Question

Northwood Company manufactures basketballs. The company has a ball that sells for $30. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $20.00 per ball, of which 67% is direct labor cost.

Last year, the company sold 30,000 of these balls, with the following results:

Sales (30,000 balls)	$	900,000
Variable expenses		600,000
Contribution margin		300,000
Fixed expenses		210,000
Net operating income	$	90,000

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 $30.00, 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, $90,000, 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 33.33%, 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, $90,000, as last year?

b. Assume the new plant is built and that next year the company manufactures and sells 30,000 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. Last year's CM ratio = Unit Contribution Margin / Unit Sales Price = $ 10 / $ 30 = 0.3333 or 33.33 %

Break-even point in balls = Total Fixed Expenses / Unit Contribution Margin = $ 210,000 / $ 10 = 21,000 balls.

b. Degree of Operating Leverage at last year's sales level = Contribution Margin / Net Operating Income = $ 300,000 / $ 90,000 = 3.333 x

2. Next year variable expense = $ 23 per ball.

Unit contribution margin = $ 30 - $ 23 = $ 7.

CM ratio = $ 7 / $ 30 = 0.2333 or 23.33 %

Break-even point in balls = Total Fixed Expenses / Unit Contribution Margin = $ 210,000 / $ 7 = 30,000 balls.

3. Last year net operating income : $ 90,000.

Number of balls to be sold to earn the same net operating income = ( Fixed Expenses + Target Income ) / Unit Contribution Margin = $ ( 210,000 + 90,000) / $ 7 = 42,857.14 balls.

4. Let the selling price per ball be P.

( P - 23) / P = 0.3333

P - 23 = 0.3333P

0.6667P = 23

P = 23 / 0.6667 = $ 34.4983 or $ 34.50.

Selling price per ball would be $ 34.50 in order to maintain the same CM ratio as in 1a.

5. New variable expense per ball = $ 20 x 2/3 = $ 13.33

Contribution margin per unit = $ 30 - $ 13.33 = $ 16.67.

New CM ratio = $ 16.67 / $ 30 = 0.5557

Break-even point in balls = $ 420,000 / $ 16.67 = 25,194.96 balls

6. a. Number of balls to be sold to earn the same net operating income = $ ( 420,000 + 90,000) / $ 16.67 = 30,593.88 balls.

b. Northwood Company

Contribution Margin Income Statement

For Next Year

Sales ( 30,000 x $ 30)	$ 900,000
Variable Expenses ( 30,000 x $ 13.33)	399,900
Contribution Margin ( 30,000 x $ 16.67)	500,100
Fixed Expenses	420,000
Net Operating Income	80,100

Degree of Operating Leverage = $ 500,100 / $ 80,100 = 6.243 x