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Take a look at our Guided Solution in Cost Accounting!

Signore Company manufactures and sells a telephone answering machine. The company's contribution format income statement for the most recent year is given below:

  Total Per Unit Percent of Sales
Sales (20,000 units) $2,400,000 $120 100%
Less Variable expenses $1,800,000 $90 ?
Contribution margin $600,000 $30 ?
Less Fixed expenses $480,000    
Net income $120,000    

Management is anxious to improve the company's profit performance and has asked for several items of information.

Required

  1. Compute the Company's CM ratio and variable expense ratio
  2. Compute the Company's break-even point in both units and sales dollars, using the equation method.
  3. Assume that the sales increase by $800,000 next year. If cost behavior patterns remain the same, what will be the increase in net income? (Hint: Use CM ratio).
  4. Assume that next year management wants the company to earn a minimum profit of $180,000. How many units will have to be sold to meet this target profit?
  5. Refer to original data. Compute the company's margin of safety in both dollar and percentage form.
  6. What is the degree of operating leverage at the present level of sales?

Solution

Given:

Contribution format income statement of Signore Company

Planning the solution:

  1. CM ratio
  2. Variable expense ratio
  3. Prepare entries to close the expenses to income summary
  4. Break-even point in units
  5. Break-even point in dollars
  6. Increase in net income when the sales increases
  7. Target profit
  8. Margin of safety
  9. Degree of operating leverage

Theoretical Concepts Used in This Solution

Contribution Margin

Contribution margin = Sales – Variable expenses

Contribution margin is the amount available after variable expenses are deducted from sales. The remaining amount is used to meet fixed expenses. If the contribution margin is in excess of fixed expenses, then a profit occurs for the period, if it is not sufficient to cover fixed expenses, then a loss occurs for the period.

CM Ratio / Contribution Margin Ratio

Contribution margin ratio is given by,

Total Contribution Margin / Total Sales
(or)
Per Unit Contribution Margin / Per Unit Sales

Contribution margin ratio indicates the change in contribution margin due to change in total sales. This ratio is useful to managers when they have to take decisions regarding trade-offs between more sales of one product versus sales of another product. Hence products which yield the greatest amount of contribution margin per dollar of sales are emphasized in such situations.

Variable Expense Ratio

Variable expense ratio is given by

Variable expenses / Selling price (or) (1 – Contribution Margin ratio)

Variable expense ratio calculates the costs which vary with production levels; it is used to decide the optimum price for a product.

Break-Even Point

Break-even point is the point where sales covers the total costs, both fixed and variable costs. At this point the company does not make any profit or loss, hence profit or loss equals zero. It can be computed using either the contribution margin method or equation method.

The Equation Method

Profit = Sales – (Variable Expenses + Fixed Expenses)

Using this method we can find break-even sales,

Sales = Variable expenses + Fixed expenses + Profit

At break-even sales, the profit is zero. Hence substitute profit = 0, in the above equation.

The Contribution Margin Method

In units,

Break-even Point (in units sold) = Fixed expenses / Unit Contribution Margin

In dollars,

Break-even Point in Total Sales (in $ made) = Fixed Expenses / CM Ratio

Graphical Representation of Break-Even Point

Graph1

Target Profit

Target profit analysis is used to find the sales volume to achieve desired/target profit. The equation used to find break-even point using the equation method can be used to find desired profit. For example, let us assume that unit selling price of product X is $100, unit variable expense is $40, and total fixed expenses are $5,000. Then in order to make a profit of $31,000, the required number of units to be sold can be found using the equation as follows.

Sales = Variable expenses + Fixed Expenses + Profit

Let us take number of units as A
Then,
$100 A = $40A + $5,000 + $31,000
$60A = $36,000
A = $36,000 / $60
A = 600 units

Thus, the target profit can be achieved by selling 600 speakers which represent $600,000 in total sales (i.e., $100 * 600).

Margin of Safety

Margin of safety is the surplus of budgeted or actual sales over the break-even sales. The amount by which sales can drop before losses begin to be incurred by the organization can be found using margin of safety.

Margin of Safety = Total Budgeted (or) Actual Sales – Break-even Sales

Degree of Operating Leverage

In order to find the effect of change in sales volume on profits, degree of operating leverage is used. In other words, it is measure used to find the sensitivity of net income to a percentage change in sales. The degree of operating leverage at a given level of sales is given by the following formula:

Degree of operating leverage = Contribution margin / Net income

Steps Used for Solving:

1.a. CM Ratio = Contribution Margin / Selling Price  
  Contribution margin is $30  
  Selling price is $120  
  Contribution margin ratio = $30 / $120 25%
     
b. Variable Expense Ratio = Variable Expense / Selling Price  
  Variable expense is $90  
  Selling price is $120  
  Variable expense ratio = $90 / $120 75%
2 Using the Equation Method    
  Break-even point in units     
  Sales = Variable expenses + Fixed expenses + Profits    
  Let us assume that number of units sold is Q    
  Unit selling price $120  
  Unit variable cost $90  
  Fixed expenses $480,000  
  Substituting in the equation, we get    
  $120Q = $90Q + $480,000 + 0    
  $30Q = $480,000    
  Q = $480,000 / $30 16,000 units
       
  Break-even point in sales dollars    
  Break-even units  16,000 units
  Unit selling price  $120  
  Break-even point in sales dollars = 16,000 units * $120 $1,920,000  
3 Increase in sales $800,000
  CM ratio 25%
  Expected increase in contribution margin= $800,000 * 25% $200,000

Increase in sales will not result in increase in fixed expenses, it will remain the same, hence the increase in net income will be same as increase in contribution margin, which is, $200,000.

4 To find target profit, we have to use the equation method.    
  Sales = Variable expenses + Fixed expenses + Profits    
  Unit selling price $120  
  Unit variable cost $90  
  Fixed expenses $480,000  
  Target profit $180,000  
  Substituting in the equation, we get    
  $120Q = $90Q + $480,000 + $180,000    
  $30Q = $660,000    
  Q = $660,000 / $30 22000 units

Therefore, the required number of units to be sold in order to achieve a target profit of $180,000 is 22,000 units.

5 Margin of Safety = Total Sales - Break-even Sales  
  Total sales (from the data provided) $2,400,000
  Break-even sales ( from 2 above) $1,920,000
  Margin of safety = $2,40,0000 - $1,920,000 $480,000
6 Degree of Operating Leverage = Contribution Margin / Net Income  
  Contribution margin $600,000
  Net income $120,000
  Therefore, degree of operating leverage is $600,000 / $120,000 5

Topics Related to Cost Accounting

Direct Cost Expired Cost Fixed Cost Full Cost
Non Manufacturing Cost Manufacturing Cost Indirect Cost Incremental Cost
Period Cost Variable Cost Business Level Cost Business Level Or Sustaining Cost

Books on Cost Accounting

Principles Of Corporate Finance, Brealey Myers Advanced Accountancy, Hrishikesh Chakraborthy Fundamentals Of Corporate Finance, Richard Financial & Managerial Accounting, Williams
Fundamentals Of Coporate Finance, Richard Managerial Accounting, Ronald W.Hilton Advanced Accounts, Shukla Grewal Company Valution A Stratagic Approach
Typical Problems In Advanced Accounting, Batliboi Public Finance Theory & Practice,Mankar & Sarma Principles Of Corporate Finance, Brealey Financial Structure And Economic Growth, Rose Lemme
Financial Accounting, Pearson Glencoe Accounting Accounting Made Easy, Agarwal Financial Accounting, Warren Deeve
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