Question

I am struggling with figureing this out as a practicing question! Please show me the work for how to get the correct answers!

XYZ Company reports a sales mix of 40% product A and 60% product B and has a tax rate of 30%. Given the following information, calculate how many bundles (assume that every bundle is 5 total units) must XYZ sell to generate an after tax profit of $250,000

Sales Mix

40% Product A                                                60% Product B

.40x5=2                                                           .60x5=3

2 Units of Product A per Bundle                     3 Units of Product B per Bundle

Product A                                Product B

Sales Price                   $500                                        $750

Direct Materials          $75                                          $100

Direct Labor                $125                                        $150

Variable Overhead      $50                                          $75

Commissions              $25                                          $50

Total Variable Costs:   $275                                        $375

Contribution Margin:  225                                          375

Fixed Manufacturing overhead:          $275,000 per year

Fixed Administrative expenses:          $300,000 per year

Total Fixed Costs:                                $575,000 per year

Answer 1

Let “x” be the total units sold

Product A = 40%

Product B = 60%

Contribution – Fixed cost = Profit

Profit after tax = 250000

Profit before tax = 250000/0.7 = 357143

Contribution of Product A = 225

Contribution of Product A = 375

(40% * x * 225) + (60% * x * 375) – 575000 = 357143

90x + 225x – 575000 = 357143

315x = 932142

X = 2959.18 or 2960

Product A units = 2960 * 40% = 1184

Product B units = 2960 * 60% = 1776

Bundle for Product A = 1184/5 = 237

Bundle for Product B = 1776/5 = 355.2 or 356