Calculate the NPV break-even level of sales for a project requiring an investment of $3,000,000 and providing as cash flows:.15 × sales less $250,000.Assume the project will generate these cash flows for 10 years and that the discount rate is 10 percent.
A)$3,254,890
B)$3,504,890
C)$4,921,549
D)$19,686,667

Question

Quizplus · Accepted Answer

The NPV break-even level of sales is the point where the NPV of cash flows is equal to zero or the point where the project starts generating a positive NPV. To calculate the break-even level of sales, we need to find the level of sales that will make the present value of the cash flows equal to the initial investment of $3,000,000.

The cash flows for this project are:

CF = .15 × sales – $250,000

Using an annuity formula, the present value of the cash flows can be calculated as:

PV = CF x [(1 – (1 + r)^-n)/r] - I

where r is the discount rate, n is the number of periods (10 years), and I is the initial investment ($3,000,000).

Setting PV to zero and solving for sales, we get:

0 = (.15 × sales – $250,000) x [(1 – (1 + 0.10)^-10)/0.10] - $3,000,000

Solving for sales, we get:

Sales = $4,921,549

Therefore, the NPV break-even level of sales for this project is $4,921,549. The correct answer is C.

Calculate the NPV Break-Even Level of Sales for a Project