Answer:
3,074 units sold or total revenue of $236,698 per year
Explanation:
cost of machine $540,000
depreciation expense per year = $540,000 / 5 = $108,000
contribution margin per unit sold = $77 - $29 = $48
we generally calculate the financial break even point of a business by using the following formula:
= EBIT × (1 - interest expense) × (1 - tax rate) - preferred dividends
But when we are dealing with projects, the financial break even point is the sales level at which the project's NPV = $0. If the sales level is lower, then the project will be rejected, and if the sales level is higher, then it should be accepted.
using an annuity formula, the free cash flow per year needed for the NPV = $0 is $540,000 / 3.8897 (PV annuity factor, 9%, 5 periods) = $138,828.19
$138,828.19 = {[(unit sales x $48) - $108,000] x 0.78} + $108,000
$30,828.19 = [(unit sales x $48) - $108,000] x 0.78
$39,523.32 = (unit sales x $48) - $108,000
$147,523.32 = unit sales x $48
unit sales = $147,523.32 / $48 = 3,073.40 units ≈ 3,074 units sold
