3
II
SOME BASIC ECONOMIC CONCEPTS
Many engineers work for corporations and businesses while others find employment with non-profit
organizations. The fundamental distinction in businesses and non-profit organizations is the difference in the
objectives. The purpose, or at least the main purpose of businesses, is to make profit. If a business does not
make profit over an extended period of time, it will fail. On the other hand, the purpose of non-profit
organizations is to provide services which are deemed beneficial to the public at large. Their objective is not
to produce a profit but to provide a needed service. This chapter deals with some general concepts and ideas
which are useful in evaluating projects in both types of environments.
2.1 TYPES OF BUSINESS ORGANIZATIONS
There are many different types of business organizations. In this section a few different ways in
which a business may be organized are discussed.
2.1.1 Individuals:
This is the simplest type of business organization. An individual sets up a
business, provides capital, and basically runs the business. Examples of these businesses are small one person
coffee shops and grocery stores, etc. In these businesses other employees may or may not work. All capital
(portion of capital may be borrowed) is provided by the owner and all profits (if any) are kept by the owner.
Advantages of this type of organization are (i) complete control of business and all business related decisions,
and (ii) owner keeps all profit. The main disadvantage of this type of business is liability. If a business fails,
4
the owner is responsible for all the liabilities (things of value which the business owes). Another disadvantage
is limited capability to raise or borrow capital for the business.
2.1.2 Partnerships: In partnerships, one or more people jointly own and run a business. Capital
is provided by the partners and all business related decisions are made jointly by the partners. A good example
of such a business is an engineer and a marketing graduate forming a partnership. The engineer can design
products while the marketing graduate can help sell it. The advantages of partnerships are more capital and
expertise for running a business. The disadvantages are loss of control over decision making and sharing of
profits from the business with partners. The major disadvantage, however, remains the liabilities against the
business. But now instead of one person, all the partners are responsible.
2.1.3
Corporations: Corporations are organized by filing a charter with an appropriate body
(State where corporation is being organized). A charter is a broad statement of types of activities a business
is planning to conduct. An example of a charter is to " manufacture and sell machinery parts". Capital for
corporations is provided by the stock holders who own it. Capital is raised by selling stocks. Stocks are traded
in open market and anyone can buy stocks at the "going" price. Generally, there are a multitude of stock
holders and therefore the control of a corporation is given to the board of directors who are responsible for
running it. For many corporations, a full management team is needed to supervise the operations. This may
include, President/Chief Executive Officer, Vice Presidents, Treasurer, Secretary, and several department
managers.
Profit earned by a corporation is primarily used for two purposes. A portion of profit earned is used
within the corporation for new and existing ventures. This portion of the profit is called "retained earnings".
Remainder of the profit is divided among the stockholders. This portion of profit distributed to the stock
holders is referred to as "dividends." A major advantage of this form of organization is that liability for an
individual stockholders is limited to the value of the stock held in the corporation.
5
It should be pointed out that the main goal of corporations, like any business, is to maximize “profit”
for the stockholders. There are many ways in which this “profit” can be measured but one obvious way is
to use dividends for the stockholders. Some other ways to measure this “profit” are (i) increase in value of
the stock and (ii) the ease of selling the stock. However, these measures cannot be quantified easily. Note
that if a corporation fails to produce profit over an extended period of time it will cease to exist.
2.1.4. Summary: In Sections 2.1.1 to 2.1.3, some important forms of business organizations were
discussed. It should be pointed out that there are many variations of the three forms of organizations discussed
here. It is beyond the scope of this book to describe all different forms of organizations. Also, only a few
important characteristics of each type of organization are discussed. For a more complete review the reader
is referred to many good references available on this topic. But one thing stands out, businesses are organized
to produce profit for the owners.
2.2
NON-PROFIT ORGANIZATIONS
The main objective of non-profit organizations is to provide services which are beneficial to the
public at large. Examples of these organizations are the Federal Government, the State Government, many
hospitals , religious organizations, and special interest groups such as The Nature Conservancy and The
Environmental Defense Fund. One of the many responsibilities of the Federal Government is to ensure that
we have an adequate defense system. State Governments provide resources for higher education, hospitals
provide a variety of health related services, and the Nature Conservancy is involved in protecting land and
environment. Note that in all these activities the idea is not to produce a profit but to provide a needed
service which benefits public at large.
2.3 EVALUATION OF PROJECTS
In most businesses (or for profit organizations) and non-profit organizations, there is generally a
shortage of funds for projects. Even if there is enough money to embark on a project, it must be justified.
6
Engineering economy deals with methods which are used for justification and selection of projects. Concepts
that are used for justification/selection of projects are similar to those used in a traditional decision making
problem. Therefore, few important characteristics of the decision making problem will be discussed.
One feature of a generalized decision problem is that there must be more than one alternative
because if there is only one alternative, then no decision is required and we must choose that particular
alternative. Therefore, more than one alternative must exist and the problem is to find the " best " one. A
decision problem can be simply stated as: determine the "best" alternative from a set of alternatives. In
general, determination of this set of alternatives is problem specific and there are no general rules for
developing it. The definition of what is "best" is not always easy but we must define what is meant by "best"
before a choice can be made. These two important concepts are further illustrated by the following example.
A student in a major urban university is trying to decide "how to commute to the school". This is a
simple but a typical decision problem. We first develop a set of alternate ways to commute to the school. This
set may include (i) Walk, (ii) Take a bus, (iii) Car, (iv) Bike, and (v) Car pool. Assuming that these are
the only alternatives, which one is the"best"? To determine this, we must specify what is meant by the "best."
Several factors may be used to define the criterion which will be used in determination of the “best”
alternative. Some of these factors are (i) Cost, (ii) Time, and (iii) Safety. Let us further assume that only
one factor, cost, will be used to make the decision. The decision can be made now and it is "to walk to
school" as it requires least cost.
From this simple example, we can see that there are two main features of a decision problem. One
is the determination of the set of the alternatives and second is the definition of "best" or the factors used in
the definition of "best". In many real life situations, more than one factor is used in the definition of “best”
For our example, one may want to use both "cost" and "safety" for determining the best alternative.
One important aspect in which traditional engineering economic analysis differs from generalized
decision problem is the use of only one factor for specification of the "best".This one factor used in
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engineering economic analysis is monetary Monetary factors are those which can be easily quantified in
terms of money or dollars. Some examples of monetary factors are profit, cost, rate of return. Non-monetary
factors cannot be easily quantified in terms of dollars. For example, safety of a machine cannot be easily
measured in terms of dollars. Safety of a machine is considered a non-monetary factor. In general, it is
difficult to measure many non-monetary factors. There is no universally accepted scale for measuring safety
of a machine. One can use an scale of 1 to 5 (with 1 being very safe and 5 unsafe) but it is not clear how
these values are to be converted to dollars.
If both monetary as well as non-monetary factors are used in evaluation of alternatives or
projects then one must use methods which allow us to measure and combine these two different types of
factors. Methods for analysis with multiple factors are developed but are beyond the scope of this book.
As stated earlier, in a business environment, profit is the most important factor in evaluating different
projects. However, for government and non-profit organizations, profit is not considered and benefit is the
most important factor. Calculation of profit for a project is, relatively, much easier than the quantification of
benefits from a project (See section 2.9).
2.4
PROFIT
Profit is calculated as follows:
Profit = Income - Expenses
(2.4.1)
It is mathematically possible to compute profit for any period of time. Many businesses have a profit
and loss statement for each quarter and they pay estimated taxes for each quarter. All businesses must file
an annual income tax return and therefore annual profit must be calculated.
Income can be derived from many sources; revenues, interest, rentals, etc. Revenues are generated
by selling products and services. For example, a company sells 20,000 die cast parts for $3.50 each. The
revenue generated by this activity is (20,000)(3.50) or $75,000. A dry cleaning business laundered 30,000
shirts this year. Charge for each shirt is $1.50. Revenue generated from this activity of the dry cleaning
8
business is $45,000. Expenses are all costs incurred in conducting the business. Many different costs are
incurred in manufacturing products or in providing services. Some examples are: labor cost, material cost,
rental of facilities, utilities etc. A detailed description of different types of cost follows.
2.5
ELEMENTS OF COST
All costs incurred in making a product or providing a service can be categorized as direct material,
direct labor and overhead costs.
2.5.1
Direct Material Cost
This category includes cost of materials which are directly used in a product. All other materials are
referred to as indirect materials. The following three criteria can be used to determine whether a material
used in a product can be classified as direct material or not?
(i) Significant amount ( in dollars )
(ii) Easily measurable
(iii) Similar quantity (amount in identical units)
For classification of a material as direct material, all three criteria must be satisfied.
Let us consider an example of a company which makes wooden furniture (tables, shelves, and
computer desks). Following is a list of materials which are used in making wooden tables:
Wood, Varnish, Screws, Nails, Glue, and Paint
Using the three criteria outlined above, it can be seen that wood can be classified as a direct
material. Amount of wood used in a table is significant in terms of dollars as cost of wood is a significant
portion of the total cost of a table. Also, amount of wood used in similar styles is easily measurable and is
same for each table. All other materials used are not direct material. For example, examine the item
screws. Cost of screws used in a table is relatively very small compared with the total cost of a table. As
one of the three criteria, significant amount is not satisfied, screws are indirect material. Using a similar logic,
varnish, paint, and nails are also classified as indirect material. In this example, only one material (wood) is
9
classified as direct material. In many products, it is entirely possible that more than one material is classified
as direct material.
Cost of direct material can be determined easily if the amount of material used per unit product and
cost of material is known. For example, if a 2.5 feet by 6 feet wood board (3/4 inch thick) is needed for one
table and cost is $2.66/square feet, then the cost of direct material is (2.5X6)(2.66) or $40.
2.5.2
Direct Labor Cost
The three criteria outlined above can also be used to classify different types of labor into direct and
indirect labor. Some of the personnel which may be needed in production of tables are as follows:
Carpenters, Foreman, Janitor, Maintenance Person
Carpenters making tables in this company will be classified as direct labor. Using the three criteria
outlined above, labor (carpenter) cost per table is certainly significant, can be measured easily, and is about
same for each similar style table manufactured. All other types of labor used can be classified as indirect. For
example, time spent per table by a janitor, in dollars, is small compared to the total cost of a table.
Cost of direct labor can be determined if the time spent by a worker per unit and the hourly rate is
known. For our example, if a carpenter spends 2.75 hours for each table and the hourly rate is $20 then direct
labor cost for a table is (2.75)(20) or $55.
2.5.3
Overhead:
All costs which are not classified as direct material or direct labor are grouped together and
designated as overhead costs. Estimation of total overhead cost, for making all the products, is straight
forward. We simply add the cost of all indirect material, all indirect labor, and all other costs which are
incurred in making products and are not included in direct material or labor. Some of the items which may
be included are property taxes, utilities, rental of facility, insurance for the facility, etc.
Allocation of overhead cost to different products is problematic. If only one product is manufactured
all of the overhead is allocated this one product. But if more than one product is made then total overhead
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must be, somehow, divided among all the products. Note that for our example of furniture company, overhead
consists of cost of glue, paint, and varnish etc. We have total cost of these items but no idea that how these
costs are to be divided among the three products manufactured.
There are several methods for distributing overhead to different products. These methods are based
on prorating overhead cost based on some common resource used in making different products. Some of
these methods are:
I.
Direct Material Cost Rate:
In this method, overhead is distributed based
theonusage of direct material cost in a product. First
we find an overhead rate as follows:
Overhead rate =
Total Overhead in a Period
Total DM cost in the Period
(2.5.1)
Overhead allocated to a product = Overhead Rate(DM Cost used for the product)
II
Direct Labor Cost Rate:
In this method, overhead rate is based on the usage of direct labor in a product. We find the
overhead rate as follows:
Overhead rate =
Total Overhead in a Period
Total DL cost in the Period
(2.5.2)
Overhead allocated to a product = (Overhead Rate)(DL Cost for the product)
III.
Direct Labor Hour Method:
In this method, overhead rate is based on the usage of direct labor hours used in a product.
The overhead rate is calculated as follows:
Overhead rate =
Total Overhead in a Period
Total DL hours in the Period
(2.5.3)
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Overhead allocated a product = Overhead rate(DL hours for the product)
It should be obvious that one can use any resource or combination of resources in allocating
overheads to different products. In general, overhead rate is determined as follows:
Overhead rate =
Total overhead in a period
Total resource / s used in the period
(2.5.4)
Overhead allocated to a product = Overhead rate(Resource/s used for the product)
Some other resources that can be used are prime cost (sum of DM and DL cost), area used, and
machine hours. The following example will clarify the allocation of overhead and determination of total cost
of manufacturing different products.
2.5.4
An Example
A furniture company is making three wooden products; tables, shelves, and computer desks. A
breakdown of all costs for making the three products for this company in one year is shown in Table 2.5.1.
Table 2.5.1
Breakdown of Costs for Fiscal Year
_________________________________________________________________
1.
Direct material cost
2.
Indirect material cost
3.
Direct labor cost
439,425
4.
Indirect labor cost
359,000
5.
Other costs
Rental of building
Utilities
Miscellaneous
Total
6.
Total Costs
$328,250
30,165
30,000
90,000
18,000
138,000
$1,294,840
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________________________________________________________________
In this table, direct material cost is the total cost of wood used in one year for making all three
products. Indirect material cost consists of varnish, paint, nails, and glue etc. used for the three products.
Direct labor cost represents total labor cost of all carpenters. This cost includes wages and all other benefits
such as health insurance, retirement etc. Indirect labor cost is the cost of all other personnel employed by
the company. These include plant managers, secretaries, payroll, etc. Cost of other resources utilized, printer
cartridges, pens, etc is shown as miscellaneous costs. Table 2.5.1 is a summary of all costs incurred by this
company in one year. Using this table, it is easy to see that overhead cost is the sum of items 2, 4, and 5.
Total overhead cost for this year is (30,165 + 359,000 + 138,000) or $527,165.
Table 2.5.2 shows breakdown of different costs by product. For example, direct material cost for
making 2,900 tables is $116,000 or $40 per table. Similarly, direct labor cost of making 2,000 computer
Table 2.5.2
Breakdown of Costs and Other Resources
Product
Units
Direct
Material Cost
Direct Labor
Cost
Direct
Labor
Hours
Square Feet
Tables
2,900
$116,000
$159,500
7,975
8,500
Shelves
1,845
92,250
89,940
5,996
5,000
Computer Desk
2,000
120,000
189,985
8,000
6,000
Total
***
328,250
439,425
21,971
19,500
desks is $189,985 or $94.99. It can be inferred from this data that each computer desk requires 8,000/(2,000)
hours of carpenter’s time. Also, production of shelves uses an area of 5,000 square feet.
Using the information in Tables 2.5.1 and 2.5.2, cost of making any product can be determined.
The cost of manufacturing a table is calculated as follows:
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Total cost of a table = DM cost + DL cost + OH cost
From Table 2.5.2;
DM cost = 116,000/(2,900) = $40.00
DL cost = 159,500/(2,900) = $55.00
Overhead cost per table is not known and only the total overhead incurred in making all the three
products is known. From Table 2.5.1, overhead is $527,165. What portion of this overhead cost should be
allocated to the production of a table? We can use any method described in section 2.5.3. Let us use direct
material cost rate. From Table 2.5.2, total direct material cost for all three products is (116,000 + 97,250 +
120,000) or $328,250. Overhead rate, using Eq. (2.5.1), is calculated as follows:
Overhead rate = (527,165)/(328,250) = $1.60/$ of DM cost
Overhead for a table = Overhead rate(DM cost of one table)
= (1.60)(40) = $64.00
Total cost of a table = DM cost + DL cost + Overhead cost
= 40.00 + 55.00 + 64.00
= $159.00
If the selling price of a table is $189, then profit per table is
Profit = Revenue - Cost
= 189.00 - 159.00
= $30.00/table
Profit from selling 2,900 tables is (2,900)(30) or $87,000.
Next, we determine cost of making a shelf using both the direct labor cost method and the prime cost
method for allocation of overhead.
From Table 2.5.2:
DM cost of a shelf = 92,250/(1,845) = $50.00
DL cost of a shelf
= 89,940/(1,845) = $48.75
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Using direct labor cost method (Eq. 2.5.2), overhead rate is:
Overhead rate = (527,165)/(439,425) = $1.20/$ of DL cost
Note that total DL cost for all three products (Table 2.5.2) is (159,500 + 89,940 + 189,985) or
$439,425.
Overhead for a shelf = Overhead rate(DL cost for a shelf)
= (1.20)(48.75)
= $58.50
Total cost of a shelf = 50.00 + 48.75 + 58.50
= $157.25
Using the prime cost method, overhead rate is obtained by dividing the total overhead by total prime
cost in this year. Total prime cost, sum of DM and DL cost, for making all the three products is
(328,250 + 439,425) or $767,675. Overhead rate, using Eq. (2.5.4) is
Overhead rate = (527,165)/(767,675) = $0.69/$ of prime cost
Overhead for one shelf = Overhead rate(Prime cost for one shelf)
= 0.69(50.00 + 48.75)
= $68.14
Total cost of a shelf = 50.00 + 48.75 + 68.14
= $166.89
It should be noted that cost per shelf is $166.89 if prime cost method for assigning the overhead is
used while it is $157.20 if the direct labor cost method is used. The difference in these two costs is due to the
difference in the allocation of overhead cost as DM and DL costs remain same. The reason for different
overhead cost is due to the assumptions made in determining the allocation of overhead. In direct labor cost
method it was assumed that products which have higher direct labor cost will also use more overhead while
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in prime cost method the assumption is that products which use more direct material and direct labor will
use more overhead.
It is not always obvious which method should be used for allocating overhead to different products.
The best way is to establish which resource or resources are most appropriate for prorating the total overhead
cost and use those in distributing the overhead. Many companies use a blanket rate for overhead, for example
150% of labor cost or 130% of prime cost. This method is simple but it may penalize some products by
unnecessarily assigning a higher overhead and thereby making their cost higher than what it is or should be.
2.6
TAXES
Taxes must be paid on all profit earned by a business. Details for calculation of taxes are contained
in Chapter 7. As stated earlier, profit is calculated as follows:
Profit = Revenue - Expenses
and
After tax profit = Profit - Taxes paid
After tax profit is money earned by the owners of a business after all expenses and taxes are paid.
Recall that for a corporation this after tax profit is divided into two parts: retained earnings and dividends. The
Board of Directors decide what portion should be given out as dividend to the stock holders. Retained
earnings are kept in the corporation for future projects.
2.7 CLASSIFICATION OF COSTS
In Section 2.5, elements of total cost were discussed. In this section we examine a variety of costs
from a different perspective and provide definitions of these costs.
2.7.1 Recurring and Non Recurring Costs: Costs which are incurred in making a product may
occur periodically or only once. This idea is used to define " first cost" (non-recurring) and "operation and
maintenance costs or "(O+M)" costs (recurring). This distinction of two types of costs is important and is
16
needed for determination of income taxes.
I. First Cost:
First cost is the total cost of an asset (things of value which a company owns)
needed to start a project. This cost includes cost of purchasing an asset and all other costs which are
necessary to put it in operation. For example, a milling machine is needed for a new product. First cost
includes purchase price of the machine , operator training, electrical connections, etc. Note that first cost
is a non-recurring cost as it occurs when a new project is started. Investment in an asset is, sometimes, also
referred to as first cost.
II. Operation and Maintenance Costs or (O+M) costs: Costs which occur periodically,
throughout the life of a project, are grouped in (O+M) costs. These costs are paid as incurred. For example,
labor cost is paid every two weeks or monthly and utility bills are paid every month.
As stated earlier, division of all costs into two types, one time(first cost or investment), also referred
to as capital expenses, and (O+M) costs is needed because of differential treatment of these costs for
income tax purposes. Capital (one time) expenses are costs of items which have a life of more than one year
and cost more than $1,000. For example, a drilling machine is purchased for $8,500. This cost is a capital
expense as it is greater than $1,000 and expected life a drilling machine is more than one year. On the other
hand a monthly payment of $24,678 for utilities is considered a (O+M) cost as utility bills are paid periodically,
generally every month. As another example, a company buys a small grinder for $800. This cost will be
classified as (O+M) cost because cost of grinder is less than $1,000 even though the expected life of this
grinder is more than one year. It should be pointed out that rules governing what cost costs are classified as
capital expense change frequently and these rules should be carefully checked out.
2.7.2 Fixed and Variable Costs:
Costs can also be classified as fixed or variable costs.
I. Fixed Costs: Fixed costs are those costs which remain fixed over a certain level of
activity. For example, let us assume that area needed to manufacture up to 50,000 units per month of a
17
product is 100,000 square feet. Rental for this building is $25,000 per month. Cost of renting can be
considered as a fixed cost as long as the number of units produced is less than 50,000 per month. Note that
if production rate increases beyond 50,000 units per month, extra space will be needed for production. The
level of activity in our example is defined by the number of units produced and rental cost is fixed in the range
of 0 to 50,000 units per month. It should be pointed out that different measures for level of activity can be
defined (See Example 2.8.1). Other costs that may remain fixed are insurance, utilities, etc.
II. Variable Costs: Variable costs change with the level of activity. Examples of variable
costs are direct material and direct labor costs. Suppose that one unit of a product uses one inch bar stock
costing $1.25 per inch. Ten units will use 10 inches of bar stock at a cost of $12.50. The higher the number
of units produced higher is the amount and cost of the material used. Similarly, if one unit requires 10 minutes
of time of a machine operator (labor cost of $3.00) then 20 units will require 200 minutes of labor time at a
cost of $60.00.
Using fixed and variable costs, total cost for manufacturing “n” units can be written as follows:
Total Cost = F + nV
where
(2.7.1)
F = fixed cost, $
V = variable cost per unit, $/unit
n = number of units produced (or level of activity)
In Eq.(2.7.1), variable cost per unit is assumed to vary linearly with the number of units produced.
Fixed and variable costs are used in determining the breakeven point. This will be discussed later in this
chapter.
2.7.3 Incremental Costs: Incremental cost is defined as extra cost needed to make additional
units. In our example in Section 2.7.2 the range of level of activity is up to 50,000 units. Suppose production
rate for past several months was 40,000 units per month. However, next month, 45,000 units or 5,000 extra
units are needed. The incremental cost of producing 5,000 extra units (40,000 to 45,000) is only the extra
18
variable costs as fixed cost remains same for up to 50,000 units. However, if 55,000 units are to be produced
then incremental cost for making these extra 5,000 units (50,000 to 55,000) will be the sum of extra fixed cost,
probably due to rental of extra space needed, and the extra variable costs.
2.7.4 Sunk Costs: In general all costs are recoverable. Costs are recovered by revenues
generated. Sunk cost is considered non-recoverable. The concept of sunk cost is best explained through an
example. Suppose a student is looking for a used car. The student finds a car for $3,500 (car A) after looking
at several used cars. The student pays $500 deposit and promises the seller to come back with rest of money
within 3 days as remaining $3,000 will be borrowed from a bank. The student applies for a loan at a bank and
has to wait for its approval. He keeps on looking for cars and finds a very similar car costing only $2,700 (car
B). The question is which car should the student should buy? The answer obviously is to buy Car B as it is
cheaper. If Car B is bought what happens to the $500 deposit? The student can try to get it back but let us
assume the seller refuses to give back the deposit because the car has been taken out of the market. If $500
deposit is not returned cost of Car B is 27,00 + 500 or $3,200. The $500 deposit is considered a sunk cost
as it cannot be recovered. In this example costs are recovered by “use of car” and not revenues. The student
is expecting to get $2,700 worth of “use” from car B and not $(2,700 + 500) or $3,200 worth of “use”.
Sunk costs should not occur. These costs are generally due to past mistakes. In our example,
probably student should have looked a little longer. Whatever is the reason for the sunk cost, it should not be
used in making future decisions.
2.7.5 Opportunity Costs: The concept of opportunity costs deals with the utilization of resources.
If a resource is used at one place it cannot be used at any other place. The cost of not using the resource at
an alternate place is the opportunity cost. For example, if $500 are available for savings, this $500 can be
saved in a savings account, or $500 worth of stock may be purchased. If stock is purchased then the
opportunity cost is the amount of interest that can be earned if $500 is put in a savings account.
2.7.6 Life Cycle Costs: Life cycle cost of a project is considered as the total of all costs incurred
19
over the entire life of the project. These costs may include cost of design and development of the product,
all recurring and nonrecurring costs, and all costs which may be associated with the abandonment of a
project. This cost is especially useful in making decisions about new products.
2.8 BREAKEVEN POINT
Breakeven point refers to the level of activity, for example number of units produced, for no profit.
E
Cost
&
Revenues, $
Profit
B
G
C
F
Loss
A
D
n*
Units, #
Figure 2.8.1 Breakeven Chart
This means that at the breakeven point total revenues equal total cost. Breakeven point can be determined
either graphically or mathematically.
A breakeven chart is used for determination of breakeven point graphically. Fig. 2.8.1 shows a typical
20
breakeven chart. In this chart, number of units are shown along the x-axis while costs and revenues are
plotted on y-axis. It is assumed that both variable costs and revenues vary linearly with the number of units.
In Fig. 2.8.1, fixed cost, F, is plotted as a horizontal line (CF) as it remains constant for a specified range of
activity. Variable costs and revenues are plotted as straight line AB and AE respectively. Note that if no
units are produced both the revenues and costs are zero. Then both increase linearly with the number of units
produced. The slope of both these lines is dictated by the variable cost and revenues per unit. Total cost, sum
of fixed and variable costs, is shown by another straight line CD. It should be noted that the total cost line
is parallel to line AB. The intersection of lines CD and AE, G, is the breakeven point as total revenues and
total costs are equal at this point.
Mathematically, breakeven point is determined by equating total cost with total revenue. In general
for “n” units,
Total cost
= F + n(V)
Total revenue
= n(R)
where
V is the variable cost/unit, $
R is the selling price per unit, $
Equating total cost and revenues, we get
F + n(V) = n(R)
Solving for n and designating breakeven point as n*
n* = (F)/(R - V)
(2.8.1)
It is obvious, and can be readily seen from Fig. 2.8.1, that profit or loss is dependent on the number
of units produced. For a specified number of units, n, if total revenue exceeds total cost then a profit is
21
realized. However, if total revenue is less than the total cost then a loss is incurred . In other words, if n >
n* profit will be realized and if n < n* , a loss will be incurred. At n = n* , the breakeven point, profit is zero.
Example 2.8.1 A professional engineering society is planning to conduct a one day technical seminar for
its members. The following cost data has been assembled.
Fixed Costs:
Brochure printing
$126
Mailing brochures
190
Room charge
150
Speaker gifts
80
Variable Costs:
The following costs are for each registrant for the seminar
Lunch
Coffee breaks
Folder
$6.50
3.75
2.50
Determine (i) the breakeven point (number of registrants is the level of activity in this example) for
this seminar if cost of attending this seminar is $50 per person and (ii) profit made if 42 people attended the
seminar.
Solution:
(i)
For determining the breakeven point, n* , we first find total fixed cost and variable cost per
person.
Total fixed cost = 126 + 190 + 150 + 80 = $546
Variable cost/ person = 6.50 + 3.75 + 2.50 = $12.75
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Next, total revenue and total cost for “n” registrants are determined. As the registration fee is $50
per person,
Total revenue
= n(50)
Total cost
= 546 + (n)(12.75)
Equating total revenue and total cost and solving for n, we have
n = n* = 14.66
This means that the breakeven point is 15 registrants for the seminar. It should be pointed out that
Eq.(2.8.1) can also be used to find the breakeven point
(ii)
Profit for 42 registrants is found as follows:
Profit = Revenues - Costs
= (42)(50) -{546 + (42)(12.75)}
= $1,081.50
2.9
Non-Profit Organizations
In section 2.2 it was pointed out that the main purpose of non-profit organizations is to provide benefit
to public at large. Costs for a project, whether in a business or non-profit organization, can be estimated
relatively easily but benefits cannot be defined and calculated as easily profit. Nonetheless, for evaluation
of projects in non-profit sector, total benefit from a project must be determined as it is usually balanced
against cost for justification of projects. Benefit-cost ratio (B-C ratio) is commonly used for justification of
projects.
B-C ratio = (Benefits in dollars)/(Cost in dollars)
(2.9.1)
If B-C ratio > 1.0; project is justified otherwise it is not.
Example 2.10.1
A suburb of a large metropolitan area with population of 12,000 has a well
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developed park. This park has a pond (30,000 sq. ft.) which freezes in winter time and many residents use
this pond for ice skating. At a Village Board meeting a proposal was submitted to build a warm house where
skaters can change, rest and get some refreshments from vending machines. This will provide (i) better and
safer ice skating facility for the residents and (ii) increased usage especially by children and senior citizens.
Should the board approve this proposal?
Solution: Following estimates of costs have been obtained.
Cost of building
Furniture(benches, lockers, etc.)
Attendant
Miscellaneous(Utilities, etc.)
$180,000
25,000
6,200/yr
4,500/yr
It will be assumed that non-recurring costs, the cost of building and furniture will be prorated over
a 20 year time period. The total nonrecurring cost is (180,000 + 25,000) or $205,000. Cost per year is
(205,000/20) or $10,500. We add to this, cost of labor and miscellaneous items. Therefore, total cost per
year is (10,0500 + 6,200 + 4,500) or $21,200. Note that total cost of operating the warm house can be easily
estimated.
The question is should the Board spend $21,200 every year for this facility? The answer is obtained
by using Benefit-Cost ratio.
Recall that expected benefits are due to better and safer park and more usage of the skating rink.
What is the value of increased safety and usage ? These questions are not easily answered but one must
evaluate the value of all the expected benefits in terms of dollars for justification of a project.
One method for evaluation of benefits is to use a charge which users will have to pay for similar
services elsewhere. For our example, we may want to use admission charge for ice skating rinks in the city.
Let us assume that charge is $6 for a 3 hour session for an indoor skating facilities. As this facility is indoor,
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we may just use 60% of this charge for our outdoor rink. Corresponding equivalent admission charge is
therefore 0.60(6.00) or $3.60. Estimated additional usage due to warm house per season (12 weeks) is 3,600
and the value of this benefit in terms of dollars is 3,600(3.60) or $12,960. Benefit Cost ratio for this project
is
B-C ratio = (12,960)/(21,200) = 0.61
As B-C ratio is less than 1.0, this project is not justified.
The Board may still decide to build the warm house if they perceive that there are other benefits such
as increased use by children and senior citizens, increase in value of homes in the area etc. These benefits
are much harder to quantify in terms of dollars and are not used in the calculation of B-C ratio. It is worth
mentioning, if the Village Board decides to build the warm house, then all additional expenses will be paid
by property taxes. As the village population is 12,000 and extra expense per year is (21,200-12,960 (benefit))
or $8,240, annual cost per household( four person in each household) is only (8,240)/(3,000) or $2.74. This
factor can play an important role in decision making. Note that Village Board has several factors to consider
which are very hard to quantify especially in terms of dollars.
PROBLEMS
2.1
Following data is available for three departments, each making a different product, in a manufacturing
company for one quarter.
Department
Direct Labor Hours
Direct Material Cost
$2,100
Square feet
3,500ft2
A
450hrs
B
375
1,700
2,750
C
280
3,200
2,900
Total overhead for this quarter is $18,750 and the labor rate for all departments is $12.50 per hour.
(a) Determine the allocation of overhead to department A using direct material cost and
for
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department C using direct labor hours.($5,628; $4,752)
(b) What is the overhead allocation for department B using (i) prime cost and (ii) area used? ($5,748;
$5,638)
2.2
Two products, automobile batteries and distributors, are manufactured using three different
departments. Both the products go through all the three departments. Direct labor and direct material cost
for these products/unit in the departments are as follows:
Department
Battery
Direct Material Direct Labor
A
$4
B
9
C
7
$6
Distributor
Direct Material Direct Labor
$12
$17
4
10
22
11
26
20
Annual production of batteries and distributors is 6,000 units and 3,500 units respectively and annual
overhead is estimated as $284,000.
(a) Determine total cost of producing one battery using direct material as the basis for
allocation of overhead. If battery is sold for $79.99, determine the annual profit.
(b) If prime cost is used for allocation of overhead, determine total cost of manufacturing
one distributor. If distributors can be sold for $209.99, determine the annual profit.($156.22;
$188,195)
2.3
A furniture company manufactures four products; chairs, office tables, computer tables, and book
shelves. Three departments, cutting, painting, and assembly are used in making these products. Direct material
cost/unit for chairs, office tables, computer tables, and book shelves is $47, $30, $51, and $65 respectively.
Direct labor hours used for each product in all the departments are as follows:
Product
Chair
Office Table
Computer Table
Book Shelf
Direct Labor Hours/Unit
Cutting
Painting
1.5
1.3
1.8
2.0
0.75
0.6
1.0
1.2
Assembly
2.0
1.25
1.85
2.15
Annual overhead for all three departments is $326,750. Direct labor cost for cutting, painting and
assembly departments are $16, $12, and $14 per hour respectively. Annual production is chairs, 1500; office
tables, 650; computer tables, 1000; book shelves, 1200.
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(a) Determine total cost of manufacturing a book shelf using direct labor cost for allocation
of overhead. ($231.01)
(b) Determine total cost of a computer table using direct labor hours for allocation of
overhead.
(c) If a chair is sold for $219.99, determine the profit per chair if direct material cost is
allocation of overhead.($41.90)
used for
2.4
Injection Molding, Inc. produces two parts using plastics, lens for automobile lamps and lane markers
for highways. Annual production of lenses and markers is 36,000 and 64,000 respectively. Total cost of
manufacturing a lens is $6.00 and a marker is$2.40. This estimate of total cost is based on the assumption
that overhead per unit of lens is twice that of a marker. Total annual overhead is $105,670. A study by IE
department found that overhead is more equitably allocated if overhead per unit of lens is 1.75 times that of
a marker.
(a) Determine total cost of manufacturing a lens based on this revised allocation of
overhead.($5.90)
(b) If markers can be sold for $2.99/unit, determine the annual profit obtained by selling
all 64,000 markers. (Use revised allocation of overhead) ($34,290)
2.5
Fixed cost of operating a campground with 200 campsites for a season (six months; 180 days) is
$120,000. Variable cost per rented campsite is $2.00 per day. Determine the number of campsites that should
be rented on an average per day to breakeven if the rental charge per campsite per day is $8.25. What is the
profit in one season if 150 campsites on average are rented per day. (107, $48,750)
2.6
Fixed cost of organizing a short course (5 days) on flexible manufacturing cells is estimated as
follows:
Printing brochures
Mailing
Managerial time
Secretarial time
Speakers
$620
1,450
850
600
3,000
If variable cost per person which includes breakfast, lunch and bound notes is $206 and registration
fees are $795, determine the breakeven point. If twenty three people paid for this course, determine the profit
for organizing this course. (12, $7,027)
2.7
A company is investigating possibility of purchasing a component, set of small gears, needed for one
of its product from outside. Relevant data for making this part in house based on last years production is as
follows:
Fixed cost
Space
Machinery
$2,650
1,500
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Supervision
4,275
Variable cost/unit
Direct material
Direct labor
$1.91
2.34
If the part can be purchased from outside vendors for $4.35/ unit, should the company make the part
or buy from outside? (Hint: Find volumes for which to make and buy)