Chapter 18, Problem 27E

To determine

Contribution Margin Income statement:

Contribution margin income statement shows the sales revenue, deduction of product and period cost from the sales revenue and then identification of contribution margin. It shows the net income while deduct the fixed income from the contribution margin.

To identify: Missing amounts.

Explanation of Solution

Company A

a

Given,
Sales are $208,000.
Selling price per unit is $65.

Formula to calculate number of units sold by Company A,

$\text{Number}\text{of}\text{units}\text{sold}=\frac{\text{Total}\text{sales}}{\text{Selling}\text{price}\text{per}\text{unit}}$

Substitute $208,000 for sales and $65 for selling price per unit.

$\begin{array}{c}\text{Number}\text{of}\text{units}\text{sold}=\frac{\$208,000}{\$65}\\ =3,200\text{units}\end{array}$

Hence, value of a is 3,200.

b

Given,
Variable cost is $150,400.

Calculated values (from part a),
Number of units sold are 3,200.

Formula to calculate per unit variable cost,

$\text{Per}\text{unit}\text{variable}\text{unit}=\frac{\text{Total}\text{Variable cost}}{\text{Number of units sold}}$

Substitute $150,400 for variable cost and 3,200 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{variable}\text{unit}=\frac{\$150,400}{3,200}\\ =\$47\end{array}$

Hence, value of b is $47.

c

Given,
Variable cost is $150,400.
Sales are $208,000.

Formula to calculate contribution margin,

$\text{Contribution}\text{margin}=\text{Sales}-\text{Variable}\text{cost}$

Substitute $208,000 for sales and $150,400 for variable cost.

$\begin{array}{c}\text{Contribution}\text{margin}=\$208,000-\$150,400\\ =\$57,600\end{array}$

Hence, value of c is $57,600.

d

Calculated values,
Number of units sold are 3,200 (from part a).
Contribution margin is $57,600 (from part c).

Formula to calculate per unit contribution margin,

$\text{Per}\text{unit}\text{contribution}\text{margin}=\frac{\text{Total}\text{contribution margin}}{\text{Number of units sold}}$

Substitute $57,600 for total contribution margin and 3,200 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{contribution margin}=\frac{\$57,600}{3,200}\\ =\$18\end{array}$

Hence, value of d is $18.

e

Calculated values,
Contribution margin is $57,600 (from part c).

Given,
Net income is $46,400.
Formula to calculate fixed cost,

$\text{Fixed}\text{cost}=\text{Contribution}\text{margin}-\text{Net}\text{income}$

Substitute $57,600 for contribution margin and $46,400 for net income.

$\begin{array}{c}\text{Fixed}\text{cost}=\$57,600-\$46,400\\ =\$11,200\end{array}$

Hence, value of e is $11,200.

f

Calculated values,
Number of units sold are 3,200 (from part a).
Fixed cost is $11,200(from part e).

Formula to calculate per unit fixed cost,

$\text{Per}\text{unit}\text{fixed}\text{unit}=\frac{\text{Total}\text{fixed cost}}{\text{Number of units sold}}$

Substitute $11,200 for fixed cost and 3,200 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{fixed}\text{unit}=\frac{\$11,200}{3,200}\\ =\$3.5\end{array}$

Hence, value of f is $3.5.

g

Calculated values,
Number of units sold are 3,200 (from part a).

Given,
Net income is $46,400.

Formula to calculate per unit income,

$\text{Per}\text{unit}\text{income}=\frac{\text{Net}\text{income}}{\text{Number of units sold}}$

Substitute $46,400 for net income and 3,200 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{income}=\frac{\$46,400}{3,200}\\ =\$14.5\end{array}$

Hence, value of g is $14.5.

Company B

h

Given,
Variable cost is $39,500.
Contribution margin is $43,450.

Formula to calculate sales,

$\text{Sales}=\text{Variable}\text{cost}+\text{Contribution}\text{margin}$

Substitute $43,450 for contribution margin and $39,500 for variable cost.

$\begin{array}{c}\text{Sales}=\$39,500+\$43,450\\ =\$82,950\end{array}$

Hence, value of h is $82,950.

i

Given,
Number of units sold are 1,975.

Calculated values (from part h),
Sales are $82,950.

Formula to calculate selling price per unit,

$\text{Selling}\text{price}\text{per}\text{unit}=\frac{\text{Total}\text{sales}}{\text{Number of units sold}}$

Substitute $82,950 for total sales and 1,975 for number of units sold.

$\begin{array}{c}\text{Selling}\text{price}\text{per}\text{unit}=\frac{\$82,950}{1,975}\\ =\$42\end{array}$

Hence, value of i is $42.

j

Given,
Variable cost is $39,500.
Number of units sold are 1,975.

Formula to calculate per unit variable cost,

$\text{Per}\text{unit}\text{variable}\text{unit}=\frac{\text{Total}\text{Variable cost}}{\text{Number of units sold}}$

Substitute $39,500 for variable cost and 1,975 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{variable}\text{unit}=\frac{\$39,500}{1,975}\\ =\$20\end{array}$

Hence, value of j is $20.

k

Given,
Number of units sold are 1,975.
Contribution margin is $43,450.

Formula to calculate per unit contribution margin,

$\text{Per}\text{unit}\text{contribution}\text{margin}=\frac{\text{Total}\text{contribution margin}}{\text{Number of units sold}}$

Substitute $43,450 for total contribution margin and 1,975 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{contribution margin}=\frac{\$43,450}{1,975}\\ =\$22\end{array}$

Hence, value of k is $22.

l

Given,
Number of units sold are 1,975.
Fixed cost is $19,750.

Formula to calculate per unit fixed cost,

$\text{Per}\text{unit}\text{fixed}\text{unit}=\frac{\text{Total}\text{fixed cost}}{\text{Number of units sold}}$

Substitute $19,750 for total fixed cost and 1,975 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{fixed}\text{unit}=\frac{\$19,750}{1,975}\\ =\$10\end{array}$

Hence, value of l is $10.

m

Given,
Contribution margin is $43,450.
Fixed cost is $19,750.

Formula to calculate net income,

$\text{Net}\text{income}=\text{Contribution}\text{margin}-\text{Fixed}\text{cost}$

Substitute $43,450 for contribution margin and $19,750 for fixed cost.

$\begin{array}{c}\text{Net}\text{income}=\$43,450-\$19,750\\ =\$23,700\end{array}$

Hence, value of m is $23,700.

n

Given,
Number of units sold are 1,975.

Calculated values,
Net income is $23,700 (from part m).

Formula to calculate per unit income,

$\text{Per}\text{unit}\text{income}=\frac{\text{Net}\text{income}}{\text{Number of units sold}}$

Substitute $23,700 for net income and 1,975 for number of units sold.

$\begin{array}{c}\text{Per}\text{unit}\text{income}=\frac{\$23,700}{1,975}\\ =\$12\end{array}$

Hence, value of n is $12.