Question

Shelly's Boutiques and Crafts had revenue of $5,700,000 this year on sales of 575,000 units. Variable costs were 35% and fixed costs totaled $3,150,000. Although the first five years were relatively profitable, increases in competition have led to a negative trend in profitability that has led them to the point where they have to make some changes to stay afloat. The company is evaluating two options to stay afloat.

Option 1: Purchase machinery to automate their operations. this machinery cost $625,000 but will decrease variable costs by 9%

Option 2: Outsource the production of one of their main components that requires a substantial amount of machinery and skilled labor. This will reduce fixed costs by $425,000, but increases variable costs from their current 35% of sales to 40% of sales.

a. determine break even points in units before changes. what is fixed cost total? what is the contribution margin per unit? what is the break even point in units?

b.) Assuming an income tax rate of 35%, what dollar value of sales is required to earn an after tax profit of $800,000 What before tax profit would be needed to earn an after tax profit of $800,000? what is the contribution margin raton? What dollar amount of sales would be required to earn the after tax profit described above?

c.) Calculate the operating leverage before applying any of the options: What is the contribution margin in Total? What is the operating income in total? what is the operating leverage factor?

d.) Calculate the break even point in units after applying Option 1: What is the new fixed cost in total? What is the new contribution margin per unit? What is the new break even point in units?

e.) Calculate the operating leverage after applying Option 1: What is the new contribution margin in Total? What is the new operating income in total? what is the new operating leverage factor?

f.) Calculate the break even point in units after applying Option 2: What is the new fixed cost in total? What is the new contribution margin per unit? What is the new break even point in units?

g.) Calculate the operating leverage after applying Option 2: What is the new contribution margin in Total? What is the new operating income in total? what is the new operating leverage factor?

Answer 1

Sales per unit (S) = total revenue/ number of units = 5,700,000/575,000 = $9.91 per unit

Variable cost per unit (VC) = Total variable cost/ number of units = 35%*total revenue/number of units

= (35%*5,700,000)/575,000 = 3.47

a). Break-even quantity Q = FC/(S - VC) = 3,150,000/(9.91 - 3.47) = 488,866.40 units

Contribution margin = S - FC = 9.91 - 3.47 = $6.44 per unit

b). To earn an after-tax profit of 800,000, the before-tax profit has to be after-tax profit/(1 - tax rate)

= 800,000/(1-35%) = 1,230,769.23

Let number of units be n.

n*(S-VC) - FC = 1,230,769.23

n*6.44 - 3,150,000 = 1,230,769.23

n = (1,230,769.23 - 3,150,000)/6.44 = 679,876.47

Dollar value of sales = S*n = 9.91*679,876.47 = 6,739,644.97

c). Operating Cash Flow (OCF) without taxes = n*(S-VC) - FC = 5,700,000 - 1,995,000 - 3,150,000 = 555,000

Operating leverage factor = Total contribution margin/operating income = (5,700,000 - 1,995,000)/555,000 = 6.68

Parts d,e,f,g:

Question		Formula	Option 1	Formula	Option 2
	Number of units (u)		5,75,000		5,75,000
	Sales (R)		5,700,000		5,700,000
	Variable cost (V)	(35%-9%)*R	1,482,000	40%*R	2,280,000
	Fixed cost (FC)	Unchanged	3,150,000	Decreases by 425,000	2,725,000
	Sales per unit (S)	R/u	9.91	R/u	9.91
	Variable cost per unit (VC)	V/u	2.58	V/u	3.97
part (d), (f)
	Break-even quantity	FC/(S-VC)	429,409.67	FC/(S-VC)	458,150.58
	New Fixed cost in total		3,150,000		2,725,000
	New contribution margin per unit	S-VC	7.34	S-VC	5.95
part (e), (g)
	Contribution margin in total (CM)	R-V	4,218,000	R-V	3,420,000
	Operating income in total (OI)	R-V-FC	1,068,000	R-V-FC	695,000
	Operating leverage factor	CM/OI	3.95	CM/OI	4.92