# Profit Center Planning and Analysis (ACCT2102)

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## Contents

### Cost Behavior Model

Variable costs

• Vary, in total, directly with the level of activity
• Remain constant on a per unit of activity basis
• v = variable cost per unit
• VC = total variable cost at a given level of activity

Fixed costs

• Remain constant in total over the relevant range of activity
• Vary, on a per unit of activity, inversely with the level of activity
• FC = total fixed cost

Mixed costs

• Combination of variable and fixed elements
• TC = v(x) + FC

Linearity Assumption

• Assume cost function can be modeled by a straight line (linear) within the relevant range
• The relevant range is the range of activity expected for the planning period of interest

#### Methods of Measuring Cost Functions

Engineering analysis

• Measures cost behavior according to what costs should be, not by what costs have been

Account analysis

• Refers to the accounting system for information about cost behavior

High-low analysis

• Measuring a linear-cost function from past cost data

Visual-fit analysis

• More reliable than the high-low method. Drawing a straight-line through a plot of all the available data, using judgment to fit the line as close as possible to all the plotted points

Least-squares regression analysis

• Measures a cost function more objectively than does the visual-fit method

#### Contribution Based Income Statement

The contribution based income statement organizes costs by behavior rather than by function. Below is an example of a Contribution Based I/S for a company with volume of sales equal to 1,000 units.

 Total Per Unit Percentage % Sales Revenue \$100,000 \$100.00 100 % Variable Costs \$80,000 \$80.00 80 % Contribution Margin \$20,000 \$20.00 20 % Fixed Costs \$5,000 Pretax Operating Income \$15,000

Contribution margin per unit represents the net dollar benefit of producing and selling a unit of product after accounting for variable costs. CM/Unit represents the marginal, or incremental, benefit of selling an additional unit. Similarly, the contribution margin ratio (CM%) represents the net percentage of revenue converted into contribution margin after accounting for variable cots.

### Basic Concepts of Cost-Volume-Profit (CVP) Analysis

CVP Analysis is an analytical tool used to evaluate the relationships between price, variable cost, fixed cost, volume, and profit (operating income) CVP Equations:

• R – VC – FC = pretax operating income
• p(x) - v(x) – FC = pretax operating income (useful for unit based computations)
• R – vc%(R) – FC = pretax operating income (useful for \$ based computations)
• Where:
• p = price/unit
• x = volume of activity
• R = revenue
• v = variable cost/unit
• vc% = variable cost ratio
• VC = total variable costs
• FC = total fixed costs

#### Breakeven Analysis

Breakeven is the level of activity for which total revenues equal total costs, or, profit = 0

• Breakeven is mainly used for businesses to determine whether or not they should promote a product, whether or not it would be profitable. Also it is used to determine how many of these units or products must be sold to determine profitability of a particular company.
• Breakeven (units) = FC / CM/unit
• Breakeven (\$) = FC / CM%

<quiz display=simple>

{The break-even level in both units and sales dollars would increase if fixed costs increase. |type="()"} + True - False

{The break-even level in both units and sales dollars would remain the same if variable cost per unit increases. |type="()"} - True + False

{Assume Elwood Consulting, Ltd. charges its clients \$150 per hour for consulting services. It estimates its variable costs to be \$80 per hour and its monthly fixed costs \$6,500. Determine the number of hours monthly that the company must bill to breakeven. |type="{}"} { 93 5% } hours per month. ||6500 / (150 - 80) = 93

{Assume Elwood Consulting, Ltd. charges its clients \$150 per hour for consulting services. It estimates its variable costs to be \$80 per hour and its monthly fixed costs \$6,500. Determine the monthly revenue that the company must bill to breakeven. |type="{}"} \${ 13930 5% } monthly revenue. ||(150 - 80) / 150 = 46.67% CM%, 6500 / .4667 = \$13,930

{Johnny's Barber Shop charges its clients \$30 per hair cut and beard trim. It estimates its variable costs to be \$10 per cut and its monthly fixed costs \$2,300. Determine the number of cuts that the company must perform to breakeven. |type="{}"} { 115 } cuts per month. ||2300 / (30 - 10) = 115 </quiz>

#### Operating Leverage

Operating leverage is a measure of a firm's relative dependence on fixed costs

• The highly leveraged alternative is more risky because it provides the highest possible net income and the highest possible net losses.
• The low-leveraged alternative is less risky because variations in sales lead to only a small variability in net income
• Degree of operating Leverage
• The degree of operating leverage is a measure, at a given level of sales of how percentage change in sales volume will effect profits.
• A manager can use the degree of operating leverage to quickly estimate what impact various percentage changes in sales will have on profits, without the necessity of preparing detailed income statements.
• The degree of operating leverage is not a constant. It is greatest at sales level near the break even point and decreases as sales and profit rise.

#### Assumptions of Cost-Volume-Profit CVP Analysis

A number of assumptions underlie cost-volume-profit CVP analysis:

• 1. Selling price is constant. The price of a product or service will not change as volume changes.
• 2. Costs are linear and can be accurately divided into variable and fixed elements. The variable element is constant per unit, and the fixed element is constant in total over the relevant range.
• 3. In multi-product companies, the sales mix is constant.
• 4. In manufacturing companies, inventories do not change. The number of units produced equal the number of units sold.
• 5. Inventory levels are fairly constant, with the number of units produced equaling the number of units sold. If inventory levels fluctuate, some of the variable and fixed products costs may flow into or out of inventory, with a variety of potential impacts on profitability.
• 6. Cost is classifired as either variable or fixed with respect to a single measure of the volume of output of activity.

#### Margin of Safety

• The planned unit sales less the break-even unit sales; it shows how far sales can fall below the planned level before losses occur.
• margin of safety = planned unit sales (-) break-even unit sales
• margin of safety (percentage form) = margin of safety in dollars / total budgeted or actual sales
• The larger the margin of safety, the less like it is that the company will have an operating loss.
• A small margin of safety may indicate a more risky situation.

#### Target Net Profit and an Incremental Approach

• Managers also use CVP analysis to determine the total sales, in units and dollars, needed to reach a target profit.
• Target Net Income = target sales - variable expenses - fixed expenses
• Target Sales Volume in units = (fixed expenses + target net income) / unit contribution margin
• This is virtually the same computation as used for breakeven analysis except that here a value other than zero is used for target income
• the term "Incremental Effect" refers to the change in total results (such as revenue, expenses, or income) under a new condition in comparison with some given or known condition.

#### CVP and Income Taxes

All of the CVP equations assume operating income on a before-tax basis. To incorporate income taxes into the analysis we need to define the relationship between operating income before-tax and income after-tax as follows:
Operating Income Before-Tax = Operating Income After-Tax / (1 - Tax Rate)

<quiz display=simple> {GA Consulting Associates has a target after-tax income of \$400,000 and is in the 30% corporate income tax bracket. What is their pre-tax income target? |type="()"} - \$120,000 - \$280,000 + \$571,429 - \$1,333,333 </quiz> <quiz display=simple> {Bob's Realty Company Inc. has a target after-tax income of \$1000,000 and has a 30% income tax rate. What is their pre-tax target income? |type="()"} - \$1,200,000 + \$1,428,571 - \$1,550,582 - \$2,760,138 </quiz> <quiz display=simple> {Jane's Place Inc. has a target after-tax income of \$500,000 and has a 35% income tax rate. What is their pre-tax target income? |type="()"} - \$1,043,092 - \$933,045 + \$769,231 - \$543,293 </quiz> Quiz 4 and 5 Check Figures

The link here is to an Excel spreadsheet that allows you to change input factor to see how those changes effects the financial results
CVP Example

#### Sales Mix and CVP Analysis

In a single product firm, we can take the price less variable cost per unit to determine CM/unit. For example, if p= \$5.00 and v = \$2.00, then CM/unit = \$3.00. In a single product firm, we can take the CM/unit divided by price to determine CM ratio. In this example, CM ratio = \$3.00 / \$5.00 = 60%

However, when a firm has multiple product lines or lines of business, we have a price and variable cost for each line. To apply CVP analysis we must be able to determine either the weighted average contribution margin per unit (WACM) or weighted average contribution margin ratio (WACM%). The average CM is a combination of all the prices, variable costs, and relative sales mix of the various lines.

##### Relative Sales Mix

Sales mix is the relative amount of sales that each line contributes to total sales. Sales mix can be computed based sales volume (quantity of product sold) or based on sales revenue (dollar amount of sales from each line).

Lets examine the following example. The company's I/S below is based on sales volume for segment A of 5,000 units and segment B of 1,000.

 Company Total Avg Per Unit Segment A Per Unit Segment B Per Unit Sales Revenue \$150,000 \$25.00 \$100,000 \$20.00 \$50,000 \$50.00 Variable Costs \$45,000 \$7.50 \$25,000 \$5.00 \$20,000 \$20.00 Contribution Margin \$105,000 \$17.50 \$75,000 \$15.00 \$30,000 \$30.00 Fixed Costs \$65,000 Pre-tax Income \$40,000

The sales mix, based on volume, is 83.3% segment A (5,000/6,000) and 16.7% segment B (1,000/6,000). WACM/unit can be computed one of two ways:

1. (15.00 * .833) + (30.00 * .167) = \$17.50 WACM/unit, or
2. \$105,000 / 6,000 = \$17.50 WACM/unit

Alternatively, sales mix, based on sale revenue (\$) is 66.7% segment A (100,000/150,000) and 33.3% segment B (50,000/150,000). WACM/% can be computed one of two ways: [note: segment A CM% is 75% (15.00/20.00) and segment B CM% is 60% (30.00/50.00)]

1. (75 * .667) + (60 * .333) = 70%, or
2. \$105,000 / \$150,000 = 70%

The WACM/unit and WACM% can be used to determine number of total units needed to achieve a target income, total revenue needed to achieve a target income, and other similar questions at the company level.

##### Using WACM/unit and WACM%
In the example above, if the company wants to determine their breakeven point, we can take FC / WACM/unit as \$65,000 / \$17.50 = 3,714 units in total. 83.3% (3,095) must be from segment A and 16.7% (619) from segment B.

### Theory of Constraints and Measuring Throughput

#### Theory of Constraints (TOC) Primer

The fundamental concept of Theory of Constraints (TOC), articulated by Eliyahu M. Goldratt and Jeff Cox in their 1984 book The Goal, is actually quite simple. TOC states that every organization is faced with at least one factor that limits the firm’s ability to earn profits or provide services. If this were not the case, then a for-profit firm would earn an infinite amount of profits!

Given this core concept, the manager who wants more profits must manage the constraint(s) faced by the enterprise. Most businesses can be viewed as a system of linked processes that convert inputs into sellable outputs (products or services). In TOC, an analogy can be drawn between such a system and a chain. What is the most effective means of strengthening a chain? Does one concentrate on the strongest or largest link? Or should the weakest link be improved upon first? TOC clearly indicates that the latter results in a better benefit-cost relationship.

The five key steps in implementing the concept of TOC are as follows:

1. Identify the first constraint or bottleneck in the system. Constraints may be internally or externally generated.
2. Determine how to exploit the system’s constraints. In other words, maximize the use of the constrained resource.
3. Let the constrained resource set the pace for the remaining elements of the process system. Subordinate other day-to-day operating decisions relative to use of the constrained resource.
4. Improve or expand the constrained resource so that it is no longer the bottleneck in the system.
5. Once the first constraint has been alleviated, return to the first step to identify the next constraint. This is the process of continuous improvement.

Although TOC was first developed to improve scheduling in a job-shop environment, the concepts and tools are sufficiently broad to be used in a wide variety of businesses including retail operations and service organizations. TOC can also be used in not-for-profit organizations wanting to maximize the delivery of services while consuming a minimum of resources.

TOC cannot be used with traditional cost accounting techniques such as absorption costing and standard cost variance reporting. Absorption costing and variance reporting create incentives to produce excessive inventories. Under absorption costing, building up inventories tends to reduce the apparent average cost of goods sold by spreading fixed overhead over more units of production. When production exceeds sales, the recognition of some of the fixed overhead is delayed by placing it on the balance sheet as a part of inventories rather than on the income statement as a part of cost of goods sold.

Under standard cost variance reporting, a work center with fixed labor costs can improve efficiency measures only by increasing output. Since this can happen more easily in a non-constrained process than in a constrained process, the result of building up inventories is inevitable. Instead of using absorption costing, most firms that have successfully implemented TOC use a variation of variable costing where only pure variable costs are subtracted from sales to arrive at profit margin or “throughput.” All other costs are subtracted from this margin as operating expenses. This form of variable costing is preferred over absorption costing for three primary reasons.

1. It reduces the incentives to build up inventories. The recognition of fixed overhead costs cannot be delayed – all of them are deducted as operating expenses to arrive at profit measures.
2. It is considered more useful in decisions. Variable costing is more compatible with cost-volume-profit analysis than is absorption costing.
3. It is closer to a cash flow concept of income measurement.
This modification to the management accounting and reporting system implies that there are only three ways to increase profits: increase throughput (sales less true variable costs), decrease operating expenses (any costs not considered part of throughput), or decrease investment, particularly inventories.

Resources for Theory of Constraints:
[Wikipedia]
[Value Based Management]

#### Measuring Throughput and Efficiency

This modification also suggests an important tool in evaluating the profitability of a firm’s output - throughput dollars per unit of constrained resource (sometimes referred to as a critical resource factor). Throughput per unit of critical resource factor (T/CRF) is THE measure of efficiency in a TOC model. T/CRF indicates the amount of benefit (throughput dollars) generated for each unit of resources consumed (input factor).

Although we have not explicitly addressed this in class, the model we have been using throughout our discussion is a throughput model. We have been using price less variable cost and calling it contribution margin. Thus, to apply the concept of theory of constraints we can assume that CM/CRF is equivalent to T/CRF.

Applying the concepts of TOC then becomes a straightforward extension of all of the CVP analysis we have been working on.

Example of applying the Theory of Constraints: Winston Shoe Company

#### Utilization of Constrained Resources

The Theory of Constraints (TOC) states that every organization is faced with at least one factor that limits the firm’s ability to earn profits or provide services. Given this core concept, the manager who wants more profits must manage the constraint(s) faced by the enterprise. To rank the segments in order of their contribution to profits, a measure of productivity must be used.

• Productivity = CM per unit / units of constrained resources used

<quiz display=simple> {Cut Right Cabinet Company Inc. Is located in GA and would like to know which of the following is not an internal constraint? |type="()"} - People + Cost - Marketing - Finance

{Cut Right Cabinet Company Inc. Is located in GA they have made 500 cherry kitchen cabinets because last year the consumers voted for cherry now this year they voted light oak. What external constraint is shown here? |type="()"} - Cost of raw material - Availability - Change in seasons + Consumer preferences </quiz>

### Summary of Important Formulas

#### Essential CVP Formulas

These formulas can be used to determine target volume or revenue for single segment companies or for individual segments of more complex organizations. Breakeven analysis simply uses 0 as target profit.

• Target Volume = (FC + Target before-tax Profit) / CM per unit
• Target Revenue \$ = (FC + Target before-tax Profit) / CM%
• Before-tax Profit = After-tax Profit) / (1 - Tax Rate)
• p(x) - v(x) – FC = pretax operating income (useful for unit based computations)
• R – vc%(R) – FC = pretax operating income (useful for \$ based computations)

#### Multi-segment CVP Formulas

CVP formulas for multi-segment organizations are extensions of those identified above.

• Target Volume = (FC + Target before-tax Profit) / WACM per unit
• Target Revenue \$ = (FC + Target before-tax Profit) / WACM%

where:

• WACM per unit = Total CM / Total volume
• WACM% = Total CM / Total Revenue

Sales mix is also an issue for Multi-segment analysis. Sales mix is the relative amount of sales that each line contributes to total sales. Sales mix can be computed based sales volume (quantity of product sold) or based on sales revenue (dollar amount of sales from each line).

• Volume-based sales mix = Segment i Volume / Total Volume
• used in conjunction with WACM per unit
• \$-based sales mix = Segment i Revenue / Total Revenue
• used in conjunction with WACM%

### Know what the abbreviations mean:

WACM per unit= Weighted Average Contribution Margin per unit
WACM% =Weighted Average Contribution Margin Ratio
FC = Fixed Cost
VC = Variable Cost
CM = Contribution Margin
P = Price
R = Rate
BE = Break Even
CVP = Cost Volume Profit
TOC = Theory Of Constraint
CRF = Critical Resource Factor
Some abbreviations may be left off please look in notes and in the book for more abbreviations and the meanings.