Answer: 47,757 units
Explanation:
To answer this we would need to first find the Contribution Margin. Contribution Margin is the differnce between the sales price and the variable cost per unit.
When the Fixed cost is divided by the Contribution margin, we get the BREAK-EVEN POINT which is where income is zero.
We will then add our required profit to find the Number of units needed.
Calculating the Variable costs we have,
= Direct Material + Direct Labor + Variable Factory overhead+ Variable Marketing Costs
= 235,800 + 241,600 + 151,600 + 51,600
= $680,600
Divide by the number of units to find the Variable cost per unit is,
= 680,609/41,000
= $16.6 per unit.
The Sales per unit will be,
= 984,000/41,000
= $24 per unit.
The Contribution Margin from earlier would therefore be,
= Sales - Variable Cost
= 24 - 16.6
= 7.4
Now we divide the Fixed Costs by that to find the Break-Even Point.
Fixed cost = Fixed factory overhead + Fixed marketing cost
= 111,600 + 108,000
= $219,000
Target sale in unit =Target profit + Fixed cost/Contribution per unit
= 133,800 + 219,000/7.4
= $353,400/7.4
= 47756.7567568
= 47,757
47,757 is the number of units that must be sold in order to achieve a target pretax income of $133,800.
