Chapter 21, Problem 7APSA

To determine

1)

Contribution Margin:

• Contribution Margin refers to the excess of Sales revenues over variable and fixed costs. Since it contributes to the overall profitability of the business it is referred to as contribution margin.

• Variable costs refer to the costs of manufacture that have a direct co-relation with the volume of the goods manufactured, i.e. the costs increase with an increase in the goods produced. Examples are costs of direct material and direct labor.

• Fixed costs refer to the costs of manufacture that have an inverse co-relation with the volume of the goods manufactured, i.e. the costs decrease with an increase in the goods produced. Examples are costs of factory rent, depreciation on plant and equipment

$\text{Contribution per unit = Sales price per unit -}\text{}\text{}\text{ Variable Costs per unit}$

Breakeven Point:

• Breakeven point is the monetary value of sales or number of units of sales where the contribution equals the fixed costs and the profit / loss is zero.

• Breakeven point is considered as the minimum sales needed to sustain a business without incurring losses.

$\begin{array}{l}\text{Breakeven point (Units) = Fixed Cost / Contribution Per Unit}\\ \\ \text{Breakeven point (Value) = Sales Price per unit x Breakeven Point (units)}\end{array}$

To Calculate:
a) Breakeven point in terms of Units

b) Breakeven point in terms of sales value

Answer to Problem 7APSA

Solution:

a) Breakeven point in terms of Units is 932.00 units 745.00 units and 373.00 units for Red, White and Blue respectively

b) Breakeven point in terms of sales value is $18,640.00, $26,075.00 and $24,245.00 for Red, White and Blue respectively

Explanation of Solution

Particulars	Red	White	Blue	Composite
Sales	$ 20.00	$ 35.00	$ 65.00	$ 370.00
Variable Costs	$ 12.00	$ 22.00	$ 50.00	$ 248.00
Contribution Margin	$ 8.00	$ 13.00	$ 15.00	$ 122.00
Sales Mix	5.00	4.00	2.00	11.00
Fixed Costs				$ 250,000.00
Breakeven point (Units)	932.00	745.00	373.00	2,050.00
Breakeven point (Value)	$ 18,640.00	$ 26,075.00	$ 24,245.00

• Sales Mix is given as 5:4:2 for Red, White and Blue respectively

• Sales price is given as $ 20.00, $ 35.00 and $ 65.00 for Red, White and Blue respectively

• Composite sales price is calculated by multiplying the Individual Sales price by value of sales mix per product respectively to calculate the weighted average sales price

• Variable Costs is given as $ 12.00 , $ 22.00 and $ 50.00 for Red, White and Blue respectively

• Composite variable cost is calculated by multiplying the Individual Variable costs price by value of sales mix per product respectively to calculate the weighted average variable costs

• Contribution margin is calculated as difference of sales price and variable costs and is $8, $13 and $15 for Red, White and Blue respectively

• Annual fixed costs are $250,000 shared by all the products. Breakeven point in units is calculated as Annual Fixed costs by Composite Contribution and is 2,050 composite units.

• Breakeven point in units for each individual product is calculated as product of proportion of sales mix per product and 2,050 composite units and is 932.00, 745.00 and 373.00 for Red, White and Blue respectively

• Breakeven point in value is calculated for each product as Breakeven point in units per product multiplied by individual selling price and is $ 18,640.00, $ 26,075.00 and $ 24,245.00 for Red, White and Blue respectively

Conclusion

Hence the individual breakeven point in units and sales are calculated.

2)

Contribution Margin:

• Contribution Margin refers to the excess of Sales revenues over variable and fixed costs. Since it contributes to the overall profitability of the business it is referred to as contribution margin.

• Variable costs refer to the costs of manufacture that have a direct co-relation with the volume of the goods manufactured, i.e. the costs increase with an increase in the goods produced. Examples are costs of direct material and direct labor.

• Fixed costs refer to the costs of manufacture that have an inverse co-relation with the volume of the goods manufactured, i.e. the costs decrease with an increase in the goods produced. Examples are costs of factory rent, depreciation on plant and equipment

$\text{Contribution per unit = Sales price per unit -}\text{}\text{}\text{ Variable Costs per unit}$

Breakeven Point:

• Breakeven point is the monetary value of sales or number of units of sales where the contribution equals the fixed costs and the profit / loss is zero.

• Breakeven point is considered as the minimum sales needed to sustain a business without incurring losses.

$\begin{array}{l}\text{Breakeven point (Units) = Fixed Cost / Contribution Per Unit}\\ \\ \text{Breakeven point (Value) = Sales Price per unit x Breakeven Point (units)}\end{array}$

To determine

To Calculate:
a) Breakeven point in terms of Units after introduction of new raw material

b) Breakeven point in terms of sales value after introduction of new raw material

Answer to Problem 7APSA

Solution:

a) Breakeven point in terms of Units is 620.00 units 496.00 units and 248.00 units for Red, White and Blue respectively after introduction of new raw material

b) Breakeven point in terms of sales value is $12,400, $17,360.00 and $16,120.00 for Red, White and Blue respectively after introduction of new raw material

Explanation of Solution

Particulars	Red	White	Blue
Sales	$ 20.00	$ 35.00	$ 65.00	$ 370.00
Variable Costs	$ 6.00	$ 10.00	$ 40.00	$ 150.00
Contribution Margin	$ 14.00	$ 25.00	$ 25.00	$ 220.00
Sales Mix	5.00	4.00	2.00	11.00
Fixed Costs				$ 300,000.00
Breakeven point (Units)	620.00	496.00	248.00	1,364.00
Breakeven point (Value)	$ 12,400.00	$ 17,360.00	$ 16,120.00

• Sales Mix is given as 5:4:2 for Red, White and Blue respectively

• Sales price is given as $ 20.00, $ 35.00 and $ 65.00 for Red, White and Blue respectively

• Composite sales price is calculated by multiplying the Individual Sales price by value of sales mix per product respectively to calculate the weighted average sales price

• Variable Costs after introduction of new raw material reduce to $ 6.00 , $ 10.00 and $ 40.00 for Red, White and Blue respectively

• Composite variable cost is calculated by multiplying the Individual Variable costs price by value of sales mix per product respectively to calculate the weighted average variable costs

• Contribution margin is calculated as difference of sales price and variable costs and is $14, $25 and $25 for Red, White and Blue respectively

• Annual fixed costs increase to $300,000, after introduction of new raw material shared by all the products. Breakeven point in units is calculated as Annual Fixed costs by Composite Contribution and is 1,364 composite units.

• Breakeven point in units for each individual product is calculated as product of proportion of sales mix per product and 1,364 composite units and is 620.00, 496.00 and 248.00 for Red, White and Blue respectively

• Breakeven point in value is calculated for each product as Breakeven point in units per product multiplied by individual selling price and is $12,400, $17,360.00 and $16,120.00 for Red, White and Blue respectively after introduction of new raw material

Conclusion

Hence the breakeven point is calculated after introduction of new raw material.

3)

Contribution Margin:

• Contribution Margin refers to the excess of Sales revenues over variable and fixed costs. Since it contributes to the overall profitability of the business it is referred to as contribution margin.

• Variable costs refer to the costs of manufacture that have a direct co-relation with the volume of the goods manufactured, i.e. the costs increase with an increase in the goods produced. Examples are costs of direct material and direct labor.

• Fixed costs refer to the costs of manufacture that have an inverse co-relation with the volume of the goods manufactured, i.e. the costs decrease with an increase in the goods produced. Examples are costs of factory rent, depreciation on plant and equipment

$\text{Contribution per unit = Sales price per unit -}\text{}\text{}\text{ Variable Costs per unit}$

Breakeven Point:

• Breakeven point is the monetary value of sales or number of units of sales where the contribution equals the fixed costs and the profit / loss is zero.

• Breakeven point is considered as the minimum sales needed to sustain a business without incurring losses.

$\begin{array}{l}\text{Breakeven point (Units) = Fixed Cost / Contribution Per Unit}\\ \\ \text{Breakeven point (Value) = Sales Price per unit x Breakeven Point (units)}\end{array}$

To determine

Management analysis of Breakeven point

Answer to Problem 7APSA

Solution:

Comparison of the contribution margins and breakeven points before and after introduction of new raw material indicate that the company should proceed with manufacture and introduction of new raw material in the production process since the breakeven point reduces.

Explanation of Solution

Calculations of Breakeven points before and after introduction of new raw material are given below:

Particulars	Red	White	Blue	Composite
Sales	$ 20.00	$ 35.00	$ 65.00	$ 370.00
Variable Costs	$ 12.00	$ 22.00	$ 50.00	$ 248.00
Contribution Margin	$ 8.00	$ 13.00	$ 15.00	$ 122.00
Sales Mix	5.00	4.00	2.00	11.00
Fixed Costs				$ 250,000.00
Breakeven point (Units)	932.00	745.00	373.00	2,050.00
Breakeven point (Value)	$ 18,640.00	$ 26,075.00	$ 24,245.00

Particulars	Red	White	Blue
Sales	$ 20.00	$ 35.00	$ 65.00	$ 370.00
Variable Costs	$ 6.00	$ 10.00	$ 40.00	$ 150.00
Contribution Margin	$ 14.00	$ 25.00	$ 25.00	$ 220.00
Sales Mix	5.00	4.00	2.00	11.00
Fixed Costs				$ 300,000.00
Breakeven point (Units)	620.00	496.00	248.00	1,364.00
Breakeven point (Value)	$ 12,400.00	$ 17,360.00	$ 16,120.00

• Comparison of the Variable Costs before and after introduction of new raw material as well as subsequent reduction of the costs to $ 6.00 , $ 10.00 and $ 40.00 for Red, White and Blue respectively indicates a favorable trend.

• Composite variable cost is calculated by multiplying the Individual Variable costs price by value of sales mix per product respectively to calculate the weighted average variable costs

• Contribution margin is calculated as difference of sales price and variable costs and increases to $14, $25 and $25 for Red, White and Blue respectively after introduction of new raw material

• Annual fixed costs increase to $300,000, after introduction of new raw material shared by all the products. However, the Breakeven point in units is calculated as Annual Fixed costs by Composite Contribution and reduces to 1,364 composite units from 2,050 units indicating a favorable change.

• Due to the positive reduction in breakeven point in units and sales value, the introduction of raw material may be initiated and long term financial goals and plans may be determined accordingly.

Conclusion

Hence the management analysis of breakeven points is presented.