Chapter 3, Problem 3.20P

1.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

The CM ratios; break-even points in balls, degree of operating leverage considering last year’s sales level.

Answer to Problem 3.20P

The CM ratio is 40%; break-even point in balls is 21000 balls; and the degree of operating leverage is 3.33.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$15 per ball. It is 60% of direct labor cost.

Sales of 30000 balls = $750000

Variable expenses = $450000

Contribution margin = $300000

Fixed expenses = $210000

Net operating income= $90000

1. Let us now calculate the CM ratio and the break-even point in balls.

Calculation of CM ratio:

CM ratio is nothing but a contribution margin ratio. It is obtained by contribution margin by sales and the amount derived has to be multiplied by 100.

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Sales}\times 100\\ =\frac{\$300000}{\$750000}\times 100\\ =0.4\times 100\\ =40\%\end{array}$

Calculation of break-even point in balls:

The following formula can be used for the calculation of break-even point.

  $\begin{array}{l}Break-evenpointinballs=\frac{Fixedexpense}{Sellingpriceperunit-variablecostperunit}\\ =\frac{\$210000}{\$25-\$15}\\ =\frac{210000}{\$10}\\ =21000balls\end{array}$

b: Let us now calculate the degree of operating leverage.

  $\begin{array}{l}Degreeofoperatingleverage=\frac{Contributionmargin}{Netoperatingincome}\\ =\frac{\$300000}{\$90000}\\ =3.33\end{array}$

Therefore, the CM ratio is 40%; break-even point in balls is 21000 balls ; and the degree of operating leverage is 3.33.

2.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

The CM ratio and break-even point in balls when there is an increase of $3 in Variable expenses.

Answer to Problem 3.20P

The CM ratio is 28% and break-even point in balls is 30000 balls when there is an increase of $3 in Variable expenses.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$15 per ball. It is 60% of direct labor cost.

Sales of 30000 balls = $750000

Variable expenses = $450000

Contribution margin = $300000

Fixed expenses = $210000

Net operating income= $90000

Calculation of contribution margin ratio:

  $Contributionmarginratio=\frac{Contributionmargin}{Sales}\times 100$

We are informed that there is an increase in the variable expense by $3.

So the variable cost per ball $=\$15+\$3=\$18$

To calculate the contribution margin, we require a total variable cost.

  $\begin{array}{l}Totalvariablecost=Variablecostperball\times Numberofballssold\\ =\$18\times 30000\\ =\$540000\end{array}$

By using this value, we will calculate the contribution margin first.

  $\begin{array}{l}Contributionmargin=Sales-totalvariablecost\\ =\$750000-\$540000\\ =\$210000\end{array}$

Since we have derived the required values, let us now calculate the contribution margin.

  $Contributionmarginratio=\frac{Contributionmargin}{Sales}\times 100$

  $\begin{array}{l}=\frac{\$2100000}{\$750000}\times 100\\ =0.28\times 100\\ =28\%\end{array}$

Calculation of break-even point in balls:

The following formula can be used for calculation of break-even point.

  $\begin{array}{l}Break-evenpointinballs=\frac{Fixedexpense}{Sellingpriceperunit-variablecostperunit}\\ =\frac{\$210000}{\$25-\$18}\\ =\frac{210000}{\$7}\\ =30000balls\end{array}$

Therefore, the CM ratio is 28% and the break-even point in balls is 30000 balls when there is an increase of $3 in Variable expenses.

3.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

The number of balls to be sold to earn a net operating profit of $90000 when there is a change in variable expenses.

Answer to Problem 3.20P

The number of units to be sold to earn a target profit of $90000 will be 42857 units.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$18 per ball.

Sales of 30000 balls = $750000

Variable expenses = $540000

Contribution margin = $210000

Fixed expenses = $210000

Net operating income= $90000

To know the expected sales units we have to use the following formula:

  $\begin{array}{l}ExpectedSalesunit=\frac{Fixedexpense+Targetprofit}{Contributionmarginperunit}\\ =\frac{\$210000+\$90000}{\$25-\$18}\\ =\frac{\$300000}{\$7}\\ =42857units\end{array}$

Therefore, the number of units to be sold to earn a target profit of $90000 will be 42857 units.

4.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

The selling price per ball to cover the increased labor costs.

Answer to Problem 3.20P

The revised selling price will be $30.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$18 per ball.

Sales of 30000 balls = $750000

Variable expenses = $450000

Contribution margin = $300000

Fixed expenses = $210000

Net operating income= $90000

We are asked to calculate the revised selling price which will help the company to cover the increased labor cost.

Initially, the variable cost per ball was $15. Then the price was modified to $18. If the same price of $15 is used for calculations, there will be a huge loss on labor cost which will remain unaccounted. So, a revised selling price is very essential to cover the increased labor cost. The following formula can be used:

  $\begin{array}{l}Revisedsellingprice=\frac{Modifiedvariablecost}{1-\frac{-\left(Oldsellingprice-oldvariablecost\right)}{oldsellingprice}}\\ =\frac{\$18}{1-\frac{\$25-\$15}{\$25}}\\ =\frac{\$18}{1-\frac{\$10}{\$25}}\\ =\frac{\$18}{1-0.4}\\ =\frac{\$18}{0.6}=\$30\end{array}$

Note: Since, the revised selling price to be calculated is for per unit, all the values taken will be per unit only

Therefore the revised selling price will be $30.

5

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

The Company’s new CM ratio and the break-even point in balls if a new plant is built.

Answer to Problem 3.20P

The CM ratio is 64% and break-even point in balls is 26250 balls when there is a decrease of 40$ in variable cost and increase in fixed cost.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$18 per ball.

Sales of 30000 balls = $750000

Variable expenses = $450000

Contribution margin = $300000

Fixed expenses = $210000

Net operating income= $90000

Additional information:

The variable expenses are going to reduce by 40%

The fixed expenses are going to double.

Calculation of contribution margin ratio:

  $Contributionmarginratio=\frac{Contributionmargin}{Sales}\times 100$

We are informed that there is a decrease in the variable expense by 40%.

So, variable cost= $100-40\%=60\%$

Variable cost per unit $=60\%\times \$15=\$9$

Therefore, the revised variable price per unit is $9.

To calculate the contribution margin, we require total variable cost.

  $\begin{array}{l}Totalvariablecost=Variablecostperball\times Numberofballssold\\ =\$9\times 30000\\ =\$270000\end{array}$

By using this value, we will calculate the contribution margin first.

  $\begin{array}{l}Contributionmargin=Sales-totalvariablecost\\ =\$750000-\$270000\\ =\$480000\end{array}$

Since we have derived the required values, let us now calculate the contribution margin.

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Sales}\times 100\\ =\frac{\$480000}{\$750000}\times 100\\ =0.64\times 100\\ =64\%\end{array}$

Calculation of break-even point in balls:

We are informed that the fixed expenses have doubled.

So, the revised fixed expense will be $\$210000\times 2=\$420000$

By using the value of fixed expense, let us calculate the break-even point. The following formula can be used for the calculation of the break-even point.

  $\begin{array}{l}Break-evenpointinballs=\frac{Fixedexpense}{Sellingpriceperunit-variablecostperunit}\\ =\frac{\$420000}{\$25-\$9}\\ =\frac{420000}{\$16}\\ =26250balls\end{array}$

Therefore, the CM ratio is 64% and the break-even point in balls is 26250 balls when there is a decrease of 40$ in variable cost and an increase in fixed cost.

6a.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

The number of balls sold to earn a net operating income of $90000 if a new plant is built.

Answer to Problem 3.20P

The number of units to be sold to earn a target profit of $90000 will be 31857 units.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$9 per ball.

Sales of 30000 balls = $750000

Contribution margin = $480000

Fixed expenses = $420000

Net operating income= $90000

To know the expected sales units we have to use the following formula:

  $\begin{array}{l}ExpectedSalesunit=\frac{Fixedexpense+Targetprofit}{Contributionmarginperunit}\\ =\frac{\$420000+\$90000}{\$25-\$9}\\ =\frac{\$510000}{\$16}\\ =31857units\end{array}$

Therefore, the number of units to be sold to earn a target profit of $90000 will be 31857 units.

6b.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

To prepare: The contribution format income statement and calculate the degree of operating leverage.

Answer to Problem 3.20P

The degree of operating leverage is 8.

Explanation of Solution

Given information:

Sale of balls= 30000 units

Selling price per unit= $25

Variable expenses=$9 per ball.

Sales of 30000 balls = $750000

Contribution margin = $480000

Fixed expenses = $420000

Let us prepare a contribution statement to know the net operating income.

Particulars	Amount in $
Sales	$30000units\times \$25=\$750000$
Less Variable cost	$30000units\times \$9=\$270000$
Contribution margin	$480000
Less Fixed expenses	$420000
Net operating profit	$60000

By using this value of net operating profit, we will calculate the degree of operating leverage.

  $\begin{array}{l}Degreeofoperatingleverage=\frac{Contributionmargin}{Netoperatingincome}\\ =\frac{\$480000}{\$60000}\\ =8\end{array}$

Therefore, the degree of operating leverage is 8.

6c.

To determine

Introduction:

CVP analysis: It refers to Cost-Volume- Proft analysis. It is an essential tool to analyze the effect on the net operating profit due to changes in sales volume and product costs.

To analyze: Whether the decision of reconstructing the new plant is good or bad.

Answer to Problem 3.20P

The decision of reconstructing the new plant is not good.

Explanation of Solution

When we consider the net operating income earned using the previous plan, it was $90000. After the construction of a new plant, there have been many changes in the costs. The available cost has reduced by 40% and the fixed cost has doubled. This change in costs has resulted in a reduction of net operating profit and amounted to $60000. So, according to my opinion, the choice of construction of a new plant was not good and it reduced the net operating income of the company.

The decision of reconstructing the new plant is not good.