Finance Quiz: Payback And Discounted Payback
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Payback And Discounted PaybackQuestion 1 of 20

A project requires an initial investment of $120,000 and is expected to generate a level annual cash flow of $40,000 for five years. If the firm's required rate of return is 10%, what is the project's discounted payback period?

3.00 years
3.75 years
2.91 years
4.17 years
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Finance Quiz: Payback And Discounted Payback

Practice Payback And Discounted Payback in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Payback And Discounted Payback, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

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Question 1

A project requires an initial investment of $120,000 and is expected to generate a level annual cash flow of $40,000 for five years. If the firm's required rate of return is 10%, what is the project's discounted payback period?

  1. 3.00 years
  2. 3.75 years (correct answer)
  3. 2.91 years
  4. 4.17 years
Explanation: First, calculate the present value (PV) of each annual cash flow at 10% and track the cumulative PV. PV of Year 1 CF = $40,000 / (1.10)^1 = $36,364. Cumulative PV = $36,364. PV of Year 2 CF = $40,000 / (1.10)^2 = $33,058. Cumulative PV = $69,422. PV of Year 3 CF = $40,000 / (1.10)^3 = $30,053. Cumulative PV = $99,475. After 3 years, the unrecovered investment is $120,000 - $99,475 = $20,525. PV of Year 4 CF = $40,000 / (1.10)^4 = $27,321. The fractional year needed to recover the remaining amount is $20,525 / $27,321 = 0.75 years. Therefore, the discounted payback period is 3 + 0.75 = 3.75 years.

Question 2

A project requires a $300,000 investment at time t=0. There is no cash flow in Year 1. The cash inflows are $120,000 in Year 2, $150,000 in Year 3, and $100,000 in Year 4. What is the project's payback period?

  1. 2.80 years
  2. 3.30 years (correct answer)
  3. 2.30 years
  4. 3.80 years
Explanation: We track the cumulative cash flow over time, starting from the initial investment. Time 0: Cumulative Flow = -$300,000 End of Year 1: No cash flow. Cumulative Flow = -$300,000. End of Year 2: Inflow of 120,000.CumulativeFlow=−120,000. Cumulative Flow = -300,000 + 120,000=−120,000 = -180,000. End of Year 3: Inflow of 150,000.CumulativeFlow=−150,000. Cumulative Flow = -180,000 + 150,000=−150,000 = -30,000. At the start of Year 4, $30,000 is still unrecovered. The cash flow during Year 4 is $100,000. The fraction of Year 4 needed is $30,000 / $100,000 = 0.30. The payback period is 3 full years plus this fraction: 3 + 0.30 = 3.30 years.

Question 3

Two mutually exclusive projects, Titan and Atlas, have the same initial cost. Project Titan has a payback period of 2.5 years and generates significant cash flows for 10 years after its payback period. Project Atlas has a payback period of 2.2 years but its cash flows cease completely after Year 3. Which of the following statements is most accurate regarding a capital budgeting decision based on the payback method?

  1. The payback method would favor Project Atlas, potentially leading to the rejection of a more profitable project. (correct answer)
  2. The payback method would favor Project Titan because its longer stream of cash flows implies lower overall risk.
  3. The payback method cannot be used to compare these projects because their total lifespans are different.
  4. The payback method correctly identifies Project Atlas as superior because it returns the initial capital more quickly.
Explanation: The primary weakness of the payback period is that it ignores all cash flows that occur after the investment is recovered. In this scenario, the payback method would favor Project Atlas due to its shorter payback period (2.2 years vs. 2.5 years). However, by ignoring the substantial cash flows generated by Project Titan after its payback period, this method could lead the firm to select the less profitable project (in terms of NPV).

Question 4

Project Alpha has high initial cash flows that decline over time. Project Beta has low initial cash flows that increase significantly in later years. Both projects have the same initial cost and the same 5-year life. Which of the following statements is most likely to be true when comparing these two projects?

  1. Project Beta will have a shorter payback period and a higher NPV.
  2. Project Alpha will have a shorter payback period, but Project Beta could have a higher NPV. (correct answer)
  3. Project Alpha will have a shorter payback period and a higher NPV.
  4. Project Beta will have a shorter payback period, but Project Alpha could have a higher NPV.
Explanation: The payback period favors projects with high cash flows in the early years. Therefore, Project Alpha, with its front-loaded cash flows, will most likely have a shorter payback period than Project Beta. However, the Net Present Value (NPV) considers all cash flows over the project's entire life and discounts them. Since Project Beta has significantly higher cash flows in later years, its total discounted cash flow could be greater than Project Alpha's, resulting in a higher NPV. The payback period's weakness is ignoring these valuable later-year cash flows.

Question 5

A project's cash flows have been forecasted, and its discounted payback period has been calculated as 4.1 years using a 9% required rate of return. If the company's management revises its required rate of return upward to 11%, what will be the effect on the discounted payback period and the simple payback period?

  1. The discounted payback period will increase, and the simple payback period will increase.
  2. The discounted payback period will decrease, and the simple payback period will remain unchanged.
  3. The discounted payback period will increase, and the simple payback period will remain unchanged. (correct answer)
  4. Both the discounted payback period and the simple payback period will remain unchanged.
Explanation: The simple payback period is calculated using nominal cash flows and is not affected by the discount rate. Therefore, it will remain unchanged. The discounted payback period, however, is calculated using the present value of future cash flows. An increase in the required rate of return (discount rate) will decrease the present value of all future cash inflows, making it take longer to recover the initial investment. Thus, the discounted payback period will increase.

Question 6

A company is evaluating a project with an initial investment of $400,000. The project's cash inflows are $150,000 in Year 1, an unknown amount (X) in Year 2, and $120,000 in Year 3. If the project's payback period is exactly 2.5 years, what is the value of the cash flow in Year 2 (X)?

  1. $200,000
  2. $250,000
  3. $190,000 (correct answer)
  4. $130,000
Explanation: The payback period of 2.5 years means the initial investment is recovered after two full years plus half of the third year's cash flow.
  1. Calculate the unrecovered investment after Year 1: $400,000 - $150,000 = $250,000.
  2. Let X be the cash flow in Year 2. The unrecovered investment at the start of Year 3 is $250,000 - X.
  3. The fractional part of the payback period (0.5 years) is the unrecovered amount at the start of Year 3 divided by the Year 3 cash flow. So, 0.5 = ($250,000 - X) / $120,000.
  4. Solve for X: 0.5 * $120,000 = $250,000 - X => $60,000 = $250,000 - X => X = $190,000.

Question 7

A project has a calculated payback period of 3.2 years, which is within the firm's maximum acceptable payback period of 4 years. What can be definitively concluded about this project's Net Present Value (NPV) and Internal Rate of Return (IRR)?

  1. The project's NPV must be positive.
  2. The project's IRR must be greater than the cost of capital.
  3. The project's NPV is positive only if the discounted payback period is also less than 4 years.
  4. No specific conclusion can be drawn about the project's NPV or IRR without more information. (correct answer)
Explanation: Meeting a payback period criterion provides no guarantee about a project's overall profitability. A project can pay back its initial investment quickly but then have small or even negative cash flows in later years. Such a project could easily have a negative NPV and an IRR below the cost of capital. Therefore, without knowing the magnitude and timing of all cash flows over the project's entire life and the discount rate, nothing can be definitively concluded about NPV or IRR.

Question 8

A firm is evaluating two mutually exclusive projects, A and B, which are part of its annual capital budget. Project A has a payback period of 2.4 years, while Project B has a payback period of 2.6 years. The company's required payback is 3.0 years. What additional information would be most critical in making the optimal investment decision?

  1. The salvage value of the assets used in each project.
  2. The depreciation method used for each project.
  3. The precise timing of cash flows within the first two years for each project.
  4. The magnitude of cash flows occurring after the payback period for each project. (correct answer)
Explanation: When evaluating capital projects using payback period analysis, you're measuring how quickly each project recovers its initial investment. However, payback period has a critical limitation: it completely ignores cash flows that occur after the payback point is reached. In this scenario, both projects meet the company's 3.0-year payback requirement, with Project A recovering its investment in 2.4 years and Project B in 2.6 years. While Project A appears superior based solely on payback period, this metric tells you nothing about the projects' profitability or total value creation. The cash flows occurring after each project's payback period could dramatically alter which investment is truly optimal. Option A is incorrect because salvage values, while relevant to overall project evaluation, are less critical than ongoing operational cash flows in determining project superiority. Option B is wrong because depreciation methods affect accounting profits and taxes but don't change the fundamental cash flow patterns that drive investment decisions. Option C misses the mark because knowing precise timing within the first two years won't change the fact that both projects already meet the payback criterion. Option D correctly identifies that the magnitude of post-payback cash flows is most critical. Project B might generate substantially higher cash flows in years 3-10, making it more valuable despite its slightly longer payback period. Without this information, you're making decisions based on incomplete data. Remember: payback period is a useful screening tool, but always consider the complete cash flow profile when choosing between acceptable projects. The real money is often made after payback is achieved.

Question 9

For any conventional investment project with a positive initial outlay followed by a series of positive cash inflows, and assuming a positive discount rate, which of the following statements correctly describes the relationship between the payback period (PP) and the discounted payback period (DPP)?

  1. DPP will always be greater than PP. (correct answer)
  2. DPP will always be less than PP.
  3. DPP will be equal to PP.
  4. The relationship between DPP and PP depends on the pattern of cash flows.
Explanation: Discounting future cash flows at a positive rate reduces their value compared to their nominal value. The simple payback period (PP) uses nominal cash flows, while the discounted payback period (DPP) uses these reduced, present-value cash flows. Since each cash inflow is smaller in present value terms, it will take longer for their cumulative sum to equal the initial investment. Therefore, for any project with positive cash flows and a positive discount rate, the discounted payback period will always be longer than the simple payback period.

Question 10

A project requires an initial investment of $500,000 for equipment and an immediate investment of $50,000 in net working capital (NWC). Annual operating cash flows are projected to be $200,000 for the next 5 years. The NWC will be fully recovered at the end of Year 5. What is the project's payback period?

  1. 2.50 years
  2. 2.25 years
  3. 2.45 years
  4. 2.75 years (correct answer)
Explanation: When calculating payback period, you need to determine how long it takes for cumulative cash inflows to recover your initial cash outflow. The key insight here is identifying what constitutes your total initial investment versus your ongoing cash flows. Your initial cash outflow includes both the $500,000 equipment investment and the $50,000 net working capital investment, totaling $550,000. This is the amount you need to recover. Your annual operating cash flows are $200,000 per year for 5 years. To find the payback period: After 2 years, you've recovered 400,000(400,000 (200,000 × 2). You still need 150,000more(150,000 more (550,000 - $400,000). In Year 3, you'll generate another $200,000, so you need $150,000200,000=0.75\frac{150,000}{200,000} = 0.75 $ of that third year. Therefore, the payback period is 2.75 years. Choice A (2.50 years) likely comes from incorrectly using only the equipment cost ($500,000) as the initial investment, giving you $500,000 ÷ $200,000 = 2.5 years. Choice B (2.25 years) might result from calculation errors or confusion about the cash flow timing. Choice C (2.45 years) appears to be a distractor with no clear logical basis. The critical mistake students make is forgetting that net working capital represents an immediate cash outflow that must be included in the initial investment for payback calculations. Even though NWC is recovered at project end, it still ties up cash initially. Always include all upfront cash requirements when calculating payback period.

Question 11

A project's payback period is calculated to be exactly 3.0 years based on an initial investment and cash flows of $50,000 in Year 1, $60,000 in Year 2, and $40,000 in Year 3. The project is also expected to generate $40,000 in Year 4. If the initial investment had been $10,000 greater, what would the new payback period have been?

  1. 3.17 years
  2. 3.25 years (correct answer)
  3. 3.50 years
  4. 3.33 years
Explanation:
  1. First, determine the original investment. A payback period of exactly 3.0 years means the initial investment equals the sum of the cash flows for the first three years: $50,000 + $60,000 + $40,000 = $150,000.
  2. The new initial investment is $10,000 greater, so it is $150,000 + $10,000 = $160,000.
  3. Now, calculate the payback period for this new investment. At the end of Year 3, the cumulative cash inflow is still $150,000. The unrecovered amount is $160,000 - $150,000 = $10,000.
  4. This remaining $10,000 must be recovered from the Year 4 cash flow, which is $40,000. The fraction of Year 4 required is $10,000 / $40,000 = 0.25 years.
  5. The new payback period is 3 full years plus this fraction: 3 + 0.25 = 3.25 years.

Question 12

A company adheres to a strict maximum payback period of 3.0 years for all capital projects. It is evaluating two mutually exclusive projects. Project Swift has a payback period of 2.8 years and an NPV of $40,000. Project Endure has a payback period of 3.4 years and an NPV of $90,000. Based only on the firm's stated payback period decision rule, what action should be taken?

  1. Accept Project Endure because its NPV is higher.
  2. Reject both projects because neither meets all capital budgeting criteria.
  3. Accept Project Swift. (correct answer)
  4. Accept both projects because they are both profitable.
Explanation: The question requires applying the firm's stated payback period rule exclusively. The rule is to accept projects with a payback period of 3.0 years or less. Project Swift has a payback of 2.8 years, which meets the criterion. Project Endure has a payback of 3.4 years, which does not. Since the projects are mutually exclusive, the firm would accept the one that meets the criteria. Therefore, Project Swift should be accepted. The information about NPV is a distractor intended to test whether the candidate can strictly follow the specified decision rule.

Question 13

A project costs $750,000 and is expected to generate a level annual cash flow of $90,000 into perpetuity. The company's policy is to reject any project with a payback period longer than 10 years. Based on the payback rule, what is the project's payback period and the correct decision?

  1. 8.33 years; accept the project. (correct answer)
  2. 10.00 years; accept the project.
  3. 11.11 years; reject the project.
  4. Cannot be determined because the cash flows are a perpetuity.
Explanation: The payback period calculation for a project with level annual cash flows (an annuity or a perpetuity) is straightforward. The fact that the cash flows continue into perpetuity is irrelevant for the payback calculation, which only considers the time to recover the initial investment. Payback Period = Initial Investment / Annual Cash Flow = $750,000 / $90,000 = 8.33 years. Since 8.33 years is less than the company's maximum acceptable payback period of 10 years, the project should be accepted based on this rule.

Question 14

A profitable company is evaluating a project and can choose between the straight-line depreciation method and an accelerated depreciation method (MACRS) for tax purposes. The choice of depreciation method will not affect sales revenue or operating costs before depreciation. How would choosing the accelerated method over the straight-line method most likely affect the project's payback period?

  1. It would have no effect on the payback period because depreciation is a non-cash expense.
  2. It would lengthen the payback period because of higher depreciation expense in early years.
  3. It would shorten the payback period because of higher cash flows in the early years of the project. (correct answer)
  4. The effect cannot be determined without knowing the firm's tax rate and the cost of capital.
Explanation: While depreciation is a non-cash expense, it affects taxes, which are a cash expense. Accelerated depreciation (like MACRS) results in higher depreciation expense in the early years of a project compared to the straight-line method. This higher expense leads to lower reported taxable income, which in turn results in lower tax payments. Lower cash outflows for taxes mean higher net operating cash flows in the early years. Higher early-year cash flows will shorten the time required to recover the initial investment, thus shortening the payback period.

Question 15

A project has an initial cost of $100,000. Its cash inflows are $50,000 in Year 1 and $70,000 in Year 2. The project's discounted payback period is exactly 2.0 years. What is the approximate discount rate being used?

  1. 8.5%
  2. 10.0%
  3. 12.0% (correct answer)
  4. 14.6%
Explanation: The discounted payback period is exactly 2.0 years, meaning the sum of the present values of the first two cash flows equals the initial investment. We can test the given discount rates to see which one satisfies this condition: 100,000 = \frac{50,000}{(1+r)^1} + \frac{70,000}{(1+r)^2} Let's test choice C, r = 12.0%: PV = \frac{50,000}{1.12} + \frac{70,000}{1.12^2} = $44,642.86 + $55,803.57 = $100,446.43 This value is very close to $100,000. Let's test the other options to be sure. Test choice D, r = 14.6%: PV = \frac{50,000}{1.146} + \frac{70,000}{1.146^2} = $43,630 + $53,299 = $96,929 Test choice B, r = 10.0%: PV = \frac{50,000}{1.10} + \frac{70,000}{1.10^2} = $45,455 + $57,851 = $103,306 The 12.0% discount rate yields a present value closest to the initial investment of $100,000, making it the best answer.

Question 16

A company is evaluating a project with an initial investment of $400,000. The project's cash inflows are $150,000 in Year 1, an unknown amount (X) in Year 2, and $120,000 in Year 3. If the project's payback period is exactly 2.5 years, what is the value of the cash flow in Year 2 (X)?

  1. $200,000
  2. $250,000
  3. $190,000 (correct answer)
  4. $130,000
Explanation: The payback period of 2.5 years means the initial investment is recovered after two full years plus half of the third year's cash flow.
  1. Calculate the unrecovered investment after Year 1: $400,000 - $150,000 = $250,000.
  2. Let X be the cash flow in Year 2. The unrecovered investment at the start of Year 3 is $250,000 - X.
  3. The fractional part of the payback period (0.5 years) is the unrecovered amount at the start of Year 3 divided by the Year 3 cash flow. So, 0.5 = ($250,000 - X) / $120,000.
  4. Solve for X: 0.5 * $120,000 = $250,000 - X => $60,000 = $250,000 - X => X = $190,000.

Question 17

A project's cash flows have been forecasted, and its discounted payback period has been calculated as 4.1 years using a 9% required rate of return. If the company's management revises its required rate of return upward to 11%, what will be the effect on the discounted payback period and the simple payback period?

  1. The discounted payback period will increase, and the simple payback period will increase.
  2. The discounted payback period will decrease, and the simple payback period will remain unchanged.
  3. The discounted payback period will increase, and the simple payback period will remain unchanged. (correct answer)
  4. Both the discounted payback period and the simple payback period will remain unchanged.
Explanation: The simple payback period is calculated using nominal cash flows and is not affected by the discount rate. Therefore, it will remain unchanged. The discounted payback period, however, is calculated using the present value of future cash flows. An increase in the required rate of return (discount rate) will decrease the present value of all future cash inflows, making it take longer to recover the initial investment. Thus, the discounted payback period will increase.

Question 18

A project requires an initial investment of $120,000 and is expected to generate a level annual cash flow of $40,000 for five years. If the firm's required rate of return is 10%, what is the project's discounted payback period?

  1. 3.00 years
  2. 3.75 years (correct answer)
  3. 2.91 years
  4. 4.17 years
Explanation: First, calculate the present value (PV) of each annual cash flow at 10% and track the cumulative PV. PV of Year 1 CF = $40,000 / (1.10)^1 = $36,364. Cumulative PV = $36,364. PV of Year 2 CF = $40,000 / (1.10)^2 = $33,058. Cumulative PV = $69,422. PV of Year 3 CF = $40,000 / (1.10)^3 = $30,053. Cumulative PV = $99,475. After 3 years, the unrecovered investment is $120,000 - $99,475 = $20,525. PV of Year 4 CF = $40,000 / (1.10)^4 = $27,321. The fractional year needed to recover the remaining amount is $20,525 / $27,321 = 0.75 years. Therefore, the discounted payback period is 3 + 0.75 = 3.75 years.

Question 19

A company adheres to a strict maximum payback period of 3.0 years for all capital projects. It is evaluating two mutually exclusive projects. Project Swift has a payback period of 2.8 years and an NPV of $40,000. Project Endure has a payback period of 3.4 years and an NPV of $90,000. Based only on the firm's stated payback period decision rule, what action should be taken?

  1. Accept Project Endure because its NPV is higher.
  2. Reject both projects because neither meets all capital budgeting criteria.
  3. Accept Project Swift. (correct answer)
  4. Accept both projects because they are both profitable.
Explanation: The question requires applying the firm's stated payback period rule exclusively. The rule is to accept projects with a payback period of 3.0 years or less. Project Swift has a payback of 2.8 years, which meets the criterion. Project Endure has a payback of 3.4 years, which does not. Since the projects are mutually exclusive, the firm would accept the one that meets the criteria. Therefore, Project Swift should be accepted. The information about NPV is a distractor intended to test whether the candidate can strictly follow the specified decision rule.

Question 20

A project requires an initial investment of $500,000 for equipment and an immediate investment of $50,000 in net working capital (NWC). Annual operating cash flows are projected to be $200,000 for the next 5 years. The NWC will be fully recovered at the end of Year 5. What is the project's payback period?

  1. 2.50 years
  2. 2.25 years
  3. 2.45 years
  4. 2.75 years (correct answer)
Explanation: When calculating payback period, you need to determine how long it takes for cumulative cash inflows to recover your initial cash outflow. The key insight here is identifying what constitutes your total initial investment versus your ongoing cash flows. Your initial cash outflow includes both the $500,000 equipment investment and the $50,000 net working capital investment, totaling $550,000. This is the amount you need to recover. Your annual operating cash flows are $200,000 per year for 5 years. To find the payback period: After 2 years, you've recovered 400,000(400,000 (200,000 × 2). You still need 150,000more(150,000 more (550,000 - $400,000). In Year 3, you'll generate another $200,000, so you need $150,000200,000=0.75\frac{150,000}{200,000} = 0.75 $ of that third year. Therefore, the payback period is 2.75 years. Choice A (2.50 years) likely comes from incorrectly using only the equipment cost ($500,000) as the initial investment, giving you $500,000 ÷ $200,000 = 2.5 years. Choice B (2.25 years) might result from calculation errors or confusion about the cash flow timing. Choice C (2.45 years) appears to be a distractor with no clear logical basis. The critical mistake students make is forgetting that net working capital represents an immediate cash outflow that must be included in the initial investment for payback calculations. Even though NWC is recovered at project end, it still ties up cash initially. Always include all upfront cash requirements when calculating payback period.