A contractor estimates their annual fixed costs at $180,000, variable costs at 65% of revenue, and wants to achieve a 15% profit margin. What annual revenue is needed to meet these goals?
Correct Answer
A) $900,000
Let R = Revenue. Equation: R = Fixed Costs + Variable Costs + Profit. R = $180,000 + 0.65R + 0.15R. Solving: R - 0.80R = $180,000, so 0.20R = $180,000, therefore R = $900,000.
Why This Is the Correct Answer
The correct answer uses the fundamental business equation where Revenue equals all costs plus desired profit. By setting up the equation R = Fixed Costs + Variable Costs + Profit, and expressing variable costs (65% of revenue) and profit (15% of revenue) as percentages of R, we get R = $180,000 + 0.65R + 0.15R. Solving this equation by combining like terms gives us 0.20R = $180,000, which yields R = $900,000.
Why the Other Options Are Wrong
Option B: $1,035,000
This answer of $553,846 appears to result from dividing fixed costs by an incorrect percentage, possibly confusing the contribution margin calculation or omitting the profit requirement entirely.
Option C: $553,846
This answer of $692,308 appears to result from incorrectly calculating the breakeven point without properly accounting for the 15% profit margin requirement, likely using only fixed costs divided by contribution margin.
Option D: $692,308
This answer of $1,035,000 suggests an error in the algebraic manipulation, possibly adding percentages incorrectly or miscalculating the coefficient when combining variable costs and profit percentages.
Memory Technique
Remember 'FVPR': Fixed + Variable + Profit = Revenue. When percentages are involved, collect all R terms on one side - the remaining percentage represents your 'contribution to fixed costs and profit.'
Reference Hint
Look up 'Business and Finance' chapter, specifically sections on breakeven analysis, profit margin calculations, and cost-volume-profit relationships
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