -$500,000
  2. Cash proceeds from sale of old asset = +$80,000
  3. The old asset is sold at a loss: Loss = Book Value - Sale Price = $120,000 - $80,000 = $40,000.
  4. This loss creates a tax shield (a tax savings): Tax Shield = Loss * Tax Rate = $40,000 * 0.25 = $10,000.
  5. Total after-tax proceeds from sale = Cash proceeds + Tax Shield = $80,000 + $10,000 = $90,000.
  6. Net initial cash outflow = -$500,000 (cost) + 90,000(after−taxproceeds)=−90,000 (after-tax proceeds) = -410,000.

Question 13

A company is evaluating two mutually exclusive projects of different initial scales. Project Small requires a $100,000 investment and has an NPV of $40,000. Project Large requires a $500,000 investment and has an NPV of $125,000. The company is not subject to capital rationing and can raise funds as needed at its cost of capital.

  1. Project Small should be selected because its Profitability Index (1.40) is higher than Project Large's (1.25).
  2. Project Large should be selected because it generates a greater total increase in shareholder wealth. (correct answer)
  3. The projects cannot be compared directly; an incremental analysis of the difference between them is required to make a decision.
  4. Project Small should be selected, and the remaining $400,000 that would have been used for Project Large should be invested elsewhere.
Explanation: When comparing mutually exclusive projects and capital is not rationed, the project with the highest positive NPV should be selected. The objective is to maximize the total dollar value added to the firm. Project Large adds $125,000 to firm value, while Project Small adds only $40,000. The Profitability Index (PI) is a measure of relative profitability and is useful for ranking projects under capital rationing, but it is not the correct decision criterion for mutually exclusive projects of different sizes when no budget constraint exists. The selection of the higher NPV project implicitly assumes that the incremental investment earns a return greater than the cost of capital.

Question 14

A company is selecting between two mutually exclusive information systems, System P and System Q. Both are expected to have a 5-year life. The company's WACC is 10%. The NPV for System P is $85,000 and its IRR is 18%. The NPV for System Q is $95,000 and its IRR is 16%. The crossover rate for the two systems is 12%.

The company's CFO has just announced that due to changing market conditions, the WACC used for project evaluation is being increased from 10% to 13%. How does this change affect the comparison of the two systems?

  1. System Q remains the preferred choice because its NPV was initially higher.
  2. System P becomes the preferred choice because the new WACC is above the crossover rate. (correct answer)
  3. System P becomes the preferred choice because its IRR of 18% is higher.
  4. The decision cannot be made without recalculating the NPVs at the new 13% WACC.
Explanation: The crossover rate is the discount rate at which the NPVs of two projects are equal. When the WACC is below the crossover rate, the project with the initially higher NPV is preferred. When the WACC is above the crossover rate, the ranking of the projects' NPVs reverses. Initially, at WACC=10% (which is < 12% crossover), System Q was preferred (NPV $95k > $85k). Now, the WACC is 13%, which is above the crossover rate of 12%. This means the NPV profiles have crossed, and System P will now have the higher NPV. Therefore, System P becomes the preferred choice.

Question 15

A firm is choosing between two mutually exclusive projects. Project A has a payback period of 2.1 years and will generate substantial positive cash flows for 8 years. Project B has a payback period of 1.8 years, but its cash flows will cease after year 3. The firm is currently facing a significant liquidity crisis and has large debt payments due in the next 24 months. The firm's standard policy is to accept projects with the highest NPV.

  1. Project A should be chosen to maximize long-term shareholder value, consistent with the firm's standard policy.
  2. Project B may be chosen despite a likely lower NPV, as its faster cash recovery directly addresses the firm's immediate and critical liquidity needs. (correct answer)
  3. The decision should be deferred until the liquidity crisis is over, as no sound capital budgeting decision can be made under these circumstances.
  4. Neither project should be chosen because the payback period is an inferior method that ignores the time value of money and later cash flows.
Explanation: While NPV is the theoretically superior capital budgeting method, its focus is on long-term value maximization. In situations of extreme financial distress or liquidity constraints, a firm's primary goal may shift to short-term survival. In this context, the payback period, despite its flaws, becomes a highly relevant measure of liquidity and risk. Choosing Project B, with its faster payback, directly addresses the critical need to generate cash quickly to meet obligations, even if it means sacrificing some long-term value (a lower NPV).

Question 16

A manufacturing firm must choose between two mutually exclusive machines. The firm's cost of capital is 12%, and it plans to replace the chosen machine indefinitely. The financial details are as follows:

  • Machine X: NPV = $45,000; Useful Life = 4 years
  • Machine Y: NPV = $60,000; Useful Life = 7 years

Using the Equivalent Annual Annuity (EAA) method to compare these projects, which machine should the firm choose?

  1. Machine X, because its EAA of approximately $14,810 is higher than Machine Y's. (correct answer)
  2. Machine Y, because its NPV of $60,000 is higher than Machine X's NPV of $45,000.
  3. Machine Y, because its longer useful life of 7 years provides more total value over time.
  4. Machine X, because its shorter replacement cycle allows for more frequent technology upgrades.
Explanation: When comparing mutually exclusive projects with unequal lives that will be replaced, one must use a method like the Equivalent Annual Annuity (EAA) to determine which project provides a higher average annual value. The formula is EAA = NPV / PVIFA(k, n), where PVIFA is the present value interest factor of an annuity. For Machine X: PVIFA(12%, 4) = 3.0373. EAA_X = $45,000 / 3.0373 ≈ $14,816. For Machine Y: PVIFA(12%, 7) = 4.5638. EAA_Y = $60,000 / 4.5638 ≈ $13,147. Since Machine X has a higher EAA, it provides more value on an annualized basis and should be selected.

Question 17

A capital projects committee is reviewing project selection methods for the firm, which operates under a strict annual capital budget. A junior analyst argues for ranking independent projects by NPV and accepting them until the budget is exhausted. The CFO argues for using the Profitability Index (PI).

  1. The analyst is correct because selecting the projects with the highest absolute NPVs directly supports the goal of wealth maximization.
  2. The CFO is correct because the PI method prioritizes projects that generate the most value per dollar of scarce capital invested. (correct answer)
  3. Both methods are suboptimal; ranking by IRR is preferred because it focuses on the highest percentage returns.
  4. The methods will always yield the same project rankings, so the choice between them is irrelevant.
Explanation: When a firm faces capital rationing, the goal is to select the combination of projects that maximizes the total NPV achievable within the budget. Simply ranking by NPV (the analyst's method) can be suboptimal because a single large project with a high NPV might use up the entire budget, preventing the firm from taking several smaller projects that, in aggregate, would have produced an even higher total NPV. The Profitability Index (PI) is designed for this situation. By measuring the NPV generated per dollar of investment, it helps identify the most efficient use of limited capital, leading to a project bundle that maximizes total value for the firm.

Question 18

A company is evaluating two large, mutually exclusive expansion projects. Project Global involves expanding into a stable, mature international market and is considered to have below-average risk. Project Venture involves launching a new product in a highly volatile tech sector and is considered to have well-above-average risk. The company's overall weighted average cost of capital (WACC) is 12%.

  1. Both projects should be discounted at the 12% WACC to ensure a consistent basis for comparison.
  2. A higher discount rate should be used for Project Global and a lower rate for Project Venture.
  3. A discount rate lower than 12% should be used for Project Global, and a rate higher than 12% for Project Venture. (correct answer)
  4. Both projects should be discounted at the firm's cost of equity, as this best represents the risk to shareholders.
Explanation: The company's WACC of 12% reflects the average risk of all its existing projects. When evaluating new projects with risk profiles that differ significantly from this average, using the overall WACC can lead to poor decisions. A risk-adjusted discount rate should be used. For a project with below-average risk like Project Global, a discount rate lower than the WACC is appropriate. For a project with above-average risk like Project Venture, a discount rate higher than the WACC is appropriate. This ensures that the required rate of return for each project correctly reflects its systematic risk.

Question 19

Global Industries must choose between two production line investments. Line A costs $1.2 million and will save $350,000 annually in operating costs for 5 years. Line B costs $1.5 million and will save $280,000 annually for 8 years. Both have zero salvage value, and the company's WACC is 10%.

If Global Industries has a capital rationing constraint of $1.3 million and cannot obtain additional funding, what is the most appropriate decision rationale?

  1. Select Line A because its NPV of $127,860 exceeds the available budget constraint and provides positive returns
  2. Select Line B because its profitability index of 0.994 is closer to break-even, maximizing capital efficiency
  3. Reject both projects because neither can be funded within the capital constraint without considering partial implementation
  4. Select Line A because it falls within the budget constraint and generates positive NPV of $127,860 (correct answer)
Explanation: Line A costs $1.2M (within the $1.3M constraint) and has NPV = $350,000 × 3.7908 - $1,200,000 = $127,860. Line B costs $1.5M (exceeds constraint) and has NPV = $280,000 × 5.3349 - $1,500,000 = $93,772. Under capital rationing, only feasible projects can be selected. Choice A incorrectly states NPV exceeds budget (confusing NPV with cost). Choice B incorrectly calculates PI and suggests inefficient capital use is desirable. Choice C ignores that Line A is feasible within the constraint.

Question 20

Phoenix Electronics is evaluating four independent projects with the following characteristics: Project W (NPV: $180K, Investment: $800K), Project X (NPV: $240K, Investment: $1.2M), Project Y (NPV: $150K, Investment: $600K), Project Z (NPV: $200K, Investment: $900K). The company has $2.1 million available for investment. Which combination maximizes total NPV under the capital rationing constraint?

  1. Projects X and Y, providing total NPV of $390,000 with investment of $1.8 million within the constraint (correct answer)
  2. Projects W and Z, providing total NPV of $380,000 with investment of $1.7 million and remaining budget flexibility
  3. Projects Y and Z plus partial funding of W, maximizing capital utilization and achieving highest possible returns
  4. Projects W, Y, and partial funding of X, utilizing the full $2.1 million budget for maximum capital efficiency
Explanation: Under capital rationing, we must find the combination that maximizes NPV within the 2.1Mconstraint.Profitabilityindices:W=0.225,X=0.20,Y=0.25,Z=0.222.RankingbyPI:Y,W,Z,X.However,combinationsmustbeevaluated:W+Y=2.1M constraint. Profitability indices: W=0.225, X=0.20, Y=0.25, Z=0.222. Ranking by PI: Y, W, Z, X. However, combinations must be evaluated: W+Y=1.4M, NPV=330K;W+Z=330K; W+Z=1.7M, NPV=380K;X+Y=380K; X+Y=1.8M, NPV=390K;Y+Z=390K; Y+Z=1.5M, NPV=350K.ThecombinationX+YprovidesthehighesttotalNPV(350K. The combination X+Y provides the highest total NPV (390K) within the constraint. Choice B provides lower NPV. Choices C and D assume partial funding is possible, which isn't stated and is typically not feasible for capital projects.