Question27 Your firm is considering expanding its current operations. The expansion requires an initial investment of $215,000 and is expected to increase the cash inflows by $60,000 in the first year, $140,000 in the second year, and $150,000 a year for the following 2 years. However, the firm has an outstanding loan that must be repaid in 2.5 years and thus will need the $215,000 at that time. Should the firm expand at this time? Why or why not? Yes; because the money will be recovered in 2.10 years No; because the project never pays back No; because the money will not be recovered in time to repay the loan Yes; because the money will be recovered in 1.69 years Yes; because the money will be recovered in 1.87 years ResetMaximum marks: 2 Flag question undefinedSingle choice
A
Yes; because the money will be recovered in 2.10 years
B
No; because the project never pays back
C
No; because the money will not be recovered in time to repay the loan
D
Yes; because the money will be recovered in 1.69 years
E
Yes; because the money will be recovered in 1.87 years

Question

Question27 Your firm is considering expanding its current operations. The expansion requires an initial investment of $215,000 and is expected to increase the cash inflows by $60,000 in the first year, $140,000 in the second year, and $150,000 a year for the following 2 years. However, the firm has an outstanding loan that must be repaid in 2.5 years and thus will need the $215,000 at that time. Should the firm expand at this time? Why or why not? Yes; because the money will be recovered in 2.10 years No; because the project never pays back No; because the money will not be recovered in time to repay the loan Yes; because the money will be recovered in 1.69 years Yes; because the money will be recovered in 1.87 years ResetMaximum marks: 2 Flag question undefinedSingle choice

A

Yes; because the money will be recovered in 2.10 years

B

No; because the project never pays back

C

No; because the money will not be recovered in time to repay the loan

D

Yes; because the money will be recovered in 1.69 years

E

Yes; because the money will be recovered in 1.87 years

BlackTom AI · Accepted Answer

Payback period: compute when cumulative cash inflows equal the $215,000 initial outlay.

1) Relevant concepts
- Payback period = time required for cumulative cash inflows to recover the initial investment.
- Decision rule here: if payback ≤ 2.5 years (loan due date), the firm will have the funds to repay the loan on time.

2) Step-by-step reasoning and cumulative totals
- Initial investment (t0): −$215,000.
- End of Year 1 inflow = $60,000. Cumulative recovered = $60,000.
  Remaining unrecovered = $215,000 − $60,000 = $155,000.
- End of Year 2 inflow = $140,000. Cumulative recovered = $60,000 + $140,000 = $200,000.
  Remaining unrecovered = $215,000 − $200,000 = $15,000.
- The remaining $15,000 is recovered during Year 3, which has a $150,000 inflow.

3) Intermediate calculation for fractional year
- Fraction of Year 3 needed = remaining unrecovered / Year 3 inflow = $15,000 / $150,000 = 0.10 year.
- Payback period = 2 full years + 0.10 year = 2.10 years.

4) Why this answer is correct
- The payback period (2.10 years) is less than the loan repayment requirement (2.5 years), so the firm will have recovered the $215,000 in time to make the required loan payment. Therefore the firm should expand now.

5) Why the other choices are incorrect
- “Never pays back” is false because cumulative inflows exceed $215,000 by Year 3.
- “Will not be recovered in time to repay the loan” is incorrect because 2.10 years < 2.5 years.
- The options giving 1.69 years or 1.87 years are calculation errors; they understate the actual time since after two years only $200,000 is recovered, leaving $15,000 for Year 3.

6) Conclusion
The correct conclusion is: Yes; because the money will be recovered in 2.10 years, which matches the provided answer.

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