Question

Praveen Co. manufactures and markets a number of rope products. Management is considering the future of Product XT, a special rope for hang gliding, that has not been as profitable as planned. Since Product XT is manufactured and marketed independently of the other products, its total costs can be precisely measured. Next year’s plans call for a \(200 selling price per 100 yards of XT rope. Its fixed costs for the year are expected to be \)270,000, up to a maximum capacity of 700,000 yards of rope. Forecasted variable costs are \(140 per 100 yards of XT rope.

Required

1. Estimate Product XT’s break-even point in terms of (a) sales units and (b) sales dollars.

2. Prepare a CVP chart for Product XT like that in Exhibit 18.14. Use 7,000 units (700,000 yards/100 yards) as the maximum number of sales units on the horizontal axis of the graph, and \)1,400,000 as the maximum dollar amount on the vertical axis.

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

Short answer

The break-even point of the business entity is 4,500 units or $900,000.

Step-by-step solution

Definition of Pre-Tax Income

Before deducting any amount paid as income tax, the income generated by the business entity is known as pre-tax income. The tax expenses are calculated on this income only.

Estimated break-even point

Calculation of contribution margin per unit and contribution margin ratio:

Particular	Amount $
Sales price per unit	$200
Less: Variable cost per unit	(140)
Contribution margin per unit	$60

$\begin{array}{rcl}\mathbf{\text{Contributionmarginratio}}& \mathbf{=}& \frac{\mathbf{\text{Contributionmarginperunit}}}{\mathbf{\text{Salespriceperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{60}}{\mathbf{\$}\mathbf{200}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{3}\end{array}$

Calculation of break-even dollar sales:

$\begin{array}{rcl}\mathbf{\text{Break-evenpointsinunits}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{60}}\\ & \mathbf{=}& \mathbf{4}\mathbf{,}\mathbf{500}\mathbf{}\mathbf{\text{units}}\end{array}$

Calculation of break-even dollar sales:

$\begin{array}{rcl}\mathbf{\text{Break-evenpointsindollars}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginperunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}}{\mathbf{0}\mathbf{.}\mathbf{3}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{900}\mathbf{,}\mathbf{000}\end{array}$

CVP chart

Contribution margin income statement

Particular	Amount $
Sales 4,500 units @ $200	$900,000
Less: Variable cost 4500 units @ $140	(630,000)
Contribution margin	$270,000
Less: Fixed cost	(270,000)
Pre-tax income	$0