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Managerial Accounting
ACCT 2330
Notes: Chapter 5
See the traditional Income Statement below. What do sales have to be in order for Happy Dan’s
to make $1,200 in net income?
Happy Dan’s Hardware Store
Income Statement
For the Year Ended December 31, 2009
Sales
Cost of Goods Sold
Gross Margin
Selling & Admin Expense
Administrative Expenses
Selling Expenses
Total Expenses
Net Income
$48,000
20,000
28,000
11,600
16,000
27,600
400
The traditional income statement is not organized in a fashion to answer these questions easily.
Additional information:
Sales Volume in units is 4,000
Cost of goods sold is $5 per unit
Administrative expenses are $6,000 plus $1.40 per unit.
Selling expenses are $8,000 plus $2 per unit.
The Basics of Cost-Volume-Profit (CVP) Analysis Cost-volume-profit (CVP) analysis is a key
step in many decisions. CVP analysis involves specifying a model of the relations among the
prices of products, the volume or level of activity, the unit variable costs, the total fixed costs,
and the mix of products sold. This model is used to predict the impact on profits of changes
in those parameters.
1.
Contribution Margin. Contribution margin is the amount remaining from sales revenue
after variable expenses have been deducted. It contributes towards covering fixed costs
and then towards profit.
2.
Unit Contribution Margin. When there is a single product, the unit contribution margin
can be used to predict changes in the contribution margin and in profits (assuming there is
no change in fixed costs) as a result of changes in unit sales. To do this, the unit
contribution margin is simply multiplied by the change in unit sales.
-23.
Contribution Margin Ratio. The contribution margin (CM) ratio is the ratio of the
contribution margin to total sales. It shows how the contribution margin is affected by a
given dollar change in total sales. Managers often find the contribution margin ratio
easier to work with than the unit contribution margin, particularly when a company has
multiple products. This is because the contribution margin ratio is denominated in sales
dollars, which is a convenient way to express activity in multi-product firms.
Applications of CVP Concepts CVP analysis is typically used to estimate the impact on profits
of changes in selling price, variable cost per unit, sales volume, and total fixed costs. CVP
analysis can be used to estimate the effect on profits of a change in any one (or any combination)
of these parameters. Target profit analysis is concerned with estimating the level of sales required
to attain a specified target profit. Break-even analysis is as a special case of target profit analysis
in which the target profit is zero.
Example:
Ace Manufacturing makes a single product, a coffee brewing machine, called “Perfect Pot.”
Ace Mfg can make 10,000 units per year.
The selling price is $160 per unit
The variable costs are $128 per unit
The fixed costs are $160,000
Current sales volume is 5,100 units.
Summary of Applications
1.
Calculate Break even point in sales dollars, or units of product.
2.
Calculate changes in income as a result of changes in volume
3.
Calculate operating leverage
4.
Calculate margin of safety
5.
Calculate sales required to attaint a specific profit. (Ace wants to make $200,000)
Break-even point using the equation method The break-even point is the level of sales at
which profit is zero. It can also be defined as the point where total sales revenue equals total
expenses or as the point where contribution margin total equals total fixed expenses. Break-even
analysis can be approached either by the equation method or by the contribution margin method.
The two methods are logically equivalent.
The Equation Method
Break Even Point in Sales:
(Price/Unit)(Units) = (Variable Cost/Units)(Units) + Fixed Cost
Or
Break Even Point in Sales:
Sales = (Variable Cost Ratio)(Sales) + Fixed Costs
-3-
Contribution Margin Method
Break Even Unit Sales =
Break Even Dollar Sales =
Fixed Expenses
Unit Contribution Margin
Fixed Expenses
Contribution Margin Ratio
Target profit analysis. Managers frequently desire to know the number of units that must be
sold to attain a target profit. Either the equation method or the contribution margin method
discussed previously can be used. In the case of the contribution margin method, the formulas
are:
Unit Sales to attain target profit =
Dollar Sales to attain target profit =
Fixed Expenses + Target Profit
Unit Contribution Margin
Fixed Expenses + Target Profit
Contribution Margin Ratio
The Graphical Representation of the Break Even Point
Graphs of CVP relationships can be used to gain insight into the behavior of expenses and
profits. The basic CVP graph is drawn with dollars on the vertical axis and volume in units on
the horizontal axis. Total fixed expense is drawn first, and then variable expense is added to the
fixed expense in order to draw the total expense line. Finally, the total revenue line is drawn. The
total profit (or loss) is the vertical difference between the total revenue and total expense lines.
-4Margin of Safety The margin of safety is the excess of budgeted (or actual) sales over the
break-even volume of sales. It is the amount by which sales can drop before losses begin to be
incurred. The margin of safety can be computed in terms of dollars, as a percent of current sales,
in units, or as a percent of capacity:
Margin of safety in dollars = Total sales - Break-even sales level
or
Margin of Safety Percent =
Margin of safety in Dollars
Current Sales in Dollars
or
Margin of Safety in units =
Margin of safety in units
Current Sales in Units
Or Margin of Safety in Dollars
Unit Sales Price
Cost Structure. Cost structure refers to the relative proportion of fixed and variable costs in an
organization. The best cost structure for a company depends on many factors, including the longrun trend in sales, year-to-year fluctuations in the level of sales, and the attitudes of owners and
managers towards risk. Understanding a company=s cost structure is important for decision
making as well as for analysis of performance.
Operating Leverage Operating leverage is a measure of how sensitive net income is to a given
percentage change in sales.
1.
Degree of operating leverage. The degree of operating leverage at a given level of sales is
computed as follows:
Contribution Margin
Net Income
2.
The math underlying the degree of operating leverage. The degree of operating leverage
can be used to estimate how a given percentage change in sales volume will affect net
income at a given level of sales, assuming there is no change in fixed expenses. To verify
this, consider the following:
Degree of Operating
Leverage
x
Percentage Change
in Sales
=
Percentage Change
In income
Thus, providing that there is no change in fixed expenses and the other assumptions of
CVP analysis are valid, the degree of operating leverage provides a quick way to predict
the percentage effect on profits of a given percentage increase in sales. The higher the
degree of operating leverage, the larger the increase in net income from a given
percentage changes in sales.
-5Degree of operating leverage is not constant. The degree of operating leverage is not
constant as the level of sales changes. For example, at the break-even point the degree of
operating leverage is infinite since the denominator of the ratio is zero. Therefore, the
degree of operating leverage should be used with some caution and should be recomputed
for each level of sales.
Structuring Sales Commissions. Which model will salespeople push hardest if they are paid a
commission of 10% of sales revenue? Which model is more profitable?
Price
Variable Cost Commission
Other Variable Cost
Unit CM
Model A
$100
10
75
$ 15
Model B
$150
15
130
$ 5
Sales Mix. The term sales mix means the relative proportions in which a company=s products are
sold. Most companies have a number of products with differing contribution margins. Thus, changes in
the sales mix can cause variations in a company’s profits. As a result, the break-even point in a multiproduct company is dependent on the mix in which the various products are sold.
Different products typically have different selling prices, costs, and contribution margins.
1.
Constant sales mix assumption. The assumption is usually made in CVP analysis
that the sales mix will not change. Under the constant sales mix assumption, the
break-even level of sales dollars can be computed using the overall contribution
margin (CM) ratio. In essence, the assumption is made that the firm has only one
product that consists of a basket of its various products in a specified proportion. The
contribution margin ratio of this basket can be easily computed by dividing the total
contribution margin of all products by total sales.
2..
Changes in sales mix. If the proportions in which products are sold change, then the
contribution margin ratio will change. Since the sales mix is not in reality constant,
the results of CVP analysis should be viewed with more caution in multi-product
firms than in single product firms
Joe’s Stuff
Income Statement
For the Year Ended December 31, 2009
Sales
Variable Costs
Contribution Margin
Fixed Costs
Net Income
Calculate the Break Even Point
Department
A
50,000
20,000
30,000
Department
B
150,000
30,000
120,000
Total
200,000
50,000
150,000
135,000
15,000
-6Limiting Assumptions in CVP Analysis. Simple CVP analysis relies on simplifying assumptions.
However, if a manager knows that one of the assumptions is violated, the CVP analysis can often be
easily modified to make it more realistic.
1.
2.
3.
4.
Selling price is constant. The assumption is that the selling price of a product will not change as
the unit volume changes. This is not wholly realistic since there is usually an inverse relationship
between price and unit volume. In order to increase volume it is often necessary to drop the price.
However, CVP analysis can easily accommodate more realistic assumptions
Costs are linear and can be accurately divided into variable and fixed elements. It is
assumed that the variable element is constant per unit and the fixed element is constant in total.
This implies that operating conditions are stable and there are no major changes in worker
efficiency
The sales mix is constant in multi-product companies. This assumption is invoked in order to
use the simple break-even and target profit formulas in multi-product firms. If unit contribution
margins are fairly uniform across products, violations of this assumption will not be important.
However, if unit contribution margins differ a great deal, then changes in the sales mix can have a
big impact on the overall contribution margin ratio and hence upon the results of CVP analysis.
In manufacturing companies, inventories do not change. It is assumed that everything the
company produces is sold in the same period. Violations of this assumption result in discrepancies
between financial accounting net income and the profits calculated using the contribution approach.
This topic is covered in detail in the next chapter.
-7In Class Examples
Implements:
Hardware:
Large equipment items such as lawnmowers and snow-blowers.
All other items sold in the store.
Ace Hardware - Monthly Information
Customers this Month
Sales – Implements
Variable Costs – Implements
Sales – Hardware
Variable Costs – Implements
Fixed Costs
8,000
$141,400
$ 84,840
$262,600
$152,308
$165,200
Required
1.
2.
3.
4.
5.
6.
7.
Contribution format income statement (Include Departments)
Calculate the break even point in sales dollars.
Calculate the average sale per customer
Calculate the break even point in customers.
Calculate the Margin of Safety
Calculate the degree of operating
Calculate the sales dollars needed to earn of profit of $18,000
Jason’s Ford Dealership – Monthly Data
Vehicles Sold
Average Selling Price
Average Cost
Fixed Costs
152
$22,000
$18,040
$396,000
Required
1.
2.
3.
4.
5.
6.
Contribution format income statement
Calculate the break even point in sales dollars.
Calculate the break even point in vehicles
Calculate the Margin of Safety
Calculate the degree of operating
Calculate the number of vehicles required to be sold in order to earn $35,000 of profit.