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 44,000 of these balls, with the following results:

Sales (44,000 balls)	$	1,100,000
Variable expenses		660,000
Contribution margin		440,000
Fixed expenses		317,000
Net operating income	$	123,000

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, $123,000, 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, $123,000, as last year?

b. Assume the new plant is built and that next year the company manufactures and sells 44,000 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) contribution margin ratio = 0.4 or 40%

break even point in balls = 31700 balls

b) operating leverage = 3.5772

Solution :

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

Where,

CM per unit = selling price per unit - variable expenses per unit.

CM per unit = $25 - $15 = $10.

Therefore,

CM ratio = $10/$25 = 0.4

Break even point in balls = fixed expenses /CM per ball.

= $317000/$10 per ball.

= 31700 balls

Operating leverage = total contribution amount /operating profit.

=$440000/$123000

= 3.5772

2) Contribution margin ratio = 0.28 or 28%

Break even point in balls = 45286 balls

Solution :

New variable expenses per unit = $15 +$3 = $18

New contribution margin per unit = $25-$18 = $7

CM ratio = $7/$25 = 0.28

Break even point in balls = $317000/$7

= 45285.71

As number of balls can't be in decimals, it is taken as 45286 balls

3) Number of balls to be sold to earn $123000 = 62858 balls.

Solution :

Number of balls to be sold to earn $123000 = (fixed expense + expected profit) /CM per unit.

= ($317000+$123000)/$7

= $440000/$7

= 62857.17

= 62858 balls

4) The new selling price should be = $30 per ball.

Solution :

New Variable expense per unit = $18 and Old CM ratio = 0.4

And new selling price be 'x'

Therefore,

CM ratio = (selling price - variable expense) /selling price.

0.4 = (x - $18)/x

0.4×x = (x - $18)

0.4x = x - $18

$18 = x - 0.4x

$18 = 0.6x

x = $18/0.6

x = $30

That means the new selling price should be $30 per ball.