Question

Detroit Disk, Inc. is a retailer for digital video disks. The projected net income for the current year is $2,580,000 based on a sales volume of 300,000 video disks. Detroit Disk has been selling the disks for $21.00 each. The variable costs consist of the $9.00 unit purchase price of the disks and a handling cost of $2.00 per disk. Detroit Disk’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 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 10 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 $21.00 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) Fixed Costs= $420,000

Selling Price/unit = $21

Total Variable costs/unit = Purchase price/unit + Handling Cost/unit

= $9 + $2 = $11

Contribution/unit = Selling Price/unit - Total Variable cost/unit

= $21 - $11 = $10

Break Even point (units) =  

= $420,000/$10

Break Even Point (units) = 42,000 units

2) Current Sales Volume = 300,000 units

Projected increase = 10%

projected increase in sales volume = 10% x 300,000 = 30,000 units

Projected sales volume = 300,000 + 30,000 = 330,000 units

  

Selling Price/unit = $21

Total Variable costs/unit = Purchase price/unit + Hnadling Cost/unit

= $9 + $2 = $11

Contribution/unit = Selling Price/unit - Total Variable cost/unit

= $21 - $11 = $10

Total contribution as per the projected sales = Projected sales volume x Contribution/unit

= 330,000 x $10

= $3,300,000

Net income as per new sales volume = Total Contribution - Total Fixed costs

= $3,300,000 - 420,000

= $2,880,000

Alternatively, this can also be done by adding the incremental contribution due to increased sale into the previous net income. Because the selling price per unit and cost per unit haven't changed.

incremental contribution = projectd increase in sales volume x contribution per unit

= 30,000 x $10

= $300,000

Net income after increased sales = Net income before increased sales + Incremental contribution

= $2,580,000 + $300,000

= $2,880,000

3)

Selling Price/unit = $21

Purchase cost/unit = $9

Increase in purchase cost = 30%

New Purchase cost per unit = $9 + 30%of $9

= $9 + $2.7 = $11.7

  

New Total Variable costs/unit = Purchase price/unit + Handling Cost/unit

= $11.7 + $2 = $13.7

New Contribution/unit = Selling Price/unit - Total Variable cost/unit

= $21 - $13.7 = $7.3

Profit required = $2,580,000

Contribution Required = Profit + Fixed Costs

= $2,580,000 + $420,000

= $3,000,000

Sales volume required to achieve this profit =

= $3,000,000/ $7.3

= 410,959 units

4)

Sales volume = 300,000 units

Selling Price/unit = $21

Total sales = Sales volume x Selling price/unit

= 300,000 x $21 = $6,300,000

Purchase cost/unit = $9

Total Variable cost/unit = Purchase cost/unit + Handling cost/unit

= $9 + $2 = $11  

Total variable cost = Total variable cost/unit x sales volume

= $11 x 300,000 = 3,300,000

Contribution/unit = Selling Price/unit - Total Variable cost/unit

= $21 - $11 = $10

Contribution margin = Total sales - Total variable costs

= $6,300,000 - $3,300,000

= $3,000,000

Increase in purchase cost = 30%

New Purchase cost per unit = $9 + 30%of $9

= $9 + $2.7 = $11.7

New Total Variable costs/unit = Purchase price/unit + Handling Cost/unit

= $11.7 + $2 = $13.7

New total variable cost = sales volume x New total variable cost/unit

= 300,000 x $13.7 = $4,110,000

New Contribution/unit = Selling Price/unit - Total Variable cost/unit

= $21 - $13.7 = $7.3

New contribution margin = New sales volume - New total variable costs

As the contribution margin is supposd to be the same

$3,000,000 = New sales volume - $4,110,000

New sales volume = $3,000,000 + $4,110,000

= $7,110,000

New selling price = Total sales volume/expected units to be sold

= $7,110,000/300,000 = $23.7

Selling price to be increased by $2.7 ($23.7-$21)

%age change in selling price = $2.7/$21 x100 = 12.86%