Question

Due to erratic sales of its sole product—a high-capacity battery for laptop computers—PEM, Inc., has been experiencing financial difficulty for some time. The company’s contribution format income statement for the most recent month is given below:

Sales (12,800 units × $30 per unit)	$	384,000
Variable expenses		230,400
Contribution margin		153,600
Fixed expenses		171,600
Net operating loss	$	(18,000	)

Required:

1. Compute the company’s CM ratio and its break-even point in unit sales and dollar sales.

2. The president believes that a $6,100 increase in the monthly advertising budget, combined with an intensified effort by the sales staff, will increase unit sales and the total sales by $88,000 per month. If the president is right, what will be the increase (decrease) in the company’s monthly net operating income?

3. Refer to the original data. The sales manager is convinced that a 10% reduction in the selling price, combined with an increase of $39,000 in the monthly advertising budget, will double unit sales. If the sales manager is right, what will be the revised net operating income (loss)?

4. Refer to the original data. The Marketing Department thinks that a fancy new package for the laptop computer battery would grow sales. The new package would increase packaging costs by $0.50 per unit. Assuming no other changes, how many units would have to be sold each month to attain a target profit of $4,100?

5. Refer to the original data. By automating, the company could reduce variable expenses by $3 per unit. However, fixed expenses would increase by $51,000 each month.

a. Compute the new CM ratio and the new break-even point in unit sales and dollar sales.

b. Assume that the company expects to sell 20,100 units next month. Prepare two contribution format income statements, one assuming that operations are not automated and one assuming that they are. (Show data on a per unit and percentage basis, as well as in total, for each alternative.)

c. Would you recommend that the company automate its operations (Assuming that the company expects to sell 20,100 units)?

Answer 1

Requirement 1:

CM ratio = 0.4 or 40%

Break-even point in unit sales = 14300 units       

Break-even point in dollar sales = $429000

Solution:

CM ratio = CM per unit/selling price per unit

Where,

CM per unit = selling price per unit – variable cost per unit

= $30 - $18

= $12

Therefore,

CM ratio = $12/$30

= 0.4

= 40%

Break-even point in unit sales = Fixed cost/ CM per unit

= $171600/$12

= 14300 units

Break-even point in dollar sales = Fixed cost/ CM ratio

= $171600/0.4

= $429000

Requirement 2:

Increase in operating profit = $29100

Solution:

	Before	Change	After
Sales	384,000	88000	472000
Variable expenses	230,400	52800	283200
Contribution margin	153,600		188800
Fixed expenses	171,600	6100	177700
Net operating profit/(loss)	(18,000)		11100

Therefore,

Increase in operating profit = 11100 – (-18000) = 11100+18000 = $29100

Requirement 3:

Increase in operating profit = $37800

Solution:

	Before	Calculations	After
Sales	384,000	$27*25600	691200
Variable expenses	230,400	$18*25600	460800
Contribution margin	153,600		230400
Fixed expenses	171,600	171600+39000	210600
Net operating profit/(loss)	(18,000)		19800

Therefore,

Increase in operating profit = 19800 – (-18000) = 19800+18000 = $37800

Requirement 4:

Units required to earn $4100 =15279

Target units = (fixed cost + target profit)/CM per unit

= ($171600+$4100)/ $11.5

= 175700/$11.5

= 15279 units [units rounded off to next whole number as units can not be in decimals]

Requirement 5:

a.

New CM ratio = 0.5 or 50%

New Break-even point in unit sales = 14840 units

New Break-even point in dollar sales = $445200

Solution:

New CM ratio = CM per unit/selling price per unit

CM ratio = $15/$30

= 0.5

= 50%

New Break-even point in unit sales = Fixed cost/ CM per unit

= $222600/$15

= 14840 units

Break-even point in dollar sales = Fixed cost/ CM ratio

= $222600/0.5

= $445200

b.

Solution:

Income statement - Not automated

	Per unit	Amount	Percentage
Sales ($30*20100 units)	$30	603000	100%
Variable expenses ($18*20100 units)	$18	361800	60%
Contribution margin	$12	241200	40%
Fixed expenses		171600
Net operating profit/(loss)		69600

Income statement - Automated

	Per unit	Amount	Percentage
Sales ($30*20100 units)	$30	603000	100%
Variable expenses ($15*20100 units)	$15	301500	50%
Contribution margin	$15	301500	50%
Fixed expenses		222600
Net operating profit/(loss)		78900

c.

I recommend the company to automate as net profit is more in automation ($78900>$69600)

Notes:

1. variable cost per unit = $230400/12800

= $18

2. Increase in variable cost(req 2) = ($88000/$384000)*$230400

= $52800

3. Number of units sold (req 3) = 12800*2 = 25600
4. New selling price (req 3) = $30-10% = $30- $3 = $27
5. New variable cost (req 4) = $18+$0.5 =$18.5      
6. New CM per unit (req 4) = $30-$18.5 = $11.5
7. New variable cost (req 5) = $18-$3 =$15      
8. New CM per unit (req 5) = $30-$15 = $15
9. New Fixed cost (req 5) = $171600+51000 = $222600