Question

Roustabout Company manufactures skateboards. Last year’s income statement is summarized below.

Skateboards(2,000 units)

  

Total   

Sales Revenue $      100,000

Variable Costs $       40,000

Contribution Margin $       60,000   

Fixed Costs $       55,500

Pre-Tax Profit $       4,500   

Required:

a. What is the CM per unit?

b. How many skateboards must be sold to breakeven?

c. What level of revenue is needed to earn a target pre-tax income of $21,000? Use CM per unit to calculate your answer.

d. If variable costs increase to $30 per skateboard, what decrease in annual fixed costs must be achieved to keep the same breakeven point as calculated in part b?

e. Back to original assumptions: What is the CM ratio?

f. Using the CM ratio, what level of revenue is needed to breakeven?

g. Using the CM ratio, how many skateboards must be sold to earn a target pre-tax profit of $51,000?

h. How many skateboards must be sold to earn after-tax profit of $147,000 (with a tax rate of 30%)?

i. What is the margin of safety for Roustabout Company in units and in dollars?

j. If Roustabout increases its sales by 5%, what will happen to profits? Use degree of operating leverage to answer this question.

Answer 1

	At Present for 2,000 units	Per unit
Sales Revenue	$       127,500	$          50
Variable Costs	$         51,000	$          20
Contribution Margin	$         76,500	$          30
Fixed Costs	$         55,500
Pre-Tax Profit	$         21,000

a	CM Per unit = Contribution Margin / Sales Units
	= $60,000 / 2,000 = $30 per unit
b	At breakeven; Contribution Margin = Fixed Cost = $55,500
	So, no. Of units required to breakeven = Fixed Cost / CM Per unit
	= $55,500 / $30 = 1,850 Units
c	Target Pre tax income = $21,000 i.e. Target Contribution = Target Pre tax income + Fixed Cost
	Target Contribution = $21,000 + $55,500 = $76,500
	No. Of units for target contribution = Target Contribution / CM Per Unit = $76,500 / $30 = 2,550 units
	So, level of revenue needed for pre tax income of $21,000 = Target Units * Sales Price per Unit
	= 2,550 units * $50 = $127,500
d	Breakeven point calculated in point b = 1,850 units
	Decrease in annual fixed costs required = Increase in Variable Costs
	=(New Variable Cost - Old Variable Cost) * Break even point units
	= ($30 - $20) * 1,850 units = $18,500
e	CM Ratio = Contribution / Sales * 100
	= $60,000 / $100,000 * 100 = 60%
f	Level of Revenue needed to breakeven = Fixed Costs / CM Ratio
	= $55,500 / 60 * 100 = $92,500
g	To earn pre tax profit of $51,000; required contribution = $55,500 + $51,000 = $106,500
	So, required sales revenue = Required Contribution / CM Ratio = $106,500 / 60 * 100 = $177,500
	So, no. Of units to be sold =Required Sales / Sale Price Per unit = $177,500 / $50 = 3,550 units
h	After tax profit of $147,000 means pre tax profit of $210,000 ($147,000 * 100 / 70)
	To earn pre tax profit of $210,000; required contribution = $55,500 + $210,000 = $265,500
	So, required sales revenue = Required Contribution / CM Ratio = $265,500 / 60 * 100 = $442,500
	So, no. Of units to be sold = Required Sales / Sale Price per unit = $442,500 / $50 = 8,850 units
i	Margin of Safety = Actual Sales - Breakeven Sales
	Breakeven Sales = 1,850 units * $50 = $92,500
	(1,850 units are breakeven units calculated in point b)
	Margin of Safety = $100,000 - $92,500 = $7,500
	Margin of Safety (in units) = (Actual Sales - Breakeven Point) / Selling Price per unit
	= ($100,000 - $92,500) / $50
	= 150 units
j	Degree of operating leverage is sensitivity of company's operating income to its sales
	Degree of operating leverage = Contribution Margin / Operating Income
	=$60,000 / $100,000 = 60%
	So, if Roustabout increases sales by 5%, its profit will increase by 3% (5% * 60%) of its sales
	i.e by $3,000 ($100,000 * 3%)