Compute The Break-Even Point In Units Using Mathematics

Compute the break-even point in units using (a) the mathematical equation and (b) unit contribution margin

Rice Company has a unit selling price of $630, variable costs per unit of $410, and fixed costs of $200,000. Compute the break-even point in units using: (a) the mathematical equation and (b) the unit contribution margin. Round answers to 0 decimal places, e.g., 1,225.

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The calculation of the break-even point is fundamental in managerial accounting, enabling businesses to determine the sales volume at which total revenues equal total costs, thereby resulting in zero profit. For Rice Company, which has a unit selling price of $630, variable costs per unit of $410, and fixed costs of $200,000, two approaches can be used: the mathematical equation and the contribution margin method.

a) Mathematical Equation Method

The mathematical formula for the break-even point in units is:

Break-even units = Fixed Costs / (Unit Selling Price - Variable Costs per Unit)

Substituting Rice Company's figures:

Break-even units = $200,000 / ($630 - $410) = $200,000 / $220 ≈ 909.09 units

Rounding to the nearest whole unit gives 909 units.

This means Rice Company needs to sell approximately 909 units to cover all fixed and variable costs, resulting in neither profit nor loss.

b) Unit Contribution Margin Method

The contribution margin per unit is calculated as:

Unit contribution margin = Unit Selling Price - Variable Costs per Unit = $630 - $410 = $220

Then, the break-even point in units is:

Break-even units = Fixed Costs / Contribution Margin per Unit = $200,000 / $220 ≈ 909.09 units

Again, rounding to 909 units aligns with the previous calculation.

In conclusion, whether using the mathematical equation or the contribution margin approach, Rice Company's break-even point is approximately 909 units. This insight guides management in setting sales targets to ensure financial stability.

References

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