Question

Disk City, Inc. is a retailer for digital video disks. The projected net income for the current year is $2,050,000 based on a sales volume of 290,000 video disks. Disk City has been selling the disks for $17 each. The variable costs consist of the $6 unit purchase price of the disks and a handling cost of $2 per disk. Disk City’s annual fixed costs are $560,000. Management is planning for the coming year, when it expects that the unit purchase price of the video disks will increase 30 percent (ignore income tax).

In order to cover a 30 percent increase in the disk’s purchase price for the coming year and still maintain the current contribution-margin ratio, what selling price per disk must Disk City establish for the coming year? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

Cost of disk = $6 per unit

Handling cost = $2 per unit

Variable cost per unit = Cost of disk + Handling cost

= 6+2

= $8 per unit

Selling price per unit = $17

Contribution margin per unit =Selling price per unit - Variable cost per unit

= 17-8

= $9

Contribution margin ratio = Contribution margin per unit / Selling price per unit

= 9/17

= 52.9411764706%

Increase in disk price = 30%

= 6 x 30%

= $1.8

Disk price will become = 6+1.8

= $7.8

Variable cost per unit after price increase = 7.8+2

= $9.8 per unit

Contribution margin rate to be maintained = 52.9411764706%

Let the new selling price = $Y

New Contribution margin per unit =new selling price -Variable cost per unit after price increase

= Y - 9.8

Contribution margin rate = Contribution margin per unit / Selling price per unit

52.9411764706% = ( Y-9.8) / Y

0.47058823529Y = 9.8

Y = 9.8 / 0.47058823529

= $20.83

Hence selling price to be charged = $20.83