Question

A new piece of equipment will have a fixed cost of $250,000 and the product it would produce has a variable cost of $22.50, and a selling price of $35.

A. What is the break-even point?

B. How many units must be sold to make a profit of $750,000?

C. How many units must be sold to average $0.50 profit per unit? $0.75 profit per unit? And $2.50 per unit?

D. If investors expect a 15% Return on Investment (ROI), how many units must be sold to achieve this goal?

Answer 1

A)

Contribution per unit

= Selling price per unit – Variable costs per unit

= $35 - $22.50

= $12.50 per unit

Break-even point in units

= Fixed costs / Contribution per unit

= $250,000 / $12.50

= 20,000 units

B)

Units required to be sold

= (Fixed costs + Target profit) / Contribution per unit

= ($250,000 + $750,000) / $12.50

= 80,000 units

C)

The following table shows the calculations

Calculations	Particulars	$0.50 profit	$0.75 profit	$2.50 profit
A	Selling price	35.0	35.0	35.0
B	Variable costs	22.5	22.5	22.5
C = A - B	Contribution	12.5	12.5	12.5
D	Target profit	0.50	0.75	2.50
E = C - D	Target Fixed costs per unit	12.00	11.75	10.00
F	Total Fixed costs	250000	250000	250000
G = F / E	Number of units required to be sold	20,833	21,277	25,000

D)

Return on Investment

= Investment x Return percentage

= $250,000 x 15%

= $ 37,500

Units required to be sold

= (Fixed costs + Target profit) / Contribution per unit

= ($250,000 + $37,500) / $12.50

= 23,000 units