Question8 A firm is evaluating a project that requires an initial investment of $10,000. The project is expected to generate cash inflows of $3,000 in Year 1, $4,000 in Year 2, and $5,000 in Year 3. a) What is the payback period for this project? Select one alternative 2.8 years 2.6 years 3.0 years 2.3 years b) Assuming a positive discount rate, how would the discounted payback period compare to the regular payback period? Select one alternative It would be longer because future cash flows are discounted It would be the same because cash flows are unchanged It cannot be determined without the discount rate It would be shorter because discounting increases cash flows ResetMaximum marks: 2 Flag question undefined

Select one alternative 2.8 years 2.6 years 3.0 years 2.3 years

Question

Question8 A firm is evaluating a project that requires an initial investment of $10,000. The project is expected to generate cash inflows of $3,000 in Year 1, $4,000 in Year 2, and $5,000 in Year 3. a) What is the payback period for this project? Select one alternative 2.8 years 2.6 years 3.0 years 2.3 years b) Assuming a positive discount rate, how would the discounted payback period compare to the regular payback period? Select one alternative It would be longer because future cash flows are discounted It would be the same because cash flows are unchanged It cannot be determined without the discount rate It would be shorter because discounting increases cash flows ResetMaximum marks: 2 Flag question undefined Select one alternative 2.8 years 2.6 years 3.0 years 2.3 years单项选择题

A

2.8 years

B

2.6 years

C

3.0 years

D

2.3 years

Select one alternative 2.8 years 2.6 years 3.0 years 2.3 years

BlackTom AI · Accepted Answer

Payback period is the time required to recover the initial investment from cumulative cash inflows.

1. Relevant knowledge points and concepts
- Payback period: sum cash inflows each year until they equal the initial outlay. If recovery occurs partway through a year, add the fraction of that year equal to the remaining amount divided by that year’s cash inflow.
- Discounted payback: same idea but uses present values of cash inflows; with a positive discount rate, future cash flows are smaller in present-value terms, so recovery takes longer (or at best equal if rates are zero).

2. Complete reasoning process step by step
- Initial investment = $10,000.
- Add Year 1, Year 2, etc., cumulatively until the $10,000 is recovered.
- When cumulative before a year is below $10,000 and after including that year’s inflow exceeds $10,000, compute the fraction of the year needed.

3. Calculations with intermediate steps
- After Year 1: cumulative = $3,000. Remaining to recover = $10,000 − $3,000 = $7,000.
- After Year 2: cumulative = $3,000 + $4,000 = $7,000. Remaining = $10,000 − $7,000 = $3,000.
- Year 3 inflow = $5,000. Fraction of Year 3 needed = remaining / Year3 inflow = $3,000 / $5,000 = 0.6 years.
- Payback period = 2 full years + 0.6 year = 2.6 years.

4. Why the correct answer is correct
- The cumulative inflows do not reach $10,000 until Year 3. The precise fraction of Year 3 required is 0.6, so total payback is 2.6 years. This directly follows the payback definition and arithmetic above.

5. Why the other options are incorrect
- 2.8 years and 2.3 years: do not match the exact fraction 3,000/5,000 = 0.6 (which yields 2.6).
- 3.0 years: would mean no recovery until the end of Year 3; but recovery occurs partway through Year 3, so payback < 3.0.

Additionally, for part (b): with a positive discount rate the discounted payback period would be longer because discounting reduces the present value of future cash inflows, so it takes more time to recover the initial investment in present-value terms.