Break-even quantity is the minimum quantity that wishes to be offered in order no longer to make a loss. In other words, at this quantity, the sales revenue just compensates for the fixed and variable prices. In phrases of contribution margin which is defined as the difference between the sales price and unit variable cost, it is the quantity at which the constant fee by myself is recovered. consequently, at a spoil-even amount, the contribution margin could be the same as the fixed cost.
Let Q be break-even quantity, then
Fixed Costs = Contribution Margin = Q * (S-V) where S and V are selling price and variable cost per unit.
Fixed costs = 6412 which does not change for the next year.
Both variable cost and selling price are set to change due to the new labor contract.
The units sold previous year can be calculated from direct labor cost and original labor cost per unit given:
Selling price = Original Price + (New labor cost - Old labor cost)/2
S2 = (33.74 + (8.41-7.91)/2) = 33.99
Direct Material Cost = Unit Material Cost * Q
Unit Material cost = Direct Material cost of previous year / Quantity sold previous year = 21313/1650 = 12.92
Similarly, Unit Carrying cost = 319/1650 = 0.19
Total Unit Variable Cost = Direct Labor + Direct material + Carrying cost
= 8.41 + 12.92 + 0.19
= 21.52
We can now derive Q at which fixed cost is the same as contribution margin
FC = CM * Q
6412 = (S2 - V2) * Q = (33.99 - 21.52) * Q
Q = 6412 / (33.99-21.52) = 514
Thus the break-even quantity at which the contribution margin will be the same as the fixed cost is 514 units.
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