Quarry Hill Systems is a mid-sized manufacturer based in Denver, Colorado, specializing in ruggedized industrial data acquisition terminals used in mining and quarry operations. Management wants to analyze the company's profitability at current production levels and determine the break-even point to better plan for fluctuating demand cycles.
Correct Answers
net Income
$11,717,500.00
break Even Sales
$3,458,146.21
break Even Units
2,907
contribution Margin Per Unit
383
Step-by-Step Solution
MIXED PROBLEM — Contribution Margin + Break-Even CONTRIBUTION MARGIN INCOME STATEMENT: Sales (33,500 units × $1,190.00) $39,865,000.00 Less: Variable Costs (33,500 × $807.00) $27,034,500.00 ───────────────────────────────────────────────────────── Contribution Margin $12,830,500.00 Less: Fixed Costs $1,113,000.00 ───────────────────────────────────────────────────────── Net Income $11,717,500.00 Per Unit: CM per Unit = $1,190.00 − $807.00 = $383.00 CM Ratio = $383.00 ÷ $1,190.00 = 32.18% BREAK-EVEN ANALYSIS: Break-Even Units = Fixed Costs ÷ CM per Unit Break-Even Units = $1,113,000.00 ÷ $383.00 = 2906.0052 → 2907 units (rounded up) Break-Even Sales = Fixed Costs ÷ CM Ratio Break-Even Sales = $1,113,000.00 ÷ 32.1849% = $3,458,146.21