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 52,000 of these balls, with the following results:

Sales (52,000 balls)	$	1,300,000
Variable expenses		780,000
Contribution margin		520,000
Fixed expenses		321,000
Net operating income	$	199,000

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, $199,000, 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, $199,000, as last year?

b. Assume the new plant is built and that next year the company manufactures and sells 52,000 balls (the same number as sold last year). Prepare a contribution format income statement and Compute the degree of operating leverage.

Answer 1

Solution

Northwood Company

1. Computation of last year’s CM ratio and break-even point in balls and the degree of operating leverage at last year’s sales level:

CM ratio –

CM ratio = (contribution margin/sales price) x 100

Contribution margin = sales price – variable cost

Sales price = $25

Variable cost = $15

Contribution margin = $10

CM ratio = (10/25) x100 = 40%

Break-even point in balls –

Break-even point in units = fixed cost/contribution margin

Fixed cost = $321,000

Contribution margin = $10

Break-even point in balls = $321,000/$10 = 32,100 balls

Degree of Operating leverage = contribution/net income

Net income = $199,000

Contribution = $520,000

Degree of operating leverage = $520,000/199,000 = 2.6

1. Estimated increase in variable expenses is $3 per ball, determination of CM ratio

New variable cost = $15 + $3 = $18

Revised contribution margin = $25- $18 = $7

CM ratio = (7/25) x 100 = 28%

Break-even point in balls –

= fixed cost/contribution margin

Fixed cost = $321,000

Contribution margin = $7

Break-even point in balls = 321,000/7 = 45,857 balls

So, the company needs to sell 45,857 balls to break-even when the variable cost increases to $18 per ball.

1. Determination of the number of balls to be sold to earn same net operating income of $199,000:

Desired units = (Fixed cost + target profit)/contribution margin

Fixed cost = $321,000

Target profit = $199,000

Contribution margin = $7 per ball

Desired units = (321,000 + 199,000)/7 = 74,286 balls

The company has to sell 74,286 balls to earn the same profit as last year.

1. Determination of increased sales price to maintain the original CM ratio of 40%:

CM ratio = 40%

Variable cost - $18

CM ratio = (sales price – variable cost)/sales price x 100

40%SP = (SP - $18)/SP

0.4SP = SP – 18

0.6 SP = 18

SP = 18/0.6 = $30

Hence, the required selling price per ball to maintain the CM ratio of 40% is $30

1. Decrease in variable expenses by 40%, so the new variable cost per unit = $15 -40% of 15

Variable cost per ball = $9

Fixed expenses doubled, = 2 x $321,000 = $642,000

New CM ratio,

Contribution margin = $25 - $9 = $16

CM ratio = (16/25) x 100 =64%

Break-even point in balls = fixed cost/contribution margin

Fixed cost = $642,000

Contribution margin = $16

Break-even point in balls = $642,000/$16 =40,125

6a. Desired units to earn the profit of $199,000 with revised variable cost and fixed cost:

Desired units = (fixed cost + target profit)/contribution margin

Fixed cost = $642,000

Target profit = $199,000

Contribution margin = $16

Desired number of balls = (642,000 + 199,000)/16

=52,563 balls

6b.

	Contribution Margin Format Income Statement
	Per Unit	Amount
Sales	$25	$1,300,000
Variable Expenses	$9	$468,000
Contribution Margin	$16	$832,000
Fixed Expenses		$642,000
Operating Income		$190,000

Degree of operating leverage = contribution/net income

Contribution = $832,000

Net income = $190,000

Degree of operating leverage = 832,000/190,000 = 4.38