Multiple-Product Analysis, Changes in Sales Mix, Sales to Earn Target Operating Income Basu Company produces two types of sleds for playing in the snow: basic sled and aerosled. The projected income for the coming year, segmented by product line, follows:

Basic Sled Aerosled Total
Sales$3,000,000 $2,400,000 $5,400,000
Total variable cost1,000,000 1,000,000 2,000,000
Contribution margin$2,000,000 $1,400,000 $3,400,000
Direct fixed cost778,000 650,000 1,428,000
Product margin$1,222,000 $750,000 $1,972,000
Common fixed cost 198,900
Operating income $1,773,100
The selling prices are $30 for the basic sled and $60 for the aerosled. (Round break-even packages and break-even units to the nearest whole unit.)

Required:

1. Compute the number of units of each product that must be sold for Basu to break even.

Basicunits
Aerounits
2. Assume that the marketing manager changes the sales mix of the two products so that the ratio is five basic sleds to three aerosleds. Compute the number of units of each product that must be sold for Basu to break even. Round your answers to the nearest whole number.

Basicunits
Aerounits
3. Conceptual Connection: Refer to the original data. Suppose that Basu can increase the sales of aerosleds with increased advertising. The extra advertising would cost an additional $195,000, and some of the potential purchasers of basic sleds would switch to aerosleds. In total, sales of aerosleds would increase by 12,000 units, and sales of basic sleds would decrease by 5,000 units. Would Basu be better off with this strategy? If so, give the amount of increase in income.

Basu Company

Multiple-Product Analysis, Changes in Sales Mix, Sales to Earn Target Operating Income

1. Break-even point:

Basic Sled = (Direct Fixed cost + Allocated Fixed Cost)/Contribution margin per unit

= $888,500/$20 = 44,425 units

Aerosled = (Direct Fixed cost + Allocated Fixed Cost)/Contribution margin per unit

= $738,400/$35 = 21,097 units

2. Break-even point:

Basic Sled = (Direct Fixed cost + Allocated Fixed Cost)/Contribution margin per unit

= $868,409/$20 = 43,420 units

Aerosled = (Direct Fixed cost + Allocated Fixed Cost)/Contribution margin per unit

= $758,491/$35 = 21,671 units

3. Operating income under scenario 3 = $1,765,600

less operating income under original  =    $1773,100

Loss = $7,500

Basu is not better off with this strategy.  It would lose $7,500 in operating income.

Explanation:

1. The projected income for the coming year, segmented by product line, follows:

                                       Basic Sled         Aerosled           Total

Selling price                        $30                   $60

Units Sold                       100,000              40,000                140,000

Sales                            $3,000,000        $2,400,000      $5,400,000

Total variable cost         1,000,000           1,000,000         2,000,000

Contribution margin  $2,000,000         $1,400,000       $3,400,000

Direct fixed cost               778,000             650,000          1,428,000

Product margin           $1,222,000           $750,000        $1,972,000

Common fixed cost                                                                198,900

Operating income                                                              $1,773,100

Variable cost per unit    $10                     $25

1b. Allocation of common

 fixed cost, using sales   $110,500           $88,400            $198,900

Total Fixed costs            $888,500         $738,400         $1,626,900

1c. Variable costs per unit

Basic Sled = $1,000,000/100,000 = $10

Aerosled = $1,000,000/40,000 = $25

1d. Contribution margin

per unit                             $20                  $35

2. New market mix

                                       Basic Sled         Aerosled           Total

Selling price                        $30                   $60

Units Sold                       87,500                  52,500                140,000

Sales                            $2,625,000        $3,150,000        $5,775,000

Total variable cost            875,000            1,312,500           2,187,500

Contribution margin    $1,750,000         $1,837,500         $3587,500

Direct fixed cost               778,000             845,000           1,623,000

Product margin             $972,000           $992,500        $1,964,500

Common fixed cost                                                                 198,900

Operating income                                                             $1,765,600

Variable cost per unit    $10                     $25

Allocation of common

 fixed cost, using sales   $90,409           $108,491            $198,900

Total Fixed costs           $868,409           $758,491         $1,626,900

Contribution margin

per unit                             $20                  $35

3. Conceptual Connection:

The projected income for the coming year, segmented by product line, follows:

                                       Basic Sled         Aerosled           Total

Selling price                        $30                   $60

Units Sold                       95,000              52,000                147,000

Sales                            $2,850,000        $3,120,000      $5,970,000

Total variable cost           950,000           1,300,000         2,250,000

Contribution margin   $1,900,000         $1,820,000       $3,720,000

Direct fixed cost               778,000             650,000          1,428,000

Product margin            $1,122,000          $1,170,000       $2,292,000

Common fixed cost                                                                198,900

Operating income                                                             $2,093,100

Variable cost per unit    $10                     $25

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