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Sagot :
Let's analyze each equation given in the options to determine which one does not accurately express the break-even point in sales dollars.
### Option 1: \[tex]$500,000 + 0.60X = X - This equation suggests that the total fixed costs plus 60% of the sales revenue should be equal to the total sales revenue. - Is this equation correct? To find the break-even point, we must consider fixed costs and the contribution margin ratio. The contribution margin ratio is 40%, meaning 60% represents the variable costs. - However, an accurate break-even calculation should account for fixed costs and the portion of sales contributing to fixed costs and profit (contribution margin). - Mathematically: \[ \text{Fixed Costs} + (\text{Variable Cost Ratio} \times X) = \text{Total Sales} \] must be correctly defined by considering the contribution margin (not variable cost ratio). - Therefore, this formulation does not align with proper break-even calculations required. ### Option 2: \$[/tex]500,000 + 0.40X = X
- This equation suggests that total fixed costs plus 40% of sales revenue should equal total sales revenue.
- The 40% is the contribution margin ratio.
- This aligns correctly with break-even point formulation because:
[tex]\[ \text{Fixed Costs} + (\text{Contribution Margin Ratio} \times X) = X \][/tex]
rearranged, this becomes:
[tex]\[ \text{Fixed Costs} = X \times (1 - \text{Contribution Margin Ratio}) \][/tex]
correctly describing the relationship and calculations for break-even point in sales dollars.
### Option 3: \[tex]$500,000 \div \$[/tex]500 = X
- This equation calculates the break-even point in sales units rather than sales dollars, using unit contribution margin.
- To find the break-even point in sales dollars, this result should be multiplied by the unit selling price, but the given formulation calculated as:
[tex]\[ \frac{\text{Fixed Costs}}{\text{Unit Contribution Margin}} = X \][/tex]
- This equation accurately calculates sales units required, not directly sale dollars.
### Option 4: \[tex]$500,000 \div 0.40 = X - This equation calculates the break-even point in sales dollars using contribution margin ratio. - Correctly formulated as: \[ \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}} = \text{Sales Dollars at Break-even} \] ### Conclusion: The equation that does not express the break-even point in sales dollars is Option 1: \$[/tex]500,000 + 0.60X = X. This formulation incorrectly represents the break-even point balance in terms of fixed costs and revenue ratios.
### Option 1: \[tex]$500,000 + 0.60X = X - This equation suggests that the total fixed costs plus 60% of the sales revenue should be equal to the total sales revenue. - Is this equation correct? To find the break-even point, we must consider fixed costs and the contribution margin ratio. The contribution margin ratio is 40%, meaning 60% represents the variable costs. - However, an accurate break-even calculation should account for fixed costs and the portion of sales contributing to fixed costs and profit (contribution margin). - Mathematically: \[ \text{Fixed Costs} + (\text{Variable Cost Ratio} \times X) = \text{Total Sales} \] must be correctly defined by considering the contribution margin (not variable cost ratio). - Therefore, this formulation does not align with proper break-even calculations required. ### Option 2: \$[/tex]500,000 + 0.40X = X
- This equation suggests that total fixed costs plus 40% of sales revenue should equal total sales revenue.
- The 40% is the contribution margin ratio.
- This aligns correctly with break-even point formulation because:
[tex]\[ \text{Fixed Costs} + (\text{Contribution Margin Ratio} \times X) = X \][/tex]
rearranged, this becomes:
[tex]\[ \text{Fixed Costs} = X \times (1 - \text{Contribution Margin Ratio}) \][/tex]
correctly describing the relationship and calculations for break-even point in sales dollars.
### Option 3: \[tex]$500,000 \div \$[/tex]500 = X
- This equation calculates the break-even point in sales units rather than sales dollars, using unit contribution margin.
- To find the break-even point in sales dollars, this result should be multiplied by the unit selling price, but the given formulation calculated as:
[tex]\[ \frac{\text{Fixed Costs}}{\text{Unit Contribution Margin}} = X \][/tex]
- This equation accurately calculates sales units required, not directly sale dollars.
### Option 4: \[tex]$500,000 \div 0.40 = X - This equation calculates the break-even point in sales dollars using contribution margin ratio. - Correctly formulated as: \[ \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}} = \text{Sales Dollars at Break-even} \] ### Conclusion: The equation that does not express the break-even point in sales dollars is Option 1: \$[/tex]500,000 + 0.60X = X. This formulation incorrectly represents the break-even point balance in terms of fixed costs and revenue ratios.
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