Corporate Finance Quiz: Profitability Index
20 questions · exam conditions
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Profitability IndexQuestion 1 of 20

A project with a 5-year life has constant annual cash inflows. Its initial cost is $150,000, and its internal rate of return (IRR) is 15%. If the company's cost of capital is 10%, what is the project's profitability index?

1.05
1.13
1.15
1.50
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Corporate Finance Quiz

Corporate Finance Quiz: Profitability Index

Practice Profitability Index in Corporate Finance 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 Profitability Index, giving you a quick way to practice the rules, question types, and explanations that matter most for Corporate Finance.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A project with a 5-year life has constant annual cash inflows. Its initial cost is $150,000, and its internal rate of return (IRR) is 15%. If the company's cost of capital is 10%, what is the project's profitability index?

  1. 1.05
  2. 1.13 (correct answer)
  3. 1.15
  4. 1.50
Explanation: This is a multi-step problem. First, use the IRR of 15% to find the annual cash inflow (CF). At the IRR, NPV=0, so the PV of inflows equals the initial cost. $150,000 = CF × PVIFA(15%, 5). The PVIFA factor is 3.3522. So, CF = $150,000 / 3.3522 = $44,747. Second, calculate the PV of these cash flows using the 10% cost of capital. PV = $44,747 × PVIFA(10%, 5). The PVIFA factor is 3.7908. So, PV = $44,747 × 3.7908 = $169,622. Finally, calculate the PI = PV of inflows / Initial Cost = $169,622 / $150,000 ≈ 1.13.

Question 2

A company is purchasing equipment for $300,000. The equipment will generate annual after-tax operating cash flows of $90,000 for four years. At the end of the fourth year, the equipment can be salvaged for an after-tax value of $50,000. If the discount rate is 11%, what is the profitability index?

  1. 0.93
  2. 1.04 (correct answer)
  3. 1.10
  4. 1.37
Explanation: The numerator of the PI is the present value (PV) of all future cash inflows. This includes both the operating cash flows and the terminal salvage value. PV of operating CFs (annuity) = $90,000 × PVIFA(11%, 4) = $90,000 × 3.1024 = $279,216. PV of salvage value (lump sum) = $50,000 / (1.11)⁴ = $50,000 / 1.5181 = $32,936. Total PV of inflows = $279,216 + $32,936 = $312,152. PI = Total PV / Initial Investment = $312,152 / $300,000 ≈ 1.04.

Question 3

A firm is evaluating two mutually exclusive projects. Project Alpha requires a $100,000 investment and has an NPV of $20,000. Project Beta requires a $500,000 investment and has an NPV of $60,000. The company is not subject to capital rationing. Which project should be selected and why?

  1. Project Beta, because it adds more total value to the firm. (correct answer)
  2. Project Alpha, because it has a higher profitability index.
  3. Project Alpha, because it is less risky due to the smaller investment.
  4. Either project is acceptable, as both have a PI greater than 1.0.
Explanation: When evaluating mutually exclusive projects without capital rationing constraints, you need to focus on which project creates the most absolute value for shareholders, not which is most efficient per dollar invested. Project Alpha generates an NPV of $20,000, while Project Beta generates an NPV of $60,000. Since both projects have positive NPVs, both are value-creating, but Project Beta adds $40,000 more value to the firm. Without capital constraints limiting your ability to fund the larger project, you should choose the one that maximizes total shareholder wealth. Looking at the incorrect answers: Option B incorrectly applies the profitability index (PI) decision rule. While Project Alpha does have a higher PI ($120,000100,000=1.20\frac{120,000}{100,000} = 1.20 vs.vs. 560,000500,000=1.12\frac{560,000}{500,000} = 1.12 $), the PI is only preferred when you face capital rationing and need to rank projects by efficiency. Here, you can fund either project fully. Option C introduces risk as a factor, but the question provides no risk information—you must assume equal risk levels when not told otherwise. Option D misses the point entirely; while both projects are acceptable individually, you must choose between them since they're mutually exclusive. The correct answer is A: Project Beta should be selected because it adds more total value to the firm. Study tip: Remember that NPV trumps PI when capital rationing isn't a constraint. Always choose the project with the highest absolute NPV for mutually exclusive decisions, regardless of investment size differences.

Question 4

Project Y has an initial cost of $400,000 and is expected to produce a single cash inflow of $450,000 in one year. The project's profitability index is 1.05. What is the approximate discount rate used to evaluate this project?

  1. 5.00%
  2. 7.14% (correct answer)
  3. 10.50%
  4. 12.50%
Explanation: First, find the present value (PV) of the future cash flows using the PI formula: PI = PV of inflows / Initial Investment. So, 1.05 = PV / $400,000, which means PV = 1.05 × $400,000 = $420,000. Next, use the present value formula to find the discount rate (r): PV = CF₁ / (1 + r). We have $420,000 = $450,000 / (1 + r). Rearranging gives 1 + r = $450,000 / $420,000 = 1.0714. Therefore, r = 0.0714 or 7.14%.

Question 5

A project requires an initial investment of $1,000. It generates cash inflows of $800 in Year 1 and $900 in Year 3. However, it requires a cash outflow of $200 for remediation in Year 2. The cost of capital is 8%. What is the project's profitability index, rounded to two decimal places?

  1. 1.21
  2. 1.28 (correct answer)
  3. 1.50
  4. 1.63
Explanation: The profitability index is the present value (PV) of all future cash flows divided by the initial investment. We must discount each future cash flow to time 0. PV = [CF₁ / (1+r)¹] + [CF₂ / (1+r)²] + [CF₃ / (1+r)³] PV = [800/(1.08)1]+[−800 / (1.08)¹] + [-200 / (1.08)²] + [$900 / (1.08)³] PV = $740.74 - $171.47 + $714.46 = $1,283.73 PI = PV of future cash flows / Initial Investment = $1,283.73 / $1,000 = 1.28.

Question 6

Two mutually exclusive projects, Titan and Saturn, have the following characteristics:

  • Project Titan: Investment = $1M, NPV = $200k
  • Project Saturn: Investment = $4M, NPV = $500k

A junior analyst recommends Project Titan because it has a higher profitability index. What is the most significant flaw in the analyst's reasoning?

  1. The analyst ignored the projects' internal rates of return.
  2. The PI rule should not be used when NPV is positive for both projects.
  3. For mutually exclusive projects, the one with the higher NPV should be chosen. (correct answer)
  4. The PI calculation may be inaccurate if the projects have different lifespans.
Explanation: The primary decision rule for mutually exclusive projects, assuming no capital rationing, is to choose the project that maximizes firm value, which is the one with the highest NPV. Project Saturn's NPV (500k)isgreaterthanTitan′s(500k) is greater than Titan's (200k). While Titan has a higher PI (1.20 vs. 1.125), the PI's focus on relative return can lead to selecting a smaller scale project that adds less absolute value to the firm. Thus, the flaw is using PI instead of NPV to rank mutually exclusive projects.

Question 7

When using the profitability index to rank projects under capital rationing, what is the implicit assumption about the reinvestment of intermediate cash flows?

  1. The cash flows can be reinvested at the company's cost of capital. (correct answer)
  2. The cash flows can be reinvested at the project's internal rate of return.
  3. The cash flows cannot be reinvested until the project's conclusion.
  4. The cash flows can be reinvested at the project-specific hurdle rate.
Explanation: When you encounter questions about profitability index (PI) and reinvestment assumptions, you're dealing with a fundamental aspect of discounted cash flow analysis. The profitability index calculates the present value of future cash flows divided by the initial investment, and like NPV, it relies on specific assumptions about what happens to cash flows received during the project's life. The profitability index implicitly assumes that any intermediate cash flows from the project can be reinvested at the company's cost of capital (the discount rate used in the PI calculation). This assumption is built into the present value formula itself - when you discount future cash flows back to today using the cost of capital, you're assuming that money received earlier could earn that same rate if invested elsewhere. Looking at the incorrect options: Choice B suggests reinvestment at the project's IRR, but this creates a circular logic problem since the PI calculation uses the cost of capital, not the IRR. Choice C assumes no reinvestment opportunity, which contradicts the time value of money principle underlying all discounted cash flow methods. Choice D mentions a "project-specific hurdle rate," but the PI formula standardly uses the company's overall cost of capital as the discount rate. The correct answer is A because the PI methodology inherently assumes intermediate cash flows earn the cost of capital rate used in the discounting process. Study tip: Remember that NPV, PI, and other DCF methods all share this same reinvestment assumption - they use the cost of capital as both the discount rate and the implied reinvestment rate.

Question 8

A firm is considering a project with the following cash flows:

  • Year 0: -$50,000
  • Year 1: +$100,000
  • Year 2: -$40,000

When calculating the profitability index for this project using the standard introductory definition, what value should be used in the denominator?

  1. $10,000
  2. $50,000 (correct answer)
  3. $81,888
  4. $90,000
Explanation: The standard definition of the profitability index is the present value of all future cash flows divided by the initial investment at time 0. Even though there is another outflow in Year 2, the denominator for the standard PI calculation is strictly the initial outlay required to start the project, which is $50,000. The Year 2 outflow is included (as a negative value) in the numerator when calculating the present value of future cash flows.

Question 9

A manager is comparing two independent projects:

  • Project Short: 2-year life, PI = 1.35
  • Project Long: 8-year life, PI = 1.30

Assuming the company is under a single-period capital constraint and the projects require similar initial investments, which of the following is the most justifiable action?

  1. Prioritize Project Long because its total NPV is likely to be higher.
  2. Calculate the Equivalent Annual Annuity (EAA) for both projects.
  3. Prioritize Project Short because it generates more value per dollar of investment. (correct answer)
  4. Choose Project Short because cash flows are returned more quickly.
Explanation: When facing a single-period capital constraint, the objective is to maximize the value generated from the limited funds available in that period. The profitability index (PI) directly measures this by indicating the present value of future cash flows per dollar of initial investment. A higher PI signifies greater capital efficiency. Therefore, Project Short should be prioritized over Project Long because its higher PI (1.35 > 1.30) indicates it creates more value for each dollar invested.

Question 10

A company with a 12% cost of capital analyzes two independent projects:

  • Project X: Cost = $60k, PV of inflows = $75k
  • Project Y: Cost = $100k, NPV = $20k

Based on the profitability index (PI) for each project, which statement is correct?

  1. The PI of Project X is 1.25, and the PI of Project Y is 1.20. (correct answer)
  2. The PI of Project X is 1.20, and the PI of Project Y is 1.25.
  3. The PI of Project X is 0.80, and the PI of Project Y is 0.83.
  4. The PI of Project X is 1.25, but the PI of Project Y cannot be determined.
Explanation: When you encounter profitability index questions, remember that PI measures how much value each dollar of investment generates. The formula is: PI=PV of Cash InflowsInitial InvestmentPI = \frac{\text{PV of Cash Inflows}}{\text{Initial Investment}} For Project X, you're given the cost (60k)andPVofinflows(60k) and PV of inflows (75k) directly. Calculate: PIX=75,00060,000=1.25PI_X = \frac{75,000}{60,000} = 1.25 For Project Y, you need to work backwards from the NPV. Since NPV = PV of inflows - Initial investment, and you know NPV = $20k and cost = $100k: PV of inflows = $20k + $100k = $120k. Therefore: $PIY=120,000100,000=1.20PI_Y = \frac{120,000}{100,000} = 1.20 $ Choice A correctly identifies PI of Project X as 1.25 and Project Y as 1.20. Choice B reverses these values, likely from mixing up the projects or miscalculating. Choice C shows values below 1.0 (0.80 and 0.83), which would indicate value-destroying projects—this happens when students incorrectly flip the PI formula or use NPV instead of PV of inflows in the numerator. Choice D suggests Project Y's PI cannot be determined, but you can always calculate PI when you have both NPV and initial investment. Study tip: Always remember that PI above 1.0 indicates value creation (positive NPV), while PI below 1.0 indicates value destruction. When given NPV instead of PV of inflows, simply add the initial investment to NPV to find the PV of inflows needed for the PI calculation.

Question 11

A company has a capital budget of $500,000 and is considering four independent projects with the following characteristics:

  • Project A: Investment $200,000, NPV $40,000
  • Project B: Investment $300,000, NPV $54,000
  • Project C: Investment $150,000, NPV $33,000
  • Project D: Investment $250,000, NPV $45,000

Using the profitability index approach to capital rationing, which set of projects should the company undertake?

  1. Projects A and B
  2. Project C and D
  3. Projects B and C
  4. Projects A and C (correct answer)
Explanation: When you encounter capital rationing problems with multiple projects, the profitability index (PI) is your best tool for maximizing value within budget constraints. The profitability index equals NPV divided by initial investment, showing how much value each dollar invested generates. Let's calculate each project's PI: Project A: $40,000 ÷ $200,000 = 0.20; Project B: $54,000 ÷ $300,000 = 0.18; Project C: $33,000 ÷ $150,000 = 0.22; Project D: $45,000 ÷ $250,000 = 0.18. Ranking by PI: Project C (0.22), Project A (0.20), then Projects B and D (both 0.18). With a $500,000 budget, you select the highest-PI projects that fit. Projects A and C require $200,000 + $150,000 = $350,000, well within budget, generating total NPV of $73,000. Option A (Projects A and B) costs $500,000 exactly but generates only $94,000 NPV. While this seems attractive due to higher absolute NPV, it's less efficient—you're leaving no room for additional opportunities. Option B (Projects C and D) costs $400,000 and generates $78,000 NPV. This beats our answer in absolute terms but ignores that we could add Project A for even more value. Option C (Projects B and C) costs $450,000 and generates $87,000 NPV, but again misses the optimal combination. Remember: under capital rationing, maximize NPV per dollar invested first, then check if your budget allows additional profitable projects. Don't just chase the highest absolute NPV—efficiency matters when capital is constrained.

Question 12

A project requires an initial investment of $80,000. Its profitability index is 1.25. The project's cash flows are an annuity lasting for 6 years, and the discount rate is 9%. What is the annual cash inflow from the project?

  1. $17,825
  2. $20,000
  3. $22,293 (correct answer)
  4. $25,000
Explanation: First, use the PI to find the total present value (PV) of the future cash inflows. PI = PV / Initial Investment => 1.25 = PV / $80,000. Solving for PV gives PV = 1.25 × $80,000 = $100,000. Second, this $100,000 PV is the present value of a 6-year annuity. We need to find the annual payment (CF). PV = CF × PVIFA(9%, 6). The PVIFA factor is 4.4859. So, $100,000 = CF × 4.4859. Solving for CF gives CF = $100,000 / 4.4859 = $22,292.56, or approximately $22,293.

Question 13

The profitability index is most accurately described as a measure of a project's:

  1. absolute increase in shareholder wealth, similar to net present value.
  2. time to recoup the initial investment, discounted for the cost of capital.
  3. safety margin, indicating how much IRR exceeds the cost of capital.
  4. relative profitability, indicating the value generated per unit of investment. (correct answer)
Explanation: The profitability index is a ratio (PV of future cash flows / Initial Investment). It provides a measure of relative profitability, often referred to as the 'bang for the buck.' It quantifies how much value (in present value terms) is created for each dollar invested. This makes it a measure of capital efficiency, not absolute value (like NPV), time to breakeven (like payback period), or a direct margin of safety for the discount rate.

Question 14

A conventional project has an internal rate of return (IRR) of 20%. The project's profitability index is currently calculated as 1.25 using a discount rate of 12%. If the firm's cost of capital increases to 15%, what will be the effect on the project's PI?

  1. It will increase.
  2. It will decrease and become less than 1.0.
  3. It will decrease but remain greater than 1.0. (correct answer)
  4. It will remain unchanged.
Explanation: An increase in the discount rate will decrease the present value of a project's future cash inflows. Since the PI's numerator (PV of inflows) decreases while its denominator (initial investment) stays the same, the PI will decrease. However, since the new discount rate (15%) is still below the IRR (20%), the project's NPV will remain positive. A positive NPV always corresponds to a PI greater than 1.0. Therefore, the PI will decrease but remain greater than 1.0.

Question 15

A project requires an initial outlay of $250,000. It is expected to generate after-tax cash inflows of $100,000 per year for 3 years. The company's cost of capital is 10%. What is the project's profitability index, rounded to two decimal places?

  1. 0.99 (correct answer)
  2. 1.01
  3. 1.20
  4. -0.01
Explanation: First, calculate the present value (PV) of the future cash inflows. This is a 3-year annuity of $100,000 at a 10% discount rate. PV = $100,000 × [1 - (1 + 0.10)⁻³] / 0.10 = $100,000 × 2.48685 = $248,685. The Profitability Index (PI) is the PV of future cash flows divided by the initial investment. PI = $248,685 / $250,000 = 0.9947, which rounds to 0.99.

Question 16

A project has a PI of 1.08 and an initial cost of $500,000. If an analyst mistakenly excluded a one-time, after-tax cash outflow of $50,000 occurring at the end of the final year from the original calculation, what is the project's correct PI? Assume a discount rate of 10% and a 5-year project life.

  1. 0.98
  2. 1.02 (correct answer)
  3. 1.06
  4. 1.18
Explanation: First, find the originally calculated PV of inflows: PV_orig = PI_orig × I₀ = 1.08 × $500,000 = $540,000. Second, find the PV of the omitted cash outflow: PV_outflow = $50,000 / (1.10)⁵ = $50,000 / 1.61051 = $31,046. Third, calculate the correct total PV of future cash flows by subtracting the PV of the outflow: PV_correct = $540,000 - $31,046 = $508,954. Finally, calculate the correct PI: PI_correct = PV_correct / I₀ = $508,954 / $500,000 ≈ 1.02.

Question 17

Consider three projects with the following characteristics: Project X has PI = 1.25 and NPV = $50,000; Project Y has PI = 1.18 and NPV = $90,000; Project Z has PI = 1.33 and NPV = $40,000. If the company faces capital rationing and can only select one project, which selection criterion provides the most appropriate guidance?

  1. Select Project Z because it has the highest profitability index, indicating the best return per dollar invested under capital constraints
  2. Select Project Y because NPV maximization should always take precedence over PI when projects are mutually exclusive due to capital rationing
  3. Select Project X because it offers the optimal balance between PI and NPV, avoiding the extremes of the other projects
  4. The selection depends on the severity of capital rationing and whether projects can be scaled or divided to optimize total portfolio NPV (correct answer)
Explanation: Under capital rationing, the optimal choice depends on the specific constraints and project characteristics. If capital is severely limited, PI helps identify efficiency per dollar invested, favoring Project Z. If the constraint is less binding and projects are indivisible, NPV maximization might favor Project Y. The ability to scale projects or combine partial investments affects the analysis. Choice A oversimplifies by always preferring highest PI. Choice B oversimplifies by always preferring highest NPV. Choice C provides no analytical basis for the 'balance' approach.

Question 18

A project has a profitability index of 1.12 when evaluated using a 10% discount rate. If inflation expectations increase, causing the discount rate to rise to 12%, and the project's cash flows are fully inflation-protected (indexed), what happens to the PI?

  1. PI increases because inflation-protected cash flows grow faster than the discount rate adjustment, improving the present value ratio
  2. PI decreases because higher nominal discount rates reduce present values more than proportional increases in nominal cash flows can offset
  3. PI decreases initially but returns to original levels as inflation-indexed cash flows compound over the project life
  4. PI remains unchanged because inflation affects both cash flows and discount rates proportionally, leaving real returns constant (correct answer)
Explanation: When analyzing profitability index under changing inflation conditions, you need to understand how inflation affects both the numerator (present value of cash flows) and denominator (initial investment) of the PI calculation. The profitability index is calculated as PI=PV of Cash FlowsInitialInvestmentPI = \frac{PV \text{ of Cash Flows}}{Initial Investment}. When inflation expectations rise from 10% to 12%, two things happen simultaneously: the discount rate increases, but the project's cash flows are fully inflation-indexed, meaning they increase by exactly the same inflation rate. Answer D is correct because inflation affects both sides of the equation proportionally. While the higher discount rate (12% vs 10%) reduces the present value calculation, the cash flows increase by the same inflation differential, creating an offsetting effect. The real return remains constant because you're essentially converting between nominal and real terms on both sides of the equation. Answer A incorrectly suggests inflation-protected cash flows grow faster than the discount rate adjustment. In reality, they grow at exactly the same rate as the inflation component of the discount rate increase. Answer B makes the common error of considering only the discount rate effect while ignoring that indexed cash flows also increase proportionally with inflation. Answer C incorrectly implies some kind of timing effect where the PI would fluctuate and then stabilize, but with full inflation indexing, the proportional relationship remains constant throughout. Remember: When cash flows are fully inflation-indexed, changes in inflation expectations affect nominal values but leave real economic relationships unchanged. Always consider both sides of valuation ratios when inflation changes.

Question 19

Company ABC is comparing two divisional projects using profitability index. Division 1's project has PI = 1.18 using a 9% divisional cost of capital, while Division 2's project has PI = 1.24 using a 13% divisional cost of capital. Both projects require $500,000 initial investment. Which statement best describes the appropriate comparison methodology?

  1. Both projects should be accepted if capital is available, but direct PI comparison is inappropriate due to different risk-adjusted discount rates (correct answer)
  2. Division 1's project is superior because lower-risk divisions should be preferred when PI values are both above 1.0 in portfolio optimization
  3. Division 2's project is superior because its higher PI indicates better risk-adjusted performance despite the higher required return
  4. The projects should be re-evaluated using the company's overall WACC to enable meaningful PI comparison across divisions
Explanation: When evaluating projects across different divisions using profitability index, you must recognize that divisions often have different risk profiles requiring different discount rates. This creates a fundamental comparison challenge that goes beyond simple PI calculations. Answer A is correct because both projects create value (PI > 1.0) and should be accepted if capital permits, but their PIs cannot be directly compared. Division 1's PI of 1.18 reflects a 9% risk-adjusted rate, while Division 2's PI of 1.24 uses a 13% rate. These different denominators make direct comparison meaningless - it's like comparing ratios with different bases. Answer B incorrectly assumes lower-risk divisions are automatically preferred in portfolio optimization. Risk preference depends on the company's overall strategy and risk tolerance, not a blanket preference for lower-risk projects. Answer C makes the critical error of treating higher PI as definitively better performance. While Division 2's 1.24 PI is numerically higher, this doesn't account for the fact that it required a much higher hurdle rate (13% vs 9%) to achieve this return, making the comparison invalid. Answer D suggests using company-wide WACC, but this would actually destroy value by applying inappropriate discount rates. Each division's cost of capital reflects its specific risk profile - using a single rate would either overstate low-risk division returns or understate high-risk division returns. Study tip: Remember that profitability index comparisons are only valid when using the same discount rate. When divisions have different risk profiles requiring different rates, focus on whether each project individually creates value (PI > 1.0) rather than direct numerical comparison.

Question 20

TechCorp is evaluating a new product line that requires $2 million in initial investment. The project is expected to generate cash flows of $600,000 annually for 5 years. However, due to rapid technological change in the industry, there is a 30% probability that the project will become obsolete after 3 years, in which case the remaining cash flows would be zero and equipment could be sold for $300,000.

Using a 12% discount rate, what is the profitability index for this project incorporating the abandonment option?

  1. 0.97, indicating the project should be rejected due to technological risk overwhelming the base case returns
  2. 1.02, indicating marginal acceptability when the abandonment value partially offsets the obsolescence risk (correct answer)
  3. 1.08, indicating clear acceptance because the expected value approach adequately captures the risk-return trade-off
  4. 0.94, indicating rejection because the probability-weighted cash flows fail to compensate for the systematic risk premium
Explanation: Calculate expected cash flows: Years 1-3 certain = $600,000 each. Years 4-5 have 70% probability = $420,000 expected each. Abandonment value in year 3 has 30% probability = $90,000 expected. Present values at 12%: PV(Years 1-3) = $600,000 × 2.4018 = $1,441,080. PV(Years 4-5) = $420,000 × (0.6355 + 0.5674) = $505,218. PV(abandonment) = $90,000 × 0.7118 = $64,062. Total PV = $2,010,360. PI = $2,010,360 ÷ $2,000,000 = 1.005, which rounds to 1.02.