Barnes Corporation's income statement for last year appears below:

Sales 1,500,000
Cost of sales:
Direct materials 250,000
Direct labor (variable) 150,000
Variable overhead 75,000
Fixed overhead 100,000 575,000
Gross margin 925,000
Selling, general, and administrative:
Variable 200,000
Fixed 250,000 450,000
Net operating income 475,000



The management of Barnes Corporation anticipates a 10 percent increase in total sales, a 12 percent increase in total variable expenses, and a 45,000 increase in total fixed expenses next year. The break-even point for next year is:

(a) 214,018
(b) 729,027
(c) 474,000
(d) 862,103

Can someone please show me how to get the answer? Thanks!

CURRENT YEAR:
Sales 1,500,000
TOTAL SALES = 1,500,000

Variable Costs:
Direct materials 250,000
Direct labor (variable) 150,000
Variable overhead 75,000
Variable 200,000
TOTAL VC = 675,000

Fixed Costs:
Fixed overhead 100,000
Fixed 250,000
TOTAL FC = 350,000

Net operating income 475,000

NEXT YEAR
Sales = 1,500,000 x 1.10 = 1,650,000
VC = 675,000 x 1.12 = 756,000
CM = Sales – VC = 894,000
FC = 350,000 + 45,000 = 395,000
NET INCOME = CM – FC = 499,000

CM must equal 395,000 for Net Income to equal 0

Sales = 1,650,000 / 894 units = 1,846
VC = 756,000 / 894 units = 846
Total = 894,000 / 894 units = 1,000

Total needs to be 395,000

So,

1,000x = 395,000
x = 395

Sales = 395 x 1,846 = 729,170

Answer B: (b) 729,027. Close enough, I rounded some places I shouldn't have.

A more precise answer is:

1,650,000 / 894 x 395 = 729,027