Finance Quiz: Cash Flow Timing And Sign Conventions
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Cash Flow Timing And Sign ConventionsQuestion 1 of 20

A firm is analyzing two projects. Project A is an investment with CF0=-100 and a positive NPV. Project B is a financing opportunity with CF0=+100 and a positive NPV. Which statement correctly interprets the sign of the initial cash flow and the project decision?

The negative CF0 for Project A is an undesirable feature, but it is acceptable because its NPV is positive.
The positive CF0 for Project B indicates it is a source of funds, and its positive NPV indicates it is an attractive source.
Both projects should be rejected because investments should have positive CF0 and financing should have negative CF0.
The sign of CF0 is arbitrary; only the positive NPV matters, so both projects should be undertaken.
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Finance Quiz

Finance Quiz: Cash Flow Timing And Sign Conventions

Practice Cash Flow Timing And Sign Conventions 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 Cash Flow Timing And Sign Conventions, 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 firm is analyzing two projects. Project A is an investment with CF0=-100 and a positive NPV. Project B is a financing opportunity with CF0=+100 and a positive NPV. Which statement correctly interprets the sign of the initial cash flow and the project decision?

  1. The negative CF0 for Project A is an undesirable feature, but it is acceptable because its NPV is positive.
  2. The positive CF0 for Project B indicates it is a source of funds, and its positive NPV indicates it is an attractive source. (correct answer)
  3. Both projects should be rejected because investments should have positive CF0 and financing should have negative CF0.
  4. The sign of CF0 is arbitrary; only the positive NPV matters, so both projects should be undertaken.
Explanation: Sign convention is crucial for interpretation. For an investment project (like A), CF0 is negative, representing an outflow. A positive NPV means the present value of future inflows exceeds this outflow, so it should be accepted. For a financing project (like B), CF0 is positive, representing an inflow of funds. A positive NPV means the present value of the future outflows (repayments) is less than the funds received, making it an attractive (i.e., low-cost) source of financing. Statement B correctly interprets the financing project.

Question 2

The standard formula for the present value of a perpetuity, PV=PMTrPV = \frac{PMT}{r}, contains an implicit assumption about the timing of the first cash flow. This formula is valid only when the first payment (PMT) occurs:

  1. immediately, at time t=0.
  2. one period from today, at time t=1. (correct answer)
  3. continuously throughout the first period.
  4. at the midpoint of the first period, at time t=0.5.
Explanation: The standard perpetuity formula is derived from the limit of an ordinary annuity formula. An ordinary annuity assumes that cash flows occur at the end of each period. Therefore, the perpetuity formula PV=PMT/rPV = PMT/r calculates the value at t=0 for a series of cash flows that begins at t=1 and continues forever.

Question 3

A project requires an initial equipment purchase of $15,000. However, the firm receives an immediate government subsidy of $2,000 for undertaking the project. The project then generates inflows of $5,000 at the end of each year for the next three years. Which of the following correctly describes the cash flow stream for calculating the project's NPV?

  1. CF0 = -15,000;CF1=+15,000; CF1 = +7,000; CF2 = +5,000;CF3=+5,000; CF3 = +5,000.
  2. CF0 = -$15,000; followed by a 4-period annuity of inflows starting at t=0.
  3. CF0 = -$13,000; followed by a 3-year ordinary annuity of $5,000. (correct answer)
  4. CF0 = -$15,000; followed by a 3-year ordinary annuity of $5,000 and a separate discounted inflow of $2,000.
Explanation: Cash flows that occur at the same point in time should be netted. At t=0, the firm has an outflow of $15,000 for equipment and an inflow of 2,000fromthesubsidy.Thenetcashflowattime0is−2,000 from the subsidy. The net cash flow at time 0 is -15,000 + 2,000=−2,000 = -13,000. The subsequent inflows of $5,000 at the end of years 1, 2, and 3 constitute a 3-year ordinary annuity.

Question 4

An analyst is saving for a goal five years from now. They will make 61 monthly deposits, with the first deposit made today (t=0) and the final deposit made exactly five years from today (at t=60 months). To calculate the future value of this series of deposits using a financial calculator, which mode and number of periods (N) should be used?

  1. END mode with N = 60.
  2. BEGIN mode with N = 60.
  3. END mode with N = 61.
  4. BEGIN mode with N = 61. (correct answer)
Explanation: This is an annuity due because the first payment occurs today (t=0). The payments occur from t=0 to t=60, which is a total of 61 payments. Therefore, BEGIN mode must be used to signify payments at the start of each period, and N must be set to 61 to account for all deposits. The future value will be calculated as of t=61, one period after the last payment, which aligns with standard BEGIN mode FV calculations.

Question 5

A project is expected to generate positive cash flows evenly throughout each year. An analyst, for simplicity, models these cash flows as occurring at the end of each respective year. Compared to a more precise valuation using a mid-year timing convention, the analyst's simplification will most likely:

  1. overstate the project's Net Present Value (NPV).
  2. understate the project's Net Present Value (NPV). (correct answer)
  3. have no systematic directional impact on the project's NPV.
  4. affect the project's IRR but have no impact on its NPV.
Explanation: Assuming all cash flows occur at the end of the year (end-of-period convention) means each cash flow is discounted for a longer period than under a mid-year convention. For example, a year 1 cash flow is discounted for a full year versus half a year. Discounting for a longer period results in a lower present value for each cash flow, thus understating the project's total NPV.

Question 6

A real estate developer purchases land for $500,000 using $100,000 of equity and a $400,000 loan. For the purpose of calculating the internal rate of return (IRR) on the equity investment, what is the correct cash flow at time 0 (CF0)?

  1. A $100,000 outflow, representing the equity investor's cash contribution. (correct answer)
  2. A $500,000 outflow, representing the total purchase price of the asset.
  3. A $400,000 inflow, representing the loan proceeds received.
  4. A $300,000 outflow, representing the land value net of the loan liability.
Explanation: When calculating the return on equity, the cash flows must be from the equity investor's perspective. The only cash that actually left the investor's pocket at time 0 was their own $100,000 contribution. The 400,000loaniscashusedfortheproject,butitisnotanoutflowfromtheequityholder.Therefore,CF0fortheequityIRRcalculationis−400,000 loan is cash used for the project, but it is not an outflow from the equity holder. Therefore, CF0 for the equity IRR calculation is -100,000.

Question 7

A project has the following non-conventional cash flows: Year 0: -1,600;Year1:+1,600; Year 1: +10,000; Year 2: -$10,000. An analyst notes that this pattern of signs creates an issue for one common capital budgeting metric. What is the primary implication of this cash flow pattern when using the Internal Rate of Return (IRR) method?

  1. The IRR will be negative, indicating that the project's costs outweigh its benefits over its lifetime.
  2. The IRR cannot be calculated because the sum of the positive cash flows equals the sum of the negative cash flows.
  3. The project may have two positive IRRs, making the standard 'accept if IRR > cost of capital' rule ambiguous. (correct answer)
  4. The project's NPV will be positive at all possible discount rates, making the IRR metric irrelevant.
Explanation: Projects with non-conventional cash flows (more than one change of sign) can have multiple IRRs or no IRR. In this case, there are two sign changes (- to + to -). This can lead to a situation where the NPV is zero at more than one discount rate, resulting in multiple IRRs. This ambiguity makes the standard IRR decision rule unreliable for such projects.

Question 8

A firm is considering a replacement project. The new machine costs $200,000. The old machine can be sold for $60,000, which results in a taxable gain and a tax liability of $8,000. Both transactions occur at t=0. What is the correct initial cash flow for this project?

  1. An outflow of $200,000, as the sale of the old asset is a separate financing decision.
  2. An outflow of $140,000, representing the cost of the new machine less the pre-tax proceeds from the old one.
  3. An outflow of $148,000, representing the net effect of the purchase, sale, and tax liability. (correct answer)
  4. An outflow of $132,000, representing the cost of the new machine less the after-tax proceeds from the old one.
Explanation: All cash flows occurring at the inception of the project must be netted to find the initial cash flow (CF0). This includes the outflow for the new machine (-200,000),theinflowfromsellingtheoldmachine(+200,000), the inflow from selling the old machine (+60,000), and the outflow for taxes on the gain (-8,000).Thenetinitialcashflowis:−8,000). The net initial cash flow is: -200,000 + $60,000 - 8,000=−8,000 = -148,000. This is an outflow of $148,000.

Question 9

A company purchases an asset for $600,000 and depreciates it straight-line to zero over a 6-year life. At the end of year 6, the company sells the asset for $70,000. If the company's marginal tax rate is 25%, what is the after-tax salvage value cash flow to be included in a capital budgeting analysis?

  1. An inflow of $70,000, since the asset was fully depreciated.
  2. An inflow of $87,500, representing the sale price plus a tax shield.
  3. An inflow of $17,500, representing only the tax consequences of the sale.
  4. An inflow of $52,500, representing the sale price net of taxes paid on the gain. (correct answer)
Explanation: The asset's book value at the time of sale is $0. The sale price is $70,000, creating a taxable gain of $70,000 - $0 = $70,000. The tax owed on this gain is 0.25 * $70,000 = $17,500. The after-tax cash flow is the sale proceeds minus the taxes paid: $70,000 - $17,500 = $52,500.

Question 10

A retiree wants to fund a series of annual withdrawals from a savings account, which earns 5% per year. The first withdrawal will be $60,000 and is needed one year from today. The retiree plans for each subsequent withdrawal to grow by 2% to offset inflation, for a total of 25 withdrawals. From the retiree's perspective, how should these cash flows be signed and timed for the purpose of calculating the required initial investment?

  1. As a series of 25 negative cash flows, starting at t=1, because they deplete the savings account balance.
  2. As a series of 25 positive cash flows, starting at t=0, to model them as an annuity due.
  3. As a series of 25 positive cash flows, starting at t=1, valued using a growing annuity formula. (correct answer)
  4. As a single positive cash flow at t=25, representing the future value of all withdrawals.
Explanation: From the retiree's perspective, the withdrawals are cash received, so they are positive cash flows. The problem states the first withdrawal is one year from today, which corresponds to t=1. This is the standard timing for an ordinary annuity. Since the payments are not level but grow at a constant rate, the present value of a growing annuity formula is the appropriate valuation tool.

Question 11

An investor purchases a 10-year, 8% annual coupon bond at its par value of $1,000. Immediately after receiving the second coupon payment, the investor sells the bond for $1,050. From the investor's perspective, which signs and timings correctly describe the cash flows for calculating the holding period return?

  1. CF0 = -1,000;CF1=+1,000; CF1 = +80; CF2 = +80+80 +1,050. (correct answer)
  2. CF0 = +1,000;CF1=−1,000; CF1 = -80; CF2 = -$80 - $1,050.
  3. CF0 = -1,000;CF1=+1,000; CF1 = +80; CF2 = +$1,050.
  4. CF0 = -1,000;CF1=+1,000; CF1 = +80; CF2 = +80;CF3..10=+80; CF3..10 = +80; CF10 = +$1000.
Explanation: From the investor's perspective: The initial purchase is a cash outflow (CF0 = -$1,000). They receive two annual coupon payments of $80 each, which are cash inflows at t=1 and t=2. At t=2, they also sell the bond, which is another cash inflow of $1,050. Therefore, the cash flow at t=2 is the sum of the second coupon and the sale price.

Question 12

A company is considering a project that will generate incremental revenues of $100,000 and incremental cash expenses of $40,000 per year. The project requires an asset that will generate $20,000 in annual depreciation expense. The firm's tax rate is 30%. What is the correct annual operating cash flow (OCF) from this project?

  1. $60,000, representing the net cash change before considering any non-cash charges.
  2. $48,000, representing the after-tax profit from the project's operations.
  3. $42,000, representing the pre-tax cash flow minus taxes on that amount.
  4. $48,000, calculated as after-tax operating income plus the depreciation amount. (correct answer)
Explanation: This question requires building the operating cash flow from its components, a key application of cash flow identification. First, calculate earnings before interest and taxes (EBIT): $100,000 (Revenue) - $40,000 (Cash Expenses) - $20,000 (Depreciation) = $40,000. Next, calculate taxes: $40,000 * 30% = $12,000. Net Operating Profit After Tax (NOPAT) is $40,000 - $12,000 = $28,000. Finally, add back the non-cash depreciation charge to get OCF: $28,000 + $20,000 = $48,000. Wait, let me re-check. EBIT = 60k - 20k = 40k. Tax = 12k. NOPAT = 28k. OCF = NOPAT + Dep = 28k + 20k = 48k. Another way: OCF = (EBITDA)(1-T) + TDep = (60k)(0.7) + 0.320k = 42k + 6k = 48k. It seems my calculation for D is correct but the explanation text is slightly off. Let me correct the explanation text for D. The correct explanation is: OCF can be calculated as (EBIT)(1-T) + Dep. Here, EBIT = $100k - $40k - $20k = 40k.SoOCF=(40k. So OCF = (40k)(1-0.3) + $20k = $28k + $20k = $48k. Let's re-evaluate the distractor B. It gives the same number. Let's rephrase D to be unique. Let's make D '...calculated as pre-tax cash flow minus taxes on EBIT.' Pre-tax cash flow is $60k. Taxes on EBIT are $12k. $60k - $12k = $48k. This is the 'tax shield' approach. OCF = (EBITDA - Dep)(1-T) + Dep = EBITDA(1-T) + T*Dep. No, let's use the standard formulas. OCF = NOPAT + Dep. NOPAT = EBIT(1-T). OCF = EBIT(1-T)+Dep. EBIT is $40k. NOPAT is $28k. OCF is $48k. Distractor B says $48k, representing after-tax profit. But after-tax profit (Net Income) is $28k. So distractor B is incorrect. Distractor D says OCF is $48k, calculated as after-tax operating income (NOPAT, 28k)plusdepreciation(28k) plus depreciation (20k). This is the correct formula and result. OK, the original setup was fine. My self-doubt was unfounded. Let's stick with the original question and answers.

Question 13

An analyst is calculating the present value of a 10-year lease with annual payments of $100,000 due at the beginning of each year. The appropriate discount rate is 7%. The analyst uses a financial calculator set to the default END mode and calculates a PV of $702,358. To correct this value for the beginning-of-year timing, which of the following adjustments is required?

  1. Divide the calculated PV by (1.07), which correctly discounts the value for one additional period.
  2. Multiply the calculated PV by (1.07), which correctly accounts for one less period of discounting for each payment. (correct answer)
  3. Add the first payment of $100,000 to the calculated PV and use N=9 in a revised calculation.
  4. No adjustment is needed, as the difference between END and BEGIN mode is immaterial over a 10-year horizon.
Explanation: An annuity due's value is always higher than an equivalent ordinary annuity's value because each cash flow is received one period earlier and is therefore discounted less. The relationship is PVdue=PVordinary×(1+r)PV_{due} = PV_{ordinary} \times (1+r). The analyst calculated the ordinary annuity PV ($702,358). To find the correct annuity due PV, they must multiply this result by (1 + 0.07).

Question 14

A project requires an investment in Net Working Capital (NWC) of $50,000 at its inception (t=0). This investment is expected to be fully recovered at the end of the project's 4-year life. How should this NWC investment and recovery be reflected in the project's free cash flow timeline?

  1. As a $50,000 outflow at t=0 and a $50,000 inflow at t=4. (correct answer)
  2. As a single $50,000 outflow at t=0, as the recovery is a non-cash accounting entry.
  3. As a depreciation-like expense of $12,500 per year for four years, with no terminal value impact.
  4. As a $50,000 inflow at t=0 representing financing and a $50,000 outflow at t=4 representing repayment.
Explanation: Investment in NWC is a cash outflow at the beginning of a project because cash is used to fund items like inventory and accounts receivable. When the project ends, this NWC is typically liquidated (e.g., inventory sold, receivables collected), resulting in a cash inflow. Therefore, it is correctly modeled as an outflow at t=0 and an equal inflow at the end of the project life (t=4).

Question 15

An analyst is modeling a retirement savings plan where a client invests $5,000 (an outflow) at the end of each year for 20 years. When using a spreadsheet's FV function, FV(rate, nper, pmt, [pv], [type]), the analyst inputs rate=0.08, nper=20, and pmt=5000. What will the function most likely return as the future value, and why?

  1. A negative value, because the function assumes the future value is a withdrawal (outflow) that must balance the implied inflows from the PMT argument. (correct answer)
  2. A positive value, because the function correctly interprets the positive payment as an investment that grows over time.
  3. An error, because the PMT and PV arguments must have opposite signs to represent inflows and outflows correctly.
  4. A value of zero, because without a negative present value (PV) input, the function cannot calculate a future accumulation.
Explanation: Most financial calculators and spreadsheet functions require a consistent sign convention. If payments (PMT) are entered as positive values (implying inflows to the user), the function assumes the resulting future value (FV) must be an outflow of the opposite sign to balance the equation. Thus, it will return a negative number. To get a positive FV, the PMT should be entered as a negative number (e.g., -5000) representing the cash outflows of the investment.

Question 16

A project requires an initial investment of $250,000 at t=0. It is expected to generate annual operating cash flows of $70,000 for five years, with the first inflow occurring at t=1. At the end of the fifth year, the project will also require a $40,000 expenditure for environmental cleanup. When calculating the project's Net Present Value (NPV), how should the environmental cleanup cost be timed and signed?

  1. As a positive cash flow of $40,000 at t=5, added to the final operating cash flow before discounting.
  2. As a negative cash flow of $40,000 at t=0, combined with the initial investment.
  3. As a negative cash flow of $40,000 at t=5, netted against the final operating cash flow before discounting. (correct answer)
  4. As five separate negative cash flows of $8,000, representing an annual provision for the future cost.
Explanation: The correct approach is to time cash flows when they actually occur. The $40,000 cleanup cost is an outflow that occurs at the end of year 5. Therefore, it should be represented as a negative cash flow at t=5. It would be netted against the year 5 operating cash flow of 70,000,resultinginanetcashflowof+70,000, resulting in a net cash flow of +30,000 for that year before discounting.

Question 17

A company must make a series of four annual payments of $25,000 to settle a legal claim. The first payment is due to be paid three years from today. If the company uses a discount rate of 6%, which of the following is the correct procedure to find the present value of this liability at t=0?

  1. Calculate the present value of a 4-period ordinary annuity at t=3, then discount this single amount back for 3 years to t=0.
  2. Calculate the present value of a 4-period ordinary annuity at t=2, then discount this single amount back for 2 years to t=0. (correct answer)
  3. Calculate the present value of a 4-period annuity due at t=3, then discount this single amount back for 3 years to t=0.
  4. Calculate the future value of a 4-period ordinary annuity, then discount this single amount back from t=6 to t=0.
Explanation: The cash flows occur at t=3, t=4, t=5, and t=6. This is a 4-period ordinary annuity. The standard formula for the PV of an ordinary annuity (PV = PMT * [...]) calculates the value one period before the first payment. Since the first payment is at t=3, the formula will value the annuity at t=2. This resulting single sum must then be discounted back two periods to find its value at t=0.

Question 18

A project requires an initial investment of $250,000 at t=0. It is expected to generate annual operating cash flows of $70,000 for five years, with the first inflow occurring at t=1. At the end of the fifth year, the project will also require a $40,000 expenditure for environmental cleanup. When calculating the project's Net Present Value (NPV), how should the environmental cleanup cost be timed and signed?

  1. As a positive cash flow of $40,000 at t=5, added to the final operating cash flow before discounting.
  2. As a negative cash flow of $40,000 at t=0, combined with the initial investment.
  3. As a negative cash flow of $40,000 at t=5, netted against the final operating cash flow before discounting. (correct answer)
  4. As five separate negative cash flows of $8,000, representing an annual provision for the future cost.
Explanation: The correct approach is to time cash flows when they actually occur. The $40,000 cleanup cost is an outflow that occurs at the end of year 5. Therefore, it should be represented as a negative cash flow at t=5. It would be netted against the year 5 operating cash flow of 70,000,resultinginanetcashflowof+70,000, resulting in a net cash flow of +30,000 for that year before discounting.

Question 19

A project has the following non-conventional cash flows: Year 0: -1,600;Year1:+1,600; Year 1: +10,000; Year 2: -$10,000. An analyst notes that this pattern of signs creates an issue for one common capital budgeting metric. What is the primary implication of this cash flow pattern when using the Internal Rate of Return (IRR) method?

  1. The IRR will be negative, indicating that the project's costs outweigh its benefits over its lifetime.
  2. The IRR cannot be calculated because the sum of the positive cash flows equals the sum of the negative cash flows.
  3. The project may have two positive IRRs, making the standard 'accept if IRR > cost of capital' rule ambiguous. (correct answer)
  4. The project's NPV will be positive at all possible discount rates, making the IRR metric irrelevant.
Explanation: Projects with non-conventional cash flows (more than one change of sign) can have multiple IRRs or no IRR. In this case, there are two sign changes (- to + to -). This can lead to a situation where the NPV is zero at more than one discount rate, resulting in multiple IRRs. This ambiguity makes the standard IRR decision rule unreliable for such projects.

Question 20

A project requires an investment in Net Working Capital (NWC) of $50,000 at its inception (t=0). This investment is expected to be fully recovered at the end of the project's 4-year life. How should this NWC investment and recovery be reflected in the project's free cash flow timeline?

  1. As a $50,000 outflow at t=0 and a $50,000 inflow at t=4. (correct answer)
  2. As a single $50,000 outflow at t=0, as the recovery is a non-cash accounting entry.
  3. As a depreciation-like expense of $12,500 per year for four years, with no terminal value impact.
  4. As a $50,000 inflow at t=0 representing financing and a $50,000 outflow at t=4 representing repayment.
Explanation: Investment in NWC is a cash outflow at the beginning of a project because cash is used to fund items like inventory and accounts receivable. When the project ends, this NWC is typically liquidated (e.g., inventory sold, receivables collected), resulting in a cash inflow. Therefore, it is correctly modeled as an outflow at t=0 and an equal inflow at the end of the project life (t=4).