Chapter 21, Problem 21.2APR

1.

To determine

Break-even Point: It refers to a point in the level of operations at which a company experiences its revenues generated is equal to its costs incurred. Thus, when a company reaches at its break-even point, it reports neither an income nor a loss from operations. The formula to calculate the break-even point in sales units is as follows:

$\text{Break-even}\text{point}\text{in}\text{Sales}\left(\text{units}\right)=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{per}\text{unit}}$

To determine: the total fixed costs and the total variable costs for the current year.

Explanation of Solution

Determine the total variable cost.

Particulars	Total cost (A)	Variable cost percentage (B)	Variable cost (A×B)
Cost of Goods sold	$25,000,000	70%	$17,500,000
Selling expenses	$4,000,000	75%	$3,000,000
Administrative expenses	$3,000,000	50%	$1,500,000
Total variable cost			$22,000,000

Table (1)

Determine the total fixed cost.

Particulars	Total cost (A)	Variable cost (B)	Fixed cost (A-B)
Cost of Goods sold	$25,000,000	$17,500,000	$7,500,000
Selling expenses	$4,000,000	$3,000,000	$1,000,000
Administrative expenses	$3,000,000	$1,500,000	$1,500,000
Total fixed cost			$10,000,000

Table (2)

Conclusion

Therefore, the total fixed costs is $10,000,000 and the total variable costs is $22,000,000 for the current year.

2.

(a)

To determine

the unit variable cost for the current year.

Explanation of Solution

Determine the unit variable cost for the current year.

Total variable cost =$22,000,000 (refer Table 1)

Number of units =500,000 units

$\begin{array}{c}\text{Unit}\text{variable cost }=\frac{\text{Total}\text{variable}\text{Costs}}{\text{Number}\text{of}\text{units}}\\ =\frac{\text{\$22,000,000}}{500,000\text{units}}\\ =\$44\text{per}\text{unit}\end{array}$

(b)

To determine

the unit contribution margin for the current year.

Explanation of Solution

Determine the unit contribution margin for the current year.

Selling price per unit =$94 per unit

Variable cost per unit =$44 per unit (refer 2 (a))

$\begin{array}{c}\begin{array}{l}\text{Contribution}\text{Margin}\\ \text{per}\text{unit}\end{array}]\text{=}\left(\begin{array}{l}\text{Selling}\text{price}\\ \text{per}\text{unit}\end{array}\right)-\left(\begin{array}{l}\text{Variable}\text{cost}\\ \text{per}\text{unit}\end{array}\right)\\ \text{=\$94}\text{per}\text{unit}-\text{\$44}\text{per}\text{unit}\\ \text{=\$50}\text{per}\text{unit}\end{array}$

Conclusion

Therefore, the unit variable cost is $44 per unit and the unit contribution margin is $50 per unit for the current year.

3.

To determine

To compute: the break-even sales (units) for the current year.

Explanation of Solution

Compute the break-even sales (unit) for the current year.

Fixed cost =$10,000,000 (refer Table 2)

Contribution margin per unit =$50 per unit (refer Part 2(b))

$\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{Sales}\left(\text{units}\right)=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{per}\text{unit}}\\ =\frac{\text{\$10,000,000}}{\text{\$50}\text{per}\text{unit}}\\ =200,000\text{units}\end{array}$

Conclusion

Therefore, the break-even point in sales (units) for the current year is 200,000 units.

4.

To determine

To compute: the break-even sales (units) under the proposed program for the following year.

Explanation of Solution

Compute the break-even point in sales (units) under the proposed program for the following year.

Fixed cost =$10,000,000 (refer Table 2)

Expected increase in fixed cost =$1,800,000

Contribution margin per unit =$50 per unit (refer Part 2(b))

$\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{Sales}\left(\text{units}\right)=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{per}\text{unit}}\\ =\frac{\$10,000,000\text{+\$1,800,000}}{\$50perunit}\\ =\frac{\$11,800,000}{\$50perunit}\\ =236,000\text{units}\end{array}$

Conclusion

Therefore, the break-even point in sales units under the proposed program for the following year is 236,000 units.

5.

To determine

the amount of sales (units) if the company desires a target profit of $15,000,000.

Explanation of Solution

Determine the amount of sales (units) if the company desires a target profit of $15,000,000.

Fixed cost under the proposed program =$11,800,000 (refer Part 4)

Target Profit =$15,000,000

Contribution margin per unit =$50 per unit (refer Part 2 (b))

$\begin{array}{c}\text{Sales}\left(\text{units}\right)=\frac{\text{Fixed}\text{Costs+Target}\text{Profit}}{\text{Unit}\text{Contribution}\text{Margin}}\\ =\frac{\$11,800,000+\$15,000,000}{\$50\text{per}\text{unit}}\\ =\frac{\$26,800,000}{\$50}\\ =536,000\text{units}\end{array}$

Conclusion

Therefore, the amount of sales (units) under the proposed program to realize the $15,000,000 of income from operations earned in the current year is 536,000 units.

6.

To determine

the maximum income from operations possible with the expanded plant.

Explanation of Solution

Determine the maximum income from operations possible with the expanded plant.

Determine the income from operations
Particulars	Amount ($)	Amount ($)
Sales	47,000,000
Add: Increase in yearly sales	3,760,000	50,760,000
Less: Fixed costs	11,800,000
Variable costs (2)	23,760,000	(35,760,000)
Income from operations		15,200,000

Table (3)

Working note:

Determine the number of units to be sold under plant expansion program.

Increase in yearly sales estimated =$3,760,000

Selling price per unit =$94 per unit

Number of units sold in the current year =500,000 units.

$\begin{array}{c}\begin{array}{l}\text{Number}\text{units}\\ \text{to}\text{be}\text{sold}\text{under}\\ \text{plant}\text{expansion}\text{program}\end{array}]=\left[\frac{\left(\begin{array}{l}\text{Increase}\text{in}\text{current}\\ \text{yearly}\text{sales}\end{array}\right)}{\left(\begin{array}{l}\text{Selling}\text{price}\\ \text{per}\text{unit}\end{array}\right)}\right]+\left(\begin{array}{l}\text{Number}\text{of}\text{units}\\ \text{sold}\text{in}\text{the}\text{current}\\ \text{year}\end{array}\right)\\ =\left[\frac{\$3,760,000}{\$94\text{per}\text{unit}}\right]+500,000\text{units}\\ =40,000\text{units}+500,000\text{units}\\ =540,000\text{units}\end{array}$ (1)

Determine the variable costs under the plant expansion program.

Number of units to be sold under the plant expansion program =540,000 units (1)

Variable cost per unit =$44 per unit (refer Part 2(a))

$\begin{array}{c}\begin{array}{l}\text{Variable}\text{cost}\\ \text{under}\text{plant}\\ \text{expansion}\text{program}\end{array}]=\left(\begin{array}{l}\text{Number}\text{of}\text{units}\text{to}\\ \text{be}\text{sold}\text{under}\text{plant}\\ \text{expansion}\text{program}\end{array}\right)\times \left(\begin{array}{l}\text{Variable}\\ \text{unit}\text{cost}\end{array}\right)\\ =540,000\text{units}\times \$44\text{per}\text{unit}\\ =\$23,760,000\end{array}$ (2)

Conclusion

Therefore, the maximum income from operations possible with the expanded plant is $15,200,000.

7.

To determine

the income or loss from operations for the following year if the proposal is accepted and the sales remains same.

Explanation of Solution

Determine the income or loss from operations for the following year if the proposal is accepted and the sales remains same.

Current year’s income from operations =$15,000,000

Estimated increase in fixed cost =$1,800,000

Particulars	Amount ($)
Current income from operations	15,000,000
Less: Fixed costs	(1,800,000)
Income from operations	13,200,000

Table (4)

Conclusion

Therefore, the income from operations for the following year if the proposal is accepted and the sales remains same is $13,200,000.

8.

To determine

To explain: whether to recommend for accepting the proposal.

Explanation of Solution

Based on the above calculated data, if the proposal is accepted, it would increase the income from operations from $15,000,000 to $15,200,000. However, there are other factors those found to be unfavorable for the acceptance of the proposals. These are stated below:

• The break-even in sales (units) would increase from 200,000 units to 236, 000 units.
• As a result, 536,000 units instead of 500,000 units would be required to be sold in order to maintain the current income from operations of $15,000,000.
• It is found that if the current sales of $47,000,000 remains same under the new proposal, it would decline the current income from operations of $15,000,000 to $13,200,000.

Conclusion

Therefore, it is suggested to the company that it would assess its sales potentials upon accepting the proposal at the first place. If the company has a good sales potential that could lead to a significant increase in sales, the proposal would be favorable. The estimated sales figures would help the company to evaluate the pros and cons of the accepting the new proposal