Question

Quikpak sells returnable containers to major food processors. The price received for the containers is $2 per unit. Of this amount $1.25 is profit contribution. Quikpak is considering an attempt to differentiate its product through quality improvement at a cost of $.05 per unit. Current profits are $40,000 on sales of 100,000 units.

(a) Assuming that average variable costs are constant at all output levels, find Quikpak‘s total cost function before the proposed change.

(b) Calculate the total cost function if the quality improvement is implemented.

(c) Calculate Quikpak‘s break-even output before and after the change, assuming it cannot increase its price.

(d) Calculate the increase in sales that would be necessary with the quality improvement to increase profits to $45,000.

Answer 1

Req A:
Sales units: 100,000
Profit: $40,000
Selling price: $2.00 per unit
Contribution margin per unit: $1.25 per unit
Variable cost per unit = Selling price- Contributin margin = 2.00 -1.25 = $0.75 per unit
Fixed cost:
Total contribution (100,000 units @$1.25)				125000
Less: profits earned:				40000
Fixed cost:				85000
Let X by Number of units sold, therefore cost function C (X) is as follows:
C(X) = 85,000 + 0.75 X
Req B:
Revised variable cost per unit: 0.75+ 0.05 = $0.80 per unit
Fixed cost: $ 85,000
Therefore, the revised cost function is as follows:
C(X) = $ 85,000 + 0.80 X
Req C:
Break even units before Improvement:
Contribution margin per unit: $ 1.25 per unit
Fixed cost: $85,000
Break even units= Fixed cost/ Contribution margin per unit
		($ 85000 /1.25 ) = 68000 units
Break even after improvement:
Revised contribution margin per unit: $ 1.25- 0.05 = $ 1.20 per unit
Break even units; fixed cost/ Revised contribution per unit
		($ 85000 /1.20 )= 70.834 units
Req D:
Desired profits after improvement: $ 45000
Revised contribution: $ 1.20 per unit
Desired contribution: Fixed cost+ Dsired profits: 85000+45000 = $130,000
Required sales in units: Desired contribution/ Contribution pe runit
		($130,000 / 1.20) = 108,333
Required sales in $:108,333 units @$2 per unit: $ 216,666