COST AND MANAGEMENT ACCOUNTING

Introduction

What is cost accounting?

The scope of cost accounting

Summary

Questions for review

Learning Objectives

Having studied this Module you should be able to:

explain the meaning and purpose of cost accounting

understand how cost accounting arises out of the need to make business decisions

differentiate between cost accounting, management accounting and financial accounting

appreciate how raw data is transformed into information

be familiar with some costing terminology

Introduction

The purpose of this Module is to introduce the subject of cost accounting, to explain its relationship to management accounting and to differentiate it from financial accounting.

The survival of any business depends on its ability to settle its debts as they fall due (liquidity) and on having products or services that obtain revenues higher than the costs incurred in producing and selling them (profitability).

The type of accounting which is concerned with recording transactions with outsiders and in determining what the business owns and what is owed to it (assets) in comparison to what it owes to the outsiders (liabilities) and to the owners of the business (capital) at any given time is termed financial accounting. Financial accounting matches the revenues earned in a period against the corresponding costs to measure the profitability of the business as a whole.

Thus, financial accounting assists in maintaining liquidity and recording overall profits of the business. Reports based on financial accounting provide useful information to users, the majority of whom are outsiders, who may be interested in the business as a whole. For instance, shareholders and creditors are only concerned with the overall profitability and viability of the business, leaving managers to focus on the profitability of individual product or service lines, using cost and management accounting techniques.

Accounting is multidisciplinary, encompassing financial accounting, cost accounting, management accounting, finance and taxation. The focus of accounting has developed over time from recording financial transactions to comply with legal requirements and for the purpose of a periodic profitability statement (profit and loss account) and position statement of assets, liabilities and capital (balance sheet) to the provision of cost data to assist management in the planning and control of activities and for the purpose of decision making.

Information on the cost incurred in producing and selling individual products or services is not readily available from the financial accounting records. When a business produces different products or services, without such information its managers cannot make sensible decisions about controlling the costs and maximizing the profits earned from a particular line of products or services. To obtain this information promptly, a mechanism of recording transactions within the business is required.

Cost accounting provides such a mechanism to record the cost of resources used by an individual product/service line, either by identifying the direct connection (cost allocation) or by sharing out the common costs on a fair basis (cost apportionment).

The role of cost accounting, a discipline arising out of the costing and estimating practices in engineering, is vital to the modern business facing increasing competition. Advances in transportation technology have eroded the geographical barriers to competition, while advances in communication technology have increased consumer awareness about alternative suppliers and their pricing.

Increasingly, businesses are facing the challenge of operating in a ‘cost continuous’ environment with little buffer to absorb poor cost management. Cost accounting assists in cost management by offering various techniques for control and reduction of the different types of costs incurred by a business.

It also helps in making the best use of the available resources.

The discipline of management accounting emerged as a natural progression from cost accounting as the information requirements of business managers were better understood and increasingly catered for by accountants.

Management accounting is more strategic in nature and encompasses various accounting disciplines such as cost accounting, financial accounting, taxation and financial management as well as behavioral psychology, management science and systems theory. This Program focuses on Cost Accounting, rather than concentrating on management accounting in great depth; however, as management accounting employs cost accounting data, there is an inevitable overlap between the two.

What is Cost Accounting?

Cost accounting is extensively used in a wide variety of businesses, including hospitals, local government, banking, retail and manufacturing. The cost accounting system is the basis of an internal financial information system to assist managers to make business decisions.

The types of business decision will vary with the nature of the organization, but typically these could include:-

Whether to provide a new service

Whether to make or buy a product

The extent to which selling prices may be altered

Whether to manufacture a new type of product

Whether to increase the levels of service provided

In an intensely competitive global marketplace, without an effective cost accounting system, it is doubtful whether a business could survive. The ability to determine the costs of products using product costing techniques, planning and controlling the enterprise using budgeting techniques and making decisions about the future of the organization using appraisal techniques is paramount.

It is important to realize that no two businesses are the same. As a consequence there is no uniform costing system that can be implemented for all businesses. Appropriate cost accounting techniques may be selected from a range of techniques and applied according to circumstances.

There is no law or statute governing the application of costing techniques. Contrast this with financial accounting, where all limited companies are required by law to produce specific prescribed financial statements.

What are the commonly used Techniques?

Cost accounting techniques arise because of specific information requirements by management. In some cases this could relate to how much a product costs to manufacture or how much a service costs to deliver. Product costing/service costing techniques address this question.

Budgeting techniques assist managers to quantify their future plans in monetary terms and enable comparisons of actual financial performance with planned. Where actual performance deviates from planned this may be recorded and subsequently investigated to ascertain the reasons why this is the case.

Management may also wish to evaluate the way a particular product/service has performed in the past to determine whether the organization is making best use of the resources available to it, and would also be interested in the future performance of existing and new products or services. In making an assessment as to the viability of a particular product or service, the level of risk associated with it would also have to be assessed and this compared with the possible rewards from the venture, with due regard to management’s attitude to differing levels of risk.

Appraisal techniques assist management to address this matter.

The techniques introduced in subsequent Modules/Chapters will be introduced under the broad headings of product costing, budgeting and appraisal. They arise primarily out of the requirement to address the information needs of the organization and provide the data for subsequent analysis by management. These three headings reflect the activities of managers: they plan (budget), measure the results of their plans (record actual product/service costs) and assess the success of those plans (appraisal).

The Scope of Cost Accounting

As we have explained, cost accounting techniques arise because of specific information requirements by management. Examples of information required by management and information provided by a typical costing system are shown in the Table below.

Summary

Cost accounting comprises a range of techniques for the purpose of:

Cost ascertainment,

Cost control and cost reduction.

Cost accounting systems and financial accounting systems are different.

Cost accounting is in effect for internal use. Financial accounting forms the basis of external reporting and is for stewardship purposes.

Cost accounting systems provide information to management for planning, control and decision making.

Financial accounting is concerned with types of expenditure for the purpose of an overall profitability statement and statement of assets and liabilities.

Cost accounting is dealt with in this text within three broad headings of product costing, budgeting and appraisal.

They arise primarily out of the need to address the information needs of the organization.

Costing information is not mutually exclusive. It may be used for many purposes.

Questions for Review

1. What is the purpose of cost accounting?

2. Discuss the similarities and differences between cost accounting and financial accounting.

3. Discuss the types of information needs that have led to the development of:

a. Product costing techniques

b. Budgeting techniques

c. Appraisal techniques

4. Give two examples of where ‘cost per unit of output’ could satisfy management’s information needs.

5. Give three examples of business decisions where cost accounting information could prove useful.

For Further Reading, Research and Reference

Essential Cost Accounting Terminology

Cost accounting terminology

Basic classification of costs

Cost accounting terminology

Determination of total cost

Cost Behavior

What is cost behavior?

Distinguishing between different cost classifications

Cost prediction

Cost behavior analysis: the accounting model vs. the economists’ model

Accounting for Labor Costs

The significance of labor costs

Distinguishing between different remuneration methods

Labor cost data

Accounting for Material Costs

What is material pricing?

Use of different pricing methods

Stock valuation

Treatment of other costs

Absorption costing

What is absorption costing?

The inclusion of overhead into cost units via cost centers

Non-manufacturing overhead

Appraisal of absorption costing

Activity Based Costing

What is activity based costing?

Marginal Costing Systems

What is marginal costing?

The treatment of overhead

Revenue statements in a marginal costing format

The role of contribution

Breakeven (CVP) analysis

Marginal costing vs. absorption (full) costing

Marginal Costing Short-term Decision Making

Planning and Budgeting

What is a budget?

Budgetary control Budgeting appraisal

Zero based budgeting

Activity based budgeting

Standard Costing and Variance Analysis

What is a standard cost?

What is variance analysis?

Variance calculation

Reasons for variances

Variance investigation

Appraisal of standard costing and variance analysis

Capital Investment Appraisal

What is capital investment appraisal?

Conventional capital investment appraisal techniques

Discounted cash flow appraisal techniques

Risk and uncertainty

MANAGERIAL & COST ACCOUNTING

Introduction to Activity Based Costing

Activity based costing (ABC) assigns manufacturing overhead costs to products in a more logical manner than the traditional approach of simply allocating costs on the basis of machine hours. Activity based costing first assigns costs to the activities that are the real cause of the overhead. It then assigns the cost of those activities only to the products that are actually demanding the activities.

Let's discuss activity based costing by looking at two products manufactured by the same company. Product 124 is a low volume item which requires certain activities such as special engineering, additional testing, and many machine setups because it is ordered in small quantities. A similar product, Product 366, is a high volume product—running continuously—and requires little attention and no special activities. If this company used traditional costing, it might allocate or "spread" all of its overhead to products based on the number of machine hours. This will result in little overhead cost allocated to Product 124, because it did not have many machine hours. However, it did demand lots of engineering, testing, and setup activities. In contrast, Product 366 will be allocated an enormous amount of overhead (due to all those machine hours), but it demanded little overhead activity. The result will be a miscalculation of each product's true cost of manufacturing overhead. Activity based costing will overcome this shortcoming by assigning overhead on more than the one activity, running the machine.

Activity based costing recognizes that the special engineering, special testing, machine setups, and others are activities that cause costs—they cause the company to consume resources. Under ABC, the company will calculate the cost of the resources used in each of these activities. Next, the cost of each of these activities will be assigned only to the products that demanded the activities. In our example, Product 124 will be assigned some of the company's costs of special engineering, special testing, and machine setup. Other products that use any of these activities will also be assigned some of their costs. Product 366 will not be assigned any cost of special engineering or special testing, and it will be assigned only a small amount of machine setup.

Activity based costing has grown in importance in recent decades because (1) manufacturing overhead costs have increased significantly, (2) the manufacturing overhead costs no longer correlate with the productive machine hours or direct labor hours, (3) the diversity of products and the diversity in customers' demands have grown, and (4) some products are produced in large batches, while others are produced in small batches.

Activity Based Costing with Two Activities

Let’s illustrate the concept of activity based costing by looking at two common manufacturing activities: (1) the setting up of a production machine for running batches of products, and (2) the actual production of the units of product.

We will assume that a company has annual manufacturing overhead costs of $2,000,000—of which $200,000 is directly involved in setting up the production machines. During the year the company expects to perform 400 machine setups. Let’s also assume that the batch sizes vary considerably, but the setup efforts for each machine are similar.

The cost per setup is calculated to be $500 ($200,000 of cost per year divided by 400 setups per year). Under activity based costing, $200,000 of the overhead will be viewed as a batch-level cost. This means that $200,000 will first be allocated to batches of products to be manufactured

(referred to as a Stage 1 allocation), and then be assigned to the units of product in each batch (referred to as Stage 2 allocation). For example, if Batch X consists of 5,000 units of product, the setup cost per unit is $0.10 ($500 divided by 5,000 units). If Batch Y is 50,000 units, the cost per unit for setup will be $0.01 ($500 divided by 50,000 units). For simplicity, let’s assume that the remaining $1,800,000 of manufacturing overhead is caused by the production activities that correlate with the company’s 100,000 machine hours.

For our simple two-activity example, let's see how the rates for allocating the manufacturing overhead would look with activity based costing and without activity based costing:

With ABC Without ABC

Mfg overhead costs assigned to setups

$200,000 $–0–

Number of setups 400Not applicable

    Mfg overhead cost per setup $500 $–0–

Total manufacturing overhead costs

$2,000,000 $2,000,000

Less: Cost traced to machine setups

200,000 –0–

Mfg O/H costs allocated on machine hours

$1,800,000 $2,000,000

Machine hours (MH) 100,000 100,000

    Mfg overhead costs per MH $18 $20

Mfg Overhead Cost Allocations$500 setup cost per batch + $18 per MH

S$20 per MH

What impact these different allocation techniques and overhead rates would have on the per unit cost of a specific unit of output. Assume that a company manufactures a batch of 5,000 units and it produces 50 units per machine hour, here is how the cost assigned to the units with activity based costing and without activity based costing compares:

With ABC Without ABC

Mfg overhead for setting up machine $500 $–0–

No. of units in batch 5,000 Not applicable

Mfg O/H caused by Setup – Per Unit $0.10 Not applicable

Mfg overhead costs per machine hour $18 $20

No. of units produced per machine hour 50 50

Mfg O/H caused by Production – Per Unit $0.36 $0.40

Total Mfg O/H Allocated – Per Unit $0.46 $0.40

If a company manufactures a batch of 50,000 units and produces 50 units per machine hour, here is how the cost assigned to the units with ABC and without ABC compares:

With ABC Without ABC

Mfg overhead for setting up machine $500 $–0–

No. of units in batch 50,000 Not applicable

Mfg O/H caused by Setup – Per Unit $0.01 Not applicable

Mfg overhead costs per machine hour $18 $20

No. of units produced per machine hour 50 50

    Mfg O/H caused by Production – Per Unit $0.36 $0.40

Total Mfg O/H Allocated – Per Unit $0.37 $0.40

As the tables above illustrate, with activity based costing the cost per unit decreases from $0.46 to $0.37 because the cost of the setup activity is spread over 50,000 units instead of 5,000 units. Without ABC, the cost per unit is $0.40 regardless of the number of units in each batch. If companies base their selling prices on costs, a company not using an ABC approach might lose the large batch work to a competitor who bids a lower price based on the lower, more accurate overhead cost of $0.37. It’s also possible that a company not using ABC may find itself being the low bidder for manufacturing small batches of product, since its $0.40 is lower than the ABC model of $0.46 for a batch size of 5,000 units. With its bid price based on manufacturing overhead of $0.40—but a true cost of $0.46—the company may end up doing lots of production for little or no profit.

Our example with just two activities (production and setup) illustrates how the cost per unit using the activity based costing method is more accurate in reflecting the actual efforts associated with production. As companies began measuring the costs of activities (instead of focusing on the accountant’s departmental classifications), they began using ABC cost information to practice activity based management. For example, with the cost of setting up a machine now being measured and discussed, managers began to ask questions such as:

Why is the cost of setting up a production machine so expensive? What can be done to reduce the setup cost? If the setup costs cannot be reduced, are the selling prices adequate to cover all of the company’s costs—including the setup cost that was previously buried in the overall machine-hour overhead rate?

Q&A: Activity Based Costing

What is cost allocation?

What is an indirect cost?

What is the difference between normal costing and standard costing?

Are direct costs fixed and indirect costs variable?

How do I compute the product cost per unit?

Are insurance premiums a fixed cost?

What is a burden rate in inventory?

Under accrual accounting, how are worker comp premiums handled?

What is meant by over absorbed?

Why would the cost behavior change outside of the relevant range of activity?

What is Cost Allocation?

Cost allocation is the assigning of a common cost to several cost objects. For example, a company might allocate or assign the cost of an expensive computer system to the three main areas of the company that use the system. A company with only one electric meter might allocate the electricity bill to several departments in the company.

Allocation implies that the assigning of the cost is somewhat arbitrary. Some people describe the allocation as the spreading of cost, because of the arbitrary nature of the allocation. Efforts have been made over the years to improve the bases for allocation. In manufacturing, the overhead allocations have moved from plant-wide rates to departmental rates, from direct labor hours to machine hours to activity based costing. The goal is to allocate or assign the costs based on the root causes of the common costs instead of merely spreading the costs.

What is an Indirect Cost?

An indirect cost is a cost that is not directly traceable to a cost object. Rather, the cost is common to several objects and requires an allocation.

For example, the depreciation of the factory building is an indirect cost of manufacturing products. The reason is that the annual cost of the factory building is not directly traceable to a specific unit of product manufactured during the year. The depreciation will be included in manufacturing overhead which is allocated to the units of  product manufactured during the year.

What is the Difference between Normal Costing and Standard Costing?

Normal costing is used to value manufactured products with the actual materials costs, the actual direct labor costs, and manufacturing overhead based on a predetermined manufacturing overhead rate. These three costs are referred to as product costs and are used for the cost of goods sold and for inventory valuation. If there is a difference between 1) the overhead costs assigned or applied to products, and 2) the overhead costs actually incurred, the difference is referred to as a variance. If the amount of the variance is not significant, it will usually be assigned to the cost of goods sold. If the variance is significant, it should be prorated to the cost of goods sold and to the work in process and finished goods inventories.

Standard costing values its manufactured products with a predetermined materials cost, a predetermined direct labor cost, and a predetermined manufacturing overhead cost. These standard costs will be used for valuing the manufacturer’s cost of goods sold and inventories. If the actual costs vary only slightly from the standard costs, the resulting variances will be assigned to the cost of goods sold. If the variances are significant, they should be prorated to the cost of goods sold and to the inventories.

Are Direct Costs Fixed and Indirect Costs Variable?

Direct product costs such as raw materials are variable costs. Variable product costs increase in total as more units of products are manufactured.

Costs that are direct to a department could be variable or fixed. For example, a supervisor in the painting department would be a direct cost to the painting department. Since the supervisor’s salary is likely to be the same amount each month regardless of the quantity of products manufactured, it is a fixed cost to the department. The supplies furnished to the painting department will be a direct cost to the department, but will be a variable cost to the department if the total amount of supplies used in the department increases as the volume or activity in the department increases.

An indirect product cost is the electricity used to operate a production machine. The cost of the electricity is variable because the total electricity used is greater when more products are manufactured on the machine. Depreciation on the production machine is also an indirect product cost, except it is usually a fixed cost. That is, the machine’s total depreciation expense is the same each year regardless of volume produced on the machine.

As you can see, costs can be direct and indirect depending on the cost object: product, department, and others such as division, customer, geographic market. The cost is fixed if the total amount of the cost does not change as volume changes. If the total cost does change in proportion to the change in the activity or volume, it is a variable cost.

How do I Compute the Product Cost Per Unit?

In accounting, we define the product cost as the direct material, direct labor, and manufacturing overhead. Costs such as advertising, preparing invoices, delivery expense, office salaries, office rent and utilities, and interest on loans are examples of expenses that are not considered to be product costs. Rather, these costs are expensed immediately to the period instead of being assigned to a product.

To be profitable, a company must have its selling prices large enough to cover both the product costs of the units sold and the period expenses.

The product cost is used for valuing the inventory and for determining the cost of goods sold. Since some of the manufacturing overhead costs are fixed in total (factory rent, factory depreciation, factory managers’ salaries), the per unit cost of a product will depend upon the number of units manufactured during a given year. In other words, the cost of a product is not know with precision, even though accountants will compute the per unit cost to the nearest penny.

Are Insurance Premiums a Fixed Cost?

The cost of the insurance premiums for a company’s property insurance is likely to be a fixed cost. The cost of worker compensation insurance is likely to be a variable cost. Whether a cost is a fixed cost, a variable cost, or a mixed cost depends on the independent variable.

Let’s illustrate this by looking at the cost of property insurance. The cost of insuring the factory building is a fixed cost when the independent variable is the number of units produced within the factory. In other words, the factory’s property insurance might be $6,000 per year whether its output is 2 million units, 3 million units, or 5 million units. On the other hand, if the independent variable is the replacement cost of the factory buildings, the insurance cost will be a variable cost. The reason is the insurance cost on $12 million of factory buildings will be more than the insurance cost on $9 million of factory buildings, and less than the insurance premiums on $18 million of factory buildings.

In the case of worker compensation insurance, the cost will vary with the amount of payroll dollars (excluding overtime premium) in each class of workers. For example, if the worker comp premiums are $5 per $100 of factory labor cost, then the worker comp premiums will be variable with respect to the dollars of factory labor cost. If the units of output in the factory correlate with the direct labor costs, then the worker compensation cost will also be variable with respect to the number of units produced. On the other hand, the worker compensation cost for the office staff is usually a much smaller rate and that worker compensation cost will not be variable with respect to the number of units of output in the factory. However, the worker compensation cost of the office staff will be variable with respect to the amount of office staff salaries and wages.

What is a Burden Rate in Inventory?

I assume that the burden rate in inventory refers to a manufacturer’s indirect manufacturing costs, which are also referred to as factory overhead, indirect production costs, and burden. In the U.S., a manufactured product’s cost consists of direct materials, direct labor, and manufacturing overhead. Since manufacturing overhead is an indirect cost, it is usually assigned or allocated through an overhead rate or burden rate. Two examples of an overhead or burden rate are 1) a percentage of direct labor, and 2) an hourly cost rate assigned on the basis of machine hours.

A product’s manufacturing cost, consisting of direct materials, direct labor and manufacturing overhead, is used to report the cost of goods sold and also the cost of units in inventory. Therefore, if you look at the detail of a product’s inventory cost, you may see the manufacturing overhead being assigned or applied to the unit through a burden rate.

Under accrual accounting, how are worker comp premiums handled?

Worker comp insurance premiums should be charged to the areas where the related wages and salaries are charged.

Let’s assume that the net cost of worker comp insurance after discounts and dividends is 5% of the wages and salaries of direct and indirect manufacturing employees. If for the month of January the direct labor is $40,000, then $2,000 of the worker comp cost should be included as direct labor. If indirect labor for January is $60,000 then $3,000 of worker comp cost should be included as the cost of the indirect labor.

If the general office worker comp rates are 0.2% of the general office wages and salaries, then 0.2% of January’s general office wages and salaries will be expensed as worker comp insurance expense.

If the employer remits each month’s worker comp cost to its insurance company each accounting period, there will be no prepaid insurance nor will there be a liability for accrued worker comp expense.

If the employer remits worker comp premiums to the insurance company in advance of the cost associated with wages and salaries, the amount that is prepaid as of the balance sheet date should be reported as Prepaid Insurance, a current asset. If the employer has remitted less than the worker comp cost associated with the wages and salaries, the amount owed to the insurance company as of the balance sheet date is reported as a current liability such as Accrued Worker Comp Payable.

What is meant by Over Absorbed?

Over absorbed is usually used in the context of a manufacturer’s production overhead costs. Since manufacturing overhead costs are not directly traceable to products, they need to be allocated, assigned, or applied to the products through an overhead rate. We also state that the products absorb the overhead costs through the overhead rate.

The overhead rate is normally a predetermined rate—meaning that it was calculated prior to the start of the accounting year by using 1) the expected amount of overhead costs, and 2) the expected volume of production. Because of these two estimates, it is unlikely that the amount of overhead allocated, applied, assigned, or absorbed will be equal to the actual overhead costs incurred.

If the actual products manufactured are assigned or absorb more overhead through the overhead rate than the actual amount of overhead costs incurred, the products have over absorbed the overhead costs.

At the end of the accounting year, the amount of the over applied, over assigned, or over absorbed overhead is often credited to the cost of goods sold. The reasons are 1) the over absorbed amount is not significant, and 2) most of the products absorbing too much overhead costs have been sold. If the over absorbed amount is significant, then the amount over absorbed must be prorated or allocated as a reduction to the cost of the inventories and to the cost of goods sold based on where the over absorbed overhead costs are residing at the end of the accounting year.

Why would the Cost Behavior Change Outside of the Relevant Range of Activity?

Cost behavior often changes outside of the relevant range of activity due to a change in the fixed costs. When volume increases to a certain point, more fixed costs will have to be added. When volume shrinks significantly, some fixed costs could be eliminated.

Here’s an illustration. A company manufactures products in its 100,000 square foot plant. The company’s depreciation on the plant is $1,000,000 per year. The capacity of the plant is 500,000 units of output and its normal output is 400,000 units per year. When the company is manufacturing between 300,000 and 500,000 units, it needs salaried managers earning $400,000 per year. Below 300,000 units of output, some of the salaried manager positions would be eliminated. Above 500,000 units, the company will need to add plant space and managers.

For this example, the relevant range is between 300,000 units and 500,000 units of output per year. In that range the total of the two fixed costs is $1,400,000 per year. Below 300,000 units, the fixed costs will drop to less than $1,400,000 because some salaries will be eliminated and some of the space might be rented. When the volume exceeds 500,000 units per year, the company will need to add fixed costs because of the additional space and the additional managers. Perhaps the total fixed costs will be $2,000,000 for output between 500,000 units and 700,000 units.

A person starting a new business often asks, "At what level of sales will my company make a profit?" Established companies that have suffered through some rough years might have a similar question. Others ask, "At what point will I be able to draw a fair salary from my company?" Our discussion of break-even point and break-even analysis will provide a thought process that may help to answer those questions and to provide some insight as to how profits change as sales increase or decrease.

Frankly, predicting a precise amount of sales or profits is nearly impossible due to a company's many products (with varying degrees of profitability), the company's many customers (with varying demands for service), and the interaction between price, promotion and the number of units sold. These and other factors will complicate the break-even analysis.

In spite of these real-world complexities, we will present a simple model or technique referred to by several names: break-even point, break-even analysis, break-even formula, break-even point formula, break-even model, cost-volume-profit (CVP) analysis, or expense-volume-profit (EVP) analysis. The latter two names are appealing because the break-even technique can be adapted to determine the sales needed to attain a specified amount of profits. However, we will use the terms break-even point and break-even analysis.

To assist with our explanations, we will use a fictional company Oil Change Co. (a company that provides oil changes for automobiles). The amounts and assumptions used in Oil Change Co. are also fictional.

Expense Behavior

At the heart of break-even point or break-even analysis is the relationship between expenses and revenues. It is critical to know how expenses will change as sales increase or decrease. Some expenses will increase as sales increase, whereas some expenses will not change as sales increase or decrease.

Variable Expenses

Variable expenses increase when sales increase. They also decrease when sales decrease.

At Oil Change Co. the following items have been identified as variable expenses. Next to each item is the variable expense per car or per oil change:

Motor oil $ 5.00

Oil filter 3.00

Grease, washer fluid 0.50

Supplies 0.20

Disposal service       0.30

Total variable expenses per car $ 9.00

The other expenses at Oil Change Co. (rent, heat, etc.) will not increase when an additional car is serviced.

For the reasons shown in the above list, Oil Change Co.'s variable expenses will be $9 if it services one car, $18 if it services two cars, $90 if it services 10 cars, $900 if it services 100 cars, etc.

Fixed Expenses

Fixed expenses do not increase when sales increase. Fixed expenses do not decrease when sales decrease. In other words, fixed expenses such as rent will not change when sales increase or decrease.

At Oil Change Co. the following items have been identified as fixed expenses. The amount shown is the fixed expense per week:

Labor including payroll taxes and benefits $1,200

Rent and utilities for the building it uses 700

Depreciation, office and professional, training, other           500

Total fixed expenses per week $2,400

Mixed Expenses

Some expenses are part variable and part fixed. These are often referred to as mixed or semi-variable expenses. An example would be a salesperson's compensation that is composed of a salary portion (fixed expense) and a commission portion (variable expense). Mixed expenses could be split

into two parts. The variable portion can be listed with other variable expenses and the fixed portion can be included with the other fixed expenses.

Revenues or Sales

Revenues (or sales) at Oil Change Co. are the amounts earned from servicing cars. Oil Change Co. charges one flat fee of $24 for performing the oil change service. For $24 the company changes the oil and filter, adds needed fluids, adds air to the tires, and inspects engine belts.

At the present time no other service is provided and the $24 fee is the same for all automobiles regardless of engine size.

As the result of its pricing, if Oil Change Co. services 10 cars its revenues (or sales) are $240. If it services 100 cars, its revenues will be $2,400.

Q&A: Break-Even Point:

o What is the margin of safety?

o How much of the contribution margin is profit on units sold in excess of the break-even point?

o Are direct costs fixed and indirect costs variable?

o What happens when the high low method ends up with a negative amount?

o What is the difference between gross margin and contribution margin?

o Why does the fixed cost per unit change?

o Are insurance premiums a fixed cost?

o How do we deal with a negative contribution margin ratio when calculating our break-even

point?

o Why would the cost behavior change outside of the relevant range of activity?

o Is the cost of land, buildings, and machinery a fixed cost?

What is the Margin of Safety?

Margin of safety is used in break-even analysis to indicate the amount of sales that are above the break-even point. In other words, the margin of safety indicates the amount by which a company’s sales could decrease before the company will become unprofitable.

How much of the contribution margin is profit on units sold in excess of the break-even point?

After the break-even point is reached, the entire contribution margin on the next units sold will be profit…provided the total fixed costs and expenses do not increase.

The reason lies in the definition of contribution margin: selling price minus the variable costs and expenses. Once the contribution margins have covered the total amount of fixed costs and expenses, the entire contribution margin on the next units will go to profit.

Are Direct Costs Fixed and Indirect Costs Variable?

Direct product costs such as raw materials are variable costs. Variable product costs increase in total as more units of products are manufactured.

Costs that are direct to a department could be variable or fixed. For example, a supervisor in the painting department would be a direct cost to the painting department. Since the supervisor’s salary is likely to be the same amount each month regardless of the quantity of products manufactured, it is a fixed cost to the department. The supplies furnished to the painting department will be a direct cost to the department, but will be a variable cost to the department if the total amount of supplies used in the department increases as the volume or activity in the department increases.

An indirect product cost is the electricity used to operate a production machine. The cost of the electricity is variable because the total electricity used is greater when more products are manufactured on the machine. Depreciation on the production machine is also an indirect product cost, except it is usually a fixed cost. That is, the machine’s total depreciation expense is the same each year regardless of volume produced on the machine.

As you can see, costs can be direct and indirect depending on the cost object: product, department, and others such as division, customer, geographic market. The cost is fixed if the total amount of the cost does not change as volume changes. If the total cost does change in proportion to the change in the activity or volume, it is a variable cost.

What Happens when the High Low Method ends up with a Negative Amount?

The high low method of determining the fixed and variable portions of a mixed cost relies on only two sets of data: 1) the costs at the highest level of activity, and 2) the costs at the lowest level of activity. If either set of data is flawed, the calculation can result in an unreasonable, negative amount of fixed cost.

To illustrate the problem, let’s assume that the total cost is $1,200 when there are 100 units of product manufactured, and $6,000 when there are 400 units of product are manufactured. The high low method computes the variable cost rate by dividing the change in the total costs by the change in the number of units of manufactured. In other words, the $4,800 change in total costs is divided by the change in units of 300 to yield the variable cost rate of $16 per unit of product. Since the fixed costs are the total costs minus the variable costs, the fixed costs will be calculated to a negative $400. This unacceptable answer results from total costs of $1,200 at the low point minus the variable costs of $1,600 (100 units times $16), or total costs of $6,000 at the high point minus the variable costs of $6,400 (400 units times $16).

The negative amount of fixed costs is not realistic and leads me to believe that either the total costs at either the high point or at the low point are not representative. This brings to light the importance of plotting or graphing all of the points of activity and their related costs before using the high low method. (The number of units uses the scale on the x-axis and the related total cost at each level of activity uses the scale on the y-axis.) It is possible that at the highest point of activity the costs were out of line from the normal relationship—referred to as an outlier. You may decide to use the second highest level of activity, if the related costs are more representative.

If the $6,000 of cost at the 400 units of activity is an outlier, you might select the next highest activity of 380 units having total costs of $4,000. Now the variable rate will be the change in total costs of $2,800 ($4,000 minus $1,200) divided by the change in the units manufactured of 280 (380 minus 100) for a variable rate of $10 per unit of product. Using the variable rate of $10 per unit manufactured will result in the fixed costs being a positive $200. The positive $200 of fixed costs is calculated at either 1) the low activity: total costs of $1,200 minus the variable costs of $1,000 (100 units at $10); or at 2) the high activity: total costs of $4,000 minus the variable costs of $3,800 (380 units at $10).

What is the Difference between Gross Margin and Contribution Margin?

Gross Margin is the Gross Profit as a percentage of Net Sales. The calculation of the Gross Profit is: Sales minus Cost of Goods Sold. The Cost of Goods Sold consists of the fixed and variable product costs, but it excludes all of the selling and administrative expenses.

Contribution Margin is Net Sales minus the variable product costs and the variable period expenses. The Contribution Margin Ratio is the Contribution Margin as a percentage of Net Sales. 

Let’s illustrate the difference between gross margin and contribution margin with the following information: company had Net Sales of $600,000 during the past year. Its inventory of goods was the same quantity at the beginning and at the end of year. Its Cost of Goods Sold consisted of $120,000 of variable costs and $200,000 of fixed costs. Its selling and administrative expenses were $40,000 of variable and $150,000 of fixed expenses. 

The company’s Gross Margin is: Net Sales of $600,000 minus its Cost of Goods Sold of $320,000 ($120,000 + $200,000) for a Gross Profit of $280,000 ($600,000 - $320,000). The Gross Margin or Gross Profit Percentage is the Gross Profit of $280,000 divided by $600,000, or 46.7%.

The company’s Contribution Margin is: Net Sales of $600,000 minus the variable product costs of $120,000 and the variable expenses of $40,000 for a Contribution Margin of $440,000. The Contribution Margin Ratio is 73.3% ($440,000 divided by $600,000).

Why does the Fixed Cost Per Unit Change?

Fixed costs such as rent or a supervisor’s salary will not change in total within a reasonable range of volume or activity. For example, the rent might be $2,500 per month and the supervisor’s salary might be $3,500 per month. This total fixed cost of $6,000 per month will be the same whether the volume is 3,000 units or 4,000 units.

On the other hand, the fixed cost per unit will change as the level of volume or activity changes. Using the amounts above, the fixed cost per unit is $2 when the volume is 3,000 units ($6,000 divided by 3,000 units). When the volume is 4,000 units, the fixed cost per unit is $1.50 ($6,000 divided by 4,000 units).

Are Insurance Premiums a Fixed Cost?

The cost of the insurance premiums for a company’s property insurance is likely to be a fixed cost. The cost of worker compensation insurance is likely to be a variable cost. Whether a cost is a fixed cost, a variable cost, or a mixed cost depends on the independent variable.

Let’s illustrate this by looking at the cost of property insurance. The cost of insuring the factory building is a fixed cost when the independent variable is the number of units produced within the factory. In other words, the factory’s property insurance might be $6,000 per year whether its output is 2 million units, 3 million units, or 5 million units. On the other hand, if the independent variable is the replacement cost of the factory buildings, the insurance cost will be a variable cost. The reason is the insurance cost on $12 million of factory buildings will be more than the insurance cost on $9 million of factory buildings, and less than the insurance premiums on $18 million of factory buildings.

In the case of worker compensation insurance, the cost will vary with the amount of payroll dollars (excluding overtime premium) in each class of workers. For example, if the worker comp premiums are $5 per $100 of factory labor cost, then the worker comp premiums will be variable with respect to the dollars of factory labor cost. If the units of output in the factory correlate with the direct labor costs, then the worker compensation cost will also be variable with respect to the number of units produced. On the other hand, the worker compensation cost for the office staff is usually a much smaller rate and that worker compensation cost will not be variable with respect to the number of units of output in the factory. However, the worker compensation cost of the office staff will be variable with respect to the amount of office staff salaries and wages.

As you have seen, determining which costs are fixed and which are variable can be a bit tricky.

How do we Deal with a Negative Contribution Margin Ratio when Calculating Our Break-Even Point?

The negative contribution margin ratio indicates that your variable costs and expenses exceed your sales. In other words, if you increase your sales in the same proportion as the past, you will experience larger losses.

My recommendation is to calculate the contribution margin and contribution margin ratio for each product (or service) that you offer. I suspect that some of your items have positive contribution margins, but the products with negative contribution margins are greater. You must get into the details.

You also need to look at each of your customers. Perhaps some customers are buying in huge quantities, but those sales are not profitable. See which customers have positive contribution margins.

By definition, the ways to eliminate the negative contribution margin are to 1) raise selling prices, 2) reduce variable costs, or 3) do some combination of the first two. If customers will not accept price increases in order for you to cover your variable costs, you are probably better off not having the sales. Remember that after covering the variable costs, those selling prices must then cover the fixed costs and expenses. A total negative contribution margin means your loss will be larger than the amount of the fixed costs and expenses.

When setting prices or bidding for new work, you must think of the bottom line—profits. Many people focus too much on the top line—sales. 

Why would the Cost Behavior Change Outside of the Relevant Range of Activity?

Cost behavior often changes outside of the relevant range of activity due to a change in the fixed costs. When volume increases to a certain point, more fixed costs will have to be added. When volume shrinks significantly, some fixed costs could be eliminated.

Here’s an illustration. A company manufactures products in its 100,000 square foot plant. The company’s depreciation on the plant is $1,000,000 per year. The capacity of the plant is 500,000 units of output and its normal output is 400,000 units per year. When the company is manufacturing between 300,000 and 500,000 units, it needs salaried managers earning $400,000 per year. Below 300,000 units of output, some of the salaried manager positions would be eliminated. Above 500,000 units, the company will need to add plant space and managers.

For this example, the relevant range is between 300,000 units and 500,000 units of output per year. In that range the total of the two fixed costs is $1,400,000 per year. Below 300,000 units, the fixed costs will drop to less than $1,400,000 because some salaries will be eliminated and some of the space might be rented. When the volume exceeds 500,000 units per year, the company will need to add fixed costs because of the additional space and the additional managers. Perhaps the total fixed costs will be $2,000,000 for output between 500,000 units and 700,000 units.

Is the Cost of Land, Buildings, and Machinery a Fixed Cost?

Some people refer to land, buildings, and machinery as fixed assets. They are also referred to as plant assets, or as property, plant, and equipment.

The depreciation expense on the buildings and machinery is often viewed as a fixed cost or fixed expense. Hence, in the calculation of the break-even point, the annual depreciation expense on the fixed assets other than land is part of the fixed costs or fixed expenses. There is no depreciation of land.

Businesses often face the need to spend large amounts of money on assets that will be functional for many years. Here are a few examples:

Equipment to improve an unsafe work situation or to protect the environment

Equipment to test the consistency of products as required by the customer

Equipment to package, label, and ship products according to the customer’s specifications

Equipment to reduce labor costs and improve the quality of products

Purchase of a building instead of leasing space

Expenditures made for long-term assets are referred to as capital expenditures and are recorded as assets on the balance sheet. During the years that these assets (other than land) are used, their costs are systematically moved from the balance sheet to the income statement through Depreciation Expense.

Capital Budgeting

Limitations such as time, money, and logistics frequently prevent a company from moving forward with too many major expenditure projects at the same time. Instead, a company will often rank its projects by priority and profitability. By using a process called capital budgeting, the company decides which capital expenditure projects will be undertaken and when.

At the top of the list of capital expenditure projects are those for which no real choice exists (e.g., installing an updated sewer line within the plant to replace one that is leaking, correcting a safety hazard, correcting a code violation, etc). The remaining capital expenditures are usually ranked according to their profitability using a capital budgeting model.

Capital Budgeting Models

There are a number of capital budgeting models available that assess and rank capital expenditure proposals. Let’s take a look at four of the most common models for evaluating business investments:

Accounting rate of return

Payback

Net present value

Internal rate of return

While each of these models has its benefits and drawbacks, sophisticated financial managers prefer the net present value and the internal rate of return methods. There are two reasons why these models are favored: (a) all of the cash flows over the entire length of the project are considered, and (b) the future cash flows are discounted to reflect the time value of money.

The following table highlights the differences among the four models:

Method Information Used Time Period Covered

1.Accounting Rate of Return

Accrual Accounting Amounts

Average of All Years or a Specific Year

2. PaybackCash Flows – Not Discounted

Until Cash is Recovered

3. Net Present Value Discounted Cash Flows Entire Life of Project

4.Internal Rate of Return

Discounted Cash Flows Entire Life of Project

Evaluating a Capital Expenditures

Let's use the capital budgeting models to evaluate a potential business investment at Treeline Manufacturing, Inc.:

Treeline Manufacturing must decide whether or not it should buy a new machine to replace its existing machine. Because the new machine is faster, it would eliminate the need for a worker now employed to run the existing machine during the evening shift. The initial annual savings are expected to be $24,000, with future cost savings expected to increase $1,000 or more per year.

The old machine is fully depreciated and would be scrapped with no expected salvage value (no proceeds).

The new machine costs $100,000 and is expected to have no salvage value at the end of its useful life of 8 years. For purposes of financial reporting, the machine would be depreciated over its 8-year life using the straight-line method. For income tax reporting, it would be depreciated over 7 years using the accelerated method. The company's income tax rate (federal and state combined) is 30%.

The new machine would be placed into service on January 1 and a full year of depreciation expense would be recorded on the financial statements during the first year. For income tax purposes our analyses uses a half-year of depreciation during the first year.

The relevant accrual basis of accounting amounts have been identified as follows (the relevant cash flow amounts will be shown later):

Treeline Manufacturing, Inc.Relevant Accrual Accounting Revenues and Expenses

Pertinent to the New Machine

Year 1  Year 2  Year 3  Year 4 

Change in revenues $   -0-  $   -0-  $   -0-  $   -0- 

Change in depreciation expense* 12,500  12,500  12,500  12,500 

Change in labor expenses (24,000) (25,000) (26,000) (27,100)

Change in accounting net income before tax 11,500  12,500  13,500  14,600 

Change in income tax expense @ 30% 3,450   3,750   4,050   4,380  

Change in accounting net income after tax $  8,050  $  8,750  $  9,450  $ 10,220 

*The depreciation expense on the income statement is based on the straight-line method.

Year 5  Year 6  Year 7  Year 8 

Change in revenues $   -0-  $   -0-  $   -0-  $   -0- 

Change in depreciation expense* 12,500  12,500  12,500  12,500 

Change in labor expenses (28,200) (29,300) (30,500) (31,733)

Change in accounting net income before tax 15,700  16,800  18,000  19,233 

Change in income tax expense @ 30% 4,710   5,040   5,400   5,770  

Change in accounting net income after tax $ 10,990  $ 11,760  $ 12,600  $ 13,463 

* The depreciation expense on the income statement is based on the straight-line method.

Non-cash, Non-discounted Model

1. Accounting Rate of Return.

This method of evaluating business investments considers the profitability of a project based on accrual accounting amounts found in the financial statements. The drawback of the accounting rate of return is that the net income amounts are not adjusted for the time value of money. In other words, $10,000 of net income in Year 4 is considered to be as valuable as $10,000 of net income in Year 1.

If the new machine is purchased, Treeline’s income statements will show a reduction of labor expense of about $24,000 in Year 1 and $31,733 in Year 8—an average of $27,729 during the 8 years. The income statements will also show additional depreciation expense of about $12,500 per year (the $100,000 cost of the machine and a useful life of 8 years with no salvage value). The net result of the average annual labor savings of $27,729 minus the additional annual depreciation expense of $12,500 is an average of $15,229 of additional net income before income tax expense. Assuming a combined federal and state income tax rate of 30%, the net income after income tax expense will average approximately $10,660 per year.

Tree line’s balance sheet will start with the new asset’s carrying amount (or the book value) of $100,000. The book value will decrease to $0 at the end of 8 years. In other words, the balance sheet amount will average about $50,000 per year during the 8-year period.

At this point, Treeline must choose one of the following calculations to estimate the accounting rate of return. (As with most "return" calculations, the numerator comes from the income statement and the denominator comes from the balance sheet.)

Average additional accounting net income before income tax expense ÷ the additional original investment:

$15,229 ÷ $100,000 = 15.2%

Average additional accounting net income after income tax expense ÷ the additional original investment:

$10,660 ÷ $100,000 = 10.7%

Average additional accounting net income before income tax expense ÷ the additional average investment:

$15,229 ÷ $50,000 = 30.5%

Average additional accounting net income after income tax expense ÷ the additional average investment:

$10,660 ÷ $50,000 = 21.3%

As you can see, the calculation Treeline chooses depends on (a) whether the company prefers to use before tax or after tax average accounting net income, and (b) whether it prefers to use the initial investment amount or the average investment amount.

Q&A: Evaluating Business Investments

What is NPV?

Are liabilities always a bad thing?

What is trading on equity?

How do I calculate IRR and NPV?

Why does the fixed cost per unit change?

Why would the cost behavior change outside of the relevant range of activity?

What is the rule of 72?

What is the difference between Present Value (PV) and Net Present Value (NPV)?

What is the difference between stockholder and stakeholder?

What is a non-discount method in capital budgeting?

What is NPV?

NPV is the acronym for net present value. Net present value is a calculation that compares the amount invested today to the present value of the future cash receipts from the investment. In other words, the amount invested is compared to the future cash amounts after they are discounted by a specified rate of return.

For example, an investment of $500,000 today is expected to return $100,000 of cash each year for 10 years. The $500,000 being spent today is already a present value, so no discounting is necessary for this amount. However, the future cash receipts of $100,000 for 10 years need to be discounted to their present value. Let’s assume that the receipts are discounted by 14% (the company’s required return). This will mean that the present value of the those future receipts will be approximately $522,000. The $522,000 of present value coming in is compared to the $500,000 of present value going out. The result is a net present value of $22,000 coming in. 

Investments with a positive net present value would be acceptable. Investments with a negative net present value would be unacceptable.

Are Liabilities always a Bad Thing?

Liabilities are obligations and are usually defined as a claim on assets. However, liabilities and stockholders’ equity are also the sources of assets. Generally, liabilities are considered to have a lower cost than stockholders’ equity. On the other hand, too many liabilities result in additional risk.

Some liabilities have low interest rates and some have no interest associated with them. For example, some of a company’s accounts payable may allow payment in 30 days. With those payables it is better to have the liability and to keep your cash in the bank until they become due.

In our personal lives, our first house was probably purchased with a down payment and mortgage loan. That mortgage loan was a big liability, but it allowed us to upgrade our living space. I viewed my mortgage loan liability as a good thing because it allowed me to own a nice home in a beautiful neighborhood.

So some liabilities are good—especially the ones that have a very low interest rate. Too many liabilities could cause financial hardships.

What is Trading on Equity?

Trading on equity is sometimes referred to as financial leverage or the leverage factor.

Trading on equity occurs when a corporation uses bonds, other debt, and preferred stock to increase its earnings on common stock. For example, a corporation might use long term debt to purchase assets that are expected to earn more than the interest on the debt. The earnings in excess of the interest expense on the new debt will increase the earnings of the corporation’s common stockholders. The increase in earnings indicates that the corporation was successful in trading on equity.

If the newly purchased assets earn less than the interest expense on the new debt, the earnings of the common stockholders will decrease.

How do I Calculate IRR and NPV?

The internal rate of return (IRR) and the net present value (NPV) are both discounted cash flow techniques or models. This means that each of these techniques looks at two things: 1) the current and future cash inflows and outflows (rather than the accrual accounting income amounts), and 2) the time at which the cash inflows and outflows occur. In other words, these models consider the time value of money: a dollar today is more valuable than a dollar in one year; a dollar received in three years is more valuable than a dollar received in five years, and so on.

The internal rate of return or IRR is the rate that will discount all cash inflows and outflows to a net present value of $0. In other words, the IRR model provides you with the true, effective interest rate being earned on a project after taking into consideration the time periods when the various cash amounts are flowing in or out. If you use present value tables to calculate the internal rate of return, it

will require some trial and error or iterations to determine the exact rate the project is earning. Software or some financial calculators will provide a quicker and more accurate answer.

The net present value (NPV) discounts all of the cash inflows and outflows by a specified interest rate. The net amount of all of the discounted amounts is the net present value. If the net present value is $0, the project is expected to earn exactly the specified rate. If the net present value is a positive amount, the project will be earning more than the specified interest rate. A negative net present value means the project is expected to earn less than the specified interest rate.

Why does the Fixed Cost per Unit Change?

Fixed costs such as rent or a supervisor’s salary will not change in total within a reasonable range of volume or activity. For example, the rent might be $2,500 per month and the supervisor’s salary might be $3,500 per month. This total fixed cost of $6,000 per month will be the same whether the volume is 3,000 units or 4,000 units.

On the other hand, the fixed cost per unit will change as the level of volume or activity changes. Using the amounts above, the fixed cost per unit is $2 when the volume is 3,000 units ($6,000 divided by 3,000 units). When the volume is 4,000 units, the fixed cost per unit is $1.50 ($6,000 divided by 4,000 units).

Why would the cost behavior change outside of the relevant range of activity?

Cost behavior often changes outside of the relevant range of activity due to a change in the fixed costs. When volume increases to a certain point, more fixed costs will have to be added. When volume shrinks significantly, some fixed costs could be eliminated.

Here’s an illustration. A company manufactures products in its 100,000 square foot plant. The company’s depreciation on the plant is $1,000,000 per year. The capacity of the plant is 500,000 units of output and its normal output is 400,000 units per year. When the company is manufacturing between 300,000 and 500,000 units, it needs salaried managers earning $400,000 per year. Below 300,000 units of output, some of the salaried manager positions would be eliminated. Above 500,000 units, the company will need to add plant space and managers.

For this example, the relevant range is between 300,000 units and 500,000 units of output per year. In that range the total of the two fixed costs is $1,400,000 per year. Below 300,000 units, the fixed costs will drop to less than $1,400,000 because some salaries will be eliminated and some of the space might be rented. When the volume exceeds 500,000 units per year, the company will need to add fixed costs because of the additional space and the additional managers. Perhaps the total fixed costs will be $2,000,000 for output between 500,000 units and 700,000 units.

What is the Rule of 72?

The rule of 72 is a simple formula that tells you the approximate amount of time or interest rate needed for an amount to double. The formula is Years X Rate per year = 72.

Here’s how it works. If you invest an amount for 8 years at 9% annual interest it will double (because 8 years X 9% = 72). If you invest an amount for 9 years at 8% it will also double (since 9 years X 8% = 72). If your investment earns 6%, it will take 12 years for it to double (since 12 years X 6% = 72; or 72 divided by 6 = 12).

If you invest $1,000 at 12% compounded annually, it will grow to approximately $2,000 in 6 years (6 X 12 = 72; or 72/12 = 6). If the $2,000 continues to earn 12% each year, six years later the investment will be worth $4,000. If the investment continues to earn 12% per year, then in six more years it will have a value of $8,000.

If successful investors were able to earn 18% each year, the value of their portfolios would have doubled every four years (72 divided by 18 = 4). If the investors live a long life and continue to earn 18% compounded annually they will become very wealthy.

What is the Difference between Present Value (PV) and Net Present Value (NPV)?

Present value is the result of discounting future amounts to the present. For example, a cash amount of $10,000 received at the end of 5 years will have a present value of $6,210 if the future amount is discounted at 10% compounded annually.

Net present value is the present value of the cash inflows minus the present value of the cash outflows. For example, let’s assume that an investment of $5,000 today will result in one cash receipt of $10,000 at the end of 5 years. If the investor requires a 10% annual return compounded annually, the net present value of the investment is $1,620. This is the result of the present value of the cash inflow $6,210 (from above) minus the present value of the $5,000 cash outflow. (Since the $5,000 cash outflow occurred at the present time, its present value is $5,000.)

Present value calculations can be seen at Present Value of a Single Amount and Present Value of an Ordinary Annuity Net present value calculations can be seen at Evaluating Business Investments.

If you received $100 today and deposited it into a savings account, it would grow over time to be worth more than $100. This fact of financial life is a result of the time value of money, a concept which says it's more valuable to receive $100 now rather than a year from now. To put it another way, the present value of receiving $100 one year from now is less than $100.

Accountants use Present Value (PV) calculations to account for the time value of money in a number of different applications. For example, assume your company provides a service in December 2007 and agrees to be paid $100 in December 2008. The time value of money tells us that the part of the $100 is interest you will earn for waiting one year for the $100. Perhaps only $91 of the $100 is service revenue earned in 2007 and $9 is interest that will be earned in 2008. The calculation of present value will remove the interest, so that the amount of the service revenue can be determined. Another example might involve the purchase of land: the owners will either sell it to you for $160,000 today, or for $200,000 if you pay at the end of two years. To help analyze the alternatives, you would use a PV calculation to tell you the interest rate implicit in the second option.

PV calculations can also tell you such things as how much money to invest right now in return for specific cash amounts to be received in the future, or how to estimate the rate of return on your investments. Our focus will be on single amounts that are received or paid in the future. We'll discuss PV calculations that solve for the present value, the implicit interest rate, and/or the length of time between the present and future amounts.

What's Involved In the Present Value Calculations of a Single Amount?

At the outset, it's important for you to understand that PV calculations involve cash amounts–not accrual amounts.

In present value calculations, future cash amounts are discounted back to the present time. (Discounting means removing the interest that is imbedded in the future cash amounts.) As a result, present value calculations are often referred to as a discounted cash flow technique.

PV calculations involve the compounding of interest. This means that any interest earned is reinvested and itself will earn interest at the same rate as the principal. In other words, you "earn interest on interest." The compounding of interest can be very significant when the interest rate and/or the number of years is sizeable.

We will use present value o(PV) to mean a single future amount such as one receipt or one payment. Here are the components of a present value (PV) calculation:

Present value amount (PV)

Future value amount (FV)

Length of time before the future value amount occurs (n)

Interest rate used for discounting the future value amount (i)

If you know any three of these four components, you will be able to calculate the unknown component. Accountants are often called upon to calculate this unknown component.

Visualizing the Present Value (PV) Amount

Let's assume that Customer X provides your company with a promissory note for $1,000 in exchange for service your company provided. The note is due at the end of two years and it does not specify any interest. The fair market value of the note and the fair market value of the service are not known. Because of the time value of money, you know that some interest is involved in a two-year note, even though it is not stated explicitly. You estimate the interest rate by considering both the length of the loan and the credit worthiness of Customer X. If Customer X is a reputable company like Google, you know there is minimal risk and a low interest rate would be used. If, however, Customer X has a bad credit history, then a high interest rate would be used. Let's assume that you have determined 10% to be the appropriate rate for Customer X. We now know three of the four components we need: (1) the future value amount ($1,000), (2) the length of time (2 years), and (3)

the interest rate (10%). With these three components, we know enough to calculate the fourth component, present value.

A timelinetime line can help us visualize what is known and what needs to be computed. The present time is noted with a "0," the end of the first period is noted with a "1," and the end of the second period is noted with a "2."

The following timeline depicts the information we know, along with the unknown component, (PV):

PV= ?? FV= $1,000

0 1 2

n = 2;  i = 10%

The letter "n" refers to the length of time (in this case, two years). The letter "i" refers to the percentage interest rate used to discount the future amount (in this case, 10%). Both (n) and (i) are stated within the context of time (e.g., two years at a 12% annual interest rate).

(Later on we will give examples where (n) and (i) pertain to a half-year, a quarter of a year, or a month.)

Visualizing the Length of Time (n)

Sometimes the present value, the future value, and the interest rate for discounting are known, but the length of time before the future value occurs is unknown. To illustrate, let's assume that $1,000 will be invested today at an annual interest rate of 8% compounded annually. The investment will be sold when its future value reaches $5,000. Because we know three components, we can solve for the unknown fourth component-the number of years it will take for $1,000 of present value to reach the future value of $5,000.

The following timeline depicts the known components and the unknown component (n):

PV= $1,000 FV= $5,000

.....

0 1 2 3 n=??

n = ??;   i = 8% compounded annually

Visualizing The Interest Rate (i)

What will our timeline look like when our unknown component is the interest rate? For this example, let's assume that we know the following: the present value is $900, the future value amount is $1,000, and the length of time before the future value occurs is two years. Since we know three of the components, the fourth one—the interest rate that will discount the future value amount to the present value—can be calculated.

The following timeline depicts the known components and the unknown component (i):

PV= $900 FV= $1,000

0 1 2

n = 2;  i = ??

Visualizing the Future Value Amount (FV)

Let's assume that the interest rate, the length of time, and the present value are known, and the future value is the component we don't know. If a present value of $1,000 is invested at 6% per year and compounded annually for four years, what is the future value amount?

The following timeline depicts the known components and the unknown component (FV):

PV= $1,000 FV= ??

0 1 2 3 4

n = 4;  i = 6%

As illustrated in the four timelines above, there is a logical connection between present value and future value. (The future value of a single amount will be discussed in a separate topic.)

MANAGEMENT ACCOUNTANCY

Depreciation

Introduction to Depreciation

Buildings, machinery, equipment, furniture, fixtures, computers, outdoor lighting, parking lots, cars, and trucks are examples of assets that will last for more than one year, but will not last indefinitely. During each accounting period (year, quarter, month, etc.) a portion of the cost of these assets is being used up. The portion being used up is reported as Depreciation Expense on the income statement. In effect depreciation is the transfer of a portion of the asset's cost from the balance sheet to the income statement during each year of the asset's life.

The calculation and reporting of depreciation is based upon two accounting principles:

1. Cost principle.

This principle requires that the Depreciation Expense reported on the income statement, and the asset amount that is reported on the balance sheet, should be based on the historical (original) cost of the asset. (The amounts should not be based on the cost to replace the asset, or on the current market value of the asset, etc.)

2. Matching principle.

This principle requires that the asset's cost be allocated to Depreciation Expense over the life of the asset. In effect the cost of the asset is divided up with some of the cost being reported on each of the income statements issued during the life of the asset. By assigning a portion of the asset's cost to various income statements, the accountant is matching a portion of the asset's cost with each period in which the asset is used. Hopefully this also means that the asset's cost is being matched with the revenues earned by using the asset.

There are several depreciation methods allowed for achieving the matching principle. The depreciation methods can be grouped into two categories: straight line depreciation and accelerated depreciation. The assets mentioned above are often referred to as fixed assets, plant assets,

depreciable assets, constructed assets, and property, plant and equipment. It is important to note that the asset land is not depreciated, because land is assumed to last indefinitely.

Book Vs Tax Depreciation

Depreciation is limited to the depreciation entered into the company's general ledger (or books) and reported on the company's financial statements. These amounts are based on accounting principles. The amounts resulting from the accounting principles are often different from the amounts based on the Internal Revenue Service code and regulations. Hence the depreciation on the financial statements will likely be legitimately different from the depreciation on the company's tax returns.

Book Depreciation Illustrated

Assumptions

To illustrate depreciation used in the accounting records and on the financial statements, let’s assume the following facts:

On July 1, 2008 a company purchases equipment having a cost of $10,500.

The Company estimates that the equipment will have a useful life of 5 years.

At the end of its useful life, the company expects to sell the equipment for $500.

The Company wants the depreciation to be reported evenly over the 5–year life.

Calculation of Straight-line Depreciation

The most common method of depreciating assets for financial statement purposes (as opposed to the method used for income tax purposes) is the straight-line method. Under this depreciation method, the depreciation for each full year is the same amount.

The depreciation expense for a full year when computed under the straight-line method is illustrated here:

Cost of the asset $10,500

Less: Expected salvage value – 500

Depreciable Cost (amount to be depreciated over

the estimated useful life) $10,000

Years of estimated useful life 5

Depreciation Expense per year $ 2,000

If a company's accounting year ends on December 31, the company will report the depreciation expense on the company's income statement as shown in the following depreciation schedule:

Depreciation Expense:

2008

$1,000

2009

$2,000

2010

$2,000

2011

$2,000

2012

$2,000

2013

$1,000

The actual cash paid by the company for this equipment will occur as follows:

Cash Paid:

2008

$10,500

2009

$ –0–

2010

$ –0–

2011

$2,000

2012

$ –0–

2013

$ –0–

As you can see, the company paid $10,500 in 2008, but the 2008 income statement reports Depreciation Expense of only $1,000. (Because the asset was acquired on July 1, 2008, only half of the annual depreciation expense amount is recorded in 2008 and 2013.) In each of the years 2009 through 2012 the company's income statements will report $2,000 of Depreciation Expense, thereby matching $2,000 of Depreciation Expense with the revenues earned in each of those years. However, the company will not pay out any cash for this expense during those years. The company's net income before income taxes will be reduced in each of the years 2009 – 2012 by $2,000—but the Cash account will not be reduced. This explains why Depreciation Expense is sometimes referred to as a noncash expense.

Journal Entries for Depreciation

The depreciation for the financial statements is entered into the accounts via a general journal entry. Assuming that the company prepares only annual financial statements the journal entries can be prepared as of the last day of each year:

Date Account Name Debit Credit

December 31, 2008 Depreciation Expense 1,000

Accumulated Depreciation 1,000

December 31, 2009 Depreciation Expense 2,000

Accumulated Depreciation 2,000

December 31, 2010 Depreciation Expense 2,000

Accumulated Depreciation 2,000

December 31, 2011 Depreciation Expense 2,000

Accumulated Depreciation 2,000

December 31, 2012 Depreciation Expense 2,000

Accumulated Depreciation 2,000

December 31, 2013 Depreciation Expense 1,000

Accumulated Depreciation 1,000

If monthly financial statements were prepared, 1/12 of the annual amounts would be entered monthly.

Note that the account credited in the journal entries is not the asset account Equipment. Instead, the credit is entered in the contra asset account Accumulated Depreciation. The use of this contra account will allow the asset Equipment to continue to report the equipment's cost, while also reporting in the account Accumulated Depreciation the amount that has been charged to Depreciation Expense since the asset was acquired.

For example, as of December 31, 2009 the Equipment account will have a debit balance of $10,500. On the same day, the account Accumulated Depreciation will have a credit balance of $3,000. In T-account form, it looks like this:

Equipment (balance sheet account) Debit

Increases an asset Credit

Decreases an asset

July 1, 2008 ENTRY 10,500

Accumulated Depreciation – Equipment (balance sheet acct.) Debit

Decreases a contra asset Credit

Increases a contra asset

1,000 ENTRY Dec. 31, 2008

2,000 ENTRY Dec. 31, 2009

3,000

Use of Estimates

Examples of Estimates

The calculation of depreciation shown above included two estimates:

1. Salvage value.

Salvage value is the estimated amount that a company will receive when it disposes of an asset at the end of the asset's useful life. Often the salvage value is estimated to be zero. However, we assumed $500 in order to demonstrate how an amount would be handled. Salvage value is also referred to as disposal value, scrap value, or residual value.

2. Useful life.

The useful life of an asset is an estimate of how long the asset will be used (as opposed to how long the asset will last). For example, a graphic artist might purchase a computer in 2008 and expects to replace it in 2010 with a more Advanced computer. Hence the graphic artist's computer will have an estimated Useful life of 2 years. An accountant purchasing a similar computer in 2008 Expects to use it until 2012. The accountant will use an estimated useful life of 4 Years when computing depreciation. Both the graphic artist and the accountant .

Are correct—the graphic artist in using 2 years and the accountant in using 4 Years—even if the computers will be in working order for many years after their Useful lives end.

Changes in Estimates

Whenever estimates are used in accounting, it is possible they will change as time moves forward. For example, a company bought a machine for $14,000 on January 1, 2004. At the time it was estimated to have no salvage value at the end of its useful life estimated to be 7 years. The company used straight-line depreciation. In 2008 the company realizes that technology will cause the machine to be obsolete by December 31, 2009 and there will be no salvage value at that time. Instead of the original useful life of 7 years, the company now estimates a total useful life of only 6 years (January 1, 2004 through December 31, 2009). This change in the estimated useful life affects only the current and future years. In other words, in this example the depreciation for 2008 and 2009 will be affected. The depreciation already reported for the years 2004, 2005, 2006, and 2007 cannot be changed. Any amount not depreciated as of December 31, 2007 will have to be depreciated over the years 2008 and 2009.

Let's first calculate the straight-line depreciation using the estimates in January 2004:

Cost of the asset $14,000 Less: Expected salvage value – 0 Depreciable Cost (amount to be depreciated over the estimated useful life) $14,000

Years of estimated useful life 7

Depreciation Expense per year $ 2,000

In the T-accounts we can see the cost of the Equipment $14,000 and the Accumulated

Depreciation of $8,000 as of December 31, 2007:

Equipment (balance sheet account) Debit

Increases an asset Credit

Decreases an asset

Jan. 1, 2004 ENTRY 14,000

Accumulated Depreciation – Equipment (balance sheet acct.) Debit

Decreases a contra asset Credit

Increases a contra asset

2,000 ENTRY Dec. 31, 2004

2,000 ENTRY Dec. 31, 2005

2,000 ENTRY Dec. 31, 2006

2,000 ENTRY Dec. 31, 2007

8,000 Balance Dec. 31, 2007

These accounts show that $6,000 ($14,000 – $8,000) remains on the books at December 31, 2007 and there are only two years remaining (2008 and 2009) in which to depreciate the remaining $6,000. The remaining $6,000 will be divided by the 2 years remaining and will result in $3,000 of depreciation in each of the years 2008 and 2009.

In general journal format the entries will be:

Date Account Name Debit Credit

December 31, 2008 Depreciation Expense 3,000

Accumulated Depreciation 3,000

December 31, 2009 Depreciation Expense 3,000

Accumulated Depreciation 3,000

For personal use by the original purchaser only

At the end of 2009 the Accumulated Depreciation account will look like this:

Accumulated Depreciation – Equipment (balance sheet acct.) Debit

Decreases a contra asset Credit

Increases a contra asset

2,000 ENTRY Dec. 31, 2004

2,000 ENTRY Dec. 31, 2005

2,000 ENTRY Dec. 31, 2006

2,000 ENTRY Dec. 31, 2007

3,000 ENTRY Dec. 31, 2008

3,000 ENTRY Dec. 31, 2009

14,000

Accelerated Depreciation

Definition:

Accelerated depreciation is an alternative to the straight-line depreciation method. Compared to the straight-line method, accelerated depreciation methods provide for more depreciation in the early years of an asset's life but then less depreciation in the later years. Under any depreciation method, the maximum depreciation during the life of an asset is limited to the cost of the asset. The difference in depreciation methods involves when you will report the depreciation. It's a matter of timing. Again, the total depreciation during the life of the asset is the same regardless of the depreciation method used.

As stated earlier, most companies use the straight-line method of depreciation for their financial statements. It is easy to compute and to understand. With straight-line depreciation the company will have the same amount of depreciation in each of the years of the asset's life. Accelerated depreciation will mean larger Depreciation Expense in the early years of the asset's life and then smaller Depreciation Expense in the later years. This larger expense in the earlier years will mean the company will report less profits in the earlier years of an asset's life (and greater profits in later years). Generally this is not appealing to most companies. As a result most companies will opt for the straight-line depreciation for their financial statements.

However, using an accelerated depreciation method on the company's income tax returns is very appealing. Higher depreciation in the early years of the asset means immediate income tax savings. Smaller depreciation in later years is far into the future.

Generally, it is better to take the income tax savings sooner rather than later. Fortunately a company is permitted to use straight-line depreciation on its financial statements and at the same time it can use accelerated depreciation on its income tax returns.

Various Accelerated Depreciation Methods:

There are various methods of accelerated depreciation. Here are some of them:

Double-declining balance (also known as the 200% declining balance)

150% declining balance

125% declining balance

Sum-of-the-years' digits

To learn more about these accelerated depreciation methods, refer to an Intermediate Accounting textbook. If you wish to use accelerated depreciation on your income tax return, refer to the Internal Revenue Service publications and/or consult with a tax professional.

Glossary

Accounting Principles

The standards, rules, guidelines, and industry-specific requirements for financial reporting. To learn more, see Explanation of Accounting Principles.

Accumulated depreciation

The amount of a long term asset's cost that has been allocated to Depreciation Expense since the time that the asset was acquired. Accumulated Depreciation is a long-term contra asset account (an asset account with a credit balance) that is reported on the balance sheet under the heading Property, Plant, and Equipment.

Accumulated depreciation - equipment

The contra asset account which accumulates the amount of Depreciation Expense taken on Equipment since the equipment was acquired. As a contra asset account it will have a credit balance.

Allocated

Costs that have been divided up and assigned to periods, departments, products, etc. In depreciation it is the asset's cost that is assigned to each of the years that the asset is in use. In cost accounting it is the assigning of common production costs to various production departments, product lines, individual products, activities.

Balance sheet

One of the main financial statements. The balance sheet reports the assets, liabilities, and owner's (stockholders') equity at a specific point in time, such as December 31. The balance sheet is also referred to as the Statement of Financial Position. To learn more, see Explanation of Balance Sheet.

Book value

The book value of an asset is the amount of cost in its asset account less the accumulated depreciation applicable to the asset. The book value of a company is the amount of owner's or stockholders' equity.

Carrying amount

Also referred to as book value; the cost of an asset minus the accumulated depreciation since the asset was acquired. This net amount is not an indication of the asset's fair market value. Also used in reference to bonds payable: the face amount in Bonds Payable plus Premium on Bonds Payable or minus.

Cash

A current asset account which includes currency, coins, checking accounts, and un deposited checks received from customers. The amounts must be unrestricted. (Restricted cash should be recorded in a different account.)

Contra asset account

An asset account which is expected to have a credit balance (which is contrary to the normal debit balance of an asset account). The contra asset account is related to another asset account. For example, the contra asset account Allowance for Doubtful Accounts is related to Accounts Receivable. The contra asset account Accumulated Depreciation is related to a constructed asset(s), and the contra asset account Accumulated Depletion is related to natural resources.

The net of the asset and its related contra asset account is referred to as the asset's book value or carrying value.

Cost principle

The accounting guideline requiring amounts in the accounts and on the financial statements to be the actual cost rather than the current value. Accountants can show an amount less than cost due to conservatism, but accountants are generally prohibited from showing amounts greater than cost. (Certain investments will be shown at fair value instead of cost.)

Depreciable cost

The amount of an asset's cost that will be depreciated. It is the cost minus the expected salvage value. For example, if equipment has a cost of $30,000 but is expected to have a salvage value of $3,000 then the depreciable cost is $27,000.

Depreciation expense

The income statement account which contains a portion of the cost of plant and equipment that is being matched to the time interval shown in the heading of the income statement. (There is no depreciation expense for land.)

Equipment

Equipment is a noncurrent or long-term asset account which reports the cost of the equipment. Equipment will be depreciated over its useful life by debiting the income statement account

Depreciation Expense and crediting the balance sheet account Accumulated Depreciation (a contra asset account).

General ledger

That part of the accounting system which contains the balance sheet and income statement accounts used for recording transactions. For personal use by the original purchaser only.

Income statement

One of the main financial statements (along with the balance sheet, the statement of cash flows, and the statement of stockholders' equity). The income statement is also referred to as the profit and loss statement, P&L, statement of income, and the statement of operations. The income statement reports the revenues, gains, expenses, losses, net income and other totals for the period of time shown in the heading of the statement. If a company's stock is publicly traded, earnings per share must appear on the face of the income statement. To learn more, see Explanation of Income Statement.

Land

A long-term asset account that reports the cost of real property exclusive of the cost of any constructed assets on the property. Land usually appears as the first item under the balance sheet heading of Property, Plant and Equipment. Generally, land is not depreciated.

Matching principle

The principle that requires a company to match expenses with related revenues in order to report a company's profitability during a specified time interval. Ideally, the matching is based on a cause and effect relationship: sales causes the cost of goods sold expense and the sales commissions expense. If no cause and effect relationship exists, accountants will show an expense in the accounting period when a cost is used up or has expired. Lastly, if a cost cannot be linked to revenues or to an accounting period, the expense will be recorded immediately. An example of this is Advertising Expense and Research and Development

Net

The result of two or more amounts being combined. For example, net sales is equal to gross sales minus sales returns, sales allowances, and sales discounts. The net realizable value of accounts receivable is the combination of the debit balance in accounts receivable and the credit balance in the allowance for doubtful accounts. The book value of equipment is also a net amount: the cost of the equipment minus the accumulated depreciation of the equipment.

Net income

This is the bottom line of the income statement. It is the mathematical result of revenues and gains minus the cost of goods sold and all expenses and losses (including income tax expense if the company is a regular corporation) provided the result is a positive amount. If the net amount is a negative amount, it is referred to as net loss.

Revenues

Fees earned from providing services and the amounts of merchandise sold. Under the accrual basis of accounting, revenues are recorded at the time of delivering the service or the merchandise, even if cash is not received at the time of delivery. Often the term income is used instead of revenues.

Examples of revenue accounts include: Sales, Service Revenues, Fees Earned, Interest Revenue, Interest Income. Revenue accounts are credited when services are performed/billed and therefore will usually have credit balances. At the time that a revenue account is credited, the account debited might be Cash, Accounts Receivable, or Unearned Revenue depending if cash was received at the time of the service, if the customer was billed at the time of the service and will pay later, or if the customer had paid in advance of the service being performed. If the revenues earned are a main activity of the business, they are considered to be operating revenues. If the revenues come from a secondary activity, they are considered to be non-operating revenues. For example, interest earned by a manufacturer on its investments is a non-operating revenue. Interest earned by a bank is considered to be part of operating revenues. To learn more.

Salvage value of fixed assets

The estimated scrap value at the end of the useful life of an asset used in the business. It is also referred to as residual value.

Straight-line method of depreciation

The depreciation method that results in the same equal amount of depreciation expense for each full year over the life of the asset. See Explanation of Depreciation for an illustration and further discussion of depreciation.

Useful life

This is the period of time that it will be economically feasible to use an asset. Useful life is used in computing depreciation on an asset, instead of using the physical life. For example, a computer might physically last for 100 years; however, the computer might be useful for only three years due to technology enhancements that are occurring. As a consequence, for financial statement purposes the computer will be depreciated over three years.