Question

This year Burchard Company sold 40,000 units of its only product for \(25 per unit. Manufacturing and selling the product required \)200,000 of fixed manufacturing costs and \(325,000 of fixed selling and administrative costs. Its per unit variable costs follow.

Material	\)8.00
Direct labor (paid on the basis of completed units)	5.00
Variable overhead cost	1.00
Variable selling and administrative costs	0.50

Next year the company will use new material, which will reduce material costs by 50% and direct labor costs by 60% and will not affect product quality or marketability. Management is considering an increase in the unit selling price to reduce the number of units sold because the factory’s output is nearing its annual output capacity of 45,000 units. Two plans are being considered. Under plan 1, the company will keep the selling price at the current level and sell the same volume as last year. This plan will increase income because of the reduced costs from using the new material. Under plan 2, the company will increase the selling price by 20%. This plan will decrease unit sales volume by 10%. Under both plans 1 and 2, the total fixed costs and the variable costs per unit for overhead and for selling and administrative costs will remain the same.

Required

1. Compute the break-even point in dollar sales for both (a) plan 1 and (b) plan 2.

2. Prepare a forecasted contribution margin income statement with two columns showing the expected results of plan 1 and plan 2. The statements should report sales, total variable costs, contribution margin, total fixed costs, income before taxes, income taxes (30% rate), and net income.

Short answer

1. Break-even point:

Plan 1:$750,000

Plan 2:$700,000

2. Forecasted net income:

Plan 1:$122,500

Plan 2:$199,500

Step-by-step solution

Definition of Net Income

The net benefit generated after adjusting every expense incurred is known as net income. It is also adjusted with the tax and interest paid by the business entity.

Break-even point

New cost due to introduction of new material:

Particular	Cost per unit
Material @ 50% of $8	$4
Direct labor @ 40% of $5	$2

1. Calculation of break-even point for plan (1):

$\begin{array}{rcl}\mathrm{contribution}\mathrm{margin}\mathrm{ratio}& =& \frac{\mathrm{Sales}-\mathrm{Variable}\mathrm{cost}}{\mathrm{Sales}}\\ & =& \frac{\$25-\$7.50}{\$25}\\ & =& 0.70\end{array}$

$\begin{array}{rcl}\mathrm{Break}-\mathrm{even}\mathrm{in}\mathrm{dollars}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\mathrm{contribution}\mathrm{margin}\mathrm{ratio}}\\ & =& \frac{\$200,000+\$325,0000}{0.70}\\ & =& \$750,000\end{array}$

b. Calculation of break-even point for the plan (2):

The new sales price will be 20% more than the previous one. Therefore, the new selling price will be 120% of $25: $30.

$\begin{array}{rcl}\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}& =& \frac{\mathrm{Sales}-\mathrm{Variable}\mathrm{cost}}{\mathrm{Sales}}\\ & =& \frac{\$30-\$7.50}{\$30}\\ & =& 0.75\end{array}$

$\begin{array}{rcl}\mathrm{Break}-\mathrm{even}\mathrm{in}\mathrm{dollars}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\mathrm{Contribution}\mathrm{in}\mathrm{margin}\mathrm{ratio}}\\ & =& \frac{\$200,000+\$325,0000}{0.75}\\ & =& \$700,000\end{array}$

Forecasted income statement

Particular	Plan 1 (40,000 units)	Plan 2 (36,000 units)
Sales	$1,000,000	$1,080,000
Less: Variable cost	(300,000)	(270,000)
Contribution margin	700,000	810,000
Less: Fixed cost	(525,000)	(525,000)
Income before tax	175,000	285,000
Less: Tax @ 30%	(52,500)	(85,500)
Net income	$122,500	$199,500