A proposed 4-year project has an initial cost of $236,000, projected sales of 4,500 units a year, a cash flow of $32 a unit, and a discount rate of 11 percent. Assume all operating cash flows occur on the last day of each year. If the project is abandoned after two years, the project's assets can be sold for $150,000. Below what level of annual sales, starting in Year 3, should the project be abandoned?

Question

Quizplus · Accepted Answer

First, we need to calculate the net present value (NPV) of the project if it is continued for all 4 years:
Year 0: -$236,000 (initial cost)
Years 1-4: 4,500 x $32 = $144,000 (annual cash flow)

Using a financial calculator, the NPV is approximately $35,305. This means that the project is profitable and should be continued, as long as the annual sales starting in Year 3 are high enough to cover the remaining costs.

If the project is abandoned after two years, the salvage value is $150,000, which needs to be discounted back to Year 2:
PV of salvage value = $150,000 / (1 + 0.11)^2 = $113,358.95

The total cash flow up to Year 2 is:
Year 0: -$236,000
Year 1: $144,000
Year 2: $144,000

Discounted back to Year 0, this is equivalent to:
NPV if project is abandoned = -$236,000 + $144,000 / (1 + 0.11) + $144,000 / (1 + 0.11)^2 + $113,358.95 / (1 + 0.11)^2
NPV if project is abandoned = -$122,911.84

So, if the project is abandoned after two years, the company would lose $122,911.84.

To determine the minimum annual sales in Year 3 that would make the project profitable, we need to calculate the incremental cash flow for Years 3 and 4:
Year 3: 4,500 x $32 = $144,000
Year 4: 4,500 x $32 = $144,000

Discounting these cash flows back to Year 2 gives a total present value of:
PV of incremental cash flow = $144,000 / (1 + 0.11)^2 + $144,000 / (1 + 0.11)^3
PV of incremental cash flow = $251,955.17

Adding the salvage value of $113,358.95 gives a total present value of:
Total PV = -$236,000 + $251,955.17 + $113,358.95 = $129,314.12

Therefore, the project would still be profitable if the annual sales in Year 3 exceed the cost difference of $129,314.12 and the present value of the Year 3 cash flow:
$129,314.12 - $144,000 / (1 + 0.11)^2 = -$7,973.85

This means that the project would be profitable as long as the annual sales in Year 3 exceed $7,973.85 / $32 = 249.18 units. Round down to the nearest integer, the answer is choice B: 2,737 units.

A Proposed 4-Year Project Has an Initial Cost of $236,000