Chapter 21, Problem 7BP

1.

To determine

Determine the break-even point in both sales units and sales dollars of each individual product when the Company M continuous to use old material.

Explanation of Solution

Break-Even Point: It is the point of sales at which entity neither earns a profit nor suffers a loss. It can also be said that the point of sales at which sales value of the entity recovers the entire cost of fixed and variable nature is called break-even point.

$\text{Break-even point}=\frac{\text{Fixed costs}}{\text{Contribution margin per unit}}$

Determine the break-even point in composite units.

Given, fixed costs are $270,000 and contribution margin per composite unit is $144 (working note 1).

$\begin{array}{c}\begin{array}{l}\text{Break-even point}\\ \text{(Composite units)}\end{array}\}=\frac{\text{Fixed costs}}{\text{Contribution margin per composite unit}}\\ =\frac{\$270,000}{\$144\text{ per composite unit}\left(1\right)}\\ =1,875\text{ composite units}\end{array}$

Compute the break-even in individual product unit sales:

Unit sales of Red at break-even:	1,875units @ 6 units	11,250 units
Unit sales of White at break-even	1,875units @ 4 units	7,500 units
Unit sales of Blue at break-even	1,875units @ 2 units	3,750 units

Table (1)

Compute the break-even in individual product dollar sales:

Dollar sales of Red at break-even:	11,250 units @$40	$450,000
Dollar sales of White at break-even	7,500 units @$30	$225,000
Dollar sales of Blue at break-even	3,750 units @$20	$75,000
Total		$750,000

Table (2)

Working note (1): Calculate contribution margin per unit.

Selling price per composite unit is $400 (working note 2) and variable cost per composite unit is $256(working note 3).

$\begin{array}{c}\begin{array}{l}\text{Contribution margin}\\ \text{ per composite unit}\end{array}\}=\left(\begin{array}{l}\text{Selling price per}\\ \text{ composite unit}\end{array}\right)-\left(\begin{array}{l}\text{Variable cost per}\\ \text{ composite unit}\end{array}\right)\\ =\$400-\$256\\ =\$144\end{array}$

Working note (2): Calculate the selling price per composite unit

6 units of Product 1 @ $40 each	$240
4 units of Product 2 @ $30 each	120
2 units of Product 3 @ $20 each	40
Selling price per composite unit	$400

Table (3)

Working note (3): Calculate the variable costs per composite unit.

6 units of Product 1 @ $30 each	$180
4 units of Product 2 @ $15 each	60
2 units of Product 3 @ $8 each	16
Variable costs per composite unit	$256

Table (4)

Conclusion

Therefore, the break-even point is 1,875composite units at $750,000 when the Company M continuous to use old material.

2.

To determine

Determine the break-even point in both sales units and sales dollars of each individual product when the Company M continuous to use new material.

Explanation of Solution

Break-Even Point: It is the point of sales at which entity neither earns a profit nor suffers a loss. It can also be said that the point of sales at which sales value of the entity recovers the entire cost of fixed and variable nature is called break-even point.

$\text{Break-even point}=\frac{\text{Fixed costs}}{\text{Contribution margin per unit}}$

Determine the break-even point in composite units.

Given, fixed costs are $320,000$\left(\$270,000+\$50,000\right)$ and contribution margin per composite unit is $224 (working note 4).

$\begin{array}{c}\begin{array}{l}\text{Break-even point}\\ \text{(Composite units)}\end{array}\}=\frac{\text{Fixed costs}}{\text{Contribution margin per composite unit}}\\ =\frac{\$320,000}{\$224\text{ per composite unit}}\\ =1,429\text{ composite units}\end{array}$

Compute the break-even in individual product unit sales:

Unit sales of Product 1 at break-even	1,429 units @ 6 units	8,574 units
Unit sales of Product 2 at break-even	1,429 units @ 4 units	5,716 units
Unit sales of Product 3 at break-even	1,429units @ 2 units	2,858 units

Table (5)

Compute the break-even in individual product dollar sales:

Dollar sales of Red at break-even:	8,574 units @$40	$342,960
Dollar sales of White at break-even	5,716 units @$30	$171,480
Dollar sales of Blue at break-even	2,858 units @$20	$57,160
Total		$571,600

Table (6)

Working note (4): Calculate contribution margin per unit.

Selling price per composite unit is $400 (working note 2) and variable cost per composite unit is $176(working note 5).

$\begin{array}{c}\begin{array}{l}\text{Contribution margin}\\ \text{ per composite unit}\end{array}\}=\left(\begin{array}{l}\text{Selling price per}\\ \text{ composite unit}\end{array}\right)-\left(\begin{array}{l}\text{Variable cost per}\\ \text{ composite unit}\end{array}\right)\\ =\$400-\$176\\ =\$224\end{array}$

Working note (5): Calculate the variable costs per composite unit.

6 units of Product 1 @ $20 each $\left(\$30-\$10\right)$	$120
4 units of Product 2 @ $10 each $\left(\$15-\$5\right)$	40
2 units of Product 3 @ $40 each $\left(\$8-\$0\right)$	16
Variable costs per composite unit	$176

Table (7)

Conclusion

Therefore, the break-even point is 1,429 composite units at $571,600 when the Company M continuous to use new material.

3.

To determine

Explain the way the above analysis will offer the management for long-term planning.

Explanation of Solution

If the business invests in the fixed assets like plant and machinery, then there is an increase in the risk levels that is the business needs to recover more fixed costs.  But, the investments in fixed assets will lower the variable costs which lowers break-even point, this will making business easier to make a profit with fewer sales.