Your firm is considering a project with a five-year life and an initial cost of $120,000. The discount rate for the project is 12%. The firm expects to sell 2,100 units a year. The cash flow per unit is $20. The firm will have the option to abandon this project after three years at which time it expects it could sell the project for $50,000. At what level of sales should the firm be willing to abandon this project?
A) 420 units
B) 1,041 units
C) 1,479 units
D) 1,618 units
E) 2,500 units

Question

Quizplus · Accepted Answer

First, we need to calculate the present value (PV) of the project's cash flows over its five-year life. The cash flow per unit is $20, and the firm expects to sell 2,100 units a year, so the annual cash flow is:

2,100 units/year x $20/unit = $42,000/year

To calculate the present value of these cash flows, we use the formula:

PV = CF/(1+r)^t, where CF is the cash flow, r is the discount rate, and t is the time period.

Using this formula for each year, we get:

PV of Year 1 cash flows = $42,000/(1+0.12)^1 = $37,500
PV of Year 2 cash flows = $42,000/(1+0.12)^2 = $33,482
PV of Year 3 cash flows = $42,000/(1+0.12)^3 = $29,881
PV of Year 4 cash flows = $42,000/(1+0.12)^4 = $26,654
PV of Year 5 cash flows = $42,000/(1+0.12)^5 = $23,764

The total present value of the cash flows is:

PV of all cash flows = $37,500 + $33,482 + $29,881 + $26,654 + $23,764 = $151,281

Next, we need to calculate the PV of the salvage value of the project at the end of Year 3. The salvage value is $50,000, and it will be received three years from now, so its present value is:

PV of salvage value = $50,000/(1+0.12)^3 = $34,452

To calculate the net present value (NPV) of the project, we subtract the initial cost from the sum of the present values of the cash flows and salvage value:

NPV = $151,281 + $34,452 - $120,000 = $65,733

If the project is abandoned after three years, the firm will lose the cash flows and the remaining salvage value. Therefore, the firm should abandon the project if the present value of the cash flows up to Year 3 is less than the initial cost:

PV of Year 1-3 cash flows = $37,500 + $33,482 + $29,881 = $100,863

If the present value of the cash flows up to Year 3 is less than $120,000, then the firm should abandon the project. Solving for the unit sales that produce a PV of $120,000, we get:

$120,000 = ($42,000 x Units/year)/(1+0.12)^1 + ($42,000 x Units/year)/(1+0.12)^2 + ($42,000 x Units/year)/(1+0.12)^3

$120,000 = $36,872 x Units/year

Units/year = $120,000/$36,872 = 3,241 units/year

Since we only need the sales up to Year 3, we divide 3,241 by 3 to get:

Units/year = 3,241/3 = 1,080

Therefore, the firm should be willing to abandon the project if it sells fewer than 1,080 units per year up to Year 3. Since the firm expects to sell 2,100 units a year, it should not abandon the project unless there is a significant drop in sales. The closest answer choice to 1,080 is 1,479, which is the correct answer.

Your Firm Is Considering a Project with a Five-Year Life