Chapter 18, Problem 7PSB

1.

To determine

To identify: Break-even point in total sales in units and in dollars when old material is used.

Explanation of Solution

Given,
Fixed cost is $270,000.

Calculated values (working note),
Unit contribution margin is $144.

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 $270,000 for fixed cost and $144 for unit margin.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$270,000}{\text{\$144}}\\ =1,875\text{units}\end{array}$

Given,
Fixed cost is $270,000.

Calculated values,
Contribution margin ratio is 36% or 0.36 (from working note).

Formula to calculate break-even point of sales in dollars,

$\text{Break}-\text{even point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution margin ratio}}$

Substitute $270,000 for fixed cost and 0.36 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$270,000}{0.36}\\ =\$750,000\end{array}$

Table represents the number of units of each product sold at break-even point.

Particulars	Ratio $\left(\text{A}\right)$	Break-even unit of composite unit $\left(\text{B}\right)$	Break-even unit $\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$	Selling price ($) $\left(\text{D}\right)$	Break-even sales in ($) $\left(\left(\text{D}\right)\times \left(\text{C}\right)\right)$
Product 1	6	1,875	11,250	40	450,000
Product 2	4	1,875	7,500	30	225,000
Product 3	2	1,875	3,750	20	75,000

Table(1)

Working note:

Given,
Sales price of product 1 is $40.
Sales price of product 2 is $30
Sales price of product 3 is $20.
Fixed cost is $270,000.
Ratio of product 1, product 2 and product 3 is 6:4:2.

Table represents the selling price per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Selling price per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Product 1	6	40	240
Product 2	4	30	120
Product 3	2	20	40
Selling price per composite unit			400

Table(2)

Hence, selling price per composite unit is $400.

Given,
Variable cost of product 2 is $15.
Variable cost of product 1 is $30.
Variable cost of product 3 is $8.
Ratio of product 1, product 2 and product 3 is 6:4:2.

Table represents the variable cost per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Variable cost per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Product 1	6	30	180
Product 2	4	15	60
Product 3	2	8	16
Variable cost per composite unit			256

Table(3)

Hence, the variable cost per composite unit is $256.

Calculated values,
Selling price per composite unit is $400.
Variable cost per composite unit is $256.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$400-\$256\\ =\$144\end{array}$

Contribution margin per composite unit is $144.

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$144}{\$400}\\ =0.36\text{or}36\text{\%}\end{array}$

Contribution margin ratio is 36%.

Hence, break-even point of sale is 1,875 composite units and $750,000.

2.

To determine

To identify: Break-even point in total sales in dollars and in units when a firm uses new material.

Explanation of Solution

Given,
Fixed cost is $320,000 $\left(\$270,000+\$50,000\right)$ .

Calculated values (working note),
Unit contribution margin is $224.

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 $320,000 for fixed cost and $224 for unit margin.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$320,000}{\text{\$224}}\\ =1,428.57\text{units}\end{array}$

Given,
Fixed cost is $320,000.

Calculated values,
Contribution margin ratio is 56% or 0.56 (from working note).

Formula to calculate break-even point of sales in dollars,

$\text{Break}-\text{even point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution margin ratio}}$

Substitute $320,000 for fixed cost and 0.56 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$320,000}{0.56}\\ =\$571,428.57\end{array}$

Table represents the number of units of each product sold at break-even point.

Particulars	Ratio $\left(\text{A}\right)$	Break-even unit of composite unit $\left(\text{B}\right)$	Break-even unit $\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$	Selling price ($) $\left(\text{D}\right)$	Break-even sales in ($) $\left(\left(\text{D}\right)\times \left(\text{C}\right)\right)$
Product 1	6	1,429	8,574	40	342,960
Product 2	4	1,429	5,716	30	171,480
Product 3	2	1,429	2,858	20	57,160

Table(4)

Working note:

Given,
Sales price of product 1 is $40.
Sales price of product 2 is $30.
Sales price of product 3 is $20.
Fixed cost is $320,000.
Ratio of product 1, product 2 and product 3 is 6:4:2.

Table represents the selling price per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Selling price per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Product 1	6	40	240
Product 2	4	30	120
Product 3	2	20	40
Selling price per composite unit			400

Table(5)

Hence, selling price per composite unit is $400.

Given,
Variable cost of product 2 is $10 $\left(\$15-\$5\right)$ .
Variable cost of product 1 is $20 $\left(\$30-\$10\right)$ .
Variable cost of product 3 is $8.
Ratio of product 1, product 2 and product 3 is 5:4:2.

Table represents the variable cost per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Variable cost per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Product 1	6	20	120
Product 2	4	10	40
Product 3	2	8	16
Variable cost per composite unit			176

Table(6)

Hence, the variable cost per composite unit is $176.

Calculated values,
Selling price per composite unit is $400.
Variable cost per composite unit is $176.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$400-\$176\\ =\$224\end{array}$

Contribution margin per composite unit is $224.

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$224}{\$400}\\ =0.56\text{or}56\text{\%}\end{array}$

Contribution margin ratio is 56%.

Hence, break-even point of sale is 1,364 composite units and $571,429 (round off).

3.

To determine

To identify: The insight provided by the break-even analysis to the management for long-term planning.

Explanation of Solution

• As per the break-even analysis, increase in fixed cost increases the risk because more contribution margin is required to cover the fixed cost.
• While variable cost decreases, break-even point also product 1uced, therefore for long term planning break-even analysis is beneficial.

Hence, break-even point is product 1uced with the decrease in variable cost.