Finance Quiz: Profitability Index
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Profitability IndexQuestion 1 of 20

Two mutually exclusive projects are being considered. Project L has a high initial cost and long-term, substantial cash flows. Project S has a low initial cost and short-term, moderate cash flows. An analyst correctly calculates that Project S has a PI of 1.8 while Project L has a PI of 1.4. In this situation, the primary weakness of using the profitability index for project selection is that it:

ignores the time value of money, which is critical for long-term projects like L.
may lead to selecting a smaller project with a lower NPV over a larger one with a higher NPV.
is more difficult to calculate than the net present value for projects with uneven cash flows.
fails to account for the recovery of the initial investment over the project's life.
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Finance Quiz: Profitability Index

Practice Profitability Index in 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 Finance.

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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

Two mutually exclusive projects are being considered. Project L has a high initial cost and long-term, substantial cash flows. Project S has a low initial cost and short-term, moderate cash flows. An analyst correctly calculates that Project S has a PI of 1.8 while Project L has a PI of 1.4. In this situation, the primary weakness of using the profitability index for project selection is that it:

  1. ignores the time value of money, which is critical for long-term projects like L.
  2. may lead to selecting a smaller project with a lower NPV over a larger one with a higher NPV. (correct answer)
  3. is more difficult to calculate than the net present value for projects with uneven cash flows.
  4. fails to account for the recovery of the initial investment over the project's life.
Explanation: This question describes the classic 'scale problem' of the profitability index. PI measures the relative profitability (value created per dollar invested), while NPV measures the absolute value created. For mutually exclusive projects, the goal is to maximize the total value added to the firm, which is measured by NPV. A smaller project (like S) can be very efficient and have a high PI, but a larger project (like L) could generate a much larger total NPV, even with a lower PI. Relying solely on PI could lead to the incorrect decision of choosing Project S, thereby forgoing the larger wealth creation from Project L. A is incorrect. The PI calculation is based on the present value of cash flows, so it explicitly incorporates the time value of money. C is incorrect. The difficulty of calculating the PV of cash flows is the same for both PI and NPV. Once the PV is found, the final calculation for both metrics is simple arithmetic. D is incorrect. PI, by its construction (comparing PV of inflows to the investment), implicitly accounts for the return of and a return on the investment.

Question 2

A financial analyst is comparing the profitability index (PI) and the net present value (NPV) methods of project evaluation. Which of the following statements is the most accurate description of the relationship between these two methods?

  1. For any single project, PI and NPV will always lead to the same accept/reject decision. (correct answer)
  2. When ranking mutually exclusive projects, PI is superior because it measures relative profitability.
  3. PI is generally preferred for all capital budgeting decisions because it is a ratio and easier to interpret.
  4. A project can have a positive NPV but a PI less than 1.0 if the discount rate is very high.
Explanation: For any single, independent project with conventional cash flows, the PI and NPV methods will always yield the same accept/reject decision. This is because the criteria are mathematically linked: If NPV > 0, then (PV of inflows - Investment) > 0, which implies PV of inflows > Investment, so (PV of inflows / Investment) > 1, meaning PI > 1 (Accept). If NPV < 0, then PI < 1 (Reject). If NPV = 0, then PI = 1 (Indifferent). Because of this direct link, they will never give conflicting signals for a single project's viability. B is incorrect. For ranking mutually exclusive projects, NPV is superior because it measures the total wealth created, while PI's focus on relative profitability can be misleading (the scale problem). C is incorrect. NPV is generally the preferred method, especially for mutually exclusive projects. PI's main advantage is in capital rationing scenarios. D is incorrect. It is mathematically impossible for a project to have a positive NPV and a PI less than 1.0.

Question 3

A project currently has a profitability index of 1.20, calculated using a discount rate of 10%. If the company's risk assessment of the project changes, leading to an increase in the discount rate to 13%, what will be the most likely impact on the project's PI and NPV?

  1. Both the PI and NPV will increase.
  2. Both the PI and NPV will decrease. (correct answer)
  3. The PI will decrease, but the NPV will increase.
  4. The impact cannot be determined without knowing the cash flow timing.
Explanation: An increase in the discount rate reduces the present value of future cash flows. The profitability index (PI) is calculated as (PV of future cash flows) / Initial Investment. Since the numerator (PV of future cash flows) decreases and the denominator (Initial Investment) remains unchanged, the PI will decrease. The Net Present Value (NPV) is calculated as PV of future cash flows - Initial Investment. Since the PV of future cash flows decreases, the NPV will also decrease. Therefore, both metrics will decrease. A is incorrect, as a higher discount rate penalizes future cash flows. C is incorrect because PI and NPV move in the same direction in response to discount rate changes for a conventional project. D is incorrect because while the magnitude of the change depends on the timing of cash flows, the direction of the change is certain: a higher discount rate will always lead to a lower PV of inflows, and thus a lower PI and NPV.

Question 4

An analyst is evaluating two mutually exclusive projects, Alpha and Beta. Project Alpha requires an initial investment of $100,000 and has a profitability index (PI) of 1.50. Project Beta requires an initial investment of $300,000 and has a PI of 1.30. Assuming no capital constraints, which project should be chosen and why?

  1. Project Alpha, because it has a higher profitability index, indicating greater efficiency.
  2. Project Beta, because it generates a higher net present value. (correct answer)
  3. Either project, as both have a PI greater than 1.0 and are therefore profitable.
  4. The project with the shorter payback period, as PI and NPV provide conflicting signals.
Explanation: When evaluating mutually exclusive projects, the project with the highest Net Present Value (NPV) should be chosen, as it adds the most absolute value to the firm. The Profitability Index (PI) can be misleading due to the 'scale problem'—it doesn't account for the magnitude of the initial investment. Let's calculate the NPV for each project: NPV = Initial Investment × (PI - 1) NPV_Alpha = $100,000 × (1.50 - 1) = $50,000 NPV_Beta = $300,000 × (1.30 - 1) = $90,000 Project Beta has a higher NPV (90,000)thanProjectAlpha(90,000) than Project Alpha (50,000). Therefore, Project Beta should be selected. A is incorrect because while Alpha is more 'efficient' per dollar invested, Beta creates more total wealth. C is incorrect because the mutually exclusive nature of the projects requires choosing the best one, not just any profitable one. D is incorrect because the payback period is an inferior metric that ignores the time value of money and cash flows beyond the payback point; NPV is the superior criterion for this decision.

Question 5

A project is considered acceptable if its profitability index (PI) is 1.15. This is equivalent to stating that the project is acceptable if its Net Present Value (NPV), calculated using the same discount rate and cash flows, is:

  1. equal to 1.15 times the discount rate.
  2. positive. (correct answer)
  3. greater than the initial investment.
  4. equal to 15% of the present value of inflows.
Explanation: There is a direct relationship between PI and NPV. PI = (PV of future cash flows) / Initial Investment. NPV = (PV of future cash flows) - Initial Investment. If the PI is 1.15, it means PI > 1.0. For this to be true, the PV of future cash flows must be greater than the initial investment. If the PV of inflows is greater than the initial investment (outflow), the NPV must be positive. Therefore, a PI > 1 (in this case, 1.15) is the equivalent acceptance criterion to NPV > 0. A is incorrect; there is no direct relationship between NPV and the discount rate in this manner. C is incorrect. The NPV could be positive but still far less than the initial investment. For example, if Investment=100andPVofinflows=100 and PV of inflows=115, PI=1.15 and NPV=$15. $15 is not greater than $100. D is incorrect. The NPV would be 15% of the initial investment (NPV = Initial Investment * (PI - 1) = I * (1.15 - 1) = 0.15 * I), not 15% of the present value of inflows.

Question 6

Two projects, East and West, have the same initial investment and the same total undiscounted cash inflows over their 5-year lives. Project East's cash flows are heavily weighted towards the later years, while Project West's cash flows are front-loaded. Assuming a positive discount rate, which project will most likely have the higher profitability index (PI)?

  1. Project East, because its larger later cash flows will grow to a larger future value.
  2. Project West, because its earlier cash flows will have a higher present value. (correct answer)
  3. The projects will have the same PI because their total cash inflows are identical.
  4. The PI cannot be determined without knowing the exact discount rate.
Explanation: The profitability index is calculated using the present value of future cash flows. Due to the time value of money, cash flows received earlier are worth more than identical cash flows received later. Project West has front-loaded cash flows, meaning more of its cash arrives in the early years. When discounted, these early cash flows will retain more of their value compared to the back-loaded cash flows of Project East. Therefore, the present value of Project West's cash flows will be higher than that of Project East. Since both projects have the same initial investment (denominator), the project with the higher PV of cash flows (numerator), which is Project West, will have the higher PI. A is incorrect because capital budgeting focuses on present value, not future value. C is incorrect as it ignores the time value of money. D is incorrect because while the exact PI values depend on the discount rate, the qualitative relationship (West > East) will hold for any positive discount rate.

Question 7

Project Atlas requires an initial outlay of $800,000 for equipment and an additional investment of $100,000 in net working capital (NWC) at t=0. The NWC will be fully recovered at the end of the project's 5-year life. The present value of the project's future operating cash inflows is $1,150,000. The present value of the NWC recovery is $62,092. What is the project's profitability index?

  1. 1.35 (correct answer)
  2. 1.28
  3. 1.44
  4. 1.21
Explanation: The profitability index is the ratio of the present value of all future cash inflows to the present value of all initial cash outflows. The numerator should include the PV of operating cash inflows and the PV of any terminal cash flows, like the recovery of NWC. Total PV of Inflows = PV(Operating CFs) + PV(NWC Recovery) = $1,150,000 + $62,092 = $1,212,092. The denominator should include all initial (t=0) cash outflows, which includes the equipment cost and the initial investment in NWC. Total Initial Investment = Equipment Cost + NWC Investment = $800,000 + $100,000 = $900,000. PI = Total PV of Inflows / Total Initial Investment = $1,212,092 / $900,000 = 1.3467 ≈ 1.35. B (1.28) incorrectly ignores the recovery of NWC in the numerator: $1,150,000 / $900,000 = 1.28. C (1.44) incorrectly ignores the initial NWC investment in the denominator: $1,150,000 / $800,000 = 1.44. D (1.21) is a combination of errors, possibly ignoring the initial NWC outlay but including the PV of recovery: ($1,150,000 + $62,092) / $1,000,000 (if they used the undiscounted NWC recovery in the denominator too, or some other error). Let's check another error: ignoring NWC altogether: $1,150,000 / 800,000=1.4375.AddingundiscountedNWCrecoverytonumerator:(800,000 = 1.4375. Adding undiscounted NWC recovery to numerator: (1,150,000 + $100,000) / $900,000 = 1.39. The distractors cover the most common mistakes.

Question 8

A project requires an initial investment of $150,000 and is expected to generate a single cash inflow of $250,000 at the end of 4 years. The firm's cost of capital is 10%. What is the project's profitability index?

  1. 1.67
  2. 1.14 (correct answer)
  3. 0.41
  4. 0.14
Explanation: First, calculate the present value (PV) of the future cash inflow. The formula for the PV of a single sum is CF/(1+r)nCF / (1+r)^n. PV = $250,000 / (1 + 0.10)^4 = $250,000 / 1.4641 = $170,753.36 Next, calculate the profitability index (PI) by dividing the PV of the inflow by the initial investment. PI = $170,753.36 / $150,000 = 1.138 ≈ 1.14 A (1.67) is the result of incorrectly dividing the undiscounted cash flow by the initial investment ($250,000 / $150,000), ignoring the time value of money. C (0.41) might result from an incorrect PV calculation, perhaps using n=10 instead of n=4. D (0.14) represents the project's NPV divided by the initial investment, not the PI itself: ($170,753 - $150,000) / $150,000 = 0.138 ≈ 0.14.

Question 9

The profitability index (PI) rule for independent projects states that a firm should accept all projects with a PI greater than 1.0. This decision rule is most likely to be consistent with maximizing shareholder wealth because a PI greater than 1.0 implies:

  1. the project's payback period is shorter than the company's target.
  2. the sum of the undiscounted cash flows exceeds the initial investment.
  3. the project's internal rate of return is positive.
  4. the present value of the project's future cash flows exceeds the initial cost. (correct answer)
Explanation: The profitability index is PI = (PV of future cash flows) / Initial Investment. If PI > 1.0, it mathematically means that the numerator (PV of future cash flows) must be greater than the denominator (Initial Investment). This is also the definition of a positive Net Present Value (NPV) project (NPV = PV of future cash flows - Initial Investment > 0). Projects with a positive NPV are expected to increase shareholder wealth. A is incorrect. PI and payback period are different metrics. A project with a PI > 1 can have a long payback period. B is incorrect. While likely true for profitable projects, this statement ignores the time value of money, which is the core concept of discounted cash flow analysis and the PI calculation. A project could have undiscounted cash flows greater than the investment but still have a PI < 1 if the cash flows occur far in the future. C is incorrect. A PI > 1 implies the IRR is greater than the discount rate used, not just that the IRR is positive. An IRR could be positive (e.g., 2%) but if the discount rate is 10%, the project would have a PI < 1 and would be rejected.

Question 10

A company is considering a project with an initial cost of $400,000. The project's internal rate of return (IRR) is calculated to be 15%, and the company's cost of capital is 12%. What can be concluded about the project's profitability index (PI)?

  1. The PI is equal to 1.15.
  2. The PI is equal to 1.0.
  3. The PI is less than 1.0.
  4. The PI is greater than 1.0. (correct answer)
Explanation: When you encounter questions linking IRR and profitability index (PI), remember that both are capital budgeting metrics that help evaluate project attractiveness, and there's a predictable relationship between them. The profitability index measures the ratio of the present value of future cash flows to the initial investment: PI=PV of future cash flowsInitial investmentPI = \frac{PV \text{ of future cash flows}}{Initial \text{ investment}}. When IRR exceeds the cost of capital, it means the project generates returns above what's required, making the present value of cash flows worth more than the initial investment. Since this project's IRR (15%) exceeds the cost of capital (12%), the present value of future cash flows must be greater than the $400,000 initial investment. This automatically means the PI is greater than 1.0, confirming answer D. Here's why the other options miss the mark: Option A (PI = 1.15) incorrectly assumes PI equals the IRR expressed as a ratio, but these are entirely different calculations. Option B (PI = 1.0) would only occur if IRR exactly equaled the cost of capital, creating a break-even scenario. Option C (PI < 1.0) would require the IRR to be below the cost of capital, indicating a value-destroying project. Remember this key relationship: when IRR > cost of capital, then PI > 1.0 and NPV > 0. These three metrics always align in their accept/reject signals. If you know one relationship, you can deduce the others without complex calculations.

Question 11

A mining project requires an initial investment of $2,000,000. It will generate positive cash flows for five years. However, at the end of the sixth year, the company must pay $500,000 in environmental cleanup costs. The present value of the positive operating cash flows (years 1-5) is $2,800,000. The present value of the cleanup cost in year 6 is $250,000. What is the project's profitability index?

  1. 1.275 (correct answer)
  2. 1.150
  3. 1.400
  4. 1.020
Explanation: The profitability index is the ratio of the present value of all future cash inflows to the present value of all cash outflows. A more general definition that works for non-conventional cash flows is PI = (PV of future cash flows) / Initial Investment. The numerator must include the PV of all future cash flows, both positive and negative. PV of future cash flows = PV of inflows - PV of outflows (occurring after t=0) PV of future cash flows = $2,800,000 - $250,000 = $2,550,000 Initial Investment = $2,000,000 PI = $2,550,000 / $2,000,000 = 1.275 B (1.150) results from incorrectly adding the cleanup cost to the denominator: 2,800,000/(2,800,000 / (2,000,000 + 250,000)=1.244,orsubtractingtheundiscountedcostfromthenumerator:(250,000) = 1.244, or subtracting the undiscounted cost from the numerator: (2.8M - 0.5M)/0.5M)/2M = 1.15. This is the correct distractor. C (1.400) is calculated by completely ignoring the future cleanup cost: $2,800,000 / $2,000,000 = 1.40. D (1.020) might result from a combination of errors, such as subtracting the undiscounted cleanup cost from the numerator and adding the PV of the cost to the denominator.

Question 12

A firm has a capital budget of $500,000. It is evaluating several independent projects. The CFO wants to use the profitability index to select the best group of projects. The analyst has prepared a list of projects ranked by their PI. Which of the following represents the most significant reason why simply selecting projects in descending order of PI until the budget is exhausted may not result in the optimal decision?

  1. This method ignores that projects may have different lifespans.
  2. The PI ranking does not consider the absolute dollar value of the NPV contributed by each project.
  3. Projects with high PIs might be riskier than projects with low PIs.
  4. This ranking method can result in a suboptimal combination of projects due to project indivisibility and budget constraints. (correct answer)
Explanation: While ranking by PI is the standard starting point for capital rationing, it is a heuristic. A 'greedy' algorithm of picking projects in descending order of PI is not guaranteed to be optimal. The primary reason is that projects have fixed sizes (they are indivisible). This can lead to a situation where the last project selected based on PI is too large for the remaining budget. A different combination of lower-PI projects might use the budget more completely and generate a higher total NPV. The truly optimal approach is to evaluate all feasible combinations of projects that fit the budget and select the combination with the highest total NPV. A is a general capital budgeting issue but not the specific flaw of the PI ranking method in a rationing context. B is related to the scale problem for mutually exclusive projects, but in a capital rationing scenario with independent projects, maximizing total NPV is the goal, and PI is a tool for that. The issue is how the ranking translates to the final selection. C is a valid point about risk, but the PI itself would have been calculated using a risk-adjusted discount rate. The flaw in the selection method itself is the main issue.

Question 13

A project has a profitability index (PI) of 0.85. The project's cash flows were discounted using the firm's weighted average cost of capital (WACC) of 10%. Which of the following statements is most accurate regarding this project?

  1. The project's internal rate of return (IRR) is greater than 10%.
  2. The project's net present value (NPV) is positive, but less than the initial investment.
  3. The present value of the project's future cash flows is less than the initial investment. (correct answer)
  4. The project should be accepted because it returns $0.85 for every dollar invested.
Explanation: The profitability index is calculated as PI = (PV of future cash flows) / Initial Investment. If the PI is 0.85, it means that (PV of future cash flows) / Initial Investment = 0.85. This directly implies that the present value of the future cash flows is only 85% of the initial investment, and thus is less than the initial investment. This indicates the project is expected to destroy value. A: A PI less than 1.0 implies that the project's NPV is negative. For a project with conventional cash flows, a negative NPV occurs when the discount rate (WACC) is greater than the IRR. Therefore, the IRR must be less than 10%. B: A PI less than 1.0 corresponds to a negative NPV. The project would destroy value. D: The statement is a misinterpretation of PI. A PI of 0.85 means the project returns only $0.85 in present value terms for every dollar invested, resulting in a loss of $0.15 per dollar invested. Therefore, the project should be rejected.

Question 14

A project has a profitability index (PI) of 0.85. The project's cash flows were discounted using the firm's weighted average cost of capital (WACC) of 10%. Which of the following statements is most accurate regarding this project?

  1. The project's internal rate of return (IRR) is greater than 10%.
  2. The project's net present value (NPV) is positive, but less than the initial investment.
  3. The present value of the project's future cash flows is less than the initial investment. (correct answer)
  4. The project should be accepted because it returns $0.85 for every dollar invested.
Explanation: The profitability index is calculated as PI = (PV of future cash flows) / Initial Investment. If the PI is 0.85, it means that (PV of future cash flows) / Initial Investment = 0.85. This directly implies that the present value of the future cash flows is only 85% of the initial investment, and thus is less than the initial investment. This indicates the project is expected to destroy value. A: A PI less than 1.0 implies that the project's NPV is negative. For a project with conventional cash flows, a negative NPV occurs when the discount rate (WACC) is greater than the IRR. Therefore, the IRR must be less than 10%. B: A PI less than 1.0 corresponds to a negative NPV. The project would destroy value. D: The statement is a misinterpretation of PI. A PI of 0.85 means the project returns only $0.85 in present value terms for every dollar invested, resulting in a loss of $0.15 per dollar invested. Therefore, the project should be rejected.

Question 15

A mining project requires an initial investment of $2,000,000. It will generate positive cash flows for five years. However, at the end of the sixth year, the company must pay $500,000 in environmental cleanup costs. The present value of the positive operating cash flows (years 1-5) is $2,800,000. The present value of the cleanup cost in year 6 is $250,000. What is the project's profitability index?

  1. 1.275 (correct answer)
  2. 1.150
  3. 1.400
  4. 1.020
Explanation: The profitability index is the ratio of the present value of all future cash inflows to the present value of all cash outflows. A more general definition that works for non-conventional cash flows is PI = (PV of future cash flows) / Initial Investment. The numerator must include the PV of all future cash flows, both positive and negative. PV of future cash flows = PV of inflows - PV of outflows (occurring after t=0) PV of future cash flows = $2,800,000 - $250,000 = $2,550,000 Initial Investment = $2,000,000 PI = $2,550,000 / $2,000,000 = 1.275 B (1.150) results from incorrectly adding the cleanup cost to the denominator: 2,800,000/(2,800,000 / (2,000,000 + 250,000)=1.244,orsubtractingtheundiscountedcostfromthenumerator:(250,000) = 1.244, or subtracting the undiscounted cost from the numerator: (2.8M - 0.5M)/0.5M)/2M = 1.15. This is the correct distractor. C (1.400) is calculated by completely ignoring the future cleanup cost: $2,800,000 / $2,000,000 = 1.40. D (1.020) might result from a combination of errors, such as subtracting the undiscounted cleanup cost from the numerator and adding the PV of the cost to the denominator.

Question 16

A project currently has a profitability index of 1.20, calculated using a discount rate of 10%. If the company's risk assessment of the project changes, leading to an increase in the discount rate to 13%, what will be the most likely impact on the project's PI and NPV?

  1. Both the PI and NPV will increase.
  2. Both the PI and NPV will decrease. (correct answer)
  3. The PI will decrease, but the NPV will increase.
  4. The impact cannot be determined without knowing the cash flow timing.
Explanation: An increase in the discount rate reduces the present value of future cash flows. The profitability index (PI) is calculated as (PV of future cash flows) / Initial Investment. Since the numerator (PV of future cash flows) decreases and the denominator (Initial Investment) remains unchanged, the PI will decrease. The Net Present Value (NPV) is calculated as PV of future cash flows - Initial Investment. Since the PV of future cash flows decreases, the NPV will also decrease. Therefore, both metrics will decrease. A is incorrect, as a higher discount rate penalizes future cash flows. C is incorrect because PI and NPV move in the same direction in response to discount rate changes for a conventional project. D is incorrect because while the magnitude of the change depends on the timing of cash flows, the direction of the change is certain: a higher discount rate will always lead to a lower PV of inflows, and thus a lower PI and NPV.

Question 17

Two mutually exclusive projects are being considered. Project L has a high initial cost and long-term, substantial cash flows. Project S has a low initial cost and short-term, moderate cash flows. An analyst correctly calculates that Project S has a PI of 1.8 while Project L has a PI of 1.4. In this situation, the primary weakness of using the profitability index for project selection is that it:

  1. ignores the time value of money, which is critical for long-term projects like L.
  2. may lead to selecting a smaller project with a lower NPV over a larger one with a higher NPV. (correct answer)
  3. is more difficult to calculate than the net present value for projects with uneven cash flows.
  4. fails to account for the recovery of the initial investment over the project's life.
Explanation: This question describes the classic 'scale problem' of the profitability index. PI measures the relative profitability (value created per dollar invested), while NPV measures the absolute value created. For mutually exclusive projects, the goal is to maximize the total value added to the firm, which is measured by NPV. A smaller project (like S) can be very efficient and have a high PI, but a larger project (like L) could generate a much larger total NPV, even with a lower PI. Relying solely on PI could lead to the incorrect decision of choosing Project S, thereby forgoing the larger wealth creation from Project L. A is incorrect. The PI calculation is based on the present value of cash flows, so it explicitly incorporates the time value of money. C is incorrect. The difficulty of calculating the PV of cash flows is the same for both PI and NPV. Once the PV is found, the final calculation for both metrics is simple arithmetic. D is incorrect. PI, by its construction (comparing PV of inflows to the investment), implicitly accounts for the return of and a return on the investment.

Question 18

A project requires an initial investment of $150,000 and is expected to generate a single cash inflow of $250,000 at the end of 4 years. The firm's cost of capital is 10%. What is the project's profitability index?

  1. 1.67
  2. 1.14 (correct answer)
  3. 0.41
  4. 0.14
Explanation: First, calculate the present value (PV) of the future cash inflow. The formula for the PV of a single sum is CF/(1+r)nCF / (1+r)^n. PV = $250,000 / (1 + 0.10)^4 = $250,000 / 1.4641 = $170,753.36 Next, calculate the profitability index (PI) by dividing the PV of the inflow by the initial investment. PI = $170,753.36 / $150,000 = 1.138 ≈ 1.14 A (1.67) is the result of incorrectly dividing the undiscounted cash flow by the initial investment ($250,000 / $150,000), ignoring the time value of money. C (0.41) might result from an incorrect PV calculation, perhaps using n=10 instead of n=4. D (0.14) represents the project's NPV divided by the initial investment, not the PI itself: ($170,753 - $150,000) / $150,000 = 0.138 ≈ 0.14.

Question 19

Project Atlas requires an initial outlay of $800,000 for equipment and an additional investment of $100,000 in net working capital (NWC) at t=0. The NWC will be fully recovered at the end of the project's 5-year life. The present value of the project's future operating cash inflows is $1,150,000. The present value of the NWC recovery is $62,092. What is the project's profitability index?

  1. 1.35 (correct answer)
  2. 1.28
  3. 1.44
  4. 1.21
Explanation: The profitability index is the ratio of the present value of all future cash inflows to the present value of all initial cash outflows. The numerator should include the PV of operating cash inflows and the PV of any terminal cash flows, like the recovery of NWC. Total PV of Inflows = PV(Operating CFs) + PV(NWC Recovery) = $1,150,000 + $62,092 = $1,212,092. The denominator should include all initial (t=0) cash outflows, which includes the equipment cost and the initial investment in NWC. Total Initial Investment = Equipment Cost + NWC Investment = $800,000 + $100,000 = $900,000. PI = Total PV of Inflows / Total Initial Investment = $1,212,092 / $900,000 = 1.3467 ≈ 1.35. B (1.28) incorrectly ignores the recovery of NWC in the numerator: $1,150,000 / $900,000 = 1.28. C (1.44) incorrectly ignores the initial NWC investment in the denominator: $1,150,000 / $800,000 = 1.44. D (1.21) is a combination of errors, possibly ignoring the initial NWC outlay but including the PV of recovery: ($1,150,000 + $62,092) / $1,000,000 (if they used the undiscounted NWC recovery in the denominator too, or some other error). Let's check another error: ignoring NWC altogether: $1,150,000 / 800,000=1.4375.AddingundiscountedNWCrecoverytonumerator:(800,000 = 1.4375. Adding undiscounted NWC recovery to numerator: (1,150,000 + $100,000) / $900,000 = 1.39. The distractors cover the most common mistakes.

Question 20

Two projects, East and West, have the same initial investment and the same total undiscounted cash inflows over their 5-year lives. Project East's cash flows are heavily weighted towards the later years, while Project West's cash flows are front-loaded. Assuming a positive discount rate, which project will most likely have the higher profitability index (PI)?

  1. Project East, because its larger later cash flows will grow to a larger future value.
  2. Project West, because its earlier cash flows will have a higher present value. (correct answer)
  3. The projects will have the same PI because their total cash inflows are identical.
  4. The PI cannot be determined without knowing the exact discount rate.
Explanation: The profitability index is calculated using the present value of future cash flows. Due to the time value of money, cash flows received earlier are worth more than identical cash flows received later. Project West has front-loaded cash flows, meaning more of its cash arrives in the early years. When discounted, these early cash flows will retain more of their value compared to the back-loaded cash flows of Project East. Therefore, the present value of Project West's cash flows will be higher than that of Project East. Since both projects have the same initial investment (denominator), the project with the higher PV of cash flows (numerator), which is Project West, will have the higher PI. A is incorrect because capital budgeting focuses on present value, not future value. C is incorrect as it ignores the time value of money. D is incorrect because while the exact PI values depend on the discount rate, the qualitative relationship (West > East) will hold for any positive discount rate.