Question

Northwood Company manufactures basketballs. The company has a ball that sells for $25. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $15.00 per ball, of which 60% is direct labor cost.

Last year, the company sold 60,000 of these balls, with the following results:

Sales (60,000 balls)	$	1,500,000
Variable expenses		900,000
Contribution margin		600,000
Fixed expenses		375,000
Net operating income	$	225,000

Required:

1. Compute (a) last year's CM ratio and the break-even point in balls, and (b) the degree of operating leverage at last year’s sales level.

2. Due to an increase in labor rates, the company estimates that next year's variable expenses will increase by $3.00 per ball. If this change takes place and the selling price per ball remains constant at $25.00, what will be next year's CM ratio and the break-even point in balls?

3. Refer to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $225,000, as last year?

4. Refer again to the data in (2) above. The president feels that the company must raise the selling price of its basketballs. If Northwood Company wants to maintain the same CM ratio as last year (as computed in requirement 1a), what selling price per ball must it charge next year to cover the increased labor costs?

5. Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 40.00%, but it would cause fixed expenses per year to double. If the new plant is built, what would be the company’s new CM ratio and new break-even point in balls?

6. Refer to the data in (5) above.

a. If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $225,000, as last year?

b. Assume the new plant is built and that next year the company manufactures and sells 60,000 balls (the same number as sold last year). Prepare a contribution format income statement and compute the degree of operating leverage.

Answer 1

1.

a.	Selling price	$25	100%
	Variable expenses	15	60%
	Contribution margin	$10	40%

Profit	= Unit CM × Q − Fixed expenses
$0	= $10 × Q − $375,000
$10Q	= $375,000
Q	= $375,000 ÷ $10
Q	= 37,500 balls

Alternative solution:

= $375,000/$10 = 37,500

b. The degree of operating leverage is:

=$600,000/225,000 = $2.67

2.

The new CM ratio will be:

Selling price	$25	100%
Variable expenses	18	72%
Contribution margin	$ 7	28%

The new break-even point will be:

Profit	= Unit CM × Q − Fixed expenses
$0	= $7 × Q − $375,000
$7Q	= $375,000
Q	= $375,000 ÷ $7
Q	= 53,571.43 balls

Alternative solution:

= $375,000/$7 = 53,571.43

Profit	= Unit CM × Q − Fixed expenses
$225,000	= $7 × Q − $375,000
$7Q	= $225,000 + $375,000
Q	= $600,000 ÷ $7
Q	= 85,714.28 balls (rounded)

Alternative solution:

= ($ 225,000+$ 375,000) / $7 =  85,714.28

Thus, sales will have to increase by 25,714.28 balls (85,714.28 balls, less 60,000 balls currently being sold) to earn the same amount of net operating income as last year. The computations above and in part (2) show the dramatic effect that increases in variable costs can have on an organization. The effects on Northwood Company are summarized below:

	Present	Expected
Combination margin ratio	40%	28%
Break-even point (in balls)	37,500	60,000
Sales (in balls) needed to earn a $225,000 profit	60,000	85,714.28

If variable costs do increase next year, then the company will just break even if it sells the same number of balls (60,000) as it did last year.

4.

The contribution margin ratio last year was 40%. If we let P equal the new selling price, then:

P =	$18 + 0.40P
0.60P =	$18
P =	$18 ÷ 0.60
P =	$30

To verify:

	Selling price.................................	$30	100%
	Variable expenses........................	18	60%
	Contribution margin....................	$12	40%

Therefore, to maintain a 40% CM ratio, a $3 increase in variable costs would require a $5 increase in the selling price.

5.

The new CM ratio would be:

Selling price........................................	$25	100%
Variable expenses...............................	9*	36%
Contribution margin...........................	$16	64%

*$15 – ($15 × 40%) = $9

The new break-even point would be:

Profit	= Unit CM × Q − Fixed expenses
$0	= $16 × Q − $750,000 (375,000*2
$16Q	= $750,000
Q	= $750,000 ÷ $16
Q	= 46,875 balls

Alternative solution:

= $750,000 ÷ $16=46,875

Although this new break-even is greater than the company’s present break-even of 37,500 balls [see Part (1) above], it is less than the break-even point will be if the company does not automate and variable labor costs rise next year [see Part (2) above].

6.

a.	Profit	= Unit CM × Q − Fixed expenses
	$225,000	= $16 × Q − $750,000
	$16Q	= $225,000 + $750,000
	Q	= $975,000 ÷ $16
	Q	= 60,937.5 balls

Alternative solution:

=($225,000 + $750,000)/$16 =60,937.5

Thus, the company will have to sell 937.5 more balls (60,937.5 – 60,000 = 1,875) than now being sold to earn a profit of $225,000 per year. However, this is still less than the 85,714.28 balls that would have to be sold to earn a $225,000 profit if the plant is not automated and variable labor costs rise next year [see Part (3) above].

b.

The contribution income statement would be:

Sales (60,000 balls × $25 per ball)	$1,500,000
Variable expenses (60,000 balls × $9 per ball)	540,000
Contribution margin	960,000
Fixed expenses	750,000
Net operating income	$ 210,000

= $960,000/$210,000 = 4.57