The York Company produces Dirt bikes Y1 and Road bikes Y2 as

The York Company produces Dirt bikes (Y1) and Road bikes (Y2) as follows: Variable Cost Per Unit S80 160 Budgeted Mix in Units 80% 20% Product Sales Price $200 400 Y1 ed costs amount to $388,800 which represents $238,800 fixed manufacturing overhead Total fix and $150,000 fixed selling and administrative expenses. Required: Determine the number of units of each product the company needs to produce and sell to break-even, assuming that unit sales are in proportion to the budget a. ed mix. b.. Determine the number of units of each product needed to generate a 20% return on sales dollars after taxes. Again assume a tax rate of 40 percent and that sales are in proportion to the budgeted mix. c. If the company is going to spend 200,000 on additional advertising, what level of sales in units of each product must be achieved in order to justify the expenditure?

Solution

a. Break-even units of each product Break even point = Total Fixed Expenses/Weighted average contribution margin per unit Total Fixed cost $388,800 Weighted Average selling price per unit Y1 ($200 x 80%) $160 Y2 ($400 x 20%) $80 Total $240 Weighted Average variable cost per unit Y1 ($80 x 80%) $64 Y2 ($160 x 20%) $32 Total $96 Weighted average contribution margin per unit Weighted Average selling price per unit $240 Weighted Average variable cost per unit $96 Weighted average contribution margin per unit $144 Break even point = $388800/$144 = 2700 units Y1 (2700 units x 80%) 2160 Y2 (2700 units x 20%) 540 b. Number of units needed to generated a 20% return on sales dollar after taxes Suppose the sales dollar is x Number of units desired = Fixed cost /contribution margin per unit - (target profit/(1-tax rate))                                                     = $388,800 /$144 -(0.20x/0.60)                                                     = $388,800/$144-(0.33x)                            $144 - 0.33x = $388,800                                       -0.33x = $388,800 -$144                                                  x = 388656/0.33                                                      = 1177745 Target profit = $1177745 x 20%/(1-tax rate)                           = 235549/0.60                           = $392582 Number of units desired = ($388800+$392582)/$144                                                    = $781382/$144                                                    = 5426 Y1 (5426 x 80%) 4341 Y2 (5426 x 20%) 1085 c. Units to justify the additional expenditure of 200,000 on advertisement Units required = (Fixed cost + additional expenditure)/weighted average contribution margin per unit                                = ($388800+$200000)/$144                                = $588,800/$144                                = 4089 Y1 (4089 x 80%) 3271 Y2 (4089 x 20%) 818