Chapter 5, Problem 7PSA

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 $250,000.

Calculated values (working note),
Unit contribution margin is $122.

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 $250,000 for fixed cost and $122 for unit margin.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$250,000}{\text{\$122}}\\ =2049.18\text{units}\end{array}$

Given,
Fixed cost is $250,000.

Calculated values,
Contribution margin ratio is 32.97% or 0.3297 (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 $250,000 for fixed cost and 0.3297 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$250,000}{0.3297}\\ =\$758,265.089\end{array}$

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 ($) $\left(\left(\text{D}\right)\times \left(\text{C}\right)\right)$
Red	5	2,050	10,250	20	205,000
White	4	2,050	8,200	35	287,000
Blue	2	2,050	4,100	65	266,500

Table(1)

Working note:

Given,
Sales price of red is $20.
Sales price of white is $35.
Sales price of blue is $65.
Fixed cost is $250,000.
Ratio of red, white and blue is 5:4:2.

Table represents the selling price per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Selling price per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Red	5	20	100
White	4	35	140
Blue	2	65	130
Selling price per composite unit			370

Table(2)

Hence, selling price per composite unit is $370.

Given,
Variable cost of white is $22.
Variable cost of red is $12.
Variable cost of blue is $50.
Ratio of red, white and blue 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 ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Red	5	12	60
White	4	22	88
Blue	2	50	100
Variable cost per composite unit			248

Table(3)

Hence, the variable cost per composite unit is $248.

Calculated values,
Selling price per composite unit is $370.
Variable cost per composite unit is $248.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$370-\$248\\ =\$122\end{array}$

Contribution margin per composite unit is $122.

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$122}{\$370}\\ =0.3297\text{or}32.97\text{\%}\end{array}$

Contribution margin ratio is 32.97%.

Hence, break-even point of sale is 2,050 composite units and $758,265 (round off).

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 $300,000 $\left(\$250,000+\$50,000\right)$ .

Calculated values (working note),
Unit contribution margin is $220.

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 $300,000 for fixed cost and $220 for unit margin.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$300,000}{\text{\$220}}\\ =1363.64\text{units}\end{array}$

Given,
Fixed cost is $300,000.

Calculated values,
Contribution margin ratio is 59.46% or 0.5946 (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 $300,000 for fixed cost and 0.5946 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$300,000}{0.5946}\\ =\$504,540.867\end{array}$

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 ($) $\left(\left(\text{D}\right)\times \left(\text{C}\right)\right)$
Red	5	1,364	6,820	20	136,400
White	4	1,364	5,456	35	190,960
Blue	2	1,364	2,728	65	177,320

Table(4)

Working note:

Given,
Sales price of red is $20.
Sales price of white is $35.
Sales price of blue is $65.
Fixed cost is $300,000.
Ratio of red, white and blue is 5:4:2.

Table represents the selling price per composite unit.

Particulars	Ratio $\left(\text{A}\right)$	Selling price per unit ($) $\left(\text{B}\right)$	Total amount ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Red	5	20	100
White	4	35	140
Blue	2	65	130
Selling price per composite unit			370

Table(5)

Hence, selling price per composite unit is $370.

Given,
Variable cost of white is $10 $\left(\$22-\$12\right)$ .
Variable cost of red is $6 $\left(\$12-\$6\right)$ .
Variable cost of blue is $40 $\left(\$50-\$10\right)$ .
Ratio of red, white and blue 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 ($) $\left(\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Red	5	6	30
White	4	10	40
Blue	2	40	80
Variable cost per composite unit			150

Table(6)

Hence, the variable cost per composite unit is $150.

Calculated values,
Selling price per composite unit is $370.
Variable cost per composite unit is $150.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$370-\$150\\ =\$220\end{array}$

Contribution margin per composite unit is $220.

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$220}{\$370}\\ =0.5946\text{or}59.46\text{\%}\end{array}$

Contribution margin ratio is 59.46%.

Hence, break-even point of sale is 1,364 composite units and $504,541 (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 reduced, therefore for long term planning break-even analysis is beneficial.

Hence, break-even point is reduced with the decrease in variable cost.