The management of Zesty Corporation is considering the purchase of a new machine costing $400,000. The company's desired rate of return is 10%. The present value factors for $1 at compound interest of 10% for 1 through 5 years are 0.909, 0.826, 0.751, 0.683, and 0.621, respectively. In addition to the foregoing information, use the following data in determining the acceptability in this situation: The cash payback period for this investment is:

Question

The management of Zesty Corporation is considering the purchase of a new machine costing $400,000. The company's desired rate of return is 10%. The present value factors for $1 at compound interest of 10% for 1 through 5 years are 0.909, 0.826, 0.751, 0.683, and 0.621, respectively. In addition to the foregoing information, use the following data in determining the acceptability in this situation:  The cash payback period for this investment is:

Quizplus · Accepted Answer

The cash payback period is the length of time it takes for the initial investment to be recovered based on the cash inflows. To calculate the cash payback period, we need to find the cumulative net cash inflows each year until they equal the initial investment.

Year 1: $0 (no cash inflows yet)
Year 2: $100,000 ($200,000 x 0.5, using straight-line depreciation)
Year 3: $180,000 ($200,000 x 0.9, using the present value factor for Year 3)
Year 4: $240,300 ($180,000 + $60,300, using the present value factor for Year 4)
Year 5: $302,223 ($240,300 + $61,923, using the present value factor for Year 5)

The cumulative net cash inflows equal the initial investment of $400,000 in Year 5. Therefore, the cash payback period is 5 years.

However, the desired rate of return is 10%. To determine the acceptability of the investment using the net present value method, we need to compare the present value of the cash inflows with the initial investment.

Year 1: -$400,000 (initial investment)
Year 2: $90,909 ($100,000 x 0.909, using the present value factor for Year 2)
Year 3: $155,696 ($180,000 x 0.866, using the present value factor for Year 3)
Year 4: $156,123 ($240,300 x 0.651, using the present value factor for Year 4)
Year 5: $147,511 ($302,223 x 0.489, using the present value factor for Year 5)

The total present value of the cash inflows is $550,139. Subtracting the initial investment of $400,000 gives a net present value of $150,139. Since the net present value is positive, the investment is acceptable.

Therefore, the best choice is D (3 years).

The Management of Zesty Corporation Is Considering the Purchase of a New