Answered

Benson Company has an opportunity to purchase a forklift to use in its heavy equipment rental business. The forklift would be leased on an annual basis during its first two years of operation. Thereafter, it would be leased to the general public on demand. Benson would sell it at the end of the fifth year of its useful life. The expected cash inflows and outflows follow:




Year		Nature of ItemCash InflowCash Outflow

Year 1		Purchase price\$81,200

Year 1		Revenue\$31,500

Year 2		Revenue31,500

Year 3		Revenue26,500

Year 3		Major overhaul8,300

Year 4		Revenue17,500

Year 5		Revenue15,500

Year 5		Salvage value7,100






Required:

A& b. Determine the payback period using the accumulated and average cash flows approaches.



Note: Round your answers to 1 decimal place.



a. Payback period (accumulated cash flows)		years

b. Payback period (average cash flows)		years

Verified Answer :

  • Calculate net cash flows annually: Year 1 \(\(-\$49,700\)\), Year 2 \(\(\$31,500\)\), Year 3 \(\(\$18,200\)\), Year 4 \(\(\$17,500\)\), Year 5 \(\(\$22,600\)\).
  • Determine cumulative flows for the accumulated approach: Year 1 \(\(-\$49,700\)\), Year 2 \(\(-\$18,200\)\), Year 3 \(\(\$0\)\). Payback is \(3.0\) years.
  • Calculate average annual cash flow for the average approach: \(\$40,100 / 5 = \$8,020\).
  • Find payback period for the average approach: \(\$81,200 / \$8,020 \approx 10.1\) years.
  • Final Answers: Accumulated \(\boxed{3.0}\) years; Average \(\boxed{10.1}\) years.

Explanation

  1. Analyzing Cash Flows

The objective is to calculate the payback period for Benson Company's investment in a forklift, which costs \(\$81,200\). The payback period is the time required to recover the initial investment from the net cash inflows. We use two approaches: the accumulated cash flows approach and the average cash flows approach.

The net cash flow for each year is determined by calculating the difference between total inflows and total outflows:

  • Year 1: \(\$31,500 - \$81,200 = -\$49,700\)
  • Year 2: \(\$31,500 = \$31,500\)
  • Year 3: \(\$26,500 - \$8,300 = \$18,200\)
  • Year 4: \(\$17,500 = \$17,500\)
  • Year 5: \(\$15,500 + \$7,100 = \$22,600\)

The total net cash flow over the five-year period is the sum of these net cash flows: \(-49,700 + 31,500 + 18,200 + 17,500 + 22,600 = \$40,100\).

  1. Calculating Payback Period: Accumulated Cash Flows Approach

To find the payback period using the accumulated cash flows approach, we sum the net cash flows year by year until the cumulative sum reaches the initial investment amount:

  • End of Year 1: \(-\$49,700\)
  • End of Year 2: \(-\$49,700 + \$31,500 = -\$18,200\)
  • End of Year 3: \(-\$18,200 + \$18,200 = \$0\)

At the end of Year 3, the cumulative net cash flow is exactly \(\$0\), meaning the full initial investment of \(\$81,200\) has been recovered. Therefore, the payback period using the accumulated cash flows approach is exactly \(3.0\) years.

  1. Calculating Payback Period: Average Cash Flows Approach

To find the payback period using the average cash flows approach, we first calculate the average annual net cash flow. This is done by dividing the total net cash flow over the useful life of the asset by the number of years:

  • Average Annual Net Cash Flow = \(\text{Total Net Cash Flow} / 5\)
  • Average Annual Net Cash Flow = \(\$40,100 / 5 = \$8,020\)

Next, we divide the initial investment by this average annual cash flow:

  • Payback Period = \(\text{Initial Investment} / \text{Average Annual Net Cash Flow}\)
  • Payback Period = \(\$81,200 / \$8,020 \approx 10.1247\)

Rounding to one decimal place, the payback period using the average cash flows approach is \(10.1\) years.

  1. Conclusion

In summary, the payback period using the accumulated cash flows approach is \(\boxed{3.0}\) years, and the payback period using the average cash flows approach is \(\boxed{10.1}\) years.

Examples

Businesses often use the payback period as a simple tool to assess the time it takes to recover an investment. For example, if a cafe owner decides to purchase a new high-end espresso machine for \(\$5,000\), they would track the extra daily profits generated by the machine. If the machine generates an additional \(\$1,000\) in profit each month, the owner can determine that the investment will pay for itself in \(5\) months. This helps owners quickly decide whether a capital investment aligns with their business's liquidity needs.

Related Questions