Chapter 3, Problem 3.22P

1.

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

The Company’s CM ratio and the break-even point in unit sales and dollar sales

Answer to Problem 3.22P

The break-even sales in dollars 600000 and in unit it is 20000 units.

Explanation of Solution

Given information:

Sales (19500units * $30 per unit) = $585000

Variable expenses     = $408500

Contribution margin     = $175500

Fixed expenses     = $180000

Net operating loss     = $ 4500

  $\begin{array}{l}Contributionmarginperunit=Sellingpriceperunit-Variablecostperunit\\ =\$30-\$21=\$9\\ Contributionmarginratio=\frac{Contributionmargin}{Sales}\times 100\\ =\frac{\$175500}{\$585000}\times 100\\ =0.30\times 100\\ =30\%\end{array}$

Therefore, the contribution margin per unit is $9 and the ratio is 30%.

Let us now calculate the break-even point in sales in both units wise and dollar sales.

  $\begin{array}{l}Break-evenpoint\text{ sales}=\frac{Fixedexpense}{Contributionmarginratio}\\ =\frac{\$180000}{30\%}\\ =\$600000\end{array}$

Let us now calculate the break-even sales unit wise.

  $\begin{array}{l}Break-evenpoint salesinunits=\frac{Fixedexpense}{Contributionmarginratio\times Sellingprice}\\ =\frac{\$180000}{30\%\times \$30}\\ =\frac{\$180000}{\$9}=20000units\end{array}$

Therefore, the break-even sales in dollars 600000 and in unit it is 20000 units.

2.

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

The increase/decrease in company’s net operating income.

Answer to Problem 3.22P

The net operating income is $8000.

Explanation of Solution

Additional information:

Monthly advertising budget increased to $16000

Sales increased by $80000.

With the help of the given information, it is clear that the sales have increased by $80000.

Here we have considered only the values which have changed.

So the contribution will be 30% of $80000= $24000

Advertising cost is a part of fixed expenses. So, the value of the advertising cost is taken as a fixed cost.

Therefore, $thenetoperatingincome/loss=Contribution–Fixedexpenses$

  $\begin{array}{l}=\$24000-\$16000\\ =\$8000\end{array}$

Since, we are given that there is a net operating loss of $4500, with a change in values, we can experience that there is an increase in the value of net operating income. Now, the net operating income is $8000.

3.

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

The revised net operating income/loss.

Answer to Problem 3.22P

The revised increase in net loss is -6000

Explanation of Solution

Given information:

Sales (19500units * $30 per unit) = $585000

Variable expenses     = $408500

Contribution margin     =$175500

Fixed expenses     =$180000

Net operating loss     =$ 4500

Selling price reduced by 10%

Advertising budget increased by $60000 per month

Advertising cost is a part of fixed expenses. So, the value of advertising cost is taken as fixed cost.

Contribution statement:

In the case of sales of 19500 units:

Income statement

Details	Amount is $	Unit cost
Sales	585000	30
Less variable cost	409500	21
Contribution margin	175000	9
Fixed expenses	180000
Net loss	-4500

In the case of proposed sales of 26000 units

Selling price $=\$30-10\%=\$27$

Income statement

Details	Amount is $	Unit cost
Sales	1053000	27
Less variable cost	819000	21
Contribution margin	234000	6
Fixed expenses	240000
Net loss	-6000

Comparison of both the income statements

	Amount in $ for 19500 units	Amount in $ for 26000 units	Change= Increase/decrease
Sales	585000	1053000	468000
Less variable cost	409500	819000	409500
Contribution margin	175000	234000	58500
Fixed expenses	180000	240000	60000
Net income/loss	-4500	-6000	-1500

Calculation of variable expenses:

  $\begin{array}{l}Variableexpense=Salesunit\times \frac{Previousvariableexpense}{Previoussalesvalue}\\ =\$39000\times \frac{\$409500}{19500}\\ =\$39000\times \$21=\$819000\end{array}$

4

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

The number of units sold to attain a target profit of $9750.

Answer to Problem 3.22P

The break-even sales in units will be 23000.

Explanation of Solution

Given information:

Sales (19500units * $30 per unit)=$585000

Variable expenses     =$408500

Contribution margin     =$175500

Fixed expenses     =$180000

Net operating loss     =$ 4500

Packaging costs increase by 75%

  $ExpectedSalesunit=\frac{Fixedexpense+Targetprofit}{Contributionmarginperunit}$

Contribution margin per unit= Selling price per unit- variable cost per unit

Revised variable cost=$21

With an increase in packaging cost, the variable expense will increase by 0.75.

Therefore, the revised variable expenses= $\$21+0.75=\$21.75$

  $\begin{array}{l}Contributionmarginperunit=Sellingpriceperunit-Variablecostperunit\\ =\$30-\$21.75=\$8.25\end{array}$

  $ExpectedSalesunit=\frac{Fixedexpense+Targetprofit}{Contributionmarginperunit}$

  $\begin{array}{l}=\frac{\$180000+\$9750}{\$8.25}\\ =23000units\end{array}$

Therefore, the break-even sales in units will be 23000.

5

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

The new CM ratio along break-even point in unit sales and dollars sales.

Answer to Problem 3.22P

The contribution ratio is 40%; the break-even sales in units is 21000 units and in dollars it is $630000.

Explanation of Solution

Additional information:

Variable expenses reduced by $3 per unit.

Fixed expenses increased by $72000 per month

Calculation of revised variable cost per unit:

  $Revisedvariablecost=\$21-\$3=\$18$

  $\begin{array}{l}Contributionmarginperunit=Sellingpriceperunit-Variablecostperunit\\ =\$30-\$18=\$12\end{array}$

Fixed expenses $=\$180000+\$72000=\$252000$

  $\begin{array}{l}Contributionmarginperunit=\frac{Contributionmargin}{Sellingpriceperunit}\times 100\\ =\frac{\$12}{\$30}\times 100\\ =0.40\times 100\\ =40\%\end{array}$

Let us now calculate the break-even sales in units and dollars.

  $\begin{array}{l}Break-evenpoint\text{ sales}=\frac{Fixedexpense}{Contributionmarginratio}\\ =\frac{\$252000}{40\%}\\ =\$630000\\ Break-evenpoint salesinunits=\frac{Fixedexpense}{Contributionmargininunits}\\ =\frac{\$252000}{\$12}=21000units\end{array}$

Therefore, the contribution ratio is 40%; the break-even sale in units is 21000 units and in dollars, it is $630000.

5b

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

To prepare: Two contribution statements showing units and percentages.

Answer to Problem 3.22P

The net operating income of both the projects is $54000 and $60000.

Explanation of Solution

Expected sales in next month=26000 units

Income statement of NA(where actual prices are considered)

Details for 26000 units	Per unit cost in $	Amount in $	Percentages
Sales value	30	780000	100%
Less variable cost	21	460000	70%
Contribution margin	9	234000	30%
less fixed expenses		180000
Net operating income		54000

Income statement of AU project (where revised prices are considered)

Details for 26000 units	Per unit cost in $	Amount in $	Percentages
Sales value	30	780000	100%
Less variable cost	18	468000	60%
Contribution margin	12	312000	40%
less fixed expenses		252000
Net operating income		60000

Note: Percentages are calculated based on the total sales value.

5c

To determine

Introduction:

Contribution margin: It is also known as gross margin. It is the value derived after deducting the variable expenses from the total sales value. It has one more feature. When the value of fixed expenses is deducted from the contribution margin, we can derive the net income.

To evaluate: Whether the automation of the company’s operations is right or wrong.

Answer to Problem 3.22P

The choice of NA project is recommended.

Explanation of Solution

When the income statements of both the projects are studied, we find that the contribution margin of AU project is more when compared to NA project. Even the fixed expenses are more in AU project resulting is higher income when compared to NA project.

The break-even sale in AU project is her than the NA project. This results in the rise of company’s risk. In case the company tries to balance its sales with NA project, it will definitely incur losses. So, choice of NA project is highly recommended.