All About Managerial Accounting

5/23/2018 All About Managerial Accounting

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Managerial Accounting

Management accounting or managerial accounting is the process of identifying, analyzing, recording and presen

financial information that is used for internally by the management for planning, decision making and control.

In contrast tofinancial accounting,managerial accounting is concerned with providing helpful information and report

internal users such as managers and entrepreneurs etc. so that they can control and plan the business activities. Few of

main areas, in which managerial accounting is used are:

Planning and Budgeting:Managers use managerial accounting techniques to plan what to sell, how much to what price is to be charged to reimburse the costs of production and also earn an optimal profit. Also they hav

plan how to finance the operations and how to manage cash etc. This is very important to keep the busin

operations working smoothly. Thecapital budgetingandmaster budgetare the two important topics in this are

Decision Making: When managers have to decide whether or not to start a particular project, they nmanagerial accounting information to estimate the benefits of various opportunities and decide which one

choose. Mangers often userelevant costingtechniques.

Measurement of Performance:Managers have to compare the actual results of operations to budgeted figureevaluate the performance of the business. They use managerial accounting techniques such asstandard costin

evaluate the performance of specific departments. They then make necessary adjustments in those departme

which are not performing well.

Financial vs. Managerial Accounting

Although financial accounting and managerial accounting are closely related and work side by side but they are differen

following aspects: Users: Users of financial accounting information are people outside the organization such as stockhold

government, investors, etc. The users of managerial accounting information are people inside the organization

example managers and entrepreneurs.

Time:Financial accounting is mainly concerned with past business activities. Financial accounting is used to recthe actual facts and figures of financial transactions. Although managerial accounting does involve the analysi

past business activities to evaluate departmental performance, it is also concerned with future planning

budgeting.

Regulation:Financial accounting practices are governed by GAAP and IFRS etc. Since financial accountants havereport about the financial performance of the business to external users therefore it is very necessary to enfo

such regulations to provide correct information to people outside the organization. Managerial accounting is

governed by such rules and regulations.

Requirement by Law: Registered companies are required by law to produce and publish financial accouninformation. But managerial accounting is not mandatory by law. It is only required internally.Cost and Cost Classifications

Cost is a sacrifice of resources to obtain a benefit or any other resource. For example in production of a car, we sacr

material, electricity, the value of machine's life (depreciation), and labor wages etc. Thus these are our costs.

Costs are usually classified as follows:

Product Costs Vs Period Costs

Product costs are costs assigned to the manufacture of products and recognized for financial reporting when sold. T

include direct materials, direct labor, factory wages, factory depreciation, etc.

Period costs are on the other hand are all costs other than product costs. They include marketing costs and administra

costs, etc.

Breakup of Product CostsThe product costs are further classified into:

Direct materials: Represents the cost of the materials that can be identified directly with the productreasonable cost. For example, cost of paper in newspaper printing, cost of

Direct labor:Represents the cost of the labor time spent on that product, for example cost of the time spent bpetroleum engineer on an oil rig, etc.

Manufacturing overhead:Represents all production costs except those for direct labor and direct materials,example the cost of an accountant's time in an organization, depreciation on equipment, electricity, fuel, etc.

The product costs that can be specifically identified with each unit of a product are called direct product costs wher

those which cannot be traced to a specific unit are indirect product costs. Thus direct material cost and direct labor cost

direct product costs whereas manufacturing overhead cost is indirect product cost.

Prime Costs Vs Conversion Costs
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Prime costs are the sum of all direct costs such as direct materials, direct labor and any other direct costs.

Conversion costs are all costs incurred to convert the raw materials to finished products and they equal the sum of di

labor, other direct costs (other than materials) and manufacturing overheads.

Cost Classification Diagram

COSTS

PRODUCT COSTS

(COST OF GOODS SOLD)

PERIOD COST

(OPERATING EXPENSES)

DIRECT MATERIAL COST DIRECT LABOUR COST OVERHEAD COST

PRIME COSTSCONVERSION COSTS

Fixed Costs Vs Variable Costs

Fixed costs are costs which remain constant within a certain level of output or sales. This certain limit where fixed c

remain constant regardless of the level of activity is called relevant range. For example, depreciation on fixed assets etc,

Variable costs are costs which change with a change in the level of activity. Examples include direct materials, direct la

etc.

Sunk Costs Vs Opportunity Costs

The costs discussed so far are historical costswhich means they have been incurred in past and cannot be avoided by

current decisions. Relevant in this regard is another cost classification, called sunk costs. Sunk costs are those costs t

have been irreversibly incurred or committed; they may also be termed unrecoverable costs.

In contrast to sunk costs are opportunity costs which are costs of a potential benefit foregone. For example the opportucost of going on a picnic is the money that you would have earned in that time.

Direct Costs and Indirect Costs

Manufacturing costs may be classified as direct costs and indirect costs on the basis of whether they can be attributed

the production of specific goods, services, departments or not.

Direct Costs

Direct costs can be defined as costs which can be accurately traced to a cost object with little effort. Cost object may b

product, a department, a project, etc. Direct costs typically benefit a single cost object therefore the classification of

cost either as direct or indirect is done by taking the cost object into perspective. A particular cost may be direct cost

one cost object but indirect cost for another cost object.

Most direct costs are variable but this may not always be the case. For example, the salary of a supervisor for a month w

has only supervised the construction of a single building is a direct fixed cost incurred on the building.

Examples: Cost of gravel, sand, cement and wages incurred on production of concrete.

Indirect Costs

Costs which cannot be accurately attributed to specific cost objects are called indirect costs. These typically benefit mult

cost objects and it is impracticable to accurately trace them to individual products, activities or departments etc.

Examples: Cost of depreciation, insurance, power, salaries of supervisors incurred in a concrete plant.

Example

Following costs are incurred by a factory on the production of identical cupboards:

1. Laborers' wages 2. Synthetic wood

3. Power consumption 4. Glass

5. Nails and screws 6. Factory insurance

7. Handles, locks and hinges 8. Wood

9. Supervisors' salaries 10. Factory depreciation

11. Varnish, glue, paints 12. Factory manager's salary

Classify the above costs as direct or indirect.

Solution

1. Direct 2. Direct

3. Indirect 4. Direct

5. Indirect 6. Indirect

7. Direct 8. Direct




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Cost Accounting Systems

A cost accounting system (also called product costing system or costing system) is a framework used by firms to estim

the cost of their products for profitability analysis, inventory valuation and cost control.

Estimating the accurate cost of products is critical for profitable operations. A firm must know which products are profit

and which ones are not, and this can be ascertained only when it has estimated the correct cost of the product. Furthe

product costing system helps in estimating the closing value of materials inventory, work-in-progress and finished go

inventory for the purpose of financial statement preparation.

There are two main cost accounting systems: the job order costing and the process costing.

Job order costing is a cost accounting system that accumulates manufacturing costs separately for each job. appropriate for firms that are engaged in production of unique products and special orders. For example, it is the cost

accounting system most appropriate for an event management company, a niche furniture producer, a producer of v

high cost air surveillance system, etc.

Process costing is a cost accounting system that accumulates manufacturing costs separately for each process. I

appropriate for products whose production is a process involving different departments and costs flow from

department to another. For example, it is the cost accounting system used by oil refineries, chemical producers, etc.

There are situations when a firm uses a combination of features of both job-order costing and process costing, in wha

called hybrid cost accounting system.

In a cost accounting system, cost allocation is carried out based on either traditional costing system or activity-ba

costing system.

Traditional costing systemcalculates a single overhead rate and applies it to each job or in each department.

Activity-based costingon the other hand, involves calculation of activity rate and application of overhead costs to produ

based on their respective activity usage.Based on whether the fixed manufacturing overheads are charged to products or not, cost accounting systems have

variations: variable costing and absorption costing. Variable costing allocates only variable manufacturing overhead

inventories, while absorption costing allocates both variable and fixed manufacturing overheads to products. Varia

costing calculates contribution margin, while absorption costing calculates the relevant gross profit.

Still further refinement to costing accounting systems include JIT-costing, back-flush costing.

Activity-Based Costing

Activity-based costing is a method of assigning indirect costs to products and services which involves finding cost of e

activity involved in the production process and assigning costs to each product based on its consumption of each activity

Activity-based costing is more refined approach to costing products and services than the traditional costing method

involves the following steps:

Identification of activities involved in the production process; Classification of each activity according to the cost hierarchy (i.e. into unit-level, batch-level, product level

facility level);

Identification and accumulation of total costs of each activity; Identification of the most appropriate cost driver for each activity; Calculation of total units of the cost driver relevant to each activity; Calculation of the activity rate i.e. the cost of each activity per unit of its relevant cost driver; Application of the cost of each activity to products based on its activity usage by the product.

Cost Hierarchy

The first step in activity-based costing involves identifying activities and classifying them according to the cost hierar

Cost hierarchy is a framework that classifies activities based the ease at which they are traceable to a product. The le

are (a) unit level, (b) batch level, (c) product level, and (d) facility level.

Unit level activities are activities that are performed on each unit of product. Batch level activities are activities that performed whenever a batch of the product is produced. Product level activities are activities that are carried

separately for each product. Facility level activities are activities that are carried out at the plant level. The unit-l

activities are most easily traceable to products while facility-level activities are least traceable.

Example

Alex Erwin started Interwood, a niche furniture brand, 10 years ago. He ran the business as a sole proprietorship. While

has 50 skilled carpenters and 5 salesmen on his payroll, he has been taking care of the accounting by himself. Now,

intends to offer 40% of the ownership to public in next couple years, and is willing to make changes and has hired you

the management accountant to organize and improve the accounting systems.

Interwood's total budgeted manufacturing overheads cost for the current year is $5,404,639 and budgeted total la

hours are 20,000. Alex applied traditional costing method during all of the 10 years period, and based the pre-determi

overhead rate on total labor hours.


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Interwood's sofa range includes the 2-set, 3-set and 6-set options. Platinum Interiors recently placed an order for 150 u

of the 6-set type. The order is expected to be delivered in 1 month time. Since it is a customized order, Platinum wil

billed at cost plus 25%.

You are not a fan of traditional product costing system. You believe that the benefits of activity-based costing syst

exceeds its costs, so you sat down with Aaron Mason, the chief engineer, to identify the activities which the f

undertakes in its sofa division. Next, you calculated the total cost that goes into each activity, identified the cost driver t

is most relevant to each activity and calculated the activity rate. The results are summarized below:

Activity

(in $)

A

Relevant Cost Driver

B C=A/B (in $)

Production of components 2,313,132 Machine hours 25,000 93

Assembly of components 1,231,312 Number of labor hours 20,000 62

Packaging 213,123 Units 5,000 43

Shipping 231,230 Units 5,000 46

Setup costs 34,243 Number of setups 240 143

Designing 123,132 Designer hours 1,000 123

Product testing 24,234 Testing hours 500 48

Rent 1,234,233 Labor cost $1,645,644 75%

Once the order was ready for packaging, Aaron gave you a summary of total cost incurred and a statement of activitie

performed (also called the bill of activities) as shown below:

Order No: 15X2013, Customer: Platinum Interiors, Units: 150, Type: 6 unit, Amounts in $

Cost of direct materials 25,000

Cost of purchased components 35,000

Labor cost 15,600

Activity Relevant Cost Driver Activity Usag

Production of components Machine hours 32

Assembly of components Number of labor hours 25

Packaging Units 15

Shipping Units 15

Setup costs Number of setups 1

Designing Designer hours 7Testing hours 22

Rent Labor cost 450

Part A

Calculate the total cost of the order and the invoice value of the order based on traditional costing system.

Solution

In the traditional costing system, cost equals materials cost plus labor cost plus manufacturing overheads charged at

pre-determined overhead rate.

The pre-determined overhead rate based on direct labor hours = $5,404,639/20,000 = $270 per labor hour

The actual number of labor hours spent on the order is 250. Once we have this data, we can estimate the manufactu

overheads and the total cost as follows:


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Direct materials 25,000

Purchased components 35,000

Labor cost 15,600

Manufacturing overheads ($270 250) 67,500

Total cost under traditional product costing system 143,100

Platinum is billed at cost plus 25%, so the amount of sales to be booked would amount to $178,875 (= $143,100 1.25).

Part B

You know activity-based costing is a more refined approach. Now, since you have all the data needed, calculate the orcost using activity based costing.

Solution

In activity-based costing, direct materials cost, cost of purchased components and labor cost remains the same a

traditional product costing. However, the value of manufacturing overheads assigned is more accurately estimated.

following worksheet estimates the manufacturing overheads that should be assigned to the order of Platinum Interiors:

(A) (B) (A B)

Activity Activity Rate Activity Usage Activity Cost Assigned

Production of components 93 320 29,760

Assembly of components 62 250 15,500Packaging 43 150 6,450

Shipping 46 150 6,900

Setup costs 143 15 2,145

Designing 123 70 8,610

Product testing 48 22 1,056

Rent 75% 15,600 11,700

82,121

Total cost of the order is hence:US$

Direct materials 25,000

Purchased components 35,000

Labor cost 15,600

Manufacturing overheads 82,121

Total cost under activity-based costing 157,721

Based on the more accurate estimation of the order cost, the invoice should be raised at $197,150 (=$157,721 1

instead of $178,875 calculated under traditional product costing system.

The example highlights the importance of correct estimation of the product cost and the usefulness of activity-ba

costing in achieving that goal.

Cost Allocation

Cost allocation or cost assignment is the process of allocating of overhead costs to costs objects. Cost object may b

product, a department or a project. Unlike direct costs, overheads cannot be traced directly to specific cost objects.

Indirect costs are assigned to cost objects using an allocation base called cost driver. Floor area, direct labor hours, mach

hours etc. may be used as cost drivers.

Cost poolis a group of costs which have been assigned to a cost object using a single cost driver.

In this chapter we will learn:

1. Allocation of individual costs to costs centers.2. Allocation of service department costs.3. Allocation of costs to individual products.


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Service Department Cost Allocation

Since service departments do not generate revenue themselves and they help other departments, all their costs must

allocated again to other departments. This will be a simple task provided that none of the service departments provi

services to other service department(s). Things are complicated when service departments receive services from each o

(which is most often the case).

The problem here is that the cost reallocation process of two service departments, both of which benefit from each oth

will repeat itself because each of them will receive a portion of reallocated service department costs which have to

allocated again and again. Assume a company has a certain number of production departments and two ser

departments, A and B, and that both of them receive services from each other. If we reallocate service department A's first and service departments B's cost later, department A's balance will no longer remain zero because it will receiv

portion of reallocated cost of department B. Thus, we will be forced to repeat the process many times.

Following are the four techniques for reallocation of service department costs for use in the situation described above:

1. Simultaneous Equation Method2. Repeated Distribution Method3. Specific Order of Closing Method4. Direct Allocation Method

Repeated Distribution Method

Repeated distribution method is a technique in which costs of each service department are repeatedly allocated to ot

departments according to the given percentages until the balance left in service departments reaches zero.

Assume a company has a certain number of production departments and two service departments, A and B, which ben

from each other. In order to reallocate the service department costs to production departments using repeated distribu

method, we follow the steps given below:

1. Start by allocating the higher service cost first, let it be A.2. Allocate department B's costs to all production departments and department A.3. Since the balance in department A no longer remains zero after reallocation of department B's cost we have

repeat the process by allocating department A's cost again to production departments and department B.

4. This process of reallocating the service department costs is repeated until the balance remaining in any serdepartment becomes negligible.

Example

The following example illustrates the repeated distribution method:

ltd. has three production departments (P, Q and R) and two service departments (X and Y). The total overheads for

departments are given below:

Department Overheads

P $35,000

Q $64,000

R $19,000

X $22,000

Y $38,000

The reallocation percentages of the service departments' costs are given below:

Department P Q R X Y

X 20% 25% 25% 10%

Y 25% 30% 30% 15%

Reallocate the service department costs in the specified percentages using repeated distribution method.Solution


Allocated Overheads 35,000 64,000 19,000 22,000 38,000

Dept. X Reallocation 4,400 5,500 5,500 (22,000) 2,200

Total 39,400 69,500 24,500 0 40,200

Dept. Y Reallocation 10,050 12,060 12,060 6,030 (40,200)

Total 49,450 81,560 36,560 6,030 0

Dept. X Reallocation 1,206 1,508 1,508 (6,030) 603

Total 50,656 83,068 38,068 0 603


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Dept. Y Reallocation 151 181 181 90 (603)

Total 50,807 83,248 38,248 90 0

Dept. X Reallocation 18 23 23 (90) 9

Total 50,825 83,271 38,271 0 9

Dept. Y Reallocation 2 3 3 1 (9)

Total 50,827 83,274 38,274 1 0

We stop when the balance left in service departments becomes negligible.

Simultaneous Equation Method

In simultaneous equation method of allocation of service department costs, we establish simultaneous equations and s

them to obtain the final balances of production departments. This method accurately allocates service department cost

the given percentages.

Simultaneous equation method is best explained using an example.

Example

In this example we use simultaneous equation method to solve the same problem we solved earlier using repea

distribution method. Following is the problem:

Y ltd. has three production departments (P, Q and R) and two service departments (X and Y). The total overheads for

departments are given below:


P $35,000Q $64,000

R $19,000

X $22,000

Y $38,000



X 20% 25% 25% 10%

Y 25% 30% 30% 15%

Use the simultaneous equation method to allocate the service department overheads to production departments.

Solution

Let,

x= total overheads of department X after reallocation

y= total overheads of department Y after reallocation

Then total overhead of department X will be 22,000 + 15% of department Y overhead after reallocation whereas the t

overhead of department Y will be 38,000 + 10% of department X overhead after reallocation. Therefore,

x= 22,000 + 0.15y

y= 38,000 + 0.10x

Solving the above equations forxand ywe get:

Total overheads of department X after reallocation = x 28,122

Total overheads of department Y after reallocation = y 40,812

The total overheads as calculated above are allocated to production departments in specified percentages as shown belo

Department P Q R

Initial Overheads 35,000 64,000 19,000

Dept. X Reallocation 5,624 7,030 7,030

Dept. Y Reallocation 10,203 12,244 12,244

Total Overheads 50,827 83,274 38,274

Specific Order of Closing Method

Specific order of closing method (also known as sequential method) is one of the techniques used to reallocate ser

departments' overheads to production departments. As the name suggests, it reallocates service department overhead

certain order.


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Under specific order of closing method, we reallocate the overheads of the largest service department first and then

overheads of the second largest service department and so on. The overheads of service departments are reallocated

production departments as well as other service departments but once the overheads of a service department

reallocated, it does not receive any reallocations back from other service departments. In this way, the balances in serv

departments reach zero in fewer steps than the repeated distribution method.

There is a major drawback however. Since there are no reallocations back, the service department overheads are

apportioned among service departments accurately according to the specified percentages.

The following example illustrates the specific order of closing method:

Example

Y ltd. has three production departments (P, Q and R) and two service departments (X and Y). The overheads befreallocation are given below:


P $35,000

Q $64,000

R $19,000

X $22,000

Y $38,000



X 20% 25% 25% 10%

Y 25% 30% 30% 15%

Use the specific order of closing method to reallocation the service department costs to

Solution

Since service department Y has large overheads than department X therefore we will reallocate department Y costs firs

all production departments and service department X. Then we will reallocate department X costs only to product

departments because in specific order of closing method we don't allocate costs back to a service department whose c

have already been reallocated. To transfer all the costs of service department X, we apportion department X cost

$27,700 after reallocation of department Y's cost among the three production departments in the ratio existing betw

their percentages from department X.

Thus, department P will get 40%/90% $27,700 and department Q and R will get 25%/90% $27,700 each.


Allocated Overheads 35,000 64,000 19,000 22,000 38,000Dept. Y Reallocation 9,500 11,400 11,400 5,700 (38,800)

Total 44,500 75,400 30,400 27,700 0

Dept. X Reallocation 12,311 7,694 7,694 (27,700)

Total 56,811 83,094 38,094 0

Direct Allocation Method

Direct allocation method is one of the four techniques used to reallocate service departments' overheads to product

departments. It is different from the other reallocation methods because it completely disregards any services provided

one service department to another. This means that no portion of the overhead of a service department is reallocated

other service departments. All is reallocated to production departments in the ratio of their specified percentages.

Direct method is generally an inaccurate method of service departments' overheads reallocations and very inaccurate wservice departments receive significant help from each other. Therefore it is only recommended in cases where ser

departments do not depend much on the services of other departments.

Direct allocation method is better explained using an example.

Example

Let us use the same problem we used earlier:

Y ltd. has three production departments (P, Q and R) and two service departments (X and Y). The overheads for

departments before reallocation are given below:


P $35,000

Q $64,000


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R $19,000

X $22,000

Y $38,000



X 40% 25% 25% 10%

Y 25% 30% 30% 15%

Use the direct allocation method to reallocate the overheads of service departments to production departments.Solution

First we have to calculate the factors to apportion service department overheads:

Department Sum of Percentages P Q R

X 40+25+25=90 40/90 25/90 25/90

Y 25+30+30=85 25/85 30/85 30/85

We then multiply the service department overhead by the above factors to obtain the amount of overhead to be alloca

to each production department.


Allocated Overheads 35,000 64,000 19,000 22,000 38,000

Dept. X Reallocation 9,778 6,111 6,111 (22,000)

Dept. Y Reallocation 11,176 13,412 13,412 (38,000)Total 55,954 83,523 38,523 0 0

Types of Costs by Behavior

Cost behavior refers to the way different types of production costs change when there is a change in level of production

There are three main types of costs according to their behavior:

Fixed Costs:

Fixed costs are those which do not change with the level of activity within the relevant range. These costs will incur eve

no units are produced. For example rent expense, straight-line depreciation expense, etc.

Fixed cost per unit decreases with increase in production. Following example explains this fact:

Total Fixed Cost $30,000 $30,000 $30,000

Units Produced 5,000 10,000 15,000

Fixed Cost per Unit $6.00 $3.00 $2.00

Variable Costs:

Variable costs change in direct proportion to the level of production. This means that total variable cost increase w

more units are produced and decreases when less units are produced. Although variable in total, these costs are const

per unit. For example

Total Variable Cost $10,000 $20,000 $30,000

Units Produced 5,000 10,000 15,000

Variable Cost per Unit $2.00 $2.00 $2.00

Mixed Costs:

Mixed costs or semi-variable costs have properties of both fixed and variable costs due to presence of both variable

fixed components in them. An example of mixed cost is telephone expense because it usually consists of a fixed compon

such as line rent and fixed subscription charges as well as variable cost charged per minute cost. Another example of mi

cost is delivery cost which has a fixed component of depreciation cost of trucks and a variable component of fuel expens

Since mixed cost figures are not useful in their raw form, therefore they are split into their fixed and variable compone

by using cost behavior analysis techniques such as High-Low Method, Scatter Diagram Method and Regression Analysis.

Cost Volume Formula

Cost volume formula is a cost accounting relation used to estimate production cost of a given number of units of a prod

A linear cost volume formula is of the following form:

y = a + bx

In the above equation,

ystands for total production cost;


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afor total fixed cost;

bfor variable cost per unit; and

xfor number of units

Total Fixed Cost is the sum of pure fixed cost, such as rent on factory building and property taxes; and the fixed compon

of mixed costs, such as total fixed cost on delivery trucks i.e. straight line depreciation expense.

Variable Cost per Unit is the sum of pure variable cost per unit, such as material cost per unit; and the variable compon

of mixed cost, such as variable cost per unit on delivery trucks i.e. fuel expense.

For this purpose, mixed costs are split into their fixed and variable components by using any of the following techniques

1. High-Low Method2. Scatter Graph Method3. Regression Method

The cost volume formula we discussed here is in the form of linear equation. Cost volume formulas can also be quadrati

other complex forms which are more accurate and thus suitable for practical use.

Example

Find total fixed cost, variable cost per unit, total cost of producing 30,000 units from the following cost volume formula:

y = $43,000 + 6x

Solution

Total Fixed Cost = $43,000

Variable Cost per Unit = $6

Total Cost of Producing 30,000 Units = $43,000 + 6 30,000 = $223,000

High-Low Method

High-Low method is one of the several techniques used to split a mixed cost into its fixed and variable components (

cost classifications). Although easy to understand, high low method is relatively unreliable. This is because it only takes

extreme activity levels (i.e. labor hours, machine hours, etc.) from a set of actual data of various activity levels and t

corresponding total cost figures. These figures are then used to calculate the approximate variable cost per unit ( b)

total fixed cost (a) to obtain acost volume formula:

y = a + bx

High-Low Method Formulas

Variable Cost per Unit

Variable cost per unit (b) is calculated using the following formula:

Variable Cost per Unit =y2 y1

x2 x1

Where,

y2is the total cost at highest level of activity;

y1is the total cost at lowest level of activity;

x2are the number of units/labor hours etc. at highest level of activity; and

x1are the number of units/labor hours etc. at lowest level of activity

The variable cost per unit is equal to the slope of the cost volume line (i.e. change in total cost change in number of un

produced).

Total Fixed Cost

Total fixed cost (a) is calculated by subtracting total variable cost from total cost, thus:

Total Fixed Cost = y2 bx2= y1 bx1

Example

Company wants to determine the cost-volume relation between its factory overhead cost and number of units produUse the high-low method to split its factory overhead (FOH) costs into fixed and variable components and create a

volume formula.The volume and the corresponding total cost information of the factory for past eight months are gi

below:

Month Units FOH

1 1,520 $36,375

2 1,250 38,000

3 1,750 41,750

4 1,600 42,360

5 2,350 55,080
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Month Units FOH

6 2,100 48,100

7 3,000 59,000

8 2,750 56,800

Solution:

We have,

at highest activity: x2= 3,000; y2= $59,000

at lowest activity: x1= 1,250; y1= $38,000Variable Cost per Unit = ($59,000 $38,000) (3,000 1,250) = $12 per unit

Total Fixed Cost = $59,000 ($12 3,000) = $38,000 ($12 1,250) = $23,000

Cost Volume Formula: y = $23,000 + 12x

Due to its unreliability, high low method is rarely used. The other techniques of variable and fixed cost estimation

scatter-graph method and least-squares regression method.

Scatter Graph Method

Scatter graph method is a graphical technique of separating fixed and variable components of mixed cost by plot

activity level along x-axis and corresponding total cost (mixed cost) along y-axis. A regression line is then drawn on

graph by visual inspection. The line thus drawn is used to estimate the total fixed cost and variable cost per unit. The p

where the line intercepts y-axis is the estimated fixed cost and the slope of the line is the average variable cost per u

Since the visual inspection does not involve any mathematical testing therefore this method should be applied with gr

care.

Procedure

Step 1: Draw scatter graph

Plot the data on scatter graph. Plot activity level (i.e. number of units, labor hours etc.) along x-axis and total mixed

along y-axis.

Step 2: Draw regression line

Draw a regression line over the scatter graph by visual inspection and try to minimize the total vertical distance betw

the line and all the points. Extend the line towards y-axis.

Step 3: Find total fixed cost

Total fixed is given by the y-intercept of the line. Y-intercept is the point at which the line cuts y-axis.

Step 4: Find variable cost per unit

Variable cost per unit is equal to the slope of the line. Take two points (x1,y

1) and (x

2,y

2) on the line and calculate vari

cost using the following formula:

Variable Cost per Unit = Slope of Regression Line =y2 y1

x2 x1

Example

Company decides to use scatter graph method to split its factory overhead (FOH) into variable and fixed compone

Following is the data which is provided for the analysis.

Month Units FOH

1 1,520 $36,375

2 1,250 38,000

3 1,750 41,750

4 1,600 42,360

5 2,350 55,080

6 2,100 48,100

7 3,000 59,000

8 2,750 56,800

Solution:

Fixed Cost = y-intercept = $18,000

Variable Cost per Unit = Slope of Regression Line


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To calculate slop we will take two points on line: (0,18000) and (3500,68000)

Variable Cost per Unit = (68000 18000) (3500 0) = $14.286

Least-Squares Regression Method

A mixed cost can be split into variable and mixed components by a statistical technique called simple linear regress

analysis. This technique mathematically calculates the y-intercept and the slope of a straight line that ideally fits throug

set of points on a graph. In least-squares method, the ideal fitting of the regression line is achieved by minimizing the s

of squares of the distances between the line and all the points on the graph.

Formulas

In cost behavior analysis, the cost volume formula "y = a + bx", is equivalent to regression line. Its y-intercept (a) and sl(b) represent the total fixed cost and variable cost per unit respectively, can be calculated by solved following simultane

linear equations of least-squares regression analysis:

By solving the above equations for total fixed cost (a) and variable cost per unit (b), we obtain:

Cost Volume Profit Analysis

Cost-Volume-Profit (CVP) analysis is a managerial accounting technique that is concerned with the effect of sales volu

and product costs on operating profit of a business. It deals with how operating profit is affected by changes in varia

costs, fixed costs, selling price per unit and the sales mix of two or more different products.

CVP analysis has following assumptions:

1. All cost can be categorized as variable or fixed.2. Sales price per unit, variable cost per unit and total fixed cost are constant.3. All units produced are sold.

Where the problem involves mixed costs, they must be split into their fixed and variable component by High-Low Meth

Scatter Plot Method or Regression Method.

CVP Analysis Formula

The basic formula used in CVP Analysis is derived from profit equation:

px = vx + FC + Profit

In the above formula,

pis price per unit;

vis variable cost per unit;

xare total number of units produced and sold; and

FCis total fixed costBesides the above formula, CVP analysis also makes use of following concepts:

Contribution Margin (CM)

Contribution Margin (CM) is equal to the difference between total sales (S) and total variable cost or, in other words,

the amount by which sales exceed total variable costs (VC). In order to make profit the contribution margin of a busin

must exceed its total fixed costs. In short:

CM = S VC

Unit Contribution Margin (Unit CM)

Contribution Margin can also be calculated per unit which is called Unit Contribution Margin. It is the excess of sales p

per unit (p) over variable cost per unit (v). Thus:

Unit CM = p v

Contribution Margin Ratio (CM Ratio)Contribution Margin Ratio is calculated by dividing contribution margin by total sales or unit CM by price per unit.

Break-even Point Equation Method

Break-even is the point of zero loss or profit. At break-even point, the revenues of the business are equal its total costs

its contribution margin equals its total fixed costs. Break-even point can be calculated by equation method, contribu

methodor graphical method. The equation method is based on thecost-volume-profit (CVP)formula:

px = vx + FC + Profit

Where,

pis the price per unit,

xis the number of units,
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vis variable cost per unit and

FCis total fixed cost.

Calculation

BEP in Sales Units

At break-even point the profit is zero therefore the CVP formula is simplified to:

px = vx + FC

Solving the above equation for x which equals break-even point in sales units, we get:

Break-even Sales Units = x =FC

p v

BEP in Sales Dollars

Break-even point in number of sales dollars is calculated using the following formula:

Break-even Sales Dollars = Price per Unit Break-even Sales Units

Example

Calculate break-even point in sales units and sales dollars from following information:

Price per Unit $15

Variable Cost per Unit $7

Total Fixed Cost $9,000

Solution

We have,p = $15

v = $7, and

FC = $9,000

Substituting the known values into the formula for breakeven point in sales units, we get:

Breakeven Point in Sales Units (x)

= 9,000 (15 7)

= 9,000 8

= 1,125 units

Break-even Point in Sales Dollars = $15 1,125 = $16,875

Break-even Point Contribution Margin Approach

The contribution margin approach to calculate the break-even point (i.e. the point of zero profit or loss) is based on the analysis concepts known as contribution margin and contribution margin ratio. Contribution margin is the differe

between sales and variable costs. When calculated for a single unit, it is called unit contribution margin. Contribu

margin ratio is the ratio of contribution margin to sales.

In this method simple formulas are derived from the CVP analysis equation by rearranging the equation and then replac

certain parts with Contribution Margin formulas.

Contribution Approach Formulas

BEP in Sales Units

We learned that, at break-even point, the CVP analysis equation is reduced to:

px = vx + FC

Where pis the price per unit, xis the number of units, vis variable cost per unit and FCis total fixed cost.

Solving the above equation for x (i.e. Break-even sales units):

Break-even Sales Units = x = FC ( p v )

Since unit contribution margin (Unit CM) is equal to unit sale price (p) less unit variable cost (v), so,

Unit CM = p v

Therefore,

Break-even Sales Units = x = FC Unit CM

BEP in Sales Dollars

Break-even point in dollars can be calculated via:

Break-even Sales Dollars = Price per Unit Break-even Sales Units ; or

Break-even Sales Dollars = FC CM Ratio


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Example

Calculate the break-even point in units and in sales dollars when sales price per unit is $35, variable cost per unit is $28 a

total fixed cost is $7,000.

Solution

Contribution Margin per Unit = ($35 $28) = $7

Break-even Point in Units = $7,000 $7 = 1,000

Break-even Point in Sales Dollars = 1,000 $35 or $7,000 20% = $35,000

Sales Mix Break-even Point Calculation

Sales mix is the proportion in which two or more products are sold. For the calculation of break-even point for sales mfollowing assumptions are made in addition to those already made for CVP analysis:

1. The proportion of sales mix must be predetermined.2. The sales mix must not change within the relevant time period.

The calculation method for the break-even point of sales mix is based on the contribution approach method. Since we h

multiple products in sales mix therefore it is most likely that we will be dealing with products with different contribut

margin per unit and contribution margin ratios. This problem is overcome by calculating weighted average contribu

margin per unit and contribution margin ratio. These are then used to calculate the break-even point for sales mix.

The calculation procedure and the formulas are discussed via following example:

Example: Formulas and Calculation Procedure

Following information is related to sales mix of product A, B and C.

Product A B C

Sales Price per Unit $15 $21 $36

Variable Cost per Unit $9 $14 $19

Sales Mix Percentage 20% 20% 60%


Calculate the break-even point in units and in dollars.

Calculation

Step 1: Calculate the contribution margin per unit for each product:

Product A B C



Contribution Margin per Unit $6 $7 $17

Step 2: Calculate the weighted-average contribution margin per unit for the sales mix using the following formula:

Product A CM per Unit Product A Sales Mix Percentage

+ Product B CM per Unit Product B Sales Mix Percentage

+ Product C CM per Unit Product C Sales Mix Percentage

= Weighted Average Unit Contribution Margin

Product A B C



Contribution Margin per Unit $6 $7 $17

Sales Mix Percentage 20% 20% 60%

$1.2 $1.4 $10.2

Sum: Weighted Average CM per Unit $12.80

Step 3: Calculate total units of sales mix required to break-even using the formula:

Break-even Point in Units of Sales Mix = Total Fixed Cost Weighted Average CM per Unit


Weighted Average CM per Unit $12.80

Break-even Point in Units of Sales Mix 3,125

Step 4: Calculate number units of product A, B and C at break-even point:


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Product A B C

Sales Mix Ratio 20% 20% 60%

Total Break-even Units 3,125 3,125 3,125

Product Units at Break-even Point 625 625 1,875

Step 5: Calculate Break-even Point in dollars as follows:

Product A B C

Product Units at Break-even Point 625 625 1,875

Price per Unit $15 $21 $36

Product Sales in Dollars $9,375 $13,125 $67,500

Sum: Break-even Point in Dollars $90,000

Contribution Margin

Contribution margin (CM) is the amount by which sales revenue exceeds variable costs. It can be calculated as contribu

margin per unit as well as total contribution margin, using the following formulas:

Unit CM = Unit Price Variable Cost per Unit

Total CM = Total Sales Total Variable Costs

Variable costs are those which vary in proportion to the level of production. Variable cost may be direct as well as indir

Direct variable cost includes direct material cost and direct labor cost. Indirect variable costs include certain varia

overheads.

Total contribution margin can also be obtained by multiplying unit contribution margin by number of units sold. Simila

contribution margin per unit can also be calculated by divided total contribution margin by number of units sold.

Contribution Margin Ratio

Contribution margin ratio is contribution margin as percentage of sales. It can be calculated as shown in the follow

formula:

CM Ratio =Unit Contribution Margin

=Total Contribution Margin

Unit Price Total Sales

Contribution margin and contribution margin ratio are used in the breakeven analysis.

Example

Use the following information to calculate unit contribution margin, total contribution margin & contribution margin rat

Price Per Unit $22Units Sold 802

Total Variable Cost $9,624

Solution

Total Sales = 802 $22 = $17,644

Total Contribution Margin = $17,644 $9,624 = $8,020

Contribution Margin Per Unit = $8,020 802 = $10

CM Ratio = $8,020 $17,644 = $10 $22 45%

Margin of Safety (MOS)

In break-even analysis, margin of safety is the extent by which actual or projected sales exceed the break-even sales. It

be calculated simply as the difference between actual or projected sales and the break-even sales. However, it is bes

calculate margin of safety in the form of a ratio. Thus we have the following two formulas to calculate margin of safety:

MOS = Budgeted Sales Break-even Sales

MOS =Budgeted Sales Break-even Sales

Budgeted Sales

Margin of Safety can be expressed both in terms of sales units and currency units.

The margin of safety is a measure of risk. It represents the amount of drop in sales which a company can tolerate. Hig

the margin of safety, the more the company can withstand fluctuations in sales. A drop in sales greater than margin

safety will cause net loss for the period.

Example

Use the following information to calculate margin of safety:


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Sales Price per Unit $40

Variable Cost per Unit $32


Budgeted Sales $40,000

Solution

Breakeven Sales Units = $7,000 ($40 - $32) = 875

Budgeted Sales Units = $40,000 $40 = 1,000

Margin of Safety = (1000 875) 1,000= 12.5%

Relevant Costing

Relevant costing is a management accounting toolkit that helps managers reach decisions when they are posed with

following questions:

1. Whether to buy a component from an external vendor or manufacture it in house?2. Whether to accept a special order?3. What price to charge on a special order?4. Whether to discontinue a product line?5. How to utilize the scarce resource optimally?

Relevant costing is an incremental analysis which means that it considers only relevant costs i.e. costs that differ betw

alternatives and ignores sunk costs i.e. costs which have been incurred, which cannot be changed and hence are irrelev

to the scenario.Example

Company A manufactures bicycles. It can produce 1,000 units in a month for a fixed cost of $300,000 and variable cos

$500 per unit. Its current demand is 600 units which it sells at $1,000 per unit. It is approached by Company B for an or

of 200 units at $700 per unit. Should the company accept the order?

Solution

A layman would reject the order because he would think that the order is leading to loss of $100 per unit assuming that

total cost per unit is $800 (fixed cost of $300,000/1,000 and variable cost of $500 as compared to revenue of $700).

On the other hand, a management accountant will go ahead with the order because in his opinion the special order

yield $200 per unit. He knows that the fixed cost of $300,000 is irrelevant because it is going to be incurred regardles

whether the order is accepted or not. Effectively, the additional cost which Company A would have to incur is the varia

cost of $500 per unit. Hence, the order will yield $200 per unit ($700 minus $500 of variable cost).

Special Order PricingSpecial order pricing is a technique used to calculate the lowest price of a product or service at which a special order m

be accepted and below which a special order should be rejected. Usually a business receives special orders from custom

at a price lower than normal. In such cases, the business will not accept the special order if it can sell all its output at nor

price. However when sales are low or when there is idle production capacity, special orders should be accepted if

incremental revenue from special order is greater than incremental costs.

This method of pricing special orders, in which price is set below normal price but the sale still generates some contribu

per unit, is called contribution approach to special order pricing. The idea is that it is better to receive something ab

variable costs, than receiving nothing at all.

The following example is used to illustrate special order pricing:

Example

A company is producing, on average, 10,000 units of product A per month despite having 30% more capacity. Costs per

of product A are as follows:Direct Material $8.00

Direct Labor 5.00

Variable Factory Overhead 2.00

Variable Selling Expense 0.50

Fixed Factory Overhead 3.00

Fixed Office Expense 2.00

$20.50


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The company received a special order of 2,000 units of product A at $17.00 per unit from a new customer. Should

company accept the special order, provided that the customer has agreed to pay the variable selling expenses in additio

the price of the product?

Solution

The increment cost per unit for the special order is calculated as:

Direct Material $8.00

Direct Labor 5.00

Variable Factory Overhead 2.00

$15.00Since the incremental cost per unit is less that the price offered in the special order, the company should accep

Accepting special order will generate additional contribution of $2.00 unit and $4,000 in total.

Make-or-Buy Decision

Make-or-Buy decision (also called the outsourcing decision) is a judgment made by management whether to mak

component internally or buy it from the market. While making the decision, both qualitative and quantitative factors m

be considered.

Examples of the qualitative factors in make-or-buy decision are: control over quality of the component, reliability

suppliers and impact of the decision on suppliers and customers, etc.

The quantitative factors are actually the incremental costs resulting from making or buying the component. For exam

incremental production cost per unit, purchase cost per unit, production capacity available to manufacture the compon

etc.The following example illustrates the numerical part of a simple make-or-buy decision.

Example

The estimated costs of producing 6,000 units of a component are:

Per Unit Total

Direct Material $10 $60,000

Direct Labor 8 48,000

Applied Variable Factory Overhead 9 54,000

Applied Fixed Factory Overhead 12 72,000

$1.5 per direct labor dollar

$39 $234,000

The same component can be purchased from market at a price of $29 per unit. If the component is purchased from mar25% of the fixed factory overhead will be saved.

Should the component be purchased from the market?

Solution

Per Unit Total

Make Buy Make Buy

Purchase Price $29 $174,000

Direct Material $10 $60,000

Direct Labor 8 48,000

Variable Overhead 9 54,000

Relevant Fixed Overhead 3 18,000

Total Relevant Costs $30 $29 $180,000 $174,000

Difference in Favor of Buying $1 $6,000

Sell-or-Process-Further Decision

A decision whether to sell a joint product at split-off point or to process it further and sell it in a more refined form is ca

a sell-or-process-further decision. Joint products are two or more products which have been manufactured from the sa

inputs and in a same production process (i.e. a joint process). The point at which joint products leave the joint proces

called split-off point.

Some of the joint products may be in final form ready for sale, while others may be processed further. In such ca

managers have to decide whether to sell the unfinished goods at split-off point or to process them further. Such decisio

known as sell-or-process-further decision and it must be made so as to maximize the profits of the business.


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A sell-or-process-further analysis can be carried out in three different ways:

Incremental (or Differential) Approach calculates the difference between the additional revenues and additional costs of further processing. If the difference is positive the product must be processed furth

otherwise not.

Opportunity Cost Approachcalculates the difference between net revenue from further processed product the opportunity cost of not selling the product at split-off point. If the difference is positive, further processing

increase profits.

Total Project Approach(or the comparative statement approach) compares the profit statements of both opti(i.e. selling or further processing) separately for each product. The option generating higher profit is chosen.

The following example illustrates the approaches to a sell-or-process-further decision:Example

Product A and B are produced in a joint process. At split-off point, Product A is complete whereas product B can be proc

further. The following additional information is available:

Product A B

Quantity in Units 5,000 10,000

Selling Price Per Unit:

At Split-Off $10 $2.5

If Processed Further $5

Costs After Split-Off $20,000

Perform sell-or-process-further analysis for product B.

Solution

Incremental Approach:

Incremental Revenue $25,000

Incremental Costs 20,000

Increase in Profits Due to Further Processing $5,000

Opportunity Cost Approach:

Sales in Case of Further Processing $50,000

Costs:

Additional Costs 20,000

Opportunity Cost of Not Selling at Split-Off 25,000

Gain on Further Processing $5,000

Total Project Approach:

Split-Off

Point

Further

Processed

Revenue $25,000 $50,000

Costs 0 20,000

Net Revenue $25,000 $30,000

Gain from Further Processing $5,000

Decision to Add or Drop Product Line

A decision whether or not to continue an old product line or department, or to start a new one is called an add-or-d

decision. An add-or-drop decision must be based only on relevant information.

Relevant information includes the revenues and costs which are directly related to a product line or department. Exam

of relevant information are sales revenue, direct costs, variable overhead and direct fixed overhead. Such decision must

be based on irrelevant information such as allocated fixed overhead because allocated fixed overhead will not

eliminated if the product line or department is dropped.

The following example illustrates an add-or-drop decision:

Example

A company has three products: Product A, Product B and Product C. Income statements of the three product lines for

latest month are given below:


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Product Line A B C

Sales $467,000 $314,000 $598,000

Variable Costs 241,000 169,000 321,000

Contribution Margin $226,000 $145,000 $277,000

Direct Fixed Costs 91,000 86,000 112,000

Allocated Fixed Costs 93,000 62,000 120,000

Net Income $42,000 $3,000 $45,000

Use the incremental approach to determine if Product B should be dropped.Solution

By dropping Product B, the company will lose the sale revenue from the product line. The company will also obtain gain

the form of avoided costs. But it can avoid only the variable costs and direct fixed costs of product B and not the alloca

fixed costs. Hence:

If Product B is Dropped

Gains:

Variable Costs Avoided $169,000

Direct Fixed Costs Avoided $86,000 $255,000

Less: Sales Revenue Lost $314,000

Decrease in Net Income of the Company $59,000

Scarce Resource Utilization Decision

Scarce resource utilization (or allocation) decision is a judgment regarding the best use of scarce resources so as

maximize the total net income of a business. Scarcity of different resources puts constraints on the amount of product t

can be produced using those resources. For example, a business may have limited number of machine hours to utiliz

production. Scarce resource allocation decision is also called limiting factors decision.

When resources are abundant, products generating relatively higher contribution margin per unit are preferred becaus

leads to highest net income. However when resources are scarce, a decision in this way is unlikely to maximize the pr

Instead the allocation of a scarce resource to various products must be based on the contribution margin per unit of

scarce resource from each product.

A simple scarce resource allocation decision involves the following steps:

1. Calculate the contribution margin per unit of the scarce resource from each product.2.

Rank the products in the order of decreasing contribution margin per unit of scarce resource.3. Estimate the number of units of each product which can be sold.

4. Allocate scarce resource first to the product with highest contribution margin per unit of scarce resource, thethe product with next highest contribution margin per unit of scarce resource.

A scarce resource decision can be better explained using an example.

Example

A company has 4,000 machine hours of plant capacity per month which are to be allocated to products A and B. T

following per unit figures relate to the products:

Product A B

Sale Price $300 $240

Costs:

Direct Material 100 70

Direct Labor 65 50

Variable Overhead 20 40

Fixed Overhead 15 30

Variable Operating Expenses 40 20

Total Costs $240 $210

Net Income $60 $30

Machine Hours Required 1.5 1.00

Assuming that the company can sell all its output, determine how many machine hours shall be allocated to each produc

Solution


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Product A B

Sale Price $300 $240

Variable Cost 225 180

CM Per Unit $75 $60

Machine Hours Required 1.50 1.00

CM Per Machine Hour $50 $60

Since the company can sell all its output the best decision is to allocate all machine hours (i.e. scarce resource) to produc

Capital Budgeting

Capital budgeting (or investment appraisal) is the process of determining the viability to long-term investments on purch

or replacement of property plant and equipment, new product line or other projects.

Capital budgeting consists of various techniques used by managers such as:

1. Payback Period2. Discounted Payback Period3. Net Present Value4. Accounting Rate of Return5. Internal Rate of Return6. Profitability Index

All of the above techniques are based on the comparison of cash inflows and outflow of a project however they

substantially different in their approach.

A brief introduction to the above methods is given below:

Payback Periodmeasures the time in which the initial cash flow is returned by the project. Cash flows are discounted. Lower payback period is preferred.

Net Present Value (NPV) is equal to initial cash outflow less sum of discounted cash inflows. Higher NPpreferred and an investment is only viable if its NPV is positive.

Accounting Rate of Return (ARR)is the profitability of the project calculated as projected total net income diviby initial or average investment. Net income is not discounted.

Internal Rate of Return (IRR)is the discount rate at which net present value of the project becomes zero. HigIRR should be preferred.

Profitability Index (PI)is the ratio of present value of future cash flows of a project to initial investment requfor the project.

The above techniques are explained in detail in next pages.

Payback Period

Payback period is the time in which the initial cash outflow of an investment is expected to be recovered from the c

inflows generated by the investment. It is one of the simplest investment appraisal techniques.

Formula

The formula to calculate payback period of a project depends on whether the cash flow per period from the project is e

or uneven. In case they are even, the formula to calculate payback period is:

Payback Period =Initial Investment

Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use

following formula for payback period:

Payback Period = A + BC

In the above formula,

Ais the last period with a negative cumulative cash flow;

Bis the absolute value of cumulative cash flow at the end of the period A;

Cis the total cash flow during the period after A

Both of the above situations are applied in the following examples.

Decision Rule

Accept the project only if its payback period is LESS than the target payback period.

Examples

Example 1: Even Cash Flows
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Company C is planning to undertake a project requiring initial investment of $105 million. The project is expected

generate $25 million per year for 7 years. Calculate the payback period of the project.

Solution

Payback Period = Initial Investment Annual Cash Flow = $105M $25M = 4.2 years

Example 2: Uneven Cash Flows

Company C is planning to undertake another project requiring initial investment of $50 million and is expected to gene

$10 million in Year 1, $13 million in Year 2, $16 million in year 3, $19 million in Year 4 and $22 million in Year 5. Calcul

the payback value of the project.

Solution

(cash flows in millions)Cumulative

Cash FlowYear Cash Flow

0 (50) (50)

1 10 (40)

2 13 (27)

3 16 (11)

4 19 8

5 22 30

Payback Period

= 3 + (|-$11M| $19M)= 3 + ($11M $19M)

3 + 0.58

3.58 years

Advantages and Disadvantages

Advantagesof payback period are:

1. Payback period is very simple to calculate.2. It can be a measure of risk inherent in a project. Since cash flows that occur later in a project's life are conside

more uncertain, payback period provides an indication of how certain the project cash inflows are.

3. For companies facing liquidity problems, it provides a good ranking of projects that would return money early.Disadvantagesof payback period are:

1. Payback period does not take into account thetime value of moneywhich is a serious drawback since it can leawrong decisions. A variation of payback method that attempts to remove this drawback is called discoun

payback periodmethod.

2. It does not take into account, the cash flows that occur after the payback period.Discounted Payback Period

One of the major disadvantages of simple payback period is that it ignores the time value of money. To counter

limitation, an alternative procedure called discounted payback period may be followed, which accounts for time value

money by discounting the cash inflows of the project.

Formulas and Calculation Procedure

In discounted payback period we have to calculate the present value of each cash inflow taking the start of the first per

as zero point. For this purpose the management has to set a suitable discount rate. The discounted cash inflow for e

period is to be calculated using the formula:

Discounted Cash Inflow =Actual Cash Inflow

(1 + i)n

Where,

iis the discount rate;

nis the period to which the cash inflow relates.

Usually the above formula is split into two components which are actual cash inflow and present value factor ( i.e. 1 / ( 1

)^n ). Thus discounted cash flow is the product of actual cash flow and present value factor.

The rest of the procedure is similar to the calculation ofsimple payback periodexcept that we have to use the discoun

cash flows as calculated above instead of actual cash flows. The cumulative cash flow will be replaced by cumula

discounted cash flow.

Discounted Payback Period = A + B
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C

Where,

A= Last period with a negative discounted cumulative cash flow;

B= Absolute value of discounted cumulative cash flow at the end of the period A;

C= Discounted cash flow during the period after A.

Note: In the calculation of simple payback period, we could use an alternative formula for situations where all the c

inflows were even. That formula won't be applicable here since it is extremely unlikely that discounted cash inflows wil

even.

The calculation method is illustrated in the example below.

Decision Rule

If the discounted payback period is less that the target period, accept the project. Otherwise reject.

Example

An initial investment of $2,324,000 is expected to generate $600,000 per year for 6 years. Calculate the discounted payb

period of the investment if the discount rate is 11%.

Solution

Step 1: Prepare a table to calculate discounted cash flow of each period by multiplying the actual cash flows by present

value factor. Create a cumulative discounted cash flow column.

Year

n

Cash Flow

CF

Present Value Factor

PV$1=1/(1+i)n

Discounted Cash Flow

CFPV$1

Cumulative Discounted

Cash Flow

0 $ 2,324,000 1.0000 $ 2,324,000 $ 2,324,000

1 600,000 0.9009 540,541 1,783,459

2 600,000 0.8116 486,973 1,296,486

3 600,000 0.7312 438,715 857,771

4 600,000 0.6587 395,239 462,533

5 600,000 0.5935 356,071 106,462

6 600,000 0.5346 320,785 214,323

Step 2: Discounted Payback Period = 5 + |-106,462| / 320,785 5.32 years

Advantages and Disadvantages

Advantage:Discounted payback period is more reliable thansimple payback periodsince it accounts for time value of

money. It is interesting to note that if a project has negative net present value it won't pay back the initial investment.

Disadvantage:It ignores the cash inflows from project after the payback period.

Accounting Rate of Return (ARR)

Accounting rate of return (also known as simple rate of return) is the ratio of estimated accounting profit of a project to

average investment made in the project. ARR is used in investment appraisal.

Formula

Accounting Rate of Return is calculated using the following formula:

ARR =Average Accounting Profit

Average Investment

Average accounting profit is the arithmetic mean of accounting income expected to be earned during each year of

project's life time. Average investment may be calculated as the sum of the beginning and ending book value of the pro

divided by 2. Another variation of ARR formula uses initial investment instead of average investment.Decision Rule

Accept the project only if its ARR is equal to or greater than the required accounting rate of return. In case of mutu

exclusive projects, accept the one with highest ARR.

Examples

Example 1: An initial investment of $130,000 is expected to generate annual cash inflow of $32,000 for 6 ye

Depreciation is allowed on the straight line basis. It is estimated that the project will generate scrap value of $10,500 at

of the 6th year. Calculate its accounting rate of return assuming that there are no other expenses on the project.

Solution

Annual Depreciation = (Initial Investment Scrap Value) Useful Life in Years

Annual Depreciation = ($130,000 $10,500) 6 $19,917
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Average Accounting Income = $32,000 $19,917 = $12,083

Accounting Rate of Return = $12,083 $130,000 9.3%

Example 2:Compare the following two mutually exclusive projects on the basis of ARR. Cash flows and salvage values ar

thousands of dollars. Use thestraight line depreciationmethod.

Project A:

Year 0 1 2 3

Cash Outflow -220

Cash Inflow 91 130 105

Salvage Value 10

Project B:Year 0 1 2 3

Cash Outflow -198


Salvage Value 18

Solution

Project A:

Step 1: Annual Depreciation = (220 10) / 3 = 70

Step 2: Year 1 2 3


Salvage Value 10

Depreciation* -70 -70 -70

Accounting Income 21 60 45

Step 3: Average Accounting Income = (21 + 60 + 45) / 3 = 42

Step 4: Accounting Rate of Return = 42 / 220 = 19.1%

Project B:

Step 1: Annual Depreciation = (198 18) / 3 = 60

Step 2: Year 1 2 3


Salvage Value 18

Depreciation* -60 -60 -60

Accounting Income 27 50 42

Step 3: Average Accounting Income = (27 + 50 + 42) / 3 = 39.666

Step 4: Accounting Rate of Return = 39.666 / 198 20.0%

Since the ARR of the project B is higher, it is more favorable than the project A.

Advantages and DisadvantagesAdvantages

1. Likepayback period,this method of investment appraisal is easy to calculate.2. It recognizes the profitability factor of investment.

Disadvantages

1. It ignorestime value of money.Suppose, if we use ARR to compare two projects having equal initial investmeThe project which has higher annual income in the latter years of its useful life may rank higher than the o

having higher annual income in the beginning years, even if the present value of the income generated by

latter project is higher.

2. It can be calculated in different ways. Thus there is problem of consistency.3. It uses accounting income rather than cash flow information. Thus it is not suitable for projects which having h

maintenance costs because their viability also depends upon timely cash inflows.

Net Present Value (NPV)

Net present value is the present value of net cash inflows generated by a project including salvage value, if any, less

initial investment on the project. It is one of the most reliable measures used in capital budgeting because it accounts

time value of moneyby using discounted cash inflows.

Before calculating NPV, a target rate of return is set which is used to discount the net cash inflows from a project. Net c

inflow equals total cash inflow during a period less the expenses directly incurred on generating the cash inflow.

Calculation Methods and Formulas

The first step involved in the calculation of NPV is the determination of the present value of net cash inflows from a pro

or asset. The net cash flows may be even (i.e. equal cash inflows in different periods) or uneven (i.e. different cash flow
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different periods). When they are even, present value can be easily calculated by using the present value formul

annuity.However, if they are uneven, we need to calculate the present value of each individual net cash inflow separate

In the second step we subtract the initial investment on the project from the total present value of inflows to arrive at

present value.

Thus we have the following two formulas for the calculation of NPV:

When cash inflows are even:

NPV = R 1 (1 + i)

-nInitial Investment

i

In the above formula,Ris the net cash inflow expected to be received each period;

iis the required rate of return per period;

nare the number of periods during which the project is expected to operate and generate cash inflows.

When cash inflows are uneven:

NPV =R1

+R2

+R3

+ ... Initial Investment(1 + i)

1 (1 + i)

2 (1 + i)

3

Where,

iis the target rate of return per period;

R1is the net cash inflow during the first period;

R2is the net cash inflow during the second period;

R3is the net cash inflow during the third period, and so on ...

Decision Rule

Accept the project only if its NPV is positive or zero. Reject the project having negative NPV. While comparing two or m

exclusive projects having positive NPVs, accept the one with highest NPV.

Examples

Example 1: Even Cash Inflows:Calculate the net present value of a project which requires an initial investment of $243,

and it is expected to generate a cash inflow of $50,000 each month for 12 months. Assume that the salvage value of

project is zero. The target rate of return is 12% per annum.

Solution

We have,

Initial Investment = $243,000

Net Cash Inflow per Period = $50,000

Number of Periods = 12

Discount Rate per Period = 12% 12 = 1%Net Present Value

= $50,000 (1 (1 + 1%)^-12) 1% $243,000

= $50,000 (1 1.01^-12) 0.01 $243,000

$50,000 (1 0.887449) 0.01 $243,000

$50,000 0.112551 0.01 $243,000

$50,000 11.2551 $243,000

$562,754 $243,000

$319,754

Example 2: Uneven Cash Inflows:An initial investment on plant and machinery of $8,320 thousand is expected to gener

cash inflows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first, second, thi

and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 thousand. Calculate the

present value of the investment if the discount rate is 18%. Round your answer to nearest thousand dollars

Solution

PV Factors:

Year 1 = 1 (1 + 18%)^1 0.8475

Year 2 = 1 (1 + 18%)^2 0.7182

Year 3 = 1 (1 + 18%)^3 0.6086

Year 4 = 1 (1 + 18%)^4 0.5158

The rest of the problem can be solved more efficiently in table format as shown below:

Year 1 2 3 4

Net Cash Inflow $3,411 $4,070 $5,824 $2,065
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Salvage Value 900

Total Cash Inflow $3,411 $4,070 $5,824 $2,965

Present Value Factor 0.8475 0.7182 0.6086 0.5158

Present Value of Cash Flows $2,890.68 $2,923.01 $3,544.67 $1,529.31

Total PV of Cash Inflows $10,888

Initial Investment 8,320

Net Present Value $2,568 thousand

Advantage and Disadvantage of NPV

Advantage:Net present value accounts for time value of money.Thus it is more reliable than other investment appra

techniques which do not discount future cash flows such payback period and accounting rate of return.

Disadvantage:It is based on estimated future cash flows of the project and estimates may be far from actual results.

Internal Rate of Return (IRR)

Internal rate of return (IRR) is the discount rate at which thenet present valueof an investment becomes zero. In ot

words, IRR is the discount rate which equates the present value of the future cash flows of an investment with the in

investment. It is one of the several measures used for investment appraisal.

Decision Rule

A project should only be accepted if its IRR is NOT less than the target internal rate of return. When comparing two or m

mutually exclusive projects, the project having highest value of IRR should be accepted.

IRR Calculation

The calculation of IRR is a bit complex than other capital budgetingtechniques. We know that at IRR, Net Present Va

(NPV) is zero, thus:

NPV = 0; or

PV of future cash flows Initial Investment = 0; or

CF1+

CF2+

CF3+ ... Initial Investment = 0

( 1 + r )1 ( 1 + r )

2 ( 1 + r )

3

Where,

ris the internal rate of return;

CF1is the period one net cash inflow;

CF2is the period two net cash inflow,

CF3is the period three net cash inflow, and so on ...But the problem is, we cannot isolate the variable r(=internal rate of return) on one side of the above equation. Howe

there are alternative procedures which can be followed to find IRR. The simplest of them is described below:

1. Guess the value of r and calculate the NPV of the project at that value.2. If NPV is close to zero then IRR is equal to r.3. If NPV is greater than 0 then increase r and jump to step 5.4. If NPV is smaller than 0 then decrease r and jump to step 5.5. Recalculate NPV using the new value of r and go back to step 2.

Example

Find the IRR of an investment having initial cash outflow of $213,000. The cash inflows during the first, second, third

fourth years are expected to be $65,200, $96,000, $73,100 and $55,400 respectively.

Solution

Assume that r is 10%.NPV at 10% discount rate = $18,372

Since NPV is greater than zero we have to increase discount rat

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