Question

Hip-Hop Co. manufactures and markets several products. Management is considering the future of one product, electronic keyboards, that has not been as profitable as planned. Since this product is manufactured and marketed independently of the other products, its total costs can be precisely measured. Next year’s plans call for a \(350 selling price per unit. The fixed costs for the year are expected to be \)42,000, up to a maximum capacity of 700 units. Forecasted variable costs are \(210 per unit.

Required

1. Estimate the keyboards’ break-even point in terms of (a) sales units and (b) sales dollars.

2. Prepare a CVP chart for keyboards like that in Exhibit 18.14. Use 700 keyboards as the maximum number of sales units on the horizontal axis of the graph, and \)250,000 as the maximum dollar amount on the vertical axis.

3. Prepare a contribution margin income statement showing sales, variable costs, and fixed costs for keyboards at the break-even point.

Short answer

The Break-even point of the business entity is 300 units or $105,000.

Step-by-step solution

Definition of Pre-Tax Income

The business entity's income generated before subtracting any amount paid as income tax is known as pre-tax income. The tax expense is calculated only on pre-tax income.

Estimated break-even point in units and dollar sales

Calculation of contribution margin per unit and contribution margin ratio:

Particular	Amount $
Sales price per unit	$350
Less: Variable cost per unit	(210)
Contribution margin per unit	$140

$\begin{array}{rcl}\mathbf{\text{Contributionmarginratio}}& \mathbf{=}& \frac{\mathbf{\text{Contributionmarginperunit}}}{\mathbf{\text{Salespriceperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{140}}{\mathbf{\$}\mathbf{350}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{4}\end{array}$

Calculation of break-even point in units:

$\begin{array}{rcl}\mathbf{\text{Break-evenpointinunits}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{42}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{140}}\\ & \mathbf{=}& \mathbf{300}\mathbf{}\mathbf{\text{units}}\end{array}$

Calculation of break-even dollar sales:

$\begin{array}{rcl}\mathbf{\text{Break-evenpointindollars}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{42}\mathbf{,}\mathbf{000}}{\mathbf{0}\mathbf{.}\mathbf{4}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{105}\mathbf{,}\mathbf{000}\end{array}$

CVP chart

Contribution margin income statement

Particular	Amount $
Sales 300 units @ $350 per unit	$105,000
Less: Variable cost 300 units @ $210 per unit	(63,000)
Contribution margin	42,000
Less: Fixed cost	(42,000)
Pre-tax income	$0