Astro Co sold 20100 units of its only product and incurred a

Astro Co. sold 20,100 units of its only product and incurred a $63,560 loss (ignoring taxes) for the current year as shown here. During a planning session for year 2018\'s activities, the production manager notes that variable costs can be reduced 40% by installing a machine that automates several operations. To obtain these savings, the company must increase its annual fixed costs by $151,000. The maximum output capacity of the company is 40,000 units per year. ASTRO COMPANY Contribution Margin Income Statement Sales Variable costs Contribution margin Fixed costs Net loss $755,760 566,820 -188,940 - 252,500 $ (63,560)

Solution

1. Break even point in dollar sales for the year 2017-

a. Break-even point (in Sales) = Fixed Cost/ Contribution margin ratio

Contribution margin ratio= Contribution margin/ Sales*100

= $188940/ $755760 * 100 = 25%

Fixed Cost = $2,52,500

Break-even point (in Sales $) = $252500/0.25 = $10,10,000

Break-even point (in units) = Fixed Cost/ Contribution per units

= $252500/$9.40 per unit = 26,861.70 units

where, Contribution per unit = 188940/20100 = $9.4 per unit

2. Break- even point in sales for the year 2018-

Unit Selling Price= $755760/20100 = $37.6 per unit

Sales = 40000 * $37.6 = $15,04,000

Variable cost = $566820 - 40% = $3,40,092

Contribution margin = Sales - Variable cost = $1504000 - $340092 = $11,63,908

Contribution margin per unit = $1163908/40,000 = $29.09 per unit

Contribution margin ratio = 1163908/1504000 *100 = 77.39%

Break-even point (in Sales dollar) = $151000/0.7739 = $1,95,115.64

4. Sales level required both in units and dollars-

Unit Sales = Fixed cost + Target profit / Contribution margin per unit

= $151,000 + $210,000 / $29.09 = 12,409.76 units

Sales (dollars) = Fixed cost + Target profit/ Contribution margin ratio

= $151,000 + $210,000/ 0.7739 = $466,468.53

where, Target profit = $210,000