Question

Disk City, Inc. is a retailer for digital video disks. The projected net income for the current year is $2,770,000 based on a sales volume of 290,000 video disks. Disk City has been selling the disks for $23 each. The variable costs consist of the $10 unit purchase price of the disks and a handling cost of $2 per disk. Disk City’s annual fixed costs are $420,000.

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 taxes.)

Required:

1. Calculate Disk City’s break-even point for the current year in number of video disks. (Round your final answer up to nearest whole number.)
2. What will be the company’s net income for the current year if there is a 10 percent increase in projected unit sales volume?
3. What volume of sales (in dollars) must Disk City achieve in the coming year to maintain the same net income as projected for the current year if the unit selling price remains at $23? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)
4. 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

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

= 23 - 12

= $11

Contribution margin ratio = Contribution margin/Selling price

= 11/23

= 0.4782608696

1.

Break even point (in units) = Fixed costs/Contribution margin per unit

= 420,000/11

= 38,182

2.

Projected sales volume = 290,000 x 110%

= 319,000 units

Net income = Sales x Contribution margin ratio - Fixed costs

= 319,000 x 23 x 0.4782608696 - 420,000

= $3,089,000

3.

unit purchase price of the video disks will increase 30 percent in the coming year

Hence, purchase price of disc = 10 x 130%

= $13

Variable cost per unit = 13 + 2

= $15

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

= 23 - 15

= $8

Contribution margin ratio = Contribution margin/Selling price

= 8/23

= 0.347826087

Sales to earn the target profit = (Fixed costs + Target profit)/Contribution margin ratio

= (420,000 + 2,770,000)/0.347826087

= 3,190,000/0.347826087

= $9,171,250

4.

Let the desired selling price be = $Y per unit

Contribution margin ratio = Contribution margin/Selling price

0.4782608696 = (Y - 15)/Y

Y - 0.4782608696Y = 15

0.5217391304Y = 15

Y = 15/0.5217391304

Y = $28.75

Hence, selling price in the coming year = $28.75