Chapter 21, Problem 7BPSB

To determine

Concept Introduction:

Composite Units:

The composite units can be defined as the variety of units produced by a business grouped together is proportion to their sales mix. A composite contribution margin per unit is calculated using the proportion of their sales mix.

Break-even point and Composite break-even point:

The break-even point can be defined as the point where the total sales revenue is equal to the total costs involved. The break-even point is calculated as –

Break-even point (in Units) –

$Break-evenpoint\left(inUnits\right)=\frac{Fixedcost}{Contributionmarginperunit}$

Break-even point (in Dollars) –

$Break-evenpoint\text{ (}inDollars)=\frac{Fixedcost}{Contributionmarginratio}$

In composite break-even point, the composite contribution margin per unit is used to find composite break-even point.

Requirement 1

To determine:

The break-even point in both sales units and sales dollars for each individual product 1, product 2 and product 3, if the company uses the old material

Answer to Problem 7BPSB

Solution:

Product	Break-even point in
	Sales units	Sales dollars
Product 1	11,250 units	$ 450,000
Product 2	7,500 units	$ 225,000
Product 3	3,750 units	$ 75,000

Explanation of Solution

The above answers can be explained as follows –

First, the composite margin per composite unit will be calculated –

Given,

Product 1 –

• Sales price per unit = $ 40

• Variable cost per unit = $ 30

• Sales mix portion = 6 out of 12 (6:4:2)

Product 2 –

• Sales price per unit = $ 30

• Variable cost per unit = $ 15

• Sales mix portion = 4 out of 12 (6:4:2)

Product 3 –

• Sales price per unit = $ 20

• Variable cost per unit = $ 8

• Sales mix portion = 2 out of 12 (6:4:2)

Total composite contribution
	Product 1	Product 2	Product 3
Sales price per unit (A)	40	30	20
Variable cost per unit (B)	30	15	8
Contribution margin per unit (C) = (A) - (B)	10	15	12
Sales mix portion (D)	6	4	2
Total contribution (E) =(C) x (D)	60	60	24
Total composite contribution	144

Contribution margin will be calculated as –

Thus, composite contribution per unit = $ 144

Now, the break-even point in sales units will be calculated as –

• Total composite contribution per unit = $ 144

• Total Fixed cost = $ 270,000

$\begin{array}{l}CompositeBreak-evenpoint\left(insalesunits\right)=\frac{Totalfixedcost}{Totalcompositecontributionperunit}\hfill \\ CompositeBreak-evenpoint\left(insalesunits\right)=\frac{\$270,000}{\$144}\hfill \\ CompositeBreak-evenpoint\left(insalesunits\right)=1,875units\hfill \end{array}$

Now, break-even point in sales units and sales dollars will be calculated as –

Product	Break-even point units (A)	Sales mix portion (B)	Total Break-even sales units (A) X (B)
Product 1	1,875	6	11250
Product 2	1,875	4	7500
Product 3	1,875	2	3750

Product	Break-even point units (A)	Sales price per unit (B)	Total Break-even sales dollars (A) X (B)
Product 1	11,250	40	450,000
Product 2	7,500	30	225,000
Product 3	3,750	20	75,000

Conclusion

Thus, the break-even point in both sales units and sales dollars for each individual product 1, product 2 and product 3, if the company uses the old material have been determined.

To determine

Requirement 2

To determine:

The break-even point in both sales units and sales dollars for each individual product 1, product 2 and product 3, if the company uses the new material

Answer to Problem 7BPSB

Solution:

Product	Break-even point in
	Sales units	Sales dollars
Product 1	8,574 units	$ 342,960
Product 2	5,716 units	$ 171,480
Product 3	2,858 units	$ 57,160

Explanation of Solution

The above answers can be explained as follows –

First, the composite margin per composite unit will be calculated –

Given,

Product 1 –

• Sales price per unit = $ 40

• Variable cost per unit = $ 20 (i.e. $ 30 - $ 10)

• Sales mix portion = 6 out of 12 (6:4:2)

Product 2 –

• Sales price per unit = $ 30

• Variable cost per unit = $ 10 (i.e. $ 15 - $ 5)

• Sales mix portion = 4 out of 12 (6:4:2)

Product 3 –

• Sales price per unit = $ 20

• Variable cost per unit = $ 8

• Sales mix portion = 2 out of 12 (6:4:2)

Total composite contribution
	Product 1	Product 2	Product 3
Sales price per unit (A)	40	30	20
Variable cost per unit (B)	20	10	8
Contribution margin per unit (C) =(A) - (B)	20	20	12
Sales mix portion (D)	6	4	2
Total contribution (E) =(C) x (D)	120	80	24
Total composite contribution per unit	224

Thus, composite contribution per unit = $ 224

Now, the break-even point in sales units will be calculated as –

• Total composite contribution per unit = $ 224

• Total Fixed cost = $ 320,000 (i.e. $ 270,000 + $ 50,000)

$\begin{array}{l}CompositeBreak-evenpoint\left(insalesunits\right)=\frac{Totalfixedcost}{Totalcompositecontributionperunit}\hfill \\ CompositeBreak-evenpoint\left(insalesunits\right)=\frac{\$\text{ 3}20,000}{\$\text{ 22}4}\hfill \\ CompositeBreak-evenpoint\left(insalesunits\right)=1,429units(roundedto\text{ t}henearestwholeunit)\hfill \end{array}$

Now, break-even point in sales units and sales dollars will be calculated as –

Product	Break-even point units (A)	Sales mix portion (B)	Total Break-even sales units (A) X (B)
Product 1	1,429	6	8,574
Product 2	1,429	4	5,716
Product 3	1,429	2	2,858

Product	Break-even point units (A)	Sales price per unit (B)	Total Break-even sales dollars (A) X (B)
Product 1	8,574	40	342,960
Product 2	5,716	30	171,480
Product 3	2,858	20	57,160

Conclusion

Thus, the break-even point in both sales units and sales dollars for each individual product 1, product 2 and product 3, if the company uses the new material have been determined.

To determine

Requirement 3

To explain:

About this analysis that offer management for long-term planning

Answer to Problem 7BPSB

Solution:

The new material reduced the variable costs for Product 1 and Product 2, but the fixed cost increased. But the overall result was, the break-even point has reduced from 1,825 units to 1,429 units. Since, the break-even point can be reached early now, it is better to use new material rather than the old material.

Explanation of Solution

The above answer can be explained as the far the break-even point is, the more distance the business has to cover to start earning profits. If the break-even point reduced to 1,429, now it can be said that, after selling 1,429 units, the business will start earning the profits, which was after 1,825 units with the old material.

The new material reduced the variable costs for Product 1 and Product 2, but the fixed cost increased. But the overall result was, the break-even point has reduced from 1,825 units to 1,429 units. Since, the break-even point can be reached early now, it is better to use new material rather than the old material

So, it is preferable to use the new material instead of old material.

Conclusion

Thus, the analysis has been explained.