Question

Use the amounts shown on the contribution margin income statement below to compute the missing amounts denoted by letters a through n.

	Company A		Company B
Number of units sold	a		1,975
	Total	Per unit	Total	Per unit
Sales	\(208,400	\)65	h	i
Variable cost	150,000	b	\(39,500	j
Contribution margin	c	d	43,450	k
Fixed cost	e	f	19,750	l
Net income	\)46,400	g	m	n

Short answer

	Company A		Company B
Number of units sold	3206		1,975
	Total	Per unit	Total	Per unit
Sales	$208,400	$65	$82,950	$42
Variable cost	150,000	$46.79	$39,500	$20
Contribution margin	$58,400	$18.21	43,450	$22
Fixed cost	$12,000	$3.74	19,750	$10
Net income	$46,400	$14.47	$23,700	$12

Step-by-step solution

Definition of Contribution Margin

Contribution is the amount left after deducting the variable cost incurred in the production process from the sales revenue. Variable cost includes labor and material expenses.

Calculation of each missing value for company A

a. Calculation of a number of units:

$\begin{array}{c}\mathrm{Number}\mathrm{of}\mathrm{units}=\frac{\mathrm{Total}\mathrm{sales}}{\mathrm{Per}\mathrm{unit}\mathrm{sales}\mathrm{price}}\\ =\frac{\mathrm{\$}208,400}{\mathrm{\$}65}\\ =3,206\mathrm{units}\end{array}$

b. Variable cost per unit:

$\begin{array}{c}\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}=\frac{\mathrm{Total}\mathrm{variable}\mathrm{cost}}{\mathrm{Total}\mathrm{units}\mathrm{sold}}\\ =\frac{\mathrm{\$}150,000}{3206}\\ =\mathrm{\$}46.78\text{\hspace{0.17em}}\mathrm{per}\mathrm{unit}\end{array}$

c. Total contribution margin:

Particular	Amount $
Sales	$208,400
Less: Variable cost	(150,000)
Contribution margin	$58,400

d. Contribution margin per unit:

Particular	Amount $
Sales	$65
Less: Variable cost	46.79
Contribution margin	$18.21

e. Total fixed cost:

Particular	Amount $
Contribution margin	$58,400
Less: Net income	(46,400)
Fixed cost	$12,000

f. Per unit fixed cost:

$\begin{array}{c}\mathrm{Fixed}\mathrm{cost}\mathrm{per}\mathrm{unit}=\frac{\mathrm{Total}\mathrm{fixed}\mathrm{cost}}{\mathrm{Total}\mathrm{units}\mathrm{sold}}\\ =\frac{\mathrm{\$}12,000}{3206}\\ =\mathrm{\$}3.74\text{\hspace{0.17em}}\mathrm{per}\mathrm{unit}\end{array}$

g. Net income per unit:

Particular	Amount $
Contribution margin per unit	$18.21
Less: Fixed cost per unit	($3.74)
Net income per unit	$14.47

Calculation of each missing value for company B

h. Calculation of variable cost

Particular	Amount $
Variable cost	$39,500
Add: Contribution margin	43,450
Total sales	$82,950

i. Sales price per unit

$\begin{array}{c}\mathrm{Sales}\mathrm{per}\mathrm{unit}=\frac{\mathrm{Total}\mathrm{sales}}{\mathrm{Total}\mathrm{units}\mathrm{sold}}\\ =\frac{\mathrm{\$}82,950}{1,975}\\ =\mathrm{\$}42\text{\hspace{0.17em}}\mathrm{per}\mathrm{unit}\end{array}$

j. Calculation of variable cost per unit

$\begin{array}{c}\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}=\frac{\mathrm{Total}\mathrm{variable}\mathrm{cost}}{\mathrm{Total}\mathrm{units}\mathrm{sold}}\\ =\frac{\mathrm{\$}39,500}{1975}\\ =\mathrm{\$}20\text{\hspace{0.17em}}\mathrm{per}\mathrm{unit}\end{array}$

K. Calculation of contribution margin per unit:

Particular	Amount $
Sales	$42
Less: Variable cost	(20)
Contribution margin per unit	$22

l. Calculation of fixed cost per unit:

$\begin{array}{c}\mathrm{Fixed}\mathrm{cost}\mathrm{per}\mathrm{unit}=\frac{\mathrm{Total}\mathrm{fixed}\mathrm{cost}}{\mathrm{Total}\mathrm{units}\mathrm{sold}}\\ =\frac{\mathrm{\$}19,750}{1975}\\ =\mathrm{\$}10\mathrm{per}\mathrm{unit}\end{array}$

m. Calculation of total net income:

Particular	Amount $
Contribution margin	$43,450
Less: Fixed cost	(19,750)
Net income	$23,700

n. Calculation of net income per unit:

Particular	Amount $
Contribution margin per unit	$22
Less: Fixed cost per unit	(10)
Net income per unit	$12