Chapter 12, Problem 12.24P

To determine

Concept Introduction:

Breakeven point

It measures whether a project will be profitable by equating its total revenues with its total expenses. At break- even point, contribution margin equals fixed expenses which can be depicted as:

  

Contribution margin

It is the difference between total revenue and variable expenses. Contribution margin equals the amount that sales exceed variable costs. It measures how efficiently a company can produce products and maintain low levels of variable cost.

  

Variable expenses

The expenses which are associated with the amount of goods produced or services provided. These vary directly with the production level i.e. company's variable cost increases as the production increases and vice-a-versa.

Fixed expenses

These expenses do not vary with the level of production. They do not change with the amount of goods or services a company produces. They remain same even if the company does not produce any product or provide any service during an accounting period.

Requirement a:

To calculate:

Number of units to be sold each month to Break- even

Answer to Problem 12.24P

Number of units to be sold each month to Break- even= 4,250 units

Explanation of Solution

To arrive at break- even point, firstly contribution margin would be calculated using the below- mentioned formula:

  

In the given problem, selling price is given as $15 per unit and Variable expenses as $9 per unit. Thus,

  $Contributionmargin=\$32perunit-\$20.8perunit=\$11.2perunit$

At break- even point, contribution margin equals fixed expenses. Fixed expenses are given in the problem as $27,000 per month. Let us assume number of units sold to be x.

  

  

Thus, break- even point in terms of sales volume= 4,250 units.

To determine

Concept Introduction:

Margin of safety

The excess of actual or budgeted sales over break- even sales volume is called margin of safety. In other words, it is the revenue earned after the company pays all of its fixed and variable costs associated with producing goods or services. It can be calculated using the following formula:

  

Margin of safety ratio can be calculated by subtracting break- even point from the current sales and dividing by the current sales as can be seen below:

  

Breakeven point

It measures whether a project will be profitable by equating its total revenues with its total expenses. At break- even point, contribution margin equals fixed expenses. Break- even point in terms of sales dollars can be computed using the following formula:

  

Requirement b:

To calculate:

Margin of safety and margin of safety ratio

Answer to Problem 12.24P

Margin of safety= $1, 36,000

Margin of safety ratio= 15%

Explanation of Solution

Firstly, Break- even point in terms of sales dollars needs to be calculated. We have determined break- even point in terms of sales volume as 4,250 units and selling price per unit is given in the problem as $32 per unit. Therefore,

  

  

Now, Margin of safety needs to be calculated. Current sales are given as $1, 60,000 in the problem and we have already calculated Break- even sales as $1, 36,000. Therefore,

  

  $=\$\mathrm{<mn>1</mn>},\mathrm{<mn>6</mn><mn>0</mn>},\mathrm{<mn>0</mn><mn>0</mn><mn>0</mn>}-\$\mathrm{<mn>1</mn>},\mathrm{<mn>3</mn><mn>6</mn>},\mathrm{<mn>0</mn><mn>0</mn><mn>0</mn>}=\$\mathrm{<mn>2</mn><mn>4</mn>},\mathrm{<mn>0</mn><mn>0</mn><mn>0</mn>}$

Margin of safety ratio can be calculated using the below- mentioned formula:

  

  $=\left(\$\mathrm{<mn>1</mn>},\mathrm{<mn>6</mn><mn>0</mn>},\mathrm{<mn>0</mn><mn>0</mn><mn>0</mn>}-\$\mathrm{<mn>1</mn>},\mathrm{<mn>3</mn><mn>6</mn>},\mathrm{<mn>0</mn><mn>0</mn><mn>0</mn>}\right)/\$\mathrm{<mn>1</mn>},\mathrm{<mn>6</mn><mn>0</mn>},\mathrm{<mn>0</mn><mn>0</mn><mn>0</mn>}=\mathrm{<mn>1</mn><mn>5</mn>}\%$

Thus, margin of safety is coming out to be $1, 36,000 and margin of safety ratio as 15%.

To determine

Concept Introduction:

Contribution margin

It is the difference between total revenue and variable expenses. Contribution margin equals the amount that sales exceed variable costs. It measures how efficiently a company can produce products and maintain low levels of variable cost.

  

Variable expenses

The expenses which are associated with the amount of goods produced or services provided. These vary directly with the production level i.e. company's variable cost increases as the production increases and vice-a-versa.

Fixed expenses

These expenses do not vary with the level of production. They do not change with the amount of goods or services a company produces. They remain same even if the company does not produce any product or provide any service during an accounting period.

Requirement c:

To calculate:

Monthly operating income (or loss) if 5,000 units are sold each month

Answer to Problem 12.24P

Monthly operating income of Miller Metal Co. = $8,400

Explanation of Solution

To arrive at monthly operating income (or loss) of Miller Metal Co. at sales volume of 5000 units, following equation would be used:

  

In the given problem, selling price is given as $32 per unit and Variable expenses as $20.8 per unit. Thus,

  $\begin{array}{l}Revenue=5,000units*\$32perunit=\$1,60,000\hfill \\ Variableexpenses=5,000units*\$20.8perunit=\$1,04,000\hfill \\ Contributionmargin=\$1,60,000-\$1,04,000=\$56,000\hfill \end{array}$

Further, monthly fixed expenses are given as $47,600. Thus, operating income would be:

  

All the above calculations can be seen from the table given below:

Calculation of monthly operating income (or loss) of Miller Metal Co. (Amount in $)

Particulars	Per unit	Sales Volume	Amount
Revenue	32	5,000 units	1,60,000
Less: Variable expenses	20.80	5,000 units	1,04,000
Contribution margin	11.20	5,000 units	56,000
Less: Fixed expenses			47,600
Operating income			8,400

Thus, monthly operating income is coming out to be $8,400.

To determine

Concept Introduction:

Contribution margin

It is the difference between total revenue and variable expenses. Contribution margin equals the amount that sales exceed variable costs. It measures how efficiently a company can produce products and maintain low levels of variable cost.

  

Variable expenses

The expenses which are associated with the amount of goods produced or services provided. These vary directly with the production level i.e. company's variable cost increases as the production increases and vice-a-versa.

Fixed expenses

These expenses do not vary with the level of production. They do not change with the amount of goods or services a company produces. They remain same even if the company does not produce any product or provide any service during an accounting period.

Requirement d:

To calculate:

Monthly operating income (or loss) if selling price is $33 per unit, advertising expenditure increases by $7,000 per month and monthly sales volume are 5,400 units

Answer to Problem 12.24P

Monthly operating income of Miller Metal Co. = $11,280

Explanation of Solution

To arrive at monthly operating income (or loss) if selling price is $33 per unit, advertising expenditure increases by $7,000 per month and monthly sales volume are 5,400 units, following equation would be used:

  

In the given problem, selling price is given as $33 and Variable expenses are given as $9 per unit. Monthly sales volume is 5,400 units. Thus,

  $\begin{array}{l}Revenue=5,400units*\$33perunit=\$1,78,200\hfill \\ Variableexpenses=5,400units*\$20.8perunit=\$1,12,320\hfill \\ Contributionmargin=\$1,78,200-\$1,12,320=\$65,880\hfill \end{array}$

Further, monthly fixed expenses are given as $47,600 and advertising expenditure increases by $7,000 per month, thereby making total fixed expenses as $54,600. Thus, operating income would be:

  

All the above calculations can be seen from the table given below:

Calculation of monthly operating income (or loss) of Miller Metal Co. (Amount in $)

Particulars	Per unit	Sales Volume	Amount
Revenue	33	5,400 units	1,78,200
Less: Variable expenses	20.80	5,400 units	1,12,320
Contribution margin	12.20	5,400 units	65,880
Less: Fixed expenses			54,600
Operating income			11,280

Thus, monthly operating income is coming out to be $11,280.

To determine

Concept Introduction:

Contribution margin

It is the difference between total revenue and variable expenses. Contribution margin equals the amount that sales exceed variable costs. It measures how efficiently a company can produce products and maintain low levels of variable cost.

  

Variable expenses

The expenses which are associated with the amount of goods produced or services provided. These vary directly with the production level i.e. company's variable cost increases as the production increases and vice-a-versa.

Fixed expenses

These expenses do not vary with the level of production. They do not change with the amount of goods or services a company produces. They remain same even if the company does not produce any product or provide any service during an accounting period.

Requirement e:

To calculate:

Monthly operating income (or loss) if new product is added

Answer to Problem 12.24P

Monthly operating income of Miller Metal Co. = $17,000

Explanation of Solution

To arrive at monthly operating income (or loss) if a new product is added, following equation would be used:

  

In the given problem, selling price of the old product is given as $32 per unit and Variable expenses are given as $20.80 per unit. Also, selling price of new product is $20 per unit, variable costs are $14 per unit and 5000 units of original and 4000 units of new product are sold. Thus,

  $\begin{array}{l}Revenue=\left(4,000units*\$20perunit\right)+\left(5,000units*\$32perunit\right)=\$2,40,000\hfill \\ Variableexpenses=\left(4,000units*\$14perunit\right)+\left(5,000units*\$20.8perunit\right)=\$1,60,000\hfill \\ Contributionmargin=\$2,40,000-\$1,60,000=\$80,000\hfill \end{array}$

Further, there has been an increase in fixed expenses making it a total of $63,000 per month. Thus, operating income would be:

  

Thus, monthly operating income is coming out to be $17,000.

To determine

Concept Introduction:

Contribution margin

It is the difference between total revenue and variable expenses. Contribution margin equals the amount that sales exceed variable costs. It measures how efficiently a company can produce products and maintain low levels of variable cost.

  

Variable expenses

The expenses which are associated with the amount of goods produced or services provided. These vary directly with the production level i.e. company's variable cost increases as the production increases and vice-a-versa.

Fixed expenses

These expenses do not vary with the level of production. They do not change with the amount of goods or services a company produces. They remain same even if the company does not produce any product or provide any service during an accounting period.

Requirement f

To calculate:

Monthly operating income (or loss) if 5,000 units of new product and 4,000 units of original product are sold

Answer to Problem 12.24P

Monthly operating income of Miller Metal Co. = $11,800

Explanation of Solution

To arrive at monthly operating income (or loss) when 4000 units of original and 5000 units of new product are sold, following equation would be used:

  

In the given problem, selling price of the old product is given as $32 per unit and Variable expenses are given as $20.80 per unit. Also, selling price of new product is $20 per unit, variable costs are $14 per unit and 4000 units of original and 5000 units of new product are sold. Thus,

  $\begin{array}{l}Revenue=\left(5,000units*\$20perunit\right)+\left(4,000units*\$32perunit\right)=\$2,28,000\hfill \\ Variableexpenses=\left(5,000units*\$14perunit\right)+\left(4,000units*\$20.8perunit\right)=\$1,53,200\hfill \\ Contributionmargin=\$2,28,000-\$1,53,200=\$74,800\hfill \end{array}$

Further, fixed expenses are given as $63,000 per month. Thus, operating income would be:

  

Thus, monthly operating income is coming out to be $11,800.

To determine

Concept Introduction:

Variable expenses

The expenses which are associated with the amount of goods produced or services provided. These vary directly with the production level i.e. company's variable cost increases as the production increases and vice-a-versa.

Fixed expenses

These expenses do not vary with the level of production. They do not change with the amount of goods or services a company produces. They remain same even if the company does not produce any product or provide any service during an accounting period.

Requirement g

Causes of difference in operating income in parts e and f

Answer to Problem 12.24P

The difference in operating income in parts e and f is due to change in the levels of product sold for both original as well as new product

Explanation of Solution

The difference in operating income in parts e and f in spite of the fact that total sales volume is 9,000 units is that there has been change in the levels of product sold in both the parts.

• In part e: 5000 units of original product and 4000 units of new product are sold, whereas
• In part f: 4000 units of original product and 5000 units of new product are sold

Also, the selling price and variable costs per unit for both the product are different, thereby causing difference in operating income.