Guerilla Radio Broadcasting has a project available with the following cash flows :

Year Cash Flow
0 −$ 14,000
1 5,800
2 7,100
3 6,100
4 4,900

What is the payback period?

Question

Guerilla Radio Broadcasting has a project available with the following cash flows :

Year	Cash Flow
0	−$ 14,000
1	5,800
2	7,100
3	6,100
4	4,900

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.

Relevant knowledge points and concepts:
- Payback period uses cumulative cash flows (usually undiscounted unless “discounted payback” is specified).
- When full recovery happens partway through a year, fractional year = (remaining unrecovered amount at start of year) / (cash inflow in that year).

Step-by-step reasoning and calculations:
1. Initial outflow at time 0 = $14,000 (amount to be recovered).
2. Year 1 inflow = $5,800. Cumulative after Year 1 = 5,800. Remaining to recover = 14,000 − 5,800 = $8,200.
3. Year 2 inflow = $7,100. Cumulative after Year 2 = 5,800 + 7,100 = $12,900. Remaining to recover = 14,000 − 12,900 = $1,100.
4. Year 3 inflow = $6,100. The unrecovered $1,100 is recovered during Year 3. Fraction of Year 3 required = 1,100 / 6,100.

Intermediate arithmetic:
- Remaining after Year 2 = $1,100.
- Fractional year = 1,100 ÷ 6,100 ≈ 0.1803278689 years.

Combine whole years and fractional year:
- Payback period = 2 years + 0.1803278689 years ≈ 2.18033 years → rounded to 2.18 years.

Why this answer is correct:
- The project has not fully recouped the $14,000 by the end of Year 2 (only $12,900 recovered). Partial recovery in Year 3 completes the payback after 0.1803 of that year, so total payback = 2.18 years.

Why other plausible answers would be incorrect:
- Saying 2 years would be incorrect because only $12,900 (not $14,000) is recovered by then.
- Saying 3 years is too conservative because full Year 3 inflow isn’t required; recovery occurs partway through Year 3.
- Any other rounded figure that does not account for the fractional year (1,100/6,100) misstates the timing.

Final confirmation:
The computed payback period is 2.18 years, matching the provided correct answer.

Guerilla Radio Broadcasting has a project available with the following cash flows : Year Cash Flow 0 −$ 14,000 1 5,800 2 7,100 3 6,100 4 4,900 What is the payback period?单项选择题

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Consider a project with the following cash flows: [table] YEAR | CASH FLOWS 0 | -10000 1 | 4000 2 | 4000 3 | 4000 4 | 4000 [/table] The payback period for this project is closest to:

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