Question

Disk City, Inc. is a retailer for digital video disks. The projected net income for the current year is $1,920,000 based on a sales volume of 290,000 video disks. Disk City has been selling the disks for $16 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 $400,000.

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 $16? (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

Disk City

Calculation of break-even point for the current year in number of video disks:

Break-even point in number of video disks = total fixed cost/contribution margin per disk

Fixed cost = $400,000

Contribution margin per disk = sales price – total variable cost

Sales price per disk = $16

Total variable cost –

Purchase price $6

Handling cost $2

Total variable cost = $8

Contribution margin per disk = $16 - $8 = $8

Break-even point in number of video disks = $400,000/$8 = 50,000 video disks

Determination of net income for the year if 10% increase in projected unit sales volume –

Change in net income = percent increase in sales x degree of operating leverage

Percent change in sales = 10% increase

Degree of operating leverage = contribution margin/net income

Contribution margin = $8 x 290,000 = $2,320,000

Net income = $1,920,000

Degree of operating leverage = 2,320,000/1,920,000 = 1.21

Change in net income = 10% x 1.21 = 12.10%

Hence, net income increases by 12.10% when sales increase by 10%.

Determination of selling price –

Assuming 30% increase in purchase price, and maintenance of current contribution margin ratio –

Revised purchase price = $6 + 30% of $6 = $7.80

Current contribution margin ratio = $8/$16 = 50%

Hence, variable cost would be 50% of sales price.

Revised variable price = $7.8 + $2 = $9.80

Hence sales price = variable cost/50% = $9.8/50% = $19.60

Desired sales price to cover 30% increase in purchase price and still maintain the current contribution margin ratio = $19.60