Chapter 5, Problem 22E

To determine

Cost-Volume-Profit Analysis:

The cost-volume analysis is the method to analyze the effect on net income due to change in fixed and variable cost and sales volume.

(1)

To identify: Selling price per composite unit.

Explanation of Solution

Given,
Sales price per window is $200.
Sales price per door is $500.
Variable cost per door is $350.
Variable cost per window is $125.
Fixed cost is $900,000.
Ratio of window and doors is 8:2.

Table represents the selling price per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Selling price per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Window	8	200	1,600
Doors	2	500	1,000
Selling price per composite unit			2,600

Table(1) Hence, selling price per composite unit is $2,600.

(2)

To determine

To identify: The variable cost per composite unit.

Explanation of Solution

Given,
Variable cost per door is $350.
Variable cost per window is $125.
Ratio of window and doors is 8:2.

Table represents the variable cost per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Variable cost per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Window	8	125	1,000
Doors	2	350	700
Variable cost per composite unit			1,700

Table(2) Hence, the variable cost per composite unit is $1,700.

(3)

To determine

To identify: The break-even point in composite units.

Explanation of Solution

Given,
Fixed cost is $900,000.

Calculated values (working note),
Unit contribution margin is $900.

Formula to calculate break- even point of sales units,

$\text{Break}-\text{even point}=\frac{\text{Fixed}\text{cost}}{\text{Unit}\text{contribution}\text{margin}}$

Substitute $900,000 for fixed cost and $900 for unit margin.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$900,000}{\text{\$900}}\\ =1,000\text{units}\end{array}$

Working note:

Calculated values from part (1) and (2),
Selling price per composite unit is $2,600.
Variable cost per composite unit is $1,700.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$2,600-\$1,700\\ =\$900\end{array}$

Contribution margin per composite unit is $900.

Hence, break-even point of sale is 1,000 composite units.

(4)

To determine

To identify: The number of units of each product sold at break-even point.

Explanation of Solution

Calculated values from part (1) and (2) and (3),
Selling price per composite unit is $2,600.
Variable cost per composite unit is $1,700.
Break-even point of sale is 1,000 composite units.

Formula to calculate break-even point for windows,

$\text{Break-even}\text{point}\text{for}\text{windows}=\left(\begin{array}{l}\text{Break-even}\text{point}\text{of}\text{composite}\text{unit}\\ \times \frac{\text{Sales}\text{amount}\text{of}\text{windows}}{\text{Selling}\text{price}\text{per}\text{composite}\text{unit}}\end{array}\right)$

Substitute 1,000 units for break-even point of composite unit, $1,600 for sales amount of windows and $2,600 for selling price per composite units.

$\begin{array}{c}\text{Break-even}\text{point}\text{for}\text{windows}=1,000\text{units}\times \frac{\$1,600}{\$2,600}\\ =1,000\text{units}\times 0.615\\ =615\text{units}\end{array}$

Formula to calculate break-even point for doors,

$\text{Break-even}\text{point}\text{for}\text{doors}=\left(\begin{array}{l}\left(\text{Break-even}\text{point}\text{of}\text{composite}\text{unit}\right)\\ \times \left(\frac{\text{Sales}\text{amount}\text{of}\text{doors}}{\text{Selling}\text{price}\text{per}\text{composite}\text{unit}}\right)\end{array}\right)$

Substitute 1,000 units for break-even point of composite unit, $1,000 for sales amount of doors and $2,600 for selling price per composite units.

$\begin{array}{c}\text{Break-even}\text{point}\text{for}\text{doors}=1,000\text{units}\times \frac{\$1,000}{\$2,600}\\ =1,000\text{units}\times 0.385\\ =385\text{units}\end{array}$

Hence, break-even point of windows and doors are 615 units or 385 units.