Question

Problem 2

	Total	Per Unit	Percent of Sales
Sales (40,000 units)	2,400,000	60	100%
Variable expenses	1,600,000	40	? %
Contribution margin	800,000		? %
Fixed expenses	500,000
Net operating income	300,000

1. Calculate variable expense ratio.
2. Calculate contribution margin ratio.
3. Calculate break even sales in units (show your work).
4. Calculate break even sales in Dollars.
5. How many units must be sold to make a profit of SAR 200,000.

Management is considering increasing quality of its units by spending SAR 3 more per unit in variable costs and adding a quality inspector for an additional SAR 60,000 annual fixed cost. Management believes this change will increase unit sales by 10% at the same price.

1. Calculate the new operating profit or loss.
2. Should management make the changes?

Answer 1

1. Variable expense ratio = 66.67%

Solution :

Variable expense ratio = (variable expense / sales )×100

= (1600000/2400000)×100

= 0.6666 × 100

= 66.67%

2. Contribution margin ratio = 33.33%

Solution :

Contribution margin ratio = (contribution margin per unit / selling price per unit) × 100

Where,

Contribution margin per unit = selling price per unit - variable cost per unit.

= 60 - 40 = 20

Therefore,

Contribution margin ratio = (20/60) × 100

= 0.333 ×100

= 33.33%

3. Break even sales in units = 25000 units.

Solution :

Break even sales in units = fixed cost / contribution margin per unit.

= 500000/20

= 25000

4. Break even sales in dollars (in amount) = 1,500,000

Solution :

Break even sales in amount = fixed cost / contribution margin ratio

= 500000/33.33%

= 1500000

OR

Break even sales in amount = break even sales in units × selling price per unit.

= 25000 × 60

= 1500000

5. Units to be sold to make profit of SAR 200000 = 35000 units.

solution :

Required units to be sold = (required profit + fixed cost) / contribution margin per unit.

= (200000 + 500000) / 20

= 700000/20

= 35000

6.

1. New operating profit = SAR 360,000

2. Should management make changes = YES (because the changes increases net operating income from 300,000 to 360,000)

Solution :

	Total (old figures)	changes	total (new figures)
Sales	2,400,000	+240000 [refer note 1]	2,640,000
(-) variable cost	(1,600,000)	+172000 [refer note 2]	(1,720,000)
Contribution margin	800,000		920,000
(-) fixed cost	500,000	+60000	(560,000)
Net operating income	300,000		360,000

note 1:

new sales units = 40000 + 10% = 44000

Change in unit sales = 44000 - 40000 = 4000 units.

Therefore,

Change in sales amount = 4000 × 60 = 240,000.

note 2:

New variable cost per unit = 40 + 3 = 43

Change in total variable cost = 4000 × 43 = 172,000.