Chapter 21, Problem 7AP

1.

To determine

Determine the break-even point in both sales units and sales dollars of each individual product when the Company P 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 $250,000 and contribution margin per composite unit is $122 (working note 1).

$\begin{array}{c}\begin{array}{l}\text{Break-even point}\\ \text{(Composite units)}\end{array}\}=\frac{\text{Fixed costs}}{\text{Contribution margin per composite unit}}\\ =\frac{\$250,000}{\$122\text{ per composite unit}\left(1\right)}\\ =2,050\text{ composite units}\end{array}$

Compute the break-even in individual product unit sales:

Unit sales of Red at break-even:	2,050 units @ 5 units	10,250 units
Unit sales of White at break-even	2,050 units @ 4 units	8,200 units
Unit sales of Blue at break-even	2,050 units @ 2 units	4,100 units

Table (1)

Compute the break-even in individual product dollar sales:

Dollar sales of Red at break-even:	10,250 units @$20	$205,000
Dollar sales of White at break-even	8,200 units @$35	$287,000
Dollar sales of Blue at break-even	4,100 units @$65	$266,500
Total		$768,265

Table (2)

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

Selling price per composite unit is $370 (working note 2) and variable cost per composite unit is $248(working note 3).

$\begin{array}{c}\begin{array}{l}\text{Contribution margin}\\ \text{ per composite unit}\end{array}\}=\left(\begin{array}{l}\text{Selling price per}\\ \text{ composite unit}\end{array}\right)-\left(\begin{array}{l}\text{Variable cost per}\\ \text{ composite unit}\end{array}\right)\\ =\$370-\$248\\ =\$122\end{array}$

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

5 units of Red @ $20 each	$100
4 units of White @ $35 each	140
2 units of Blue @ $65 each	130
Selling price per composite unit	$370

Table (3)

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

5 units of Red @ $12 each	$60
4 units of White @ $22 each	88
2 units of Blue @ $50 each	100
Variable costs per composite unit	$248

Table (4)

Conclusion

Therefore, the break-even point is 2,050 composite units at $768,265 when the Company P 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 P 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 $300,000$\left(\$250,000+\$50,000\right)$ and contribution margin per composite unit is $220 (working note 4).

$\begin{array}{c}\begin{array}{l}\text{Break-even point}\\ \text{(Composite units)}\end{array}\}=\frac{\text{Fixed costs}}{\text{Contribution margin per composite unit}}\\ =\frac{\$300,000}{\$220\text{ per composite unit}\left(4\right)}\\ =1,364\text{ composite units}\end{array}$

Compute the break-even in individual product unit sales:

Unit sales of Red at break-even:	1,364 units @ 5 units	6,820 units
Unit sales of White at break-even	1,364 units @ 4 units	5,456 units
Unit sales of Blue at break-even	1,364 units @ 2 units	2,728 units

Table (5)

Compute the break-even in individual product dollar sales:

Dollar sales of Red at break-even:	6,820 units @$20	$136,400
Dollar sales of White at break-even	5,456 units @$35	$190,960
Dollar sales of Blue at break-even	2,728 units @$65	$177,320
Total		$504,680

Table (6)

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

Selling price per composite unit is $370 (working note 2) and variable cost per composite unit is $150(working note 5).

$\begin{array}{c}\begin{array}{l}\text{Contribution margin}\\ \text{ per composite unit}\end{array}\}=\left(\begin{array}{l}\text{Selling price per}\\ \text{ composite unit}\end{array}\right)-\left(\begin{array}{l}\text{Variable cost per}\\ \text{ composite unit}\end{array}\right)\\ =\$370-\$150\\ =\$220\end{array}$

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

5 units of Red @ $ $6 each $\left(\$12-\$6\right)$	$30
4 units of White @ $10 each $\left(\$22-\$12\right)$	40
2 units of Blue @ $40 each $\left(\$50-\$10\right)$	80
Variable costs per composite unit	$150

Table (7)

Conclusion

Therefore, the break-even point is 1,364 composite units at $504,680 when the Company P 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.