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Rice Company has a unit selling price of $730, variable costs per unit of $500, and fixed costs of $208,400. Compute the break-even point in units using (a) the mathematical equation and (b) unit contribution margin. (Round answers to 0 decimal places, e.g. 1,225.)

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Answer:

Rice Company

a) Break-even point in units using the mathematical equation = 906 units

b) Break-even point in units using the unit contribution margin = 906 units

Explanation:

a) Data and Calculations:

Selling price per unit = $730

Variable costs per unit = $500

Contribution margin per unit = $230 ($730 - $500)

Fixed costs for the period = $208,400

Break-even point in units:

a) Mathematical equation:

(Total Revenue = Expenses at the BEP)/

Profit  =  Selling price  −  Variable Expenses  −  Fixed Expenses

$ 0  =  Unit CM  *  Q  −  Fixed expenses

$ 0  =  $ 230  * Q  −  $208,400

$208,400  =  $230 * Q

=  $230Q = $208,400  

= Q = $208,400/$230

= 906 units

b) Unit contribution margin:

Break-Even point (units) = Fixed Costs ÷ (Sales price per unit – Variable costs per unit)

= $208,400/ ($730 - $500)

= 906 units

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