Question

Pronghorn produces one single product, a small reading tablet, and sells it at $100 per unit. Its current annual sales are $200,000. Its annual fixed costs include factory rent, $38,000; depreciation expense; equipment, $10,000; utilities, $18,000; insurance, $8,000. Its variable costs include materials, $30 per unit, and direct labour, $40 per unit. Pronghorn’s income tax rate is 20%.

1.What is the contribution margin per unit?

2.What is the contribution margin ratio?

3.How many units must Pronghorn sell to break even?

4.If Pronghorn would like to earn a profit after tax of $11,000, what should the sales be? At this sales level, what is the degree of operating leverage? What is the margin of safety in unit?

5.If Pronghorn would like to earn a profit after tax that is 8% of sales, what should the sales be? How many units does Pronghorn need to increase from the current sales level?

Answer 1

* All working forms part of the answer

Requirement 1

Sales price per unit		$100
Variable cost per unit:
Direct Material	$30
Direct labor	$40	$70
Contribution margin per unit		$30

Requirement 2

A	Contribution margin per unit	$30
B	Sales price per unit	$100
C = A/B	Contribution margin ratio	30%

Requirement 3

	Fixed Expenses:
	Factory Rent	$38,000
	Depreciation expense	$10,000
	Utilities	$18,000
	Insurance expense	$8,000
A	Total Fixed expense	$74,000
B	Contribution margin per unit	$30
C = A/B	No. of units required to be sold to Break Even	2,467

Requirement 4

A	After Tax profits	$11,000
B = A/80%	Hence, before tax profits =	$13,750
C	Total Fixed expense	$74,000
D = B+C	Total Contribution margin required	$87,750
E	Contribution margin ratio	30%
F = D/E	Sales should be	$292,500
G = F x 30%	Contribution margin would be	$87,750
H = G - C	Net Operating Income	$13,750
I = G/H	Degree of Operating Leverage	6.38
J = F/$100	Sales in Units	2,925
K	Break Even units, calculated above	2,467
L = J - K	Margin of Safety	458

--Requirement 5

Let sales be $'x'

Profit after tax tax required = 8% of Sales = 0.08x

Profit before tax = 0.08x/80% = 0.1x

Contribution margin = 30% of x = 0.3x

Fixed cost = 74000

Contribution margin - Fixed Cost = Before tax profits

0.3x - 74000 = 0.1x

0.3x - 0.1x = 74000

0.2x = 74000

x = 74000/0.2

x = 370,000

Sales should be $ 370,000 = ANSWER This means 3700 units. while currently it sells 2000 units. Units need to be increased by 1700 units