MC algo 8-3 Calculating Payback Period

There is a project with the following cash flows :

Year Cash Flow
0 −$ 23,900
1 7,100
2 7,750
3 7,150
4 5,200

What is the payback period?

Question

MC algo 8-3 Calculating Payback Period

There is a project with the following cash flows :

Year	Cash Flow
0	−$ 23,900
1	7,100
2	7,750
3	7,150
4	5,200

What is the payback period?

BlackTom AI · Accepted Answer

Payback period is the time required to recover the initial investment from the project’s cumulative (undiscounted) cash inflows.

1) Relevant concepts
- Payback period: number of years until cumulative cash inflows equal the initial cash outflow. It is usually computed using undiscounted cash flows (simple payback), so no time value of money adjustment is made here.
- If full recovery doesn’t occur at an integer year, compute the fractional year = (remaining unrecovered amount at start of the year) / (cash inflow during that year).

2) Step-by-step reasoning and calculations
Initial investment at Year 0 = −$23,900.

Compute cumulative cash flows year by year:
- End of Year 1: cumulative = −23,900 + 7,100 = −16,800
- End of Year 2: cumulative = −16,800 + 7,750 = −9,050
- End of Year 3: cumulative = −9,050 + 7,150 = −1,900
- End of Year 4: cumulative = −1,900 + 5,200 = +3,300

At the end of Year 3 the project has not yet recovered the initial outlay (cumulative = −$1,900). During Year 4 the cash inflow is $5,200, which is enough to recover the remaining $1,900.

3) Fractional year calculation (showing intermediate steps)
Remaining amount to recover at start of Year 4 = $1,900
Cash inflow in Year 4 = $5,200
Fraction of Year 4 required = 1,900 / 5,200 = 0.3653846...

Total payback period = 3 full years + 0.3653846 year = 3.3653846 years ≈ 3.37 years

4) Why the correct answer is correct
The calculated payback (3.365... years) rounds to 3.37 years, matching the provided correct answer. The method directly follows the definition of payback using cumulative undiscounted cash flows and the fractional-year adjustment.

5) Why the other options are incorrect
- 3.63, 3.81, 4.00, and 2.73 years do not match the precise cumulative recovery calculation above. For example, 4.00 would imply recovery only at the end of Year 4 (ignoring fractional recovery during Year 4), and 2.73 or 3.63/3.81 are inconsistent with the remaining $1,900 and Year 4 cash inflow of $5,200.

6) Conclusion
The payback period is 3.37 years, which confirms the provided answer.

MC algo 8-3 Calculating Payback Period There is a project with the following cash flows : Year Cash Flow 0 −$ 23,900 1 7,100 2 7,750 3 7,150 4 5,200 What is the payback period?单项选择题

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