Glenmore Advanced Systems manufactures the ProShield X7, a high-performance industrial sensor array used in automated safety systems for large-scale manufacturing facilities. The company sold 36,000 units this year at $777 each, incurring variable costs of $557 per unit and total fixed costs of $1,759,000. Management wants to evaluate overall profitability through contribution margin analysis and determine the break-even point in both units and sales dollars.
Correct Answers
net Income
$6,161,000.00
break Even Sales
$6,212,468.18
break Even Units
7,996
contribution Margin Per Unit
220
Step-by-Step Solution
MIXED PROBLEM — Contribution Margin + Break-Even CONTRIBUTION MARGIN INCOME STATEMENT: Sales (36,000 units × $777.00) $27,972,000.00 Less: Variable Costs (36,000 × $557.00) $20,052,000.00 ───────────────────────────────────────────────────────── Contribution Margin $7,920,000.00 Less: Fixed Costs $1,759,000.00 ───────────────────────────────────────────────────────── Net Income $6,161,000.00 Per Unit: CM per Unit = $777.00 − $557.00 = $220.00 CM Ratio = $220.00 ÷ $777.00 = 28.31% BREAK-EVEN ANALYSIS: Break-Even Units = Fixed Costs ÷ CM per Unit Break-Even Units = $1,759,000.00 ÷ $220.00 = 7995.4545 → 7996 units (rounded up) Break-Even Sales = Fixed Costs ÷ CM Ratio Break-Even Sales = $1,759,000.00 ÷ 28.3140% = $6,212,468.18