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A small shop fabricates threshers for rice producers in the locality
A small shop fabricates threshers for rice producers in the locality. The shop can produce each thresher at a labor cost of $1,800.00. The cost of materials for each unit is $2,500.00. The variable costs amounts to $650.00 per unit, while fixed charges incurred per annum totals $69,000.00 If the portable threshers are sold at $7,800.00 per unit, how many units must be produced and sold per annum to break-even?
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Expert Solution
The cost data is as follows -
Labor cost = $1,800 per unit
Material cost = $2,500 per unit
Variable cost = $650 per unit
Fixed charges = $69,000
Price per unit = $7,800
Let the number of units that must be sold per annum to breakeven is X units
At break even, total revenue equals total cost.
Total revenue = Total cost
Price per unit * Break even number of units = Total labor cost + Total material cost + Total variable cost + Fixed charges
Price per unit * Breakeven number of units = [Labor cost per unit * Breakeven number of units] + [Material cost per unit * Breakeven number of units] + [Variable cost per unit * Breakeven number of units] + Fixed charges
$7,800 * X = [$1,800 * X] + [$2,500 * X] + [$650 * X] + $69,000
7800X = 1800X + 2500X + 650X + 69000
7800X = 4950X + 69000
7800X - 4950X = 69000
2850X = 69000
X = 69000/2850 = 24.12
Thus,
The small shop must produce and sold approximately 24 units per annum to break even.
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