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.
