Question

Speedy Sports manufactures basketballs that sell for $ 25. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Therefore, variable costs are high, totaling $ 15 per ball, of which 60% is direct labor cost. Fixed costs are $ 210,000. Last year, the firm sold 30,000 balls.

1. Compute (1) the CM ratio and the breakeven point in units and (2) the degree of operating leverage.
2. Due to an increase in labor rates, the firm estimates that variable expenses will increase by $ 3 per ball next year. If this change takes place and the selling price remains the same, what will be the new CM ratio and breakeven point in balls?
3. Refer to the data in (b) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same before tax operating income as last year?
4. Refer to the data in (b) above. The CEO feels that the company must raise the selling price of its basketballs. If the firm wants to maintain the same CM ratio as last year, what unit selling price must it charge next year to cover the increased labor costs?
5. Refer to the original data. The firm is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 40%, but it would cause fixed costs per year to double. If the new plant is built, what would be the firm’s new CM ratio and new breakeven point in balls?
6. Refer to the data in (e) above.
   1. If the new plant is built, how many balls will have to be sold next year to earn the before tax operating income as last year?
   2. Presume the new plant is built and that next year the firm manufactures and sells 30,000 balls (the same number as last year). Prepare a contribution margin income statement and compute the degree of operating leverage.
   3. If you were a member of top management, would you have been in favor of constructing the new plant? Explain.

Answer 1

a) 1. Contribution margin ratio = Contribution margin / Selling price

Seliing price = $25

Contribution margin = Selling price - Variable cost

Variable cost = $15

Contribution margin = $25 - $15 = $10

Contribution margin ratio = $10 / $25 = 0.4

Contribution margin ratio in percentage = 0.4*100 = 40%

Break even point in units = Fixed cost / Contribution margin per unit

Fixed cost = $210,000 Contribution margin per unit = $10

Break even point in units = $210,000 / $10 = 21,000 units

2. Degree of operating leverage leverage = Contribution margin / Operating income

Calculation of operating income and contribution margin of 30,000 basket balls

	Basket ball
Per ball	30,000 balls
Sales	$ 25	$ 750,000
Less:Variable cost	($ 15)	($ 450,000)
Contribution margin	$ 10	$ 300,000
Less: Fixed cost		($ 210,000)
Operating profit		$ 90,000

Degree of operating leverage = $300,000 / $90,000 = 3.33

b) Variable cost is increased by $3 and new variable cost = $15 + $3 = $18

Contribution margin = Selling price - Variable cost = $25 - $18 = $7

Contribution margin ratio = Contribution margin / seliing price = $7 / $25 = 0.28

Contribution margin ratio in percentage = 0.28 * 100 = 28%

Break even point in units = Fixed cost / contribution margin = $210,000 / $7 = 30,000 units

c) operating income in (b) = $90,000

Variable cost has increased by $3.

No: of balls to be sold to earn an operating income of $90,000 = (Fixed cost + target profit) / Contribution margin

Fixed cost = $210,000 Target profit = $90,000 Contribution margin = $7

Required sales of balls = ($210,000 + $90,000) / $7 = $300,000 / $7 = 42,857.14 rounded to 42,857 balls

To earn an operating income of $90,000, 42,857 basket balls must be sold.

d) Contribution margin ratio before increase in labor cost = 0.4

if contribution margin ratio is 0.4, Variable cost ratio must be 0.6 (1 - 0.4)

Variable cost after increase in labor cost = $18

Desired unit selling price = Variable cost / Variable cost ratio = $18 / 0.6 = $30

So, unit selling price must be $30 to get a CM ratio of 0.4.

Let's check:

CM ratio = Contribuiton margin / selling price

Contribution margin = Selling price - vaeriable cost = $30 - $18 = $12

CM ratio = $12 / $30 = 0.4

e) if new plant is built, variable costs will decrease by 40% and fixed cost get doubled;

(refer to original data)

Variable cost = $15 Fixed cost in a year = $210,000

if plant is built,

Variable cost = $15 - ($15*40%) = $15 - $6 = $9

Fixed cost = $210,000 * 2 = $420,000

New CM ratio = Contribution margin / Selling price

Selling price = $25

Contribution margin = Selling price - variable cost = $25 - $9 = $16

CM ratio = $16 / $25 = 0.64

Break even point in units = Fixed cost / contribution margin

= $420,000 / $16 = 26,250 units

f) Operating income of last year = $90,000

if plant is built, number of basket balls to be sold to get operating income of $90,000

=(Fixed cost + target profit) / contribution margin

Fixed cost = $420,000 Target profit = $90,000 contribution margin = $16

Required sales(number of basket balls) =($420,000 + $90,000) / $16 = $510,000 / $16 = 31,875 basket balls.

31,875 basket balls must be sold to earn an operating income of $90,000 if new plant is built.

CONTRIBUTION FORMAT INCOME STATEMENT IF 30,000 BASKET BALLS ARE SOLD.

SPEEDY SPORTS
Income statement
Sales	$750,000
Less:Variable cost	($270,000)
Contribution margin	$480,000
Less: Fixed cost	($420,000)
Operating income	$60,000

notes;

sales = $25 * 30,000

variable cost = $9 * 30,000

OPERATING LEVERAGE = CONTRIBUTION MARGIN / OPERATING INCOME

= $480,000 / $60,000 = 8

My opininion ; As a member of top management, I don't agree with the new plant construction. The only benefit is the decrease in variable cost. But it doubles the fixed cost and didn't bring any increase in the sales. As a result The operating income has decreased to $60,000. In the previous year, operating income was $90,000. The construction of new plant decreased operating income by $30,000. And the opearting leverage is too high comparing to previous year which means high risk of loss. The costs can't be reduced during decrease in sales in this situation since high fixed cost is involved.So, I can't agree with it's construction.