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?

Question

Quizplus · Accepted Answer

To determine the level of sales at which the firm should be willing to abandon the project, we need to compare the present value of the cash inflows and outflows at the end of year 3 with the present value of the cash inflows and outflows if the project is continued for the full 5 years.

If the project is continued for the full 5 years, the total cash inflow will be calculated as follows:

Total cash inflow = Number of units sold × Cash flow per unit × Number of years

Total cash inflow = 2,100 × €20 × 5

Total cash inflow = €210,000

The total cost of the project, including the initial cost of €120,000, can be discounted back to year 0 using the discount rate of 12%.

PV(cost of project) = €120,000 / (1 + 0.12)^0

PV(cost of project) = €120,000

PV(total cash inflow) = €210,000 / (1 + 0.12)^5

PV(total cash inflow) = €111,720

NPV = PV(total cash inflow) - PV(cost of project)

NPV = €111,720 - €120,000

NPV = -€8,280

This means that if the project is continued for the full 5 years, it will result in a negative net present value.

If the project is abandoned after 3 years, the total cash inflow will be calculated as follows:

Total cash inflow = Number of units sold × Cash flow per unit × Number of years

Total cash inflow = 2,100 × €20 × 3

Total cash inflow = €126,000

The total cost of the project, including the initial cost of €120,000 and the salvage value of €50,000, can be discounted back to year 0 using the discount rate of 12%.

PV(cost of project) = (€120,000 - €50,000) / (1 + 0.12)^3

PV(cost of project) = €52,394

PV(total cash inflow) = €126,000 / (1 + 0.12)^3

PV(total cash inflow) = €83,113

NPV = PV(total cash inflow) - PV(cost of project)

NPV = €83,113 - €52,394

NPV = €30,719

Therefore, the firm should abandon the project if the net present value of continuing with the project for the full 5 years is negative and the net present value of abandoning the project after 3 years is positive. This occurs when sales fall below 1,479 units per year (i.e. the level of sales at which the total cash inflow for 3 years equals the cost of the project including salvage value). Therefore, the answer is C).

Your ﬁRm Is Considering a Project with a ﬁVe-Year Life