Skip to main content
Sign in Create a free account
Varsity Tutors
Sign in

Profitability Index - Corporate Finance

  1. 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?
    Answer: Both projects should be accepted if capital is available, but direct PI comparison is inappropriate due to different risk-adjusted discount rates 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.
  2. 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?
    Answer: Prioritize Project Short because it generates more value per dollar of investment. 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.
  3. A financial analyst determines that a proposed project has a profitability index of 0.95. Which of the following statements is the most accurate conclusion based on this finding?
    Answer: The present value of the project's future cash flows is less than its initial cost. A profitability index (PI) less than 1.0 indicates that the present value (PV) of the project's future cash flows is less than the initial investment. This also implies that the project's net present value (NPV = PV of inflows - Investment) is negative. A negative NPV project should be rejected as it is expected to destroy firm value.
  4. 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?
    Answer: $22,293 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.
  5. 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?
    Answer: Project Beta, because it adds more total value to the firm. 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. 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.
  6. 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?
    Answer: 7.14% 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%.
  7. A project's profitability index is 1.10. Which of the following statements is a correct interpretation of this value?
    Answer: The present value of the project's future cash flows is 110% of the initial investment. The profitability index is defined as PI = (PV of future cash flows) / (Initial Investment). A PI of 1.10 means that the PV of future cash flows is 1.10 times, or 110% of, the initial investment. This also means that for every dollar invested, the project creates $0.10 in net present value (NPV = PV - Investment = 1.10 - 1.00 = 0.10). Choice C is the most direct and accurate interpretation of the ratio itself.
  8. A company calculates a profitability index of 1.15 for a 4-year project using quarterly cash flows and quarterly compounding at 8% annual rate. If the same project were analyzed using annual cash flows (summing quarterly flows) and annual compounding, what would most likely happen to the PI?
    Answer: PI would decrease because annual compounding at 8% is less frequent than quarterly compounding at 2% per quarter, reducing present values When switching from quarterly to annual compounding while maintaining the same nominal rate, the effective annual rate decreases from (1.02)4(1.02)^4 - 1 = 8.24% to 8.00%. Additionally, if cash flows are received annually rather than quarterly, the timing disadvantage (later receipts) combined with the different compounding pattern will generally result in lower present values and thus a lower PI. Choice A incorrectly describes the relationship between compounding frequency and present values. Choice C incorrectly suggests the compounding effect dominates the timing effect. Choice D incorrectly assumes the effects offset each other.
  9. 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?
    Answer: It will decrease but remain greater than 1.0. 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.
  10. 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?
    Answer: The selection depends on the severity of capital rationing and whether projects can be scaled or divided to optimize total portfolio NPV 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.
  11. 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?
    Answer: 0.99 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.
  12. 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?
    Answer: 1.28 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] + [-$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.
  13. When calculating the profitability index for this project using the standard introductory definition, what value should be used in the denominator?
    Answer: $50,000 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.
  14. Using a 12% discount rate, what is the profitability index for this project incorporating the abandonment option?
    Answer: 1.02, indicating marginal acceptability when the abandonment value partially offsets the obsolescence risk 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.
  15. The profitability index is most accurately described as a measure of a project's:
    Answer: relative profitability, indicating the value generated per unit of investment. 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.
  16. Based on the profitability index (PI) for each project, which statement is correct?
    Answer: The PI of Project X is 1.25, and the PI of Project Y is 1.20. 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) 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.
  17. A junior analyst recommends Project Titan because it has a higher profitability index. What is the most significant flaw in the analyst's reasoning?
    Answer: For mutually exclusive projects, the one with the higher NPV should be chosen. 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) 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.
  18. A project requires an initial investment of $600,000 and generates cash flows with a present value of $720,000. If the company can only fund this project by borrowing at 8% (higher than the 6% rate used in the original analysis), how should the profitability index calculation be modified?
    Answer: Recalculate PI using 8% discount rate: PI = PV of cash flows at 8% ÷ $600,000 The profitability index should use the actual cost of capital for the project, which is now 8% due to the financing constraint. The PI formula requires discounting future cash flows at the appropriate rate, so the entire analysis must be recalculated using 8%. Choice B incorrectly adjusts only the initial investment rather than the discount rate. Choice C incorrectly applies the separation principle—while conceptually valid, practical capital budgeting must consider actual financing costs. Choice D incorrectly attempts to adjust the previously calculated present value rather than recalculating from original cash flows.
  19. 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.
    Answer: 1.02 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.
  20. Project Atlas has a net present value (NPV) of $45,000 and a profitability index (PI) of 1.18. What was the initial investment required for Project Atlas?
    Answer: $250,000 The formula relating PI and NPV is PI = (NPV + Initial Investment) / Initial Investment. Let I₀ be the initial investment. We have 1.18 = ($45,000 + I₀) / I₀. Rearranging the formula: 1.18 × I₀ = $45,000 + I₀. This simplifies to 0.18 × I₀ = $45,000. Solving for I₀ gives I₀ = $45,000 / 0.18 = $250,000.

Start this quiz