What is the NPV break-even level of sales for a project costing $4,000,000 and generating cash flows according to.30 × sales - $450,000? Assume the project will last 10 years and requires a discount rate of 12 percent.
A)$2,093,654
B)$2,359,047
C)$3,859,798
D)$13,783,333

Question

Quizplus · Accepted Answer

The NPV equation for this project is:

NPV = (PV of cash inflows) - (PV of cash outflows)
PV of cash inflows = Σ(FCF / (1 + r)^n) where n = year of cash flow
PV of cash outflows = initial investment = $4,000,000

Setting the NPV to zero and solving for sales:

0 = Σ(0.3S - 450,000) / (1 + 0.12)^n - 4,000,000
0 = Σ(0.3S / 1.12^n) - Σ(450,000 / 1.12^n) - 4,000,000

To find the break-even level of sales, we need to solve for S:

Σ(0.3S / 1.12^n) = Σ(450,000 / 1.12^n) + 4,000,000
Σ(0.3S / 1.12^n) = 450,000 * Σ(1 / 1.12^n) + 4,000,000

Using the formula for the sum of a geometric series:

Σ(1 / 1.12^n) = (1 - 1 / 1.12^10) / (1 - 1 / 1.12) = 6.784

Substituting and solving for S:

0.3S / 1.12^10 = 450,000 * 6.784 + 4,000,000
S = (450,000 * 6.784 + 4,000,000) * 1.12^10 / 0.3
S = $3,859,798.77

Therefore, the NPV break-even level of sales for this project is $3,859,798.77.

What Is the NPV Break-Even Level of Sales for a Project