- An investment of $240,000 generates the following cash flows: Year 1: $80,000, Year 2: $90,000, Year 3: $100,000, Year 4: $110,000. At what approximate discount rate would the discounted payback period equal the regular payback period?
Answer: 0% discount rate, since only then are nominal and present values equivalent for comparison purposes
Regular payback = 2 + ($70,000/$100,000) = 2.7 years. Discounted payback equals regular payback only when present values equal nominal values, which occurs only at a 0% discount rate. At any positive rate, discounting reduces early cash flows, requiring more time to recover the initial investment, making discounted payback longer than regular payback.
- A manufacturing company is comparing two equipment purchases. Machine A costs $400,000 and generates cash flows of $120,000, $140,000, $160,000, and $180,000 in years 1-4. Machine B costs $400,000 and generates $180,000, $160,000, $140,000, and $120,000 in years 1-4. At a 14% cost of capital, which statement about their payback characteristics is most accurate?
Answer: Machine B has both shorter regular payback and shorter discounted payback periods due to front-loaded cash flows
Machine A regular payback: $120K + $140K + $140K (of Year 3's $160K) = $400K, so 2 + ($140K/$160K) = 2.88 years. Machine B: $180K + $160K + $60K (of Year 3's $140K) = $400K, so 2 + ($60K/$140K) = 2.43 years. For discounted payback at 14%, Machine B's advantage increases because earlier cash flows are discounted less heavily. Machine B's front-loaded pattern results in faster recovery in both nominal and present value terms.
- A project has a regular payback period of 2.4 years and a discounted payback period of 3.1 years at 15% cost of capital. If the project's cash flows were to increase by 20% each year while maintaining the same timing pattern, what would happen to both payback measures?
Answer: Regular payback decreases to 2.0 years; discounted payback decreases to 2.58 years proportionally
When all cash flows increase by 20%, both numerator (investment recovery needed) and denominator (annual cash flows) scale proportionally. New regular payback = 2.4/1.2 = 2.0 years. For discounted payback, the same proportional relationship applies since all cash flows scale equally: 3.1/1.2 = 2.58 years. The discount rate doesn't change this proportional scaling effect.
- If a project's discounted payback period is determined to be shorter than the project's economic life, which of the following can be concluded with certainty?
Answer: The project's net present value (NPV) is positive.
The discounted payback period is the time it takes for the cumulative discounted cash inflows to equal the initial investment. If this occurs before the end of the project's life, it means that by the end of its life, the sum of the discounted cash inflows will be greater than the initial investment. This is the definition of a positive Net Present Value (NPV). Option A is not necessarily true - the simple payback could still exceed the project life even when discounted payback doesn't. The IRR would be greater than, not equal to, the discount rate (C). Profitability relative to other projects cannot be determined (D).
- A project's payback period is calculated to be 3.4 years, while the company's maximum acceptable payback period is 3.0 years. However, the project's NPV is highly positive. What is the most appropriate recommendation an analyst should make to management?
Answer: Recommend accepting the project, but highlight the conflict with the payback policy and explain why the NPV signal is more reliable.
While the project fails the payback test, its highly positive NPV indicates it is expected to create significant shareholder value. The payback period is a secondary, non-value-based metric often used as a liquidity or risk screen. The NPV rule is the gold standard for capital budgeting decisions. The most professional and appropriate action is to recommend accepting the value-creating project while acknowledging the policy exception and justifying it based on the superiority of the NPV metric for wealth maximization.
- When calculating a project's payback period, which of the following items is most likely to be incorrectly excluded from the initial investment at time 0?
Answer: The required increase in net working capital.
The full initial investment at time 0 includes all outlays necessary to begin the project. This consists of the equipment's purchase price plus any shipping and installation costs (which are capitalized). A frequent error is to forget the initial outlay for net working capital (e.g., increased inventory or accounts receivable). NWC is a cash outflow at the beginning of the project and must be included in the initial investment to be 'paid back.' Depreciation (D) is a non-cash expense and is not part of the initial investment calculation.
- For a conventional project with positive cash flows, the discounted payback period will always be longer than the simple payback period, assuming a positive discount rate. How does the difference between the discounted payback period and the simple payback period change as the firm's required rate of return increases?
Answer: The difference increases because the present value of each cash inflow is reduced more significantly.
A higher required rate of return (discount rate) leads to lower present values for all future cash flows. This means it will take longer for the cumulative discounted cash flows to recover the initial investment. As the rate increases, the PV of each cash flow decreases, stretching out the discounted payback period even further relative to the simple payback period. Therefore, the difference between the two periods widens.
- A project has an initial cost of $400,000 and is expected to generate the following cash flows: Year 1: $120,000; Year 2: $150,000; Year 3: $180,000; Year 4: $200,000. The company's required rate of return is 12%. What is the project's discounted payback period?
Answer: 3.35 years
To find the discounted payback period, first discount each cash flow to its present value.
PV(CF1) = $120,000 / (1.12)1 = $107,143
PV(CF2) = $150,000 / (1.12)2 = $119,579
PV(CF3) = $180,000 / (1.12)3 = $128,116
PV(CF4) = $200,000 / (1.12)4 = $127,100
Next, find the cumulative discounted cash flows:
Year 1: -$400,000 + $107,143 = -$292,857
Year 2: -$292,857 + $119,579 = -$173,278
Year 3: -$173,278 + $128,116 = -$45,162
Recovery happens in Year 4. The fractional year is the remaining amount to recover divided by the discounted cash flow in that year: $45,162 / $127,100 = 0.355.
Discounted Payback Period = 3 + 0.355 = 3.35 years. - A company is analyzing a project with an initial cost of $250,000. The after-tax cash flows are: Year 1: $70,000, Year 2: $90,000, Year 3: $110,000, and Year 4: $100,000. The company's policy is to accept projects with a payback period of 3 years or less. Which statement is correct?
Answer: The project should be accepted as its payback period is 2.82 years.
When evaluating capital investment projects, the payback period measures how long it takes to recover the initial investment from after-tax cash flows. This straightforward metric helps companies assess liquidity risk and compare projects against predetermined acceptance criteria.
To calculate the payback period, you accumulate cash flows year by year until they equal or exceed the initial investment. Here, the initial cost is $250,000. By the end of Year 1, you've recovered $70,000. After Year 2, the cumulative recovery is $160,000 ($70,000 + $90,000). After Year 3, you've recovered $270,000 ($160,000 + $110,000), which exceeds the $250,000 initial investment.
Since the full recovery occurs partway through Year 3, you need to calculate the exact timing. At the start of Year 3, you still need $90,000 ($250,000 - $160,000). Year 3 generates $110,000, so the recovery takes 110,00090,000=0.818 of Year 3. The total payback period is 2+0.818=2.82 years. Since this is less than the 3-year threshold, the project should be accepted.
Answer A uses an incorrect calculation method, likely dividing the remaining amount by a wrong cash flow figure. Answer B shows a computational error in the fractional year calculation. Answer C reflects a common misconception—the simple payback period uses undiscounted cash flows, so no discount rate is needed. The discounted payback period would require a discount rate, but that's not what's being asked here.
Remember: Simple payback calculations always use nominal cash flows and straightforward addition—no discounting required. - Which of the following statements most accurately describes the conflict in ranking these two projects?
Answer: Both payback methods will favor Project Lux, potentially creating a conflict with the NPV rule's preference for Project Rea.
Payback and discounted payback methods are biased towards liquidity and quick returns. Project Lux, with its high initial cash inflows, will have a shorter payback and discounted payback period than Project Rea. However, the NPV rule considers all cash flows and the time value of money, and it indicates that Project Rea creates more value. This creates a classic conflict: payback methods favor the project with early cash flows (Lux), while NPV favors the project with the highest overall value (Rea).
- A project has the following unconventional cash flows: an initial outflow of $200,000, inflows of $150,000 in both Year 1 and Year 2, and a required outflow of $120,000 in Year 3 for environmental cleanup. What is the project's payback period?
Answer: 1.33 years
The conventional payback period calculation stops once the initial investment is recovered.
Year 0: -$200,000 (Initial Investment)
Year 1: -$200,000 + $150,000 = -$50,000 (Unrecovered)
Year 2: The cash inflow is $150,000. The amount needed to recover is $50,000. Payback occurs during Year 2.
Fractional Year = $50,000 / $150,000 = 0.33
Payback Period = 1 + 0.33 = 1.33 years.
The subsequent outflow in Year 3 is ignored by the standard payback calculation. While unconventional cash flows can lead to multiple payback periods if the cumulative cash flow becomes negative again, the standard definition measures the first time the initial investment is recovered.
- A manager uses the payback period to select Project A over Project B. Project A has a payback of 2.5 years and total cash inflows of $1M over its 5-year life. Project B has a payback of 3.1 years but generates a very large cash inflow in Year 4, leading to total cash inflows of $3M over its 5-year life. Both projects have identical initial investments. This decision most clearly illustrates which critical weakness of the payback period rule?
Answer: It is biased against long-term projects and may not reflect overall profitability.
When evaluating capital budgeting questions involving payback period, focus on what specific weakness is being highlighted by the scenario's details.
The payback period measures how quickly a project recovers its initial investment, but this scenario reveals its most critical flaw. Project A recovers its investment in 2.5 years with $1M total cash flows, while Project B takes 3.1 years but generates $3M total—three times more cash flow over the same 5-year period. By choosing Project A solely based on faster payback, the manager is sacrificing $2M in additional cash flows to recover the investment just 0.6 years sooner.
Answer A correctly identifies this weakness: payback period is biased against long-term projects and ignores overall profitability. The method stops counting once the initial investment is recovered, completely disregarding any cash flows afterward. Project B's "very large cash inflow in Year 4" never factors into the payback calculation, even though it dramatically improves the project's total value.
Answer B is incorrect because while payback does ignore time value of money, that's not the primary issue illustrated here—the problem is ignoring cash flows entirely after payback. Answer C is wrong because no arbitrary cutoff point is mentioned in this scenario. Answer D is incorrect because both projects have identical initial investments, so this isn't about how initial investment is handled.
Study tip: When you see payback period questions, immediately check what happens to cash flows after the payback point. The method's biggest weakness is treating post-payback cash flows as worthless, potentially leading to poor long-term investment decisions.
- A company is considering a project with an initial investment of $750,000. The projected cash inflows are $200,000 in Year 1, $300,000 in Year 2, and an unknown amount in Year 3. If the project's payback period is exactly 2.80 years, what is the required cash inflow for Year 3?
Answer: $312,500
First, calculate the unrecovered investment at the end of Year 2.
Initial Investment: $750,000
Cumulative Inflow after Year 2: $200,000 (Y1) + $300,000 (Y2) = $500,000
Unrecovered Amount at start of Year 3: $750,000 - $500,000 = $250,000.
The payback period is 2.80 years, meaning the fractional year is 0.80. The formula for the payback period is: Full Years + (Unrecovered Amount / Cash Flow in Next Year).
So, 2.80 = 2 + ($250,000 / CF_Year3).
This simplifies to 0.80 = $250,000 / CF_Year3.
Solving for CF_Year3: CF_Year3 = $250,000 / 0.80 = $312,500.
- Compared to the simple payback period, the discounted payback period is considered a superior evaluation method because it:
Answer: adjusts the cash inflows for the time value of money.
The primary advantage of the discounted payback period over the simple payback period is its recognition of the time value of money. It discounts future cash flows back to their present value before calculating the recovery period. However, it still suffers from the other major flaws of the payback method: it ignores cash flows after the payback point (A) and it is not a measure of profitability like NPV (B). It is also more complex to calculate, not easier (D).
- A project requires an initial investment that includes a $1.2 million equipment purchase and a $150,000 increase in net working capital (NWC). The project generates after-tax cash flows of $450,000 per year for five years. The NWC is fully recovered at the end of the project's life. What is the project's payback period?
Answer: 3.00 years
Payback period questions test your ability to determine how long it takes to recover the initial investment from project cash flows. The key is correctly identifying the total initial outlay and then tracking cumulative cash flows until they equal that investment.
Your initial investment includes both the equipment purchase ($1.2 million) and the increase in net working capital ($150,000), totaling $1.35 million. While the NWC is recovered at the end, it still represents cash tied up initially that needs to be "paid back" through the project's cash flows.
With annual after-tax cash flows of $450,000, you can calculate: Payback Period=$450,000$1,350,000=3.00 years
Choice A (2.67 years) incorrectly uses only the equipment cost as the initial investment: $1,200,000 ÷ $450,000 = 2.67. This ignores the working capital requirement entirely. Choice B (2.89 years) appears to result from some calculation error, possibly mixing up components of the initial investment. Choice C (3.33 years) might come from incorrectly adding the NWC recovery to the denominator instead of recognizing it as part of the initial outlay, or from other computational mistakes.
Remember that payback period calculations must include all initial cash outflows, including working capital increases, even though working capital is typically recovered later. The working capital recovery at project end doesn't affect the payback calculation—it's simply additional cash flow beyond the payback point. - A firm has a strict policy of only accepting projects with a payback period of 3.0 years or less. It is evaluating a project with a $600,000 initial outlay. Expected annual cash inflows are $220,000 in Year 1 and $250,000 in Year 2. The cash inflow for Year 3 is uncertain due to market conditions. What is the minimum cash inflow required in Year 3 for the project to be accepted?
Answer: $130,000
First, determine the unrecovered investment at the beginning of Year 3.
Cumulative cash flow after Year 2 = $220,000 (Y1) + $250,000 (Y2) = $470,000.
Unrecovered amount = $600,000 - $470,000 = $130,000.
To meet a payback period of exactly 3.0 years, the project must recover this remaining $130,000 during Year 3. Therefore, the minimum cash inflow required in Year 3 is $130,000. Any amount less than this would result in a payback period longer than 3.0 years.
- A project has a discounted payback period of 3.5 years using a 10% discount rate. If the company's chief financial officer decides to lower the discount rate to 8% due to a change in the firm's risk profile, what will be the effect on the project's discounted payback period?
Answer: It will become shorter than 3.5 years.
Lowering the discount rate from 10% to 8% will increase the present value of all future cash inflows. Because each year's discounted cash flow is now larger, the cumulative discounted cash flow will reach the initial investment amount more quickly. Therefore, the discounted payback period will become shorter than 3.5 years.
- A startup firm operating in a rapidly changing technology sector might prefer the payback period method for capital budgeting primarily because it:
Answer: emphasizes liquidity and provides an implicit measure of a project's risk.
For firms in high-risk, uncertain environments like a tech startup, quickly recovering the initial investment is a major concern. The payback period provides a simple measure of how long capital is at risk. A shorter payback period implies lower risk and faster return of capital (liquidity), which is highly valued when future cash flows are very uncertain. NPV is a better measure of profitability (A) and long-term value (D), but payback's focus on risk and liquidity is its main appeal in such contexts.
- A capital project shows a discounted payback period of 4.6 years when evaluated at the company's 12% cost of capital. If inflation expectations increase, causing the company to raise its cost of capital to 16%, and assuming project cash flows remain nominally unchanged, what is the most likely outcome for the discounted payback analysis?
Answer: Discounted payback period will extend beyond 4.6 years, potentially making the project unacceptable if it exceeds the maximum threshold
Higher discount rates reduce the present value of future cash flows, especially those further in the future. This means it takes longer (more years) to accumulate enough discounted cash flow to recover the initial investment. Therefore, discounted payback period increases from 4.6 years to something longer, potentially making a previously acceptable project unacceptable if it exceeds the company's maximum payback threshold.
- A project costs $300,000 and has cash inflows of $90,000 in Year 1, $120,000 in Year 2, and $150,000 in Year 3. Which of the following is closest to the amount of unrecovered investment at the beginning of the year in which payback occurs?
Answer: $90,000
This question requires identifying the start of the payback year.
Initial Investment: $300,000.
After Year 1: Unrecovered amount is $300,000 - $90,000 = $210,000.
After Year 2: Unrecovered amount is $210,000 - $120,000 = $90,000.
At the beginning of Year 3, the project still needs to recover $90,000. The cash flow in Year 3 is $150,000, which is sufficient to cover the remaining balance. Therefore, payback occurs during Year 3, and the unrecovered investment at the beginning of that year is $90,000.
