If fixed costs are $561,000 and the unit contribution margin is $8.00, what is the break-even point in units if variable costs are decreased by $0.50 a unit?

The break even point is the point where in the total cost and the total revenue of the business are of the same value which means there is no profit or no loss. It is would be the minimum point that a business to reach in order to be able to recover the costs without any loss. At this point selling cost is equal to the sum of the fixed cost and the variable cost. To determine the break even point in units, we do as follows:

SC = FC + VC
Px = FC + Vx
where x is the number of units, P is the price per unit and V is the variable cost per unit.

x = FC / P - V
x = 561000 / (8.00 - 0.50)
x = 74800 units