Question

Disk City, Inc. is a retailer for digital video disks. The projected net income for the current year is $2,660,000 based on a sales volume of 260,000 video disks. Disk City has been selling the disks for $22 each. The variable costs consist of the $8 unit purchase price of the disks and a handling cost of $2 per disk. Disk City’s annual fixed costs are $460,000.

Management is planning for the coming year, when it expects that the unit purchase price of the video disks will increase 20 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 $22? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)
4. In order to cover a 20 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

I have Figured out the first 2 but am struggling on the last 2.

Answer 1

Solution :

(1) Current Breakeven

Break-even point in number of video disks = Total fixed cost / Contribution Margin per disk

= $ 460,000 / ($ 22 - $ 8 - $ 2)

= $ 460,000 / $ 12

= 38,333 Disks

(2) Net Income :

New sales volume = 260,000 * 110% = 286,000 disks

Company's net income if 10% increase in Sales volume = Total Contribution - Fixed Costs

= (286,000 * $ 12) - $ 460,000

= $ 2,972,000.

(3) Sales Volume in Dollars :

New variable cost per unit = ($ 8 * 1.20) - 2 = $ 11.60 per unit

Contribution margin per unit = $ 22 - $ 11.60 = $ 10.40

Desired sales volume = (Fixed cost + Projected net income) / Contribution margin ratio

Contribution margin ratio = CM Per Unit / Sales Price per Unit

= $ 10.40 / $ 22

= 47.272727%

Projected Net Income = (260,000 * $ 12) - $ 460,000 = $ 2,660,000

Desired sales volume = ($ 460,000 + $ 2,660,000 ) / 47.272727%

Desired sales volume = $ 3,120,000 / 47.272727%

= $ 6,600,000

(4) Selling Price per Unit :

Current CM Ratio = ($ 22 - $ 8 - $ 2) / $ 22 = 54.545454%

Assume Sale price is fixed is X

CM Ratio = (CM per Unit / Sale Price per Unit) * 100

54.545454    = [( $ X - $ 11.60 ) / $ X ] * 100

0.54545454 = ( $ X - $ 11.60 ) / $ X   

$ 0.54545454 X = $ X - $ 11.60

$ X - $ 0.54545454 X = $ 11.60

X = $ 11.60 / 0.45454545

X    = $ 25.52

New Sale Price = $ 25.52.

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