# Agenda: Cost Behavior

TM 2b-1

**AGENDA: COST BEHAVIOR**

1.Variable cost behavior.

2.Types of fixed costs: committed and discretionary.

3.Behavior of fixed costs in total and on a unit basis.

4.Mixed costs (combination of fixed and variable).

5.Scattergraph plot of a mixed cost.

6.High-low method of mixed cost analysis.

7.Least-squares regression method of mixed cost analysis.

8.Contribution income statement.

**VARIABLE COST BEHAVIOR**

Many costs can be described as variable, fixed, or mixed.

A variable cost changes in total in proportion to changes in activity; a variable cost is constant on a per-unit basis.

EXAMPLE: Each bicycle requires one bicycle chain costing $8.

**EXAMPLES OF COSTS THAT ARE NORMALLY VARIABLE WITH RESPECT TO OUTPUT VOLUME**

Merchandising company

Costs of goods (merchandise) sold

Manufacturing company

Manufacturing costs:

Prime costs:

Direct materials

Direct labor*

Variable portion of manufacturing overhead:

Indirect materials

Lubricants

Supplies

Power

Both merchandising and manufacturing companies

Selling, general, and administrative costs:

Commissions

Clerical costs, such as invoicing

Shipping costs

Service organizations

Supplies, travel, clerical

*Whether direct labor is fixed or variable will depend on the labor laws of the country, custom, and the company’s employment contracts and policies.

**FIXED COST BEHAVIOR**

A fixed cost remains constant in total amount throughout wide ranges of activity.

EXAMPLE: Fashion photographer Lori Yang rents studio spaces in a prestige location for $50,000 a year. She measures her company’s activity in terms of the number of photo sessions.

**FIXED COST BEHAVIOR (cont’d)**

A fixed cost varies inversely with activity if expressed on a per unit basis.

**TYPES OF FIXED COSTS**

•Committed fixed costs relate to investment in plant, equipment, and basic administrative structure. It is difficult to reduce these fixed costs in the short-term. Examples include:

•Depreciation on plant facilities.

•Taxes on real estate.

•Salaries of key operating personnel.

•Discretionary fixed costs arise from annual decisions by management to spend in certain areas. These costs can often be reduced in the short-term. Examples include:

•Advertising.

•Research.

•Public relations.

•Management development programs.

**TREND TOWARD FIXED COSTS**

The trend is toward greater fixed costs relative to variable costs. The reasons for this trend are:

•Increased automation of business processes.

•Shift from laborers paid by the hour to salaried knowledge workers.

MIXED COSTS

A mixed (or semi-variable) cost contains elements of both variable and fixed costs.

Example: Lori Yang leases an automated photo developer for $2,500 per year plus 2¢ per photo developed.

Equation of a straight line: Y = a + bX

Y = $2,500 + $0.02X

**MIXED COSTS (cont’d)**

A cost that is considered fixed in one company might be considered variable or mixed in another company.

**SCATTERGRAPH METHOD**

As the first step in the analysis of a mixed cost, the cost and its activity base should be plotted on a scattergraph. This helps to quickly diagnose the nature of the relation between the cost and the activity base.

Example: Piedmont Wholesale Florists has maintained records of the number of orders and billing costs in each quarter over the past several years.

Quarter / Number of Orders / Billing CostsYear 1—1st / 1,500 / $42,000

2nd / 1,900 / $46,000

3rd / 1,000 / $37,000

4th / 1,300 / $43,000

Year 2—1st / 2,800 / $54,000

2nd / 1,700 / $47,000

3rd / 2,100 / $51,000

4th / 1,100 / $42,000

Year 3—1st / 2,000 / $48,000

2nd / 2,400 / $53,000

3rd / 2,300 / $49,000

These data are plotted on the next page, with the activity (number of orders) on the horizontal X axis and the cost (billing costs) on the vertical Y axis.

**A COMPLETED SCATTERGRAPH**

The relation between the number of orders and the billing cost is approximately linear. (A straight line that seems to reflect this basic relation was drawn with a ruler on the scattergraph.)

Since a straight line seems to be a reasonable fit to the data, we can proceed to estimate the variable and fixed elements of the cost using one of the following three methods.

1)Quick-and-dirty method based on the line in the scattergraph.

2)High-low method.

3)Least-squares regression method.

**THE QUICK-AND-DIRTY METHOD**

The straight line drawn on the scattergraph can be used to make a quick-and-dirty estimate of the fixed and variable elements of billing costs.

Recall that we are trying to estimate the fixed cost, a, and the variable cost per unit, b, in the linear equation Y= a + bX.

•The vertical intercept, approximately $30,000 in this case, is a rough estimate of the fixed cost.

•The slope of the straight line is an estimate of the variable cost per unit

Select a point falling on the line (in this case 2,000 orders):

Total billing cost for 2,000 orders.... / $48,000Less fixed cost element (intercept)... / 30,000

Variable cost element for 2,000 orders / $18,000

Variable cost per unit = $18,000 ÷ 2,000 orders = $9 per order.

Therefore, the cost formula for billing costs is $30,000 per quarter plus $9 per order or:

Y = $30,000 + $9X,

where X is the number of orders.

Because of the imprecision of this method of estimating the variable and fixed cost components of a mixed cost, it is seldom used in practice.

Nevertheless, it is always a good idea to plot the data on a scattergraph before using the more precise high-low or least-squares regression methods.

**ANALYSIS OF MIXED COSTS: HIGH-LOW METHOD**

EXAMPLE: Kohlson Company has incurred the following shipping costs over the past eight months:

Units Sold / Shipping CostJanuary.. / 6,000 / $66,000

February. / 5,000 / $65,000

March... / 7,000 / $70,000

April..... / 9,000 / $80,000

May..... / 8,000 / $76,000

June.... / 10,000 / $85,000

July..... / 12,000 / $100,000

August... / 11,000 / $87,000

With the high-low method, only the periods in which the lowest activity and the highest activity occurred are used to estimate the variable and fixed components of the mixed cost.

Units Sold / Shipping CostHigh activity level, July... / 12,000 / $100,000

Low activity level, February / 5,000 / 65,000

Change...... / 7,000 / $35,000

The cost formula for shipping cost is:

Y = $40,000 + $5X

**EVALUATION OF THE HIGH-LOW METHOD**

The high-low method suffers from two major defects:

1.It throws away all but two data points.

2.The high and low volume periods are often unusual.

**LEAST-SQUARES REGRESSION METHOD**

The least-squares regression method for analyzing mixed costs uses mathematical formulas to determine the regression line that minimizes the sum of the squared “errors.”

**LEAST-SQUARES REGRESSION (cont’d)**

Example: Montrose Hospital operates a cafeteria for employees. Management would like to know how cafeteria costs are affected by the number of meals served.

Meals ServedX / Total Cost

Y

April...... / 4,000 / $9,500

May...... / 1,000 / $4,000

June...... / 3,000 / $8,000

July...... / 5,000 / $10,000

August.... / 10,000 / $19,500

September. / 7,000 / $14,000

Statistical software or a spreadsheet program can do the computations required by the least-squares method. The results in this case are:

Intercept (fixed cost)..... / $2,433Slope (variable cost)...... / $1.68

R2...... / 0.99

The fixed cost is therefore $2,433 per month and the variable cost is $1.68 per meal served, or:

Y = $2,433 + $1.68X,

where X is meals served.

R2 is a measure of the goodness of fit of the regression line. In this case, it indicates that 99% of the variation in cafeteria costs is due to the number of meals served. This suggests a very good fit.

*© The McGraw-Hill Companies, Inc., 2006. All rights reserved.*

TM 5-1

**TRADITIONAL VERSUS CONTRIBUTION INCOME STATEMENT**

(costs organized by function) / Contribution Approach

(costs organized by behavior)

Sales...... / $60,000 / Sales / $60,000

Less cost of goods sold*. / 34,000 / Less variable expenses:

Gross margin...... / 26,000 / Variable production... / $12,000

Less operating expenses: / Variable selling...... / 3,000

Selling*...... / $15,000 / Variable administrative / 1,000 / 16,000

Administrative*...... / 6,000 / 21,000 / Contribution margin.... / 44,000

Net operating income... / $5,000 / Less fixed expenses:

Fixed production..... / 22,000

Fixed selling...... / 12,000

Fixed administrative.. / 5,000 / 39,000

Net operating income.. / $5,000

* Contains both variable and fixed elements since this is the income statement for a manufacturing company. If this were a merchandising company, then the cost of goods sold would be entirely variable.

*© The McGraw-Hill Companies, Inc., 2006. All rights reserved.*