Given a break?even point of 88,000 units and a contribution margin per unit of $9.60, the total number of units that must be sold to reach a net pre-tax profit of $18,096 is _____.
A)89,885 units
B)88,000 units
C)1,885 units
D)indeterminable

Question

Quizplus · Accepted Answer

First, we need to calculate the total contribution margin necessary to reach the desired net pre-tax profit:

Net pre-tax profit = (sales - variable costs) - fixed costs 
$18,096 = (P - $9.60)88,000 - fixed costs

Solving for fixed costs, we get:

Fixed costs = (P - $9.60)88,000 - $18,096

We do not know the selling price (P), but we can find it by using the break-even equation:

88,000P = 88,000($9.60) + fixed costs 
88,000P = $844,800 + [(P - $9.60)88,000 - $18,096] 
88,000P = $826,704 + 88,000P - $844,800 
P = $10.26

Now we can substitute P back into the equation for fixed costs:

Fixed costs = ($10.26 - $9.60)88,000 - $18,096 
Fixed costs = $58,080

Finally, we can find the total units needed to reach the desired profit:

Net pre-tax profit = (P - $9.60)Q - $58,080 
$18,096 = ($10.26 - $9.60)Q - $58,080 
Q = 89,885

Therefore, the answer is A (89,885 units).

Given a Break?even Point of 88,000 Units and a Contribution