Question

Detroit Disk, Inc. is a retailer for digital video disks. The projected net income for the current year is $1,880,000 based on a sales volume of 240,000 video disks. Detroit Disk has been selling the disks for $23.00 each. The variable costs consist of the $11.00 unit purchase price of the disks and a handling cost of $2.00 per disk. Detroit Disk’s annual fixed costs are $520,000.

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.) 1. Calculate Detroit Disk’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 20 percent increase in projected unit sales volume? 3. What volume of sales (in dollars) must Detroit Disk achieve in the coming year to maintain the same net income as projected for the current year if the unit selling price remains at $23.00 but the unit purchase price of the disks increases by 30 percent as expected? (Do not round intermediate calculations and 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 Detroit Disk establish for the coming year? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

1. Break Even Point : Fixed Cost ÷ Contribution per unit ( Selling Price - Variable Cost)

= $ 5,20,000 ÷ ($23 - $11 - $2)

= $52,000

2. Projected Sales Volume = Current Sales Volume * 1.20 (Increase by 20 %)

= 2,40,000 units * 1.2

= 2,88,000 units

Net income if sales volume increase by 20% = {Total increased sale volume * (Selling Price - Variable Cost)} - Fixed Cost

= {2,88,000 units * ($23 - $11 - $2)} - $5,20,000

=$23,60,000

3. Volume of sales (in $) = {(Net Income + Fixed Cost) ÷ Contribution p.u.} * Selling Price

= {($18,80,000 +$ 5,20,000) ÷ ($23 - ($11*1.3) - $2)} * 23

=$82,38,806

4. Current Contribution Margin Ratio = Contribution p.u. ÷ sales price p.u.

= 10 ÷ 23

= 43.48 %

Calculating new sales price per unit =

(Sales price p.u. - Variable cost p.u.) ÷ Sales price p.u. = contribution Margin Ratio

={ Sales price p.u. - ($11*1.3) - $2) ÷ Sales price p.u. = 43.48%

Sales p.u. - 0.4348 Sales p.u. = $16.30

= Sales price = $16.30 ÷ 0.5652

= Sale Price = $28.84 per unit.