Break Even Answer
Step By Step Solution
Step 1: Calculate Contribution Margin (CM) per Unit for Each Product
To calculate the break-even point for a multi-product company, we need to determine a weighted-average contribution margin. This approach assumes that the sales mix remains constant at all sales volumes, including at the break-even point.
The contribution margin per unit is calculated as Selling Price per Unit minus Variable Cost per Unit .
The weighted-average contribution margin per unit considers the proportion of each product in the sales mix .
Step 2: Calculate the Weighted-Average Contribution Margin per Unit
Gizmo CM per Unit: $150 (Selling Price) - $70 (Variable Cost) = $80
Widget CM per Unit: $200 (Selling Price) - $90 (Variable Cost) = $110
Gizmo's Weighted CM: $80 (CM per Unit) * 0.60 (Sales Mix Percentage) = $48
Widget's Weighted CM: $110 (CM per Unit) * 0.40 (Sales Mix Percentage) = $44
The total break-even units are found by dividing total fixed costs by the weighted-average contribution margin per unit .
Step 3: Calculate Total Break-Even Units
Weighted-Average CM per Unit: $48 (Gizmo) + $44 (Widget) = $92
Since units must be whole numbers, we typically round up to ensure all fixed costs are covered. Rounded Total Break-Even Units: 2,392 units
Total Break-Even Units: $220,000 (Fixed Costs) / $92 (Weighted-Average CM per Unit) = 2,391.30 units
Now, distribute the total break-even units back to each product based on the sales mix .
Step 4: Calculate Break-Even Units for Each Product
Gizmo Break-Even Units: 2,392 (Total Break-Even Units) * 0.60 (Gizmo Sales Mix) = 1,435.2 units (round to 1,435 units)
Widget Break-Even Units: 2,392 (Total Break-Even Units) * 0.40 (Widget Sales Mix) = 956.8 units (round to 957 units)
Verification: 1,435 (Gizmo) + 957 (Widget) = 2,392 units. (Slight difference due to rounding individual product units up). Alternatively, if we use the precise total break-even units before rounding: Gizmo: 2,391.30 * 0.60 = 1,434.78 units (round to 1,435 units) Widget: 2,391.30 * 0.40 = 956.52 units (round to 957 units) Total: 1,435 + 957 = 2,392 units.
The contribution margin ratio is the contribution margin as a percentage of sales revenue.
Step 5: Calculate Contribution Margin Ratio for Each Product
Therefore, GadgetCo needs to sell approximately 1,435 Gizmos and 957 Widgets to break even.
Gizmo CM Ratio: $80 (CM per Unit) / $150 (Selling Price) = 0.5333 or 53.33%
Widget CM Ratio: $110 (CM per Unit) / $200 (Selling Price) = 0.5500 or 55.00%
Similar to the per-unit calculation, we weight the individual CM ratios by their sales mix .
Step 6: Calculate the Weighted-Average Contribution Margin Ratio
Gizmo's Weighted CM Ratio: 0.5333 (CM Ratio) * 0.60 (Sales Mix Percentage) = 0.31998
Widget's Weighted CM Ratio: 0.5500 (CM Ratio) * 0.40 (Sales Mix Percentage) = 0.22000
Step 7: Calculate Total Break-Even Sales Dollars
Weighted-Average CM Ratio: 0.31998 (Gizmo) + 0.22000 (Widget) = 0.53998 or 53.998%
Total Break-Even Sales Dollars: $220,000 (Fixed Costs) / 0.53998 (Weighted-Average CM Ratio) = $407,414.79
The total break-even sales in dollars are found by dividing total fixed costs by the weighted-average contribution margin ratio .
Summary
Summary of Break-Even Point for GadgetCo
Therefore, GadgetCo needs to achieve approximately $407,414.79 in total sales revenue to break even.
Total Break-Even Units: 2,392 units
Break-Even Units by Product:
Gizmo: 1,435 units
Widget: 957 units
Total Break-Even Sales Dollars: $407,414.79
Gizmo Sales Dollars
Widget Sales Dollars