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 48,000 of these balls, with the following results:

Sales (48,000 balls)	$	1,200,000
Variable expenses		720,000
Contribution margin		480,000
Fixed expenses		319,000
Net operating income	$	161,000

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, $161,000, 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, $161,000, as last year?

b. Assume the new plant is built and that next year the company manufactures and sells 48,000 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. CM ratio = Contribution Margin / Sales

=> CM ratio = 480000 / 1200000

=> CM ratio = 0.4 = 40%

and,

Break even point = Total fixed cost / CM per unit

Total number of balls sold = 48000

CM = 480000

Therefore, CM per unit = 480000 / 48000 = 10

Hence,

Break even point = 319000 / 10

=>  Break even point = 31900 balls

1. b Degree of operating leverage = CM / Net operating Income

=> Degree of operating leverage = 480000 / 161000

=> Degree of operating leverage = 2.98

2. Last year's variable expense = $15 per ball

The company estimates variable expense to increase by $3 per ball

Therefore, next year's variable expense = 15 + 3 = $18 per ball

Now, CM per ball = sales per ball - variable expense per ball

=> CM per ball = 25 - 18 = $7

Therefore, CM ratio = CM per ball / Sales per ball

=> CM ratio = 7 / 25 = 0.28 = 28%

and,

Break even point = Total fixed cost / CM per unit

=>  Break even point = 319000 / 7

=>  Break even point = 45571.43 balls

3. Net operating profit = $161000

Fixed cost = $319000

Contribution Margin = 160000 + 319000 = $480000

As we calculated in the last question, CM per ball = $7

Therefore, Number of balls = CM / CM per ball = 480000 / 7 = 68571.43 balls

4. CM ratio in question 1a = 40%

The company wants to maintain the CM ratio

As we know,

CM ratio = Contribution Margin per ball / Sales per ball

=> 0.4 = 7 / Sales per ball

=> Sales per ball = 7 / 0.4

=> Sales per ball = $17.5

5. Given

If the new plant is manufactured

Variable expense per ball = 15 * (1-0.4) = $9

Fixed expense = 2 * 319000 = $638000

Sales per ball = $25

Therefore,

CM per ball = Sales per ball - Variable expense per ball

=> CM per ball = 25 - 9 = $16

Now,

CM Ratio = CM per ball / Sales per ball

=> CM Ratio = 16 / 25

=> CM Ratio = 0.64 = 64%

and,

Break even point = Total fixed cost / CM per unit

=> Break even point = 638000 / 16

=> Break even point = 39875 balls

6.a if the net operating income remains same = $161000

then,

CM = Fixed expense + net operating income

=> CM = 638000 + 161000 = $799000

As we calculated in the last question, CM per ball = 16

Therefore, Number of balls to be sold = CM / CM per ball = 799000 / 16 = 49937.5 = 49938

6.b

Sales per ball = $25

Total Sales = 48000 * 25 = $1200000

Variable expense per ball = $9

Total variable expense = 48000 * 9 = 432000

Contribution margin per ball = 16

Total contribution Margin = 48000 * 16 = 768000

Fixed expense = $638000

Net operating income = CM - Fixed expense

=> Net operating income = 768000 - 638000 = $400000

Contribution format income statement will be as follows:

	Total (in $)	per ball (in $)
Sales (48000 balls)	1200000	25
Variable expense	432000	9
Contribution Margin	768000	16
Fixed expense	638000
Net Operating income	400000

Degree of operating leverage = CM / Net operating Income

=> Degree of operating leverage = 768000 / 400000 = 1.92