A firm produces three products in a repetitive process facility. Product A sells for $60; its variable costs are $20. Product B sells for $200; its variable costs are $80. Product C sells for $25; its variable costs are $15

The firm has annual fixed costs of $320,000. Last year, the firm sold 1000 units of A, 2000 units of B, and 10,000 units of C. Calculate the break-even point of the firm. The firm has some idle capacity at these volumes, and chooses to cut the selling price of A from $60 to $45, believing that its sales volume will rise from 1000 units to 2500 units. What is the revised break-even point?

Calculations for the original version of this problem are:

Product Selling price P Variable cost V V/P 1-V/P Sales Percent of sales Weighted contrib.
A $60 $20 .333 .667 $60,000 .0845 .0564
B $200 $80 .400 .600 $400,000 .5634 .3380
C $25 $15 .600 .400 $250,000 .3521 .1408
$710,000 1.0000 0.5352
The original break-even for this firm was $320,000/.5352 = $597,907. This is a calculator-based result; Excel reports $597,895

When the price of A is reduced, the revised calculations are:

Product Selling price P Variable cost V V/P 1-V/P Sales Percent of sales Weighted contrib.
A $45 $20 .444 .556 $112,500 .1475 .0820
B $200 $80 .400 .600 $400,000 .5246 .3148
C $25 $15 .600 .400 $250,000 .3279 .1312
$762,500 1.0000 0.5280

The firm's breakeven point has increased to $320,000 /.5280 = $606,061. (Calculator-based; Excel reports $606,211).