B.tech Civil Notes for 7th Semester

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ENGINEERING ECONOMICS - ECO202
Written & Composed BY ENGINEER SAQIB IMRAN
WhatsApp & Contact No: 0341-7549889
Email: Saqibimran43@gmail.com
Student of B.TECH(Civil) at Sarhad University of Science &
Information Technology Peshawer.

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ENGINEERING: The application of scientific and mathematical principles to practical ends such
as the design, manufacture and operation of efficient and economical structures, machines,
processes, and systems.
ECONOMICS: The social science that deals with the production, distribution and consumption
of goods and services and with the theory and management of economies or economic system.
In engineering, economics is the efficient use or management of limited or available resources.
ENGINEERING ECONOMICS: Engineering economics is the application of economic principles
and calculations to engineering projects. It is important to all fields of engineering because no
matter how technically sound an engineering project is; it will fail if it is not economically
feasible.
IMPORTANCE: Engineering economics is the application of economic principles and calculations
to engineering projects. It is important to all fields of engineering because no matter how
technically sound an engineering project is; it will fail if it is not economically feasible.
Engineering economics has an important role on investment analysis, especially in the case of
expressing advantages and disadvantages in monetary terms, when you want to invest a capital
or buy a capital good, checking all technically feasible alternatives of investment.
One of the engineering economics objectives is to do economic analysis of investment
decisions. It has quite extensive applications since the investment may come from private
companies or government entities. The analysis or evaluation of projects involves a set of
techniques that establish feasibility parameters.
SCOPE: According to the Institute of Industrial Engineers (IIE), engineering economics is
defined as the application of economic analysis and synthesis or mathematics or engineering
decisions to a body of knowledge and techniques involved in the assessment of the value of
goods and services in relation to the cost and methods to estimate the data. In this sense, it is
understood as a set of techniques that allow the monetary quantification and economic
evaluation of investment alternatives, providing the necessary information and knowledge for
decision-making. Many basic economic principles may be applied in an engineering economic
analysis, depending on their applicability. Time value of money is one such principle with wide
applicability. This principle is used to calculate the future value of something given the present
value, or the present value given the future value, at a given interest rate. For example, time
value of money may be used to calculate how much a project will cost once it is actually
completed; annual investments or withdrawals may also be calculated. A cash-flow diagram is
often used to aid in the calculation of the time value of money.
When comparing costs among two or more possible alternatives, engineering economics may
use either present or future worth analysis or annual cost. Present or future worth analysis
converts all the costs of a project into equivalent present or future worth. The time period of
analysis must be the same for all options for this method to be valid.
VALUE AND COST CONCEPTS
ECONOMIC VALUE: The worth of a good or service as determined by people’s preferences and
the tradeoffs they choose to make given their scarce resources, or the value the market places

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on an item. Economic value is represented by the maximum amount a consumer is willing to
pay for an item in a free market economy.
TERMINOLOGY
Variable Costs (VC): Costs which depend on the output produced. For example, if you produce
more cars, you have to use more raw materials such as metal. This is a variable cost.
Fixed Costs (FC): The costs which don’t vary with changing output. Fixed costs might include the
cost of building a factory, insurance and legal bills. Even if your output changes or you don’t
produce anything, your fixed costs stay the same.
Total Costs (TC) – Fixed + Variable Costs
Sunk Costs: These are costs that have been incurred and cannot be recouped. For example, if
you spend money on advertising to enter an industry, you can never claim these costs back.
Direct cost: A direct cost is related to producing a good or service. It can be accurately and
easily traced to a product, department or project. For example, suppose a worker spends
eight hours building a car for a car manufacturing company. The direct costs associated with the
car are the wages paid to the worker and the parts used to build the car.
Indirect cost: An indirect cost is an expense unrelated to producing a good or service. An
indirect cost cannot be easily traced to a product, department, activity or project. For example,
a semiconductor company rents office space in a building and produces microchips. The wages
paid to the workers and the material used to produce the microchips is direct costs. However,
the electricity used to power the entire building is considered an indirect cost.
Opportunity cost: Opportunity cost is the next best alternative foregone. It is the difference in
return between a chosen investment and one that is necessarily passed up. Say you invest in
a stock and it returns 2% over the year. In placing your money in the stock, you gave up the
opportunity of another investment - say, a risk-free government bond yielding 6%. In this
situation, your opportunity costs are 4% (6% - 2%).
Cash Cost: A cash cost requires the cash transaction of dollars "out of one person's pocket" into
"the pocket of someone else." When you buy dinner for your friends or make your monthly
automobile payment you are incurring a cash cost.
Book Cost: Book costs do not require the transaction of dollars "from one pocket to another."
Rather, book costs are cost effects from past decisions that are recorded "in the books"
(accounting books) of a firm. Book costs do not ordinarily represent cash flows and thus are not
included in engineering economic analysis.
Life cycle cost: Sum of all recurring and one-time (non-recurring) costs over full life span or
specified period of goods, services, structures or system. In includes purchase price, installation
cost, operating costs, maintenance and upgrade costs, and remaining (residual or salvage) value
at the end of ownership or its useful life.
COST DRIVEN DESIGN OPTIMIZATION
Engineers must maintain a life-cycle viewpoint as they design products, processes, and services.
Such a complete perspective ensures that engineers consider initial investment costs, operation
and maintenance expenses and other annual expenses in later years, and environmental and

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social consequences over the life of their designs. Cost-Driven Design Optimization" is simple
design models intended to illustrate the importance of cost in the design process. These
problems show the procedure for determining an optimal design, using cost concepts. For cost-
driven design optimization problems, the two main tasks are as follows:
1. Determine optimal value for certain alternative’s design variable
2. Select the best alternative, each with its own unique value for the design variable
In general the cost models developed in these problems consist of three types of costs:
 Fixed cost(s)
 Cost(s) that vary directly with the design variable
 Cost(s) that vary indirectly with the design variable
GENERAL APPROACH FOR OPTIMIZING A DESIGN WITH RESPECT TO COST
 Identify primary cost-driving design variable.
 Write an expression for the cost model in terms of the design variable.
 Set first derivative of cost model with respect to continuous design variable equal to 0.
 Solve equation in step 3 for optimum value of continuous design variables.
 For continuous design variables, use the second derivative of the cost model with respect to
the design variable to determine whether optimum corresponds to global maximum or
minimum.
TIME VALUE FOR MONEY
Definition: The change in the amount of money over given time period is called the time value
of money. It is the most important concept in the engineering economy.
INTRODUCTION: One of the most fundamental concepts in finance is that money has a “time
value.” That is to say that money in hand today is worth more than money that is expected to
be received in the future. The reason is straightforward: A dollar that you receive today can be
invested such that you will have more than a dollar at some future time. This leads to the saying
that we often use to summarize the concept of time value: “A dollar today is worth more than a
dollar tomorrow."
CONCEPT: Time Value of Money (TVM) is an important concept in financial management. It can
be used to compare investment alternatives and to solve problems involving loans, mortgages,
leases, savings, and annuities. TVM is based on the concept that a dollar that you have today is
worth more than the promise or expectation that you will receive a dollar in the future. Money
that you hold today is worth more because you can invest it and earn interest. After all, you
should receive some compensation for foregoing spending. For instance, you can invest your
dollar for one year at a 6% annual interest rate and accumulate $1.06 at the end of the year.
You can say that the future value of the dollar is $1.06 given a 6% interest rate and a one-year
period. It follows that the present value of the $1.06 you expect to receive in one year is only
$1. The Time Value of Money concepts will be grouped into two areas:
PRESENT VALUE & FUTURE VALUE
PRESENT VALUE: Present value is the amount of money today that is equivalent to a single
payment or a stream of payments earned in the future, invested at a certain interest rate. The

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formula for present value takes a future payment, or payments, and discounts them using the
interest rate to find the worth of this money today. The higher the interest rate is, the lower
the present value is today. The lower the interest rate is, the higher the present value is today.
The present value of $100 one year later is going to be worth less than $100 today. Why?
Because of the 5% interest. To make things easy, we use the formula for present value:
Present value =
𝐹𝑉
(1+ 𝑖) 𝑛
Where i is the interest rate and n is the number of time periods.
FUTURE VALUE: Future value is amount that is obtained by enhancing the value of a present
payment or a series of payments at the given rate of interest to reflect the time value of
money. Future value is the future worth of an amount of money invested today, paying a
certain interest rate. If we invest $100 today in an account earning 5% per year, then 5% of
$100 is $5, and in exactly 1 year, our $100 turns into $105. How do we figure that out? By using
the formula for future value:
Present value = PV x (1 + 𝑖) 𝑛
PV stands for present value, which is $100 in this case. i is the interest rate, which we said was
5%, and n is the number of periods - in this case we're talking about years, specifically 1 year -
so n = 1. When you plug all this into the future value formula, the future value of our $100
invested at 5% is equal to $100 * (1 + .05) ^1 = $105.
Example 1: Jefferson University has recently received a bequest of $1 million to establish a
trust for providing annual scholarships in perpetuity. The trust fund is deposited in a bank that
pays 7% interest per annum, and only the annual interest will be spent for the designated
purpose. What is the annual amount that is available for scholarships?
Sol: Since the interest will be withdrawn at the end of the interest period, the simple interest
per annum is ($1,000,000)(0.07) = $70,000
Note that at the end of each year, the trust fund remains intact after the interest is withdrawn
from the bank. Thus, $70,000 is available annually for scholarships in perpetuity.
Example 2: A sum of$1,00 0 is invested in a 2-year savings certificate that pays 8% interest per
year compounded annually. What is the total amount to be received at the end of 2 years?
Sol: The principal and interest at the end of each year for the 2 years are as follows:
End of year 1: 1,000 + (l,000)(0.08) = 1,080.00
End of year 2: 1.080 + (l,080)(0.08) = 1,166.40
Hence, the total amount to be received at the end of two years is $1,166.40.
Example 3: A manufacturer expects to receive $20,200 one month after the shipment of goods
to a retailer. The manufacturer needs the cash and has arranged with a bank for a loan of
$20,000 upon the shipment of goods on the condition that the bank will collect all of the
$20,200 from the retailer a month later. What is the monthly interest rate charged by the
bank?
Sol: Since there is only one interest period, the interest rate per month is:

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20,000−20,000
20,000
= 0.01 = 1%. This is also the discount rate by which the future sum of $20,200 is
discounted to a present value of $20,000.
THE CONCEPT OF EQUIVALENCE
Another important concept is the concept of equivalence between a current lump sum
of money and a lump sum to be received in the future. Offering someone a choice
between receiving $100 today and receiving $101 one year from today can
demonstrate this. Most people will opt for the $100 today. If we increase the amount of
future money to $115 or $125 or perhaps $200 and guarantee payment, there will be
a point at which the future sum of money will become more attractive than the current
$100. The amount of future money necessary to sway the person to choose the future
sum is dependent upon many things, which include, among others:  The inflation rate.
 Current opportunities to invest the $100.  Perceived risk.
No matter what the amount of money necessary to tip the scales, the concept that
money has a time value is established.
In the case just discussed, if the person is indifferent to receiving $125 one year from
now or $100 now, we say that the two sums are "equivalent." This concept of
equivalence is fundamental to the evaluation of all engineering projects. By
determining the equivalence between money received today and money received in the
future, we can make an informed decision.
UNIFORM SERIES
It is a sum of money payable yearly or at other regular intervals. Many times we will find
uniform series of receipts or disbursements. Automobile loans, house payments, and many
other loans are based on a uniform payment series
Figure: The general relationship between A and F.

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A = An end-of-period cash receipt or disbursement in a uniform series, continuing for n periods,
the entire series equivalent to P or F at interest rate i.
The horizontal line in figure is a representation of time with four interest periods.
Uniform payments ‘A’ have been placed at the end of each interest period, and there are as
many A's as there are interest periods n. above figure uses January 1 and December 31, but
other periods could be used.
DISCOUNTED CASH FLOW
Discounted cash flow (DCF) is a valuation method used to estimate the attractiveness of an
investment opportunity. DCF analysis uses future free cash flow projections and discounts them
to arrive at a present value estimate, which is used to evaluate the potential for investment. If
the value arrived at through DCF analysis is higher than the current cost of the investment, the
opportunity may be a good one.
APPLICATIONS OF MONEY-TIME RELATIONSHIPS
All engineering economy studies of capital projects should consider the return that a given
project will or should produce. A basic question is whether a proposed capital investment and
its associated expenditures can be recovered by revenue (or savings) over time in addition to a
return on the capital that is sufficiently attractive in view of the risks involved and the potential
alternative uses. The interest and money-time relationship emerges as essential ingredients in
answering this question, and they are applied to many different types of problems. For
answering these questions following methods are applied to evaluate the profit or returns
resulting from an investment.
1. MINIMUM ATTRACTIVE RATE OF RETURN (MARR): In business and engineering, the
minimum attractive rate of return, often abbreviated MARR, or hurdle rate is the minimum rate
of return on a project a manager or company is willing to accept before starting a project, given
its risk and the opportunity cost of forgoing other projects. MARR is the minimum interest rate
that encourages the investor to invest in financial projects. When a project has been proposed,
it must first go through a preliminary analysis in order to determine whether or not it has a
positive net present value using the MARR as the discount rate. The MARR is the target rate for
evaluation of the project investment. This is accomplished by creating a cash flow diagram for
the project, and moving all of the transactions on that diagram to the same point, using the
MARR as the interest rate. If the resulting value at that point is zero or higher, then the project
will move on to the next stage of analysis. Otherwise, it is discarded. The MARR generally
increases with increased risk.
2. INTERNAL RATE OF RETURN (IRR): Internal rate of return (IRR) is the interest rate at which
the net present value of all the cash flows (both positive and negative) from a project or
investment equal zero. Internal rate of return is used to evaluate the attractiveness of a project
or investment. IRR is used in capital budgeting to measure and compare the profitability of
investments. IRR calculations are commonly used to evaluate the desirability of investments or
projects. The higher a project's IRR, the more desirable it is to undertake the project. Assuming
all projects require the same amount of up-front investment, the project with the highest IRR

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would be considered the best and undertaken first.
3. EXTERNAL RATE OF RETURN: ERR method directly takes into account the interest rate (𝜀)
external to a project at which net cash flows generated or required by the project over its life
can be reinvested or borrowed. If ERR = IRR, then the ERR method produces results identical to
those IRR methods. If ERR ≥ MARR, the project is economically justified.
4. PRESENT WORTH: Present worth analysis is most frequently used to determine the present
value of future money receipts and disbursements. It would help us, for example, to determine
a present worth of income-producing property, like an oil well or an apartment house. If the
future income and costs are known, then using a suitable interest rate, the present worth of the
property may be calculated. This should provide a good estimate of the price at which the
property could be bought or sold
5. FUTURE WORTH: A primary objective of all time value of money methods is to maximize the
future wealth of the owners of a firm. The economic information provided by the future worth
method is very useful in capital investment decision situations. The future worth is based on
the equivalent worth of all cash inflows and outflows at the end of the study period at an
interest rate that is generally the MARR. Also, the FW of a project is equivalent to its PW. The
equivalent future worth is obtained by using following formula:
FW = PW(
𝐹
𝑃
, i, n,)
6. THE ANNUAL WORTH METHOD: The Annual Worth method evaluates the desirability of an
alternative as an equal annual series of cash flows during the study period. Basically, it looks at
the annual equivalent of all the cash flows of an alternative. The AW worth is most useful when
comparing alternatives with unequal expected lives. The AW of a project is annual equivalent
revenues or savings (R) minus annual equivalent annual expenses (E), less its annual equivalent
Capital Recovery (CR) amount, which is can be calculated by,
CR (i %) =I (A/P, i%, N) - S (A/F, i%, N). Where, I = initial investment for the project, S = salvage
(market) value at the end of the study period, N = project study period In evaluation form the
AW, which is a function of i%, is N, which is usually in years. The AW can be calculated by the
following formula, AW (i %) = R – E - CR (i %). Also, we need to notice that the AW of a project is
equivalent to its PW and FW. That is, AW = PW (A/P, i%, N), and AW = FW (A/F, i%, N).
Hence, it can be computed for a project from these equivalent values.
COST/BENEFIT RATIO
Cost–benefit analysis (CBA), is a systematic approach to estimating the strengths and
weaknesses of alternatives that satisfy transactions, activities or functional requirements for a
business. It is a technique that is used to determine options that provide the best approach for
the adoption and practice in terms of benefits in labor, time and cost savings etc. The CBA is
also defined as a systematic process for calculating and comparing benefits and costs of a
project, decision or government policy. Broadly, CBA has two purposes: To determine if it is a
sound investment/decision (justification/feasibility), To provide a basis for comparing projects.
It involves comparing the total expected cost of each option against the total expected benefits,
to see whether the benefits outweigh the costs, and by how much Cost-benefit analysis

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assesses the profitability of a financial endeavor by considering the present value of each cost
and benefit. Present values are used under the assumption that money available now is worth
more than money in the future. That is generally true in an economy with positive inflation, so
values need to be discounted for this effect.
BENEFIT-COST RATIO (BCR): A benefit-cost ratio (BCR) is an indicator, used in the formal
discipline of Cost-Benefit Analysis,, that attempts to summarize the overall value of money of a
project or proposal. Benefit cost ratios are most often used in corporate finance to detail the
relationship between possible benefits and costs, both quantitative and qualitative, of
undertaking new projects or replacing old ones.
ADVANTAGES OF COST BENEFIT ANALYSIS: Using the benefit cost ratio allows businesses and
governments to make decisions on the negatives and positives of investing in different projects.
In other words, using benefit cost ratio analysis allows an entity to decide whether or not the
benefits of a given project or proposal outweighs the actual costs that go into the creation of
the project or proposal. Businesses and governments can benefit greatly by figuring out the
cost of a project versus its returns. For this reason alone, the benefit cost ratio is an important
formula to be used in the decision making process for any project that might be presented.
DEPRECIATION AND OBSOLESCENCE
DEPRECIATION: Depreciation is the decrease in the value of physical properties with the
passage of time and use. More specifically, depreciation is an accounting concept that
establishes an annual deduction against before time-tax income such that the effect of time
and use on an asset value can be reflected in a firm’s financial statement. It may be tangible or
intangible Assets depreciate for two reasons:
 Wear and tear. For example, a car will decrease in value because of the mileage, wear on
tires, and other factors related to the use of the vehicle.
 Obsolescence. Assets also decrease in value as they are replaced by newer models. Last
year's car model is less valuable because there is a newer model in the marketplace.
METHODS OF DEPRECIATION: Depreciation is classified into following two categories:
1. CLASSICAL (HISTORICAL) DEPRECIATION METHOD
i. Straight Line Method: The simplest and most commonly used method, straight-line
depreciation is calculated by taking the purchase or acquisition price of an asset, subtracting
the salvage value (value at which it can be sold once the company no longer needs it) and
dividing by the total productive years for which the asset can reasonably be expected to benefit
the company (or its useful life). Straight-line depreciation produces a constant depreciation
expense. At the end of the asset's useful life, the asset is accounted for in the balance sheet at
its salvage value
ii. Straight Line Depreciation: Example A company purchases a machine for $60,000. It has an
estimated salvage value of $10,000 and a useful life of five years. Company calculates the
annual straight-line depreciation for the machine as: Purchase cost of $60,000 – estimated
salvage value of $10,000 = Depreciable asset cost of $50,000 1 / 5-year useful life = 20%
depreciation rate per year 20% depreciation rate x $50,000 depreciable asset cost = $10,000

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annual depreciation
iii. Sum-of-the-Years Digits Method: Sum-of-years' digits is a depreciation method that results
in a more accelerated write off than straight line, but less accelerated than that of the double-
declining balance method. Under this method, annual depreciation is determined by
multiplying the depreciable cost by a series of fractions based on the sum of the asset's useful
life digits. The sum of the digits can be determined by using the formula (n2+n)/2, where n is
equal to the useful life of the asset. To calculate depreciation expense under the sum-of-years-
digits -- assume a piece of machinery is purchased for USD 100,000 with a residual value of
40,000 and a useful life of 5 years. First, calculate the depreciation rate by adding the years of
useful life, or 1 + 2 + 3 + 4 + 5 (equal to 15). Second, calculate the depreciation expense for year
5 -- 100,000 - 40,000 * 5/15, or USD 20,000. For year 4, the calculation uses the asset's book
value (100,000 - 20,000) subtracted by its residual value (40,000) and multiplied by the rate for
year 4 (4/15).
iv. Declining balance method Declining balance method of depreciation is a technique of
accelerated depreciation in which the amount of depreciation that is charged to an asset
declines over time. In other words, more depreciation is charged during the beginning of the
life time and less is charged during the end. Why more depreciation is charged in beginning
years? The reason is that assets are usually more productive when they are new and their
productivity declines gradually. Thus, in the early years of their life time, assets generate more
revenue as compared to the revenue generated in later years of their life.
2. MODIFIED ACCELARATED COST RECOVERY SYSTEM (MACRS): MACRS stands for modified
accelerated cost recovery system. It is the current system to calculate tax deductions on
account of depreciation for depreciable assets (other than intangible assets). It allows a larger
deduction in early years and lower deductions in later years when compared to the straight-line
method. There are two sub-systems of MACRS: the general depreciation system (GDS) and
alternate depreciation system (ADS). GDS is the most relevant and is used for most assets.
Formulas Depreciation in 1st Year = Cost ×
1
Useful Life
× A × Depreciation Convention.
Depreciation in Subsequent Years = (Cost − Depreciation in Previous Years) ×
1
Recovery Period
× A Where A is 100% or 150% or 200%.
However, where the depreciation calculated using the above formula is lower than depreciation
under straight line method, the straight line depreciation for the previous year is taken as the
relevant depreciation deduction for the rest of the recovery period. OR
Depreciation: Any equipment which is purchased today will not work for ever. This may be due
to wear and tear of the equipment or obsolescence of technology. Hence, it is to be replaced at
the proper time for continuance of any business. The replacement of the equipment at the end
of its life involves money. This must be internally generated from the earnings of the equipment.
The recovery of money from the earnings of an equipment for its replacement purpose is called
depreciation fund since we make an assumption that the value of the equipment decreases with
the passage of time. Thus, the word “depreciation” means decrease in value of any physical

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asset with the passage of time.
METHODS OF DEPRECIATION: There are several methods of accounting depreciation fund.
These are as follows: 1. Straight line method of depreciation. 2. Declining balance method of
depreciation. 3. Sum of the years—digits method of depreciation. 4. Sinking-fund method of
depreciation. 5. Service output method of depreciation. These are now discussed in detail.
1: Straight Line Method of Depreciation: In this method of depreciation, a fixed sum is charged as
the depreciation amount throughout the lifetime of an asset such that the accumulated sum at
the end of the life of the asset is exactly equal to the purchase value of the asset.
Here, we make an important assumption that inflation is absent.
Let, P = first cost of the asset, F = salvage value of the asset, n = life of the asset, 𝐁𝐭 = book value of
the asset at the end of the period t, 𝐃𝐭 = depreciation amount for the period t.
The formulae for depreciation and book value are as follows: Dt = (P – F)/n
𝐁𝐭 = Bt – 1 – Dt = P – t [(P – F)/n]
EXAMPLE 1: A company has purchased an equipment whose first cost is Rs. 1,00,000 with an
estimated life of eight years. The estimated salvage value of the equipment at the end of its
lifetime is Rs. 20,000. Determine the depreciation charge and book value at the end of various
years using the straight line method of depreciation.
Solution: P = Rs. 1,00,000. F = Rs. 20,000, n = 8 years.
Dt = (P – F)/n = (1,00,000 – 20,000)/8 = Rs. 10,000.
In this method of depreciation, the value of Dt is the same for all the years. The calculations
pertaining to Bt for different values of t are summarized in Table 1.
Table 1 Dt and Bt Values under Straight Line Method of Depreciation
End of the year (t) Depreciation (𝑫𝒕) Book Value (𝑩𝒕 = 𝑩𝒕−𝟏 - 𝑫𝒕)
0 1,00,000
1 10,000 90,000
2 10,000 80,000
3 10,000 70,000
4 10,000 60,000
5 10,000 50,000
6 10,000 40,000
7 10,000 30,000
8 10,000 20,000
If we are interested in computing Dt and Bt for a specific period (t), the formulae can be used.
In this approach, it should be noted that the depreciation is the same for all the periods.
2: Declining Balance Method of Depreciation: In this method of depreciation, a constant
percentage of the book value of the previous period of the asset will be charged as the
depreciation amount for the current period. This approach is a more realistic approach, since
the depreciation charge decreases with the life of the asset which matches with the earning
potential of the asset. The book value at the end of the life of the asset may not be exactly
equal to the salvage value of the asset. This is a major limitation of this approach.
Let, P = first cost of the asset, F = salvage value of the asset, n = life of the asset,

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𝐁𝐭 = book value of the asset at the end of the period t, K = a fixed percentage, and
𝐃𝐭 = depreciation amount at the end of the period t.
The formulae for depreciation and book value are as follows: Dt = K x Bt−1
Bt = Bt−1 – Dt = Bt−1 – K x Bt−1 = (1 – K) Bt−1
The formulae for depreciation and book value in terms of P are as follows: Dt = K(1 – K)t–1 x P
Bt = (1 – K)t x P
While availing income-tax exception for the depreciation amount paid in each year, the rate K is
limited to at the most 2/n. If this rate is used, then the corresponding approach is called the
double declining balance method of depreciation.
EXAMPLE 2: Consider Example 1 and demonstrate the calculations of the declining balance
method of depreciation by assuming 0.2 for K.
Solution: P = Rs. 1,00,000. F = Rs. 20,000. n = 8 years. K = 0.2
The calculations pertaining to Dt and Bt for different values of t are summarized in Table 2
using the following formulae:
Dt = K x Bt−1 ⇒ Bt = Bt−1 - Dt
Table 2 Dt and Bt according to Declining Balance Method of Depreciation.
End of the year (n) Depreciation (𝑫𝒕) Book Value (𝑩𝒕)
0 1,00,000.00
1 20,000.00 80,000.00
2 16,000.00 64,000.00
3 12,000.00 51,200.00
4 10,240.00 40,960.00
5 8,192.00 32,768.00
6 6,553.60 26,214.40
7 5,242.88 20,971.52
8 4,194.30 16,777.22
If we are interested in computing Dt and Bt for a specific period t, the respective formulae can
be used.
3: Sum-of-the-Years-Digits Method of Depreciation: In this method of depreciation also, it is
assumed that the book value of the asset decreases at a decreasing rate. If the asset has a life
of eight years, first the sum of the years is computed as:
Sum of the years = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = n(n + 1)/2
The rate of depreciation charge for the first year is assumed as the highest and then it
decreases. The rates of depreciation for the years 1–8, respectively are as follows: 8/36, 7/36,
6/36, 5/36, 4/36, 3/36, 2/36, and 1/36. For any year, the depreciation is calculated by
multiplying the corresponding rate of depreciation with (P – F).
Dt = Rate (P – F) ⇒ Bt = Bt−1 – Dt

13. 13 | P a g e
The formulae for Dt and Bt for a specific year t are as follows:
𝐷𝑡 =
𝑛−𝑡+1
𝑛(𝑛+1)/2
(P – F) ⇒ 𝐵𝑡 = (P – F) =
(𝑛−𝑡)
𝑛
𝑛−𝑡+1
(𝑛+1)
+ 𝐹
EXAMPLE 3: Consider Example 1 and demonstrate the calculations of the sum-of-the-years-
digits method of depreciation.
Solution: P = Rs. 1,00,000. F = Rs. 20,000. n = 8 years. Sum = n (n + 1)/2 = 8 9/2 = 36
The rates for years 1–8, are respectively 8/36, 7/36, 6/36, 5/36, 4/36, 3/36, 2/36 and 1/36.
The calculations of Dt and Bt for different values of t are summarized in Table 3 using the
following formulae: Dt = Rate (P – F) ⇒ Bt = Bt−1 – Dt.
Table 3 Dt and Bt under Sum-of-the-years-digits Method of Depreciation.
End of the year (n) Depreciation (𝑫𝒕) Book Value (𝑩𝒕)
0 1,00,000.00
1 17,777.77 82,222.23
2 15,555.55 66,666.68
3 13,333.33 53,333.35
4 11,111.11 42,222.24
5 8,888.88 33,333.36
6 6,666.66 26,666.70
7 4,444.44 22,222.26
8 2,222.22 20,000.04
If we are interested in calculating Dt and Bt for a specific t, then the usage of the formulae
would be better.
4: Sinking Fund Method of Depreciation: In this method of depreciation, the book value
decreases at increasing rates with respect to the life of the asset.
Let, P = first cost of the asset, F = salvage value of the asset, n = life of the asset,
i = rate of return compounded annually, A = the annual equivalent amount,
Bt = the book value of the asset at the end of the period t, and Dt = the depreciation amount at
the end of the period t.
The loss in value of the asset (P – F) is made available on the form of cumulative depreciation
amount at the end of the life of the asset by setting up an equal depreciation amount (A) at the
end of each period during the lifetime of the asset.
A = (P – F) [A/F, i, n]
The fixed sum depreciated at the end of every time period earns an interest at the rate of i%
compounded annually, and hence the actual depreciation amount will be in the increasing

14. 14 | P a g e
manner with respect to the time period. A generalized formula for Dt is
Dt = (P – F) (A/F, i, n) (F/P, i, t – 1)
The formula to calculate the book value at the end of period t is
Bt = P – (P – F) (A/F, i, n) (F/A, i, t)
The above two formulae are very useful if we have to calculate Dt and Bt for any specific
period. If we calculate Dt and Bt for all the periods, then the tabular approach would be better.
EXAMPLE 4: Consider Example 1 and give the calculations regarding the sinking fund method of
depreciation with an interest rate of 12%, compounded annually.
Solution: P = Rs. 1,00,000. F = Rs. 20,000. n = 8 years. i = 12%.
A = (P – F) [A/F, 12%, 8] = (1,00,000 – 20,000) x 0.0813 = Rs. 6,504
In this method of depreciation, a fixed amount of Rs. 6,504 will be depreciated at the end of
every year from the earning of the asset. The depreciated amount will earn interest for the
remaining period of life of the asset at an interest rate of 12%, compounded annually. For
example, the calculations of net depreciation for some periods are as follows:
Depreciation at the end of year 1 (D1) = Rs. 6,504.
Depreciation at the end of year 2 (D2) = 6,504 + 6,504 x 0.12 = Rs. 7,284.48
Depreciation at the end of the year 3 (D3) = 6,504 + (6,504 + 7,284.48) x 0.12 = Rs. 8,158.62
Depreciation at the end of year 4 (D4) = 6,504 + (6,504 + 7,284.48 + 8,158.62) x 0.12
= Rs. 9,137.65. These calculations along with book values are summarized in Table 4.
Table 4 Dt and Bt according to Sinking Fund Method of Depreciation
End of the
year (t)
Fixed Depreciation (Rs.) Net Depreciation (Rs.) Book Value 𝑩𝒕 (Rs.)
0 6,504 ------ 1,00,000.00
1 6,504 6,504.00 93,496.00
2 6,504 7,284.48 86,211.52

15. 15 | P a g e
3 6,504 8,158.62 78,052.90
4 6,504 9,137.65 68,915.25
5 6,504 10,234.17 58,681.08
6 6,504 11,462.27 47,218.81
7 6,504 12,837.74 34,381.07
8 6,504 14,378.27 20,002.80
𝐵𝑡 = 𝐵𝑡−1 − 𝐷𝑡
5: Service Output Method of Depreciation: In some situations, it may not be realistic to
compute depreciation based on time period. In such cases, the depreciation is computed based
on service rendered by an asset.
Let, P = first cost of the asset. F = salvage value of the asset. X = maximum capacity of service of
the asset during its lifetime. x = quantity of service rendered in a period.
Then, the depreciation is defined per unit of service rendered:
Depreciation/unit of service = (P – F)/X.
Depreciation for x units of service in a period =
𝑃−𝐹
𝑋
(𝑥).
EXAMPLE 5: The first coat of a road laying machine is Rs. 80,00,000. Its salvage value after five
years is Rs. 50,000. The length of road that can be laid by the machine during its lifetime is
75,000 km. In its third year of operation, the length of road laid is 2,000 km. Find the
depreciation of the equipment for that year.
Solution: P = Rs. 80,00,000. F = Rs. 50,000. X = 75,000 km. x = 2,000 km.
Depreciation for x units of service in a period =
𝑃−𝐹
𝑋
(𝑥).
Depreciation for year 3 =
80,00,000−50,000
75,000
× 2,000 = Rs. 2,12,000.
OBSOLESCENCE
OBSOLESCENCE: Obsolescence is the state of being which occurs when an object, service, or
practice is no longer wanted even though it may still be in good working order. Obsolescence
occurs generally due to the availability of alternatives that perform better or are cheaper or
both, or due to changes in user preferences or requirements. There are three types of
obsolescence or flaws that cause properties to lose value:
1. Functional Obsolescence: Functional obsolescence occurs when a property loses value due
to its architectural design, building style, size, outdated amenities, local economic conditions
and changing technology.
2. Economic Obsolescence: Economic obsolescence occurs when a property loses value
because of external factors such as local traffic pattern changes or the construction of public
nuisance type properties and utilities such as county jails and sewer treatment plants on
adjoining property.
3. Physical obsolescence: Physical obsolescence occurs when a property loses value due to
gross mismanagement and physical neglect resulting in deferred maintenance that's usually too
costly to repair.
COSTING

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Intelligent pricing is one of the most important elements of any successful business venture. Yet
many entrepreneurs fail to educate themselves adequately about various pricing components
and strategies before launching a new business. As the Small Business Administration (SBA)
indicated in The Facts about Pricing Your Products and Services, "you must understand your
market, distribution costs, and competition. You must keep abreast of the factors that affect
pricing and be ready to adjust quickly."
COST FACTORS
There are three primary cost factors that need to be considered by small businesses when
determining the prices that they charge for their goods or services. After all, price alone means
little if it is not figured within the context of operating costs.
1. Labor Costs: Labor costs consist of the cost of the work that goes into the manufacturing of a
product or the execution of a service. Direct labor costs can be figured by multiplying the cost
of labor per hour by the number of employee-hours required to complete the job. Business
owners, however, need to keep in mind that the "cost of labor per hour" includes not only
hourly wage or salary of the relevant employees, but also the costs of the fringe benefits that
those workers receive. These fringe benefits can include social security, retirement benefits,
insurance, unemployment compensation, workers compensation, and other benefits.
2. Material Costs: Material costs are the costs of all materials that are part of the final product
offered by the business. As with labor, this expense can apply to both goods and services. In the
case of goods, material costs refer to the costs of the various components that make up a
product, while material costs associated with services rendered typically include replacement
parts, building parts, etc. A deck builder, for example, would include such items as lumber,
nails, and sealer as material costs.
3. Overhead Costs: Overhead costs are costs that cannot be directly attributed to one particular
product or service. Some business consultants simply refer to overhead costs as those business
expenses that do not qualify as labor costs or material costs. These costs include indirect
expenses such as general supplies, heating and lighting expenditures, depreciation, taxes,
advertising, rental or leasing costs, transportation, employee discounts, damaged merchandise,
business memberships, and insurance.
PRODUCT COST AND SELLING PRICE
PRODUCT COST: Product cost refers to the costs used to create a product. These costs include
direct labor, direct materials, consumable production supplies, and factory overhead. Product
cost can also be considered the cost of the labor required to deliver a service to a customer. In
the latter case, product cost should include all costs related to a service, such as compensation,
payroll taxes, and employee benefits.
The cost of a product on a unit basis is typically derived by compiling the costs associated with a
batch of units that were produced as a group, and dividing by the number of units
manufactured. The calculation is: (Total direct labor + Total direct materials + Consumable
supplies + Total allocated overhead) / Total number of units= Product unit cost Product cost can
be recorded as an inventory asset if the product has not yet been sold. It is charged to the cost

17. 17 | P a g e
of goods sold as soon as the product is sold, and appears as an expense on the income
statement
SELLING PRICE: The actual final price of a product or service that company charges a purchaser
to buy the item. OR The market value, or agreed exchange value, that will purchase a definite
quantity, weight, or other measure of a good or service. It may be fixed by a contract (such as
sale of goods contract), left to be determined by an agreed upon formula at a future date, or
discovered or negotiated during the course of dealings between the parties involved. In
commerce, it boils down to what:  Buyer is willing to pay.  Seller is willing to accept
 The competition is allowing to be charged. With product, promotion, and place of marketing
mix, it is one of the business variables over which a company can exercise some degree of
control.
PROJECT CASH FLOWS
The sums of money recorded as receipts or disbursements in a project's financial records are
called cash flows. Examples of cash flows are deposits to a bank, dividend interest payments,
loan payments, operating and maintenance costs. To run a successful business project, you
have to understand your cash inflows and outflows. A cash flow enables you to create a short-
term forecast that enables you to determine how you are going to get money for the project
and how you are going to pay for your expenses. Cash inflows usually arise from financing,
operations and investing. While cash outflows mainly result from expenses. Estimating the cash
flow of a project is necessary and one of the most challenging parts of capital budgeting.
ABSORPTION COSTING
Absorption costing is defined as a method for accumulating the costs associated with a
production process and apportioning them to individual products. This type of costing is
required by the accounting standards to create an inventory valuation that is stated in an
organization's balance sheet.
Absorption costing includes or "absorbs" all the costs of manufacturing a product including
both fixed and variable costs. That means that all costs including direct, like material costs, and
indirect, like overhead costs, are included in the price of inventory. Absorption costing gives a
much more comprehensive and accurate view on how much it really costs to produce your
inventory then the variable costing method. This method ensures that all incurred costs are
recovered from the selling price of a good or service. Also called full absorption costing
Absorption Costing Components: The key costs assigned to products under an absorption
costing system are:
 Direct materials. Those materials that are included in a finished product.
 Direct labor. The factory labor costs required to construct a product.
 Variable manufacturing overhead. The costs to operate a manufacturing facility, which vary
with production volume. Examples are supplies and electricity for production equipment.
 Fixed manufacturing overhead. The costs to operate a manufacturing facility, which do not
vary with production volume. Examples are rent and insurance.
MARGINAL COSTING

18. 18 | P a g e
Marginal cost is the change in the total cost when the quantity produced is incremented by
one. That is, it is the cost of producing one more unit of a good.
Need for Marginal Costing: Let us see why marginal costing is required:
 Variable cost per unit remains constant; any increase or decrease in production changes the
total cost of output.
 Total fixed cost remains unchanged up to a certain level of production and does not vary with
increase or decrease in production. It means the fixed cost remains constant in terms of total
cost.
 Fixed expenses exclude from the total cost in marginal costing technique and provide us the
same cost per unit up to a certain level of production. OR
Marginal Cost: Marginal cost of a product is the cost of producing an additional unit of that
product. Let the cost of producing 20 units of a product be Rs. 10,000, and the cost of
producing 21 units of the same product be Rs. 10,045. Then the marginal cost of producing the
21st unit is Rs. 45.
The marginal cost is defined as the change in total costs with one-unit increase or decrease in
the current quantity produced. Marginal cost 
Δ Total cost
Δ Quantity produced
.
BREAKEVEN ANALYSIS
Break-even analysis is a technique widely used by production management and management
accountants. It is based on categorizing production costs between those which are "variable"
and those that are "fixed". Total variable and fixed costs are compared with sales revenue in
order to determine the level of sales volume, sales value or production at which the business
makes neither a profit nor a loss (the "break-even point"). A break-even analysis is a key part of
any good business plan. It can also be helpful even before you decide to write a business plan,
when you're trying to figure out if an idea is worth pursuing. Long after your company is up and
running, it can remain helpful as a way to figure out the best pricing structure for your
products.
a) Performing a Break-Even Analysis: Fixed Costs Fixed costs are ones like rent and
administrative payroll that don't change much from month to month, regardless of how many
units you sell. SCORE lists many common fixed costs.
b) Performing a Break-Even Analysis: Variable Costs Variable costs are ones like inventory,
shipping and sales commissions that rise or fall with your sales volume. As with fixed costs, talk
to trade associations, vendors and even other business owners in your field to come up with
the most accurate estimate.
c) Performing a Break-Even Analysis: Pricing This is the trickiest of your three pieces of data,
since you're able to choose exactly where to set your prices. Start by looking at your
competition, and how they price their products. You can also do informal focus groups to see
what people might be willing to pay for your wares or services.
THE BREAK-EVEN CHART: In its simplest form, the break-even chart is a graphical
representation of costs at various levels of activity shown on the same chart as the variation of
income (or sales, revenue) with the same variation in activity. The point at which neither profit

19. 19 | P a g e
nor loss is made is known as the "break-even point" and is represented on the chart below by
the intersection of the two lines: In the diagram above, the line OA represents the variation of
income at varying levels of production activity ("output"). OB represents the total fixed costs in
the business. As output increases, variable costs are incurred, meaning that total costs (fixed +
variable) also increase. At low levels of output, Costs are greater than Income. At the point of
intersection, P, costs are exactly equal to income, and hence neither profit nor loss is made
Illustration 2 shows a break-even chart. As sales increase, the profit line passes through the
zero or break-even line at the break-even point.
Illustration 2: Break-even chart: The illustration shows that the company needs to sell
approximately 1,222 units in order to cross the breakeven line. This is a classic business chart
that helps you consider your bottom line financial realities.
BENEFITS: The following are the benefits out of break-even analysis:
 Make or buy decision: The C-V-P analysis assists in making a choice between two courses of
action to make versus to buy. If the variable cost is less than the price that has to be paid to an
outside supplier, it may be better to manufacture than to buy.
 Production planning; The C-V-P analysis helps in planning the production of items giving

20. 20 | P a g e
maximum contribution towards profit and fixed costs.
 Cost control: As a cost control device, the C-V-P analysis can be used to detect insidious
upward creep of costs that might otherwise go unnoticed.
 Financial structure: Break-even analysis provides an understanding of the behavior of profits
in relation to output. This understanding is significant in planning the financial structure of a
company.
 Conditions of uncertainty: When some reasonable basis for subjective extrapolation is
available, the breakeven analysis provides the financial management with information helpful
in its decision making activities.
LIMITATIONS: The following limitations of break-even analysis have to be kept in mind while
making use of this tool:
1. Many costs and their components do not fall into neatly compartmentalized fixed or variable
cost categories as they possess the characteristics of both types.
2. If company sells several products, the financial manager has to prepare and evaluate a
number of profit-graphs covering integrated segments of independent activities.
3. A break-even chart represents a short-run static relationship of costs and output and become
obsolete very quickly.
4. The relations indicated in the break-even chart do not help for all levels of operations. Costs
tend to be higher than shown on the static break-even chart when the plant’s operation
approaches 100 percent of its capacity.
5. The frequent changes happening in the selling price of the product affect the reliability of the
break-even analysis. The cost of securing funds to expand is disregarded in break-even chart.
6. In spite of the above mentioned limitations, the breakeven analysis has high place in financial
management. OR
Break-even analysis: It is a situation where there is a no profit and no losses. Revenue =
Expenses. Break even analysis is based on the cost behavior pattern to the level of production.
It is a key consideration in the pricing decisions of any businesses.
The main objective of break-even analysis is to find the cut-off production volume from where a
firm will make profit. Let, s = selling price per unit. v = variable cost per unit.
FC = fixed cost per period. Q = volume of production.
The total sales revenue (S) of the firm is given by the following formula: S = s x Q
The total cost of the firm for a given production volume is given as
TC = Total variable cost + Fixed cost ⇒ = v x Q + FC.
The linear plots of the above two equations are shown in Fig. 1.3. The intersection point of the
total sales revenue line and the total cost line is called the break-even point. The corresponding
volume of production on the X-axis is known as the break-even sales quantity. At the
intersection point, the total cost is equal to the total revenue. This point is also called the no-
loss or no-gain situation. For any production quantity which is less than the break-even
quantity, the total cost is more than the total revenue. Hence, the firm will be making loss.

21. 21 | P a g e
For any production quantity which is more than the break-even quantity, the total revenue will
be more than the total cost. Hence, the firm will be making profit.
Profit = Sales – (Fixed cost + Variable costs) ⇒ = s x Q – (FC + v x Q)
The formulae to find the break-even quantity and break-even sales quantity
Break-even quantity =
Fixed cost
Selling price/unit − Variable cost/unit
𝐹𝐶
𝑠−𝑣
(in units).
Break-even sales =
Fixed cost
Selling price/unit − Variable cost/unit
× Selling price/unit =
𝐹𝐶
𝑠−𝑣
x s (Rs.).
The contribution is the difference between the sales and the variable costs. The margin of
safety (M.S.) is the sales over and above the break-even sales. The formulae to compute these
values are: Contribution = Sales – Variable costs
Contribution/unit = Selling price/unit – Variable cost/unit
M.S. = Actual sales – Break-even sales
𝑃𝑟𝑜𝑓𝑖𝑡
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
x sales
M.S. as a per cent of sales = (M.S./Sales) x 100
EXAMPLE 1: Alpha Associates has the following details: Fixed cost = Rs. 20,00,000.
Variable cost per unit = Rs. 100. Selling price per unit = Rs. 200.
Find (a) The break-even sales quantity, (b) The break-even sales (c) If the actual production
quantity is 60,000, find (i) contribution; and (ii) margin of safety by all methods.
Solution: Fixed cost (FC) = Rs. 20,00,000. Variable cost per unit (v) = Rs. 100.
Selling price per unit (s) = Rs. 200.

22. 22 | P a g e
Break-even quantity =
𝐹𝐶
𝑠−𝑣
=
20,00,000
200−100
x 200 = 20,00,000/100 = 20,000 units
(b) Break-even sales =
𝐹𝐶
𝑐−𝑣
x s (Rs.) =
20,00,000
200−100
x 200 =
20,00,000
100
x 200 = Rs. 40,00,000.
(c) (i) Contribution = Sales – Variable cost
= s x Q – v x Q ⇒ = 200 x 60,000 – 100 x 60,000 ⇒ = 1,20,00,000 – 60,00,000 = Rs. 60,00,000.
(ii) Margin of safety: METHOD I: M.S. = Sales – Break-even sales
= 60,000 x 200 – 40,00,000 = 1,20,00,000 – 40,00,000 = Rs. 80,00,000.
METHOD II: M.S. =
𝑃𝑟𝑜𝑓𝑖𝑡
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
x sales
Profit = Sales – (FC + v x Q)
= 60,000 x 200 – (20,00,000 + 100 x 60,000) = 1,20,00,000 – 80,00,000 = Rs. 40,00,000.
M.S. =
40,00,000
60,00,000
x 1,20,00,000 = Rs. 80,00,000.
M.S. as a per cent of sales =
40,00,000
60,00,000
x 100 = 67%.
EXAMPLE 2: A manufacturer of TV buys TV cabinet at Rs. 500 each. In case the company makes
it within the factory, the fixed and variable costs would be Rs. 4,00,000 and Rs. 300 per cabinet
respectively. Should the manufacturer make or buy the cabinet if the demand is 1,500 TV
cabinets?.
Solution: Selling price/unit (SP) = Rs. 500. Variable cost/unit (VC) = Rs. 300.
Fixed cost (FC) = Rs. 4,00,000.
BEP = =
40,00,000
500−300
= 2,000 units
Since the demand (1,500 units) is less than the break-even quantity, the company should buy
the cabinets for its TV production.
REPLACEMENT ANALYSIS
A machine which is purchased today cannot be used forever. It has a definite economic lifetime.
After the economic life, the machine should be replaced with a substitute machine with similar
operational capabilities. This kind of analysis is called replacement analysis.
Replacement may be defined as the acquisition of a new asset to fulfill a particular function,
together with the simultaneous scrapping or transference to another use of an old asset which
has hitherto fulfilled more or less the same function.
CAUSES OF REPLACEMENT
1. Physica1 Impairment (Deterioration): These are changes that occur in the physical condition
of the assets. Normally, continuing use (aging) results in the operation of an asset becoming
less efficient. Routine maintenance as well as breakdown repair costs increase, energy use may
increase per unit of output, more operator time is required. Or, some unexpected incident such
as an accident occurs that affects the physical condition and the economics of ownership and
use of the asset.
2. Altered Requirements: Altered Requirements Capital assets are used to produce goods and
services that satisfy human wants. When the demand for a good or service either increases or
decreases or the design of a good or service changes, the related asset(s) may have the

23. 23 | P a g e
economics of its use affected.
3. Technology: The impact of changes in technology varies among different types of assets. For
example, the relative efficiency of heavy highway construction equipment is impacted less
rapidly by technological changes than automated manufacturing equipment. In general, the
costs per unit of production, as well as quality and other factors, are favorably impacted by
changes in technology, which result in more frequent replacement of existing assets with new
and better challengers.
FACTORS TO BE CONSIDERED
There are several factors that must be considered in replacement studies. Once a proper
perspective has been established regarding these factors, little difficulty should be experienced
in making replacement studies. Factors and related concepts are discussed below:
1. Past Estimation Errors: The economic focus in a replacement study is the future. Any
estimation errors made in a previous study related to the defender are not relevant. For
example, when an asset's book value (BV) is greater than its current market value (MV), the
difference frequently has been designated as an estimation error. Such errors also arise when
capacity is inadequate, maintenance expenses are higher than anticipated, and so forth.
2. The Sunk-Cost Trap: Only present and future cash flows should be considered in replacement
studies. A sunk cost is the difference between an asset's BV and its MV at a particular point in
time. Sunk costs have no relevance to the replacement decisions that must be made. When
income tax considerations are involved, we must include them an engineering economy study.
Clearly, serious errors can be made in practice when sunk costs are incorrectly handled in
replacement studies.
3. Economic Life of the Challenger: The economic life of an asset minimizes the EUAC of owning
and operating the asset, and it is often shorter than the useful or physical life. It is essential to
know a challenger's economic life, in view of the principle that new and existing assets should
be compared over their economic (optimum) lives. Economic data regarding challengers are
periodically updated (often annually), and replacement studies are then repeated to ensure an
ongoing evaluation of improvement opportunities.
4. Economic Life of the Defender: The economic life of the defender is often one year.
Consequently, care must be taken when comparing the defender asset with a challenger asset,
because different lives are involved in the analysis. We shall see that the defender should be
kept longer than its apparent economic life, as long as its marginal cost is less than the
minimum EUAC of the challenger over its economic life.
5. Income Tax Consequences: The replacement of assets often results in gains or losses from
the sale of depreciable property, as discussed. Consequently, to perform an accurate economic
analysis in such cases, the studies must be made on an after-tax basis. It is evident that the
existence of a taxable gain or loss, in connection with replacement, can have a considerable
effect on the results of an engineering study. A prospective gain from the disposal of assets can
be reduced by as much as 40% or 50%, depending on the effective income tax rate used in a
particular study.

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COMPARISON AND REPLACEMENT
When the useful lives of the best challenger and the defender are known or can be estimated,
but are not the same then two assumptions are used for economic comparison. Under either
assumption, the analysis period used is the same for all alternatives in the study. These
assumptions are:
1. Repeatability The Repeatability assumption, applied to replacement problems involving
assets with different useful lives, often simplifies the economic comparison of the alternatives.
When a replacement analysis involves a defender that cannot be continued in service because
of changes in technology, service requirements, and so on, a choice among two or more new
challengers must be made. Under this situation, the repeatability assumption may be a
convenient economic modeling approach for comparing the alternatives and making a present
decision.
2. Cotermination Whenever the repeatability assumption is not applicable, the coterminated
assumption may be used; it involves using a finite study period for all alternatives. Use of the
coterminated assumption requires detailing what and when cash flows are expected to occur
for each alternative and then determining which it most economical, using any of the correct
economic analysis methods. When the effects of price changes and taxes are to be considered
in replacement studies, it is recommended that the coterminated assumption be used.
ECONOMIC LIFE OF ASSET
ECONOMIC LIFE Economic life is the period of time (years) that results in the minimum
“equivalent uniform annual Cost” (EUAC) of owning and operating an asset. Assuming good
asset management, economic life should coincide with time from date of acquisition to date of
abandonment, demotion in use, or replacement from primary intended service. The economic
life of an asset could be different than the actual physical life of the asset. Estimating the
economic life of an asset is important for businesses so that they can determine when it is
worthwhile to invest in new equipment. In addition, businesses must plan so that they have
sufficient funds to purchase replacements for expensive equipment once it has exceeded its
useful life.
DETERMINITION OF ECONOMIC LIFE OF NEW ASSET (CHALLENGER): For a new asset, its
Equivalent uniform annual cost (EUAC) can be computed if the capital investment, annual
expenses, and year-by-year MVs are known or can be estimated. The estimated initial capital
investment as well as annual expanse and market value estimates may be used to determine
the PW. The total marginal cost for each year is calculated by finding the increase in the present
worth (PW) of total cost and then determining the equivalent worth (EW) of this increase at the
end of the year. Total marginal cost is then used to find the EUAC through each year. The
minimum EUAC value during the useful life of the asset identifies its economic life.
DETERMINITION OF ECONOMIC LIFE OF OLD ASSET (DEFENDER): In replacement analyses, we
must also determine the economic lift that is most favorable to the defender. When a major
outlay (cash) for defender alteration or overhaul is needed, the life that will yield the least
EUAC is likely to be the period that will elapse before the next major alteration or overhaul will

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be needed. Alternatively, when there is no defender MV now or later and when defender
operating expenses are expected to increase annually, the remaining life that will yield the least
EUAC will be one year. When MVs are greater than zero and expected to decline from year to
year, it is necessary to calculate the apparent remaining economic life, which is done in the
same manner as for a new asset.
RISK ANALYSIS
UNCERTAINTY: Uncertainty is unknown unknowns. Uncertainty is the observation that the
future is not known. You don't know what might happen tomorrow. You might step in a puddle
of mud on the way to class. Or you might anger an intelligent extraterrestrial life form that
retaliates by destroying all life on the planet. You just never know.
RISK: Risk is known unknown. Risk is assigning quantitative probabilities to alternative future
outcomes. While it is possible that you could either step in a mud puddle or you could cause
total destruction of the planet, both are not equally likely outcomes. Risk is the process of
assigning probabilities to these alternatives.
SOURCES OF UNCERTAINTY
SOURCES OF UNCERTAINITY: It is useful to consider some of the factors that affect the
uncertainty involved in the analysis of the future economic consequences of an engineering
project. There are four major sources of uncertainty.
1. Inaccurate Cash Flows: The first source that is always present is the possible inaccuracy of
the cash-flow estimates used in the study. The accuracy of the cash-inflow estimates is difficult
to determine. If they are based on past experience or have been determined by adequate
market surveys, a fair degree of reliance may be placed on them. On the other hand, if they are
based on limited information with a considerable element of hope thrown in, they probably
contain a sizable element of uncertainty.
2. Type of Business: The second major source affecting uncertainty is the type of business
involved in relation to the future health of the economy. Some types of business operations are
less stable than others. For example, most mining enterprises are riskier than one engaged in
manufactured homes. Whenever capital is to be invested in an engineering project, the nature
of the business as well as expectations of future economic conditions (e.g., interest rates)
should be considered in deciding what risk is present.
3. Type of Plant and Equipment: A third source affecting uncertainty is the type of physical
plant and equipment involved. Some types of structures and equipment have rather definite
lives and market values. A good engine lathe generally can be used for many purposes in nearly
any fabrication shop. Quite different would be a special type of lathe that was built to do only
one unusual job. Its value would be dependent almost entirely upon the demand for the special
task that it can perform. Thus, the type of physical property involved affects the accuracy of the
estimated cash-flow patterns.
4. Period of Analysis: The fourth important source of uncertainty that must always be
considered is the length of the study period used in the analysis. A long study period naturally

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decreases the probability of all the factors turning out as estimated. Therefore, a long study
period, all else being equal, generally increases the uncertainty of a capital investment.
SENSITIVITY ANALYSIS
SENSITIVITY ANALYSIS Sensitivity analysis is an analysis that finds out how sensitive an output
is to any change in an input while keeping other inputs constant. This is a way to predict the
outcome of a decision. Sensitivity analysis is useful because it tells the model user how
dependent the output value is on each input. It gives him an idea of how much room he has for
each variable to go adverse. It helps in assessing risk. Sensitivity analysis is a group of
techniques that can be used to examine the degree of uncertainty in a cost-benefit analysis
(CBA) and how that affects a study’s results. There are several advantages of sensitivity analysis.
First, it shows how significant a single input variable is in determining project outcomes.
Second, it recognizes the uncertainty associated with the input. Third, it gives information
about the range of output variability. And fourth, it does all of these when there is little
information, resources, or time to use more sophisticated techniques. In engineering economy
studies, sensitivity analysis is a general non-probabilistic methodology readily available, to
provide information about the potential impact of uncertainty in selected estimates. Its routine
use is fundamental to developing economic information useful in the decision process. Several
techniques are usually included in discussion of sensitivity analysis in engineering economy.
Following are most important:
1. Break Even Analysis: This technique is commonly used when the selection among project
alternatives or the economic acceptability of an engineering project is heavily dependent upon
a single factor, we can solve the value of that factor. That value is known as the breakeven
point, that is, the value at which we are indifferent between the two alternatives. Then, if the
best estimate of the actual outcome of the common factor is higher or lower than the
breakeven point, and assumed certain, the best alternative becomes apparent.
2. Sensitivity graph: The sensitivity graph technique is an analysis tool applicable when break
even analysis does not fit the project situation. This approach is used when two or more project
factors are of concern and an understanding of the sensitivity of the economic measure of
merit to changes in the value of each factor is needed.
3. Combination of factors: When the combined effects of uncertainty in two or more project
factors need to be examined, this analysis approach may be used. When this situation occurs,
the following approach should be used in developing additional information to assist decision
making.  Develop a sensitivity graph for the project. Also for the most sensitive factors
 Select the most sensitive project factors based on the information in the sensitivity graph
 Analyze the combined effects of these factors on the project’s economic measure of merit.
OPTIMISTIC-PESSIMISTIC ESTIMATES
During the late 1950s, U.S. Navy developed distribution tool called the program
evaluation and review technique (PERT) to manage the thousands of tasks and
estimates that were required for the complex project. The PERT measured three values
for time estimates, cost estimates and work effort estimates (i.e., man-hours, machine
hours). These values were categorized as “optimistic,” “most likely” and “pessimistic”

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times. With the three estimates, practitioners can calculate the expected time, or
weighted average of an activity, and a probability estimate of a completion time for the
entire project. An optimistic estimate for a factor is one that is in the favorable
direction (say, the minimum capital investment cost). The pessimistic estimate for a
factor is one that is in the unfavorable direction (say, the maximum capital investment
cost). In applications of this technique, the optimistic condition for a factor is often
specified as a value that has 19 out of 20 chances of being better than the actual
outcome. Similarly, the pessimistic condition has 19 out of 20 chances of being worse
than the actual outcome. In operational terms, the optimistic condition for a factor is
the value when things occur as well as can be reasonably expected, and the
pessimistic estimate is the value when things occur as detrimentally as can be
reasonably expected.
CAPITAL FINANCING
DEBT FINANCING:
Debt financing is cash borrowed from a lender at a fixed rate of interest and with a
predetermined maturity date. The principal must be paid back in full by the maturity date. Debt
may take the form of a loan or the sale of bonds. The lender retains a right to the money lent
and may demand it back under conditions specified in the borrowing arrangement. Debt
financing means borrowing money and not giving up ownership. Debt financing often comes
with strict conditions or covenants in addition to having to pay interest and principal at
specified dates. Failure to meet the debt requirements will result in severe consequences. Debt
financing includes both secured and unsecured loans. Security involves a form of collateral
(security) as an assurance the loan will be repaid. Most lenders will ask for some sort of security
on a loan. Few, if any, will lend you money based on your name or idea alone. Here are some
types of security you can offer a lender:
 Guarantors sign an agreement stating they'll guarantee the payment of the loan.
 Co-makers are in effect principals, who are responsible for payment of the loan.
 Equipment provides 60 to 65 percent of its value as collateral for a loan.
 Securities allow publicly held companies to offer stocks and bonds as collateral for repaying a
loan. You can also try to acquire debt financing through an unsecured loan. In this type of loan,
your credit reputation is the only security the lender will accept. You may receive a personal
loan for several thousand dollars--or more--if you have a good relationship with the bank. But
these are usually short-term loans with very high rates of interest in addition to secured or
unsecured loans, most debt will be subject to a repayment period. There are three types of
repayment terms:
 Short-term loans are typically paid back within six to 18 months.
 Intermediate-term loans are paid back within three years.
 Long-term loans are paid back from the cash flow of the business in five years or less.
SOURCES OF DEBT FINANCE
i. Financial institutions: Financial institutions such as banks, building societies and credit unions
offer a range of finance products with both short and long-term finance solutions. Some

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products include business loans, lines of credit, overdraft facilities, invoice financing, equipment
leases and asset financing.
ii. Retailers: If you require finance to purchase goods such as furniture, technology or
equipment, many stores offer store credit through a finance company. Generally, this is a
higher interest option and is suited to businesses that can pay the loan off quickly within the
interest-free period.
iii. Suppliers: Most suppliers offer trade credit that allow businesses to delay payment for
goods. The terms often vary and trade credit may only be offered to businesses that have an
established relationship with the supplier.
iv. Finance companies: Most finance companies offer finance products via a retailer. Finance
companies must be registered, so before you obtain finance check the Professional registers on
the Australian Securities and Investments Commission (ASIC) website.
v. Factor companies: Factor companies offer a form of finance where they purchase a business'
outstanding invoices at a discount. The factor company then chases up the debtors. While
factoring is a way to get quick access to cash, it can be quite expensive compared to traditional
financing options.
vi. Family or friends: If a friend or relative offers you a loan that is expected to be repaid, it's
called a debt finance arrangement. If you decide on this option, carefully consider how this
arrangement could affect your relationship.
EQUITY FINANCING:
Equity financing is the method of raising capital by selling company stock to investors. In return
for the investment, the shareholders receive ownership interests in the company.
SOURCES OF EQUITY FINANCE
i. Self-funding: Often called 'bootstrapping', self-funding is often the first step in seeking
finance and involves funding purely through personal finances and revenue from the business.
Investors and lenders will both expect some amount of self-funding before they agree to offer
you finance.
ii. Family or friends: Offering a partnership or share in your business to family or friends in
return for equity is often an easy way of obtaining finance. However, this option must be
carefully considered to ensure your relationship is not adversely affected.
iii. Private investors: Investors can contribute funds to your business in return for a share in
your profits and equity. Investors such as business angels can also work in the business
providing expertise or advice as well as providing funds.
iv. Venture capitalists: Venture capitalists are generally large corporations that invest large
sums in start-up businesses with the potential for high growth and large profits. They typically
require a large controlling share of the business and often provide management or industry
expertise.
v. Stock market: Also known as an Initial Public Offering (IPO), floating on the stock market
involves publicly offering shares to raise capital. This can be a more expensive and complex
option and carries the risk of not raising the funds needed due to poor market conditions.
vi. Government: In general, the government doesn't provide finance for starting up or buying a

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business. However, you may be eligible for a grant in certain circumstances, such as business
expansion, research and development, innovation or exporting.
vii. Crowd funding: Some social media websites offer entrepreneurs a 'crowd funding' platform
for their product prototypes or innovative projects. It involves setting a funding goal, providing
project and budget details and inviting people to contribute to a startup capital pool.
LEASING
Leasing is a modern financing method that allows individuals to own and make use of certain
assets for medium to long term financing periods in return for previously-set interim payments.
The lesser, who is the finance company, purchases the identified asset and becomes its legal
owner. The lessee, in turn, will be able to use the asset throughout the determined leasing
period, paying a series of rentals or installments for the use of that asset. A lease falls into this
category if any of the following requirements are met:
a) The life of the lease is 75% or greater of the assets useful life.
b) The lease contains a purchase agreement for less than market value.
c) The lessee gains ownership at the end of the lease period.
d) The present value of lease payments is greater than 90% of the asset's market value.
Throughout the duration of the leasing period, the lesser (finance company) remains the legal
owner of the asset. However, the lessee also has control over the asset, making use of the
benefits and assuming the risks of economic (defector) ownership. OR
Leasing: A lease is a contract for the use of a physical asset over a specific period of time
without acquiring its ownership. Under a lease contract, the user of the asset is referred to as
the lessee, and the owner or provider is called the lessor. From the viewpoint of the lessee,
there are two major categories of lease contracts: the operating lease and the capital lease. An
operating lease refers to a short term contract whereby the lessee is entitled to use the asset
for a fraction of its useful life, while the lessor may provide services such as maintenance and
insurance. A capital lease refers to a non-cancellable contract with the intention of transferring
the ownership of the property to the lessee at or near the end of its useful life either
through prior agreement or through a bargain purchase option in the contract.
If a physical asset can only be leased but not purchased, the decision whether to lease such an
asset is an investment decision. Other than this exception, a leasing decision is a financing
decision. In other words, the decision whether to acquire a physical asset for production or
operation against other alternatives is an investment decision. Once a decision is made to
acquire this asset, the decision whether to buy or lease is a financial decision. Consequently,
leasing can be viewed as an instrument of financing in capital budgeting.
Renting is another means for allowing the use of a physical asset without owning it. In this
context, it can be treated as an operating lease even though the two may have different legal
and/or accounting implications. Both serve the purpose of reducing capital expenditures while
retaining the use of a physical asset under capital rationing.
Example: The owner of a small business plans to lease a personal computer for 5 years.
In talking to a sales representative, she learned that a new model with the same performance

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characteristics but lower price may be available every one or two years. She was offered three
different options representing the changing prices of the newer models that may be provided
when they become available. The cash flow profiles representing the costs of these non-
cancellable lease options are shown in Table 9.12. Assuming that the level of performance is
identical for all options and using a MARR of 10%, which option should be selected?
The present values of costs of these options are computed as follows:
[𝐶𝑃𝑉1]10% = 24,000 + 16,000(P | U, 10%, 4) = $74,71 8
[𝐶𝑃𝑉2]10% = 22,000 + ll,000(P | U, 10%, 2) + 11,000(P | U, 10%, 4) = $75,959.
[𝐶𝑃𝑉3]10% = 18,000 + 18,000(P | U, 10%, 4) = $75,058
The first option has the minimum present value and is preferable.
TABLE 9.1 2 CASHFLOW PROFILES FOR THREE OPTIONS
t 𝐶𝑡.1 𝐶𝑡.2 𝐶𝑡.3
0 24,000 22,000 18,000
1 16,000 22,000 18,000
2 16,000 22,000 18,000
3 16,000 11,000 18,000
4 16,000 11,000 18,000
CAPITAL ALLOCATION
A process of how businesses divide their financial resources and other sources of capital to
different processes, people and projects. Overall, it is management's goal to optimize capital
allocation so that it generates as much wealth as possible for its shareholders. The goal of
capital allocation is to maximize output per dollar spent.
PAST PAPERS
i. The main purpose of breakeven analysis is to determine the level of output at which
total revenue is equal to total cost. (T / F)
ii. The downward pointing arrows on a cash flow diagram represent revenues. (T / F)
iii. Cost added by producing one additional unit of a product is called Marginal Cost. (T / F)
iv. A situation involving exposure to danger is called Risk. (T / F)
v. An increase in the value of an asset over a period of time is called depreciation. (T / F).
decrease
vi. A positive NPV means that the project is expected to add value to the firm and will
increase the wealth of the firm. (T / F) Wealth of the owners.
a. In engineering economics, two things are said to be equivalent when they have the
same effect. (TRUE / FALSE)
b. IRR stands for Internal Rate of Return. (TRUE / FALSE)
c. NPV stands for Net Present Value. (TRUE / FALSE)
d. Pakistan is an industrialist country. (TRUE / FALSE)
e. A place where different economic activities are performed is called economy. (TRUE
/ FALSE)
Q: Explain the purpose of preparing balance sheet and write the important details furnished
in a balance sheet of a company?

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Purposes
1. One purpose behind these financial documents is to allow key decision makers to evaluate
the company's current situation and make changes as needed.
2. Banks want to see balance sheets and income statements to determine if you’re earning
enough to repay the loan you’re requesting.
3. Stock investors use these statements to determine whether the company represents a good
investment. Balance sheets and income statements can highlight trouble areas, such as chronic
late payment fees for bills, or back taxes that you owe. A financial adviser or business mentor
can review your financial statements with you and help you make wise decisions for your
business.
PARTS OF A BALANCE SHEET: The balance sheet is divided into two parts that, based on the
following equation, must equal each other, or balance each other out. The main formula behind
balance sheets is: Assets = Liabilities + shareholders/equity
Assets: Assets are things that the company owns. They are the resources of the company that
have been acquired through transactions, and have future economic value that can be
measured and expressed in dollars. Assets also include costs paid in advance that have not yet
expired, such as prepaid advertising, prepaid insurance, prepaid legal fees, and prepaid rent.
Liabilities: On the other side of the balance sheet are the liabilities. These are the financial
obligations a company owes to outside parties. Like assets, they can be both current and long-
term. Long-term liabilities are debts and other non-debt financial obligations, which are due
after a period of at least one year from the date of the balance sheet. Current liabilities are the
company's liabilities that will come due, or must be paid, within one year.
Shareholders' Equity: Shareholders' equity is the initial amount of money invested into a
business. If, at the end of the fiscal year, a company decides to reinvest its net earnings into the
company (after taxes), these retained earnings will be transferred from the income statement
onto the balance sheet and into the shareholder's equity account. This account represents a
company's total net worth.
Q: Balancing ,replacement and modernization improves the productivity comment?
BALANCING: Statement of a company’s assets, liabilities and stockholder equity at a given
period of time, such as the end of year. A balance sheet is a record of what a company has and
how it has come to have it. A balance sheet is divided into two main sections, and stockholder
equity. The assets should generally equal the liabilities and stockholder equity. Projects have
many production units that are linked with one another. The flow of material, resources or
information through different production units should be such that the output of one
production unit exactly matches the input requirement for the next production unit. If this is,
then the efficiency of the production line will be the maximum and there will be perfect
utilization of production capacity. This process of utilization among different productions units
is said to be Balancing. While, a project that is carry out to improve the production capacity of
one or more production units that will result in improvement in the overall production capacity
of the whole project is called Balancing project. Perfectly balanced organizations/projects are
rare but attempts should be made for near perfect balance as far as possible. The following are

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the effects of an unbalanced organization:  There is less utilization of production capacity.
 Slow production capacity between units will result in wastage of time and lower return on
investment.  If the balanced project remains unbalanced, there is possibility that challenger
may be able to offer product at relatively cheaper price, resulting in lower efficiency.
 The unbalanced project may face severe threat for its continued existence.
MODERNIZATION Technological innovation is a continuous process. When a new technology is
developing and becomes operative, the existing technology becomes out of date. Then the
project is set up with the latest available technology. However, with the passage of time the
projects become outdated in technology. Modernization is meant for such upgrading of
technology or the existing equipment for improving productivity. It may be because of ageing or
technological obsolescence of machinery and process. Obsolescence is the major reason for
modernization. There are two aspects of technological obsolescence that need modernization:
1. The production process becomes old-fashioned in view of the latest technological
innovations. For example, for painting of metal components heat painting was used long ago
which was replaced by spray painting and powder coating.
2. More advanced features have included in the plant and machinery, by which the existing old
plant and machinery might have become outdated in technology. When modernization is
ignored, it will result in any of the following two situations:
1. The organization that has ignored modernization will be producing products which are lesser
in quality as compared to the products produced by its competitors.
2. Even if there is no difference in quality, the cost of production would be higher than that of
competitors. Hence for the survival of any organization/project, modernization with the latest
developments is must. While ignoring the modernization will only mean that the organization is
moving towards its end.
REPLACEMENT: Due to ageing and wear and tear, the maintenance cost of any machinery or
unit of production starts rising up and a stage will come when it will be no more beneficial to
keep them in the production line because of high maintenance costs, poor quality of output,
reduction in capacity of output, breakdown etc. Replacement involves replacing of such old
parts of machinery or complete machinery or unit of production with new unit, machinery or
part of the same capacity. Hence, replacement is implemented to reduce the maintenance cost
and to keep the perfect utilization of production without any obstruction so that delivery
schedules are met in time. Thus, replacement is undertaken with view to maintaining the same
level of operational efficiency or to the better level of operational efficiency. Following is the
importance of the replacement:
 It ensures that equipment’s are always ready and in reliable condition, which ensures
organization is able to respond any sudden change in demand.
 It ensures that there are no sudden and repeated breakdowns.
 It ensures that costs are always in control. If any organization is not able to implement an
effective replacement, than there will be following results:
 Full capacity utilization may not be achieved
 Increase in production cost cannot be reduced

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 Increase in maintenance cost is required
 Reduction in product quality and increase in wastage
 Safety of workers and operators in danger
Q: WRITE SHORT NOTES:
Engineering Cost is the engineering practice devoted to the management of project cost,
involving such activities as estimating, cost control, cost forecasting, investment appraisal and
risk analysis. Cost Engineers budget, plan and monitor investment projects. An engineering cost
analysis may involve many types of costs. Here is a list of cost types, including definitions and
examples.
i. A fixed cost is constant, independent of the output or activity level. The annual cost of
property taxes for a production facility is a fixed cost, independent of the production level and
number of employees.
ii. A variable cost does depend on the output or activity level. The raw material cost for a
production facility is a variable cost because it varies directly with the level of production.
iii. The total cost to provide a product or service over some period of time or production
volume is the total fixed cost plus the total variable cost, where:
iv. Total variable cost = (Variable cost per unit) (Total number of units)
v. A marginal cost is the variable cost associated with one additional unit of output or activity. A
direct labor marginal cost of $2.50 to produce one additional production unit is an example
marginal cost.
vi. The average cost is the total cost of an output or activity divided by the total output or
activity in units. If the total direct cost of producing 400,000 is $3.2 million, then the average
total direct cost per unit is $8.00.
INCOME STATEMENT: The income statement is one of the major financial statements used by
accountants and business owners. The income statement is sometimes referred to as the profit
and loss statement (P&L), statement of operations, or statement of income. The income
statement summarizes the revenues and expenses generated by the company over the entire
reporting period. The period of time that the statement covers is chosen by the business and
will vary. The basic equation on which an income statement is based is: Revenues – Expenses =
Net Income All companies need to generate revenue to stay in business. Revenues are used to
pay expenses, interest payments on debt and taxes owed to the government. After the costs of
doing business are paid, the amount left over is called net income. Income statements are all
organized the same way, regardless of industry.
Differentiate between Present Value and Future Value.
Present value is the value today of an amount of money to be received in the future. For
example: if annual interest rate is 10%, then $90.90 is the present value of $100 received one
year from now. If someone gives you $90.90 today or $100 in one year, you should be
indifferent.
Future value is just another way of looking at what we said above. Future value is the value in
the future of an amount you plan to invest today. For example: if annual interest rate is 20%,

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$120 is the future value in one year of $100 invested today. If someone gives you $100 today or
$120 in one year, you should be indifferent. OR
Sr. Description Present Value Future Value
1 Meaning Present value is defined as the
current value of the cash flow
in future. It is basically the
amount of cash in hand on
today’s date.
It is defined as the value of the
future cash flow after a certain
future period. This is the amount
of cash which will be received at
a specified future date.
2 Time Frame It is the current value of an
asset or investment at the
starting of a particular time
period.
It is that value of the asset or
investment at the end of a
particular time period.
3 Inflation Effect For present value inflation is
considered.
For future value inflation is not
considered.
4 Rates Applicable While calculating present value
both discount rate and interest
rate are taken into account.
While calculating Future value
only interest rate are taken into
account.
5 Decision Making Present value is very much
important for the investors as it
helps to decide whether to
invest to invest or not.
Since the reflects the future
profits from an investment it has
lesser importance in decision
making regarding investments.
6 Calculation
Method
While calculating present value
discounting is applied to find
out the present value of every
cash flow and then all these
values are added up to find the
investment’s value on today’s
date.
Future value calculation uses the
compounding technique to arrive
at the future value of every cash
flow after a certain time period
and then all these values are
added up to get the investment’s
future value.
7 Nature Present value is that amount
which is required to obtain the
future value.
Future value is that amount
which an individual will get from
cash on hand.
Difference between Selling Costs from Production Cost
The term “selling costs” is broader than advertisement expenditure. Whereas advertisement
expenditure includes costs incurred only on getting product advertised in newspapers and
magazines, on radio and television, selling costs include the salaries and wages of salesmen,
allowances to retailers for the purpose of getting their product displayed by them and so many
other types of promotional activities besides advertisement.
Chamberlin who introduced the analysis of selling costs in price theory distinguished selling
costs from production costs. According to Chamberlin, cost of production includes all those
expenses which are incurred to manufacture and provide a product to the consumer to meet
his given demand or want, while the selling costs are those which are incurred to change, alter
or create the demand for a product.

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Costs of production therefore include manufacturing costs, transportation costs, and cost of handling,
storing and delivering a product to the consumers, since all of these activities add utilities to a
commodity. And the addition or creation of utilities to satisfy the given wants is called production in
economics.
To quote Chamberlin, “Cost of production includes all expenses which must be met in order to
provide the commodity or service, transport it to the buyer, and put it into his hands ready to
satisfy his wants. Cost of selling includes all outlays made in order to secure a demand or
market for the product. The former costs create utilities in order that given demands may be
satisfied; the latter create and shift the demands themselves. A simple criterion is this: of all the
costs incurred in the manufacture and sale of a given product, those which alter the demand
curve for it are selling costs, and those which do not care costs of production.”
The selling costs, according to Chamberlin, include “advertising in its many forms, salaries of
salesmen and the expenses of sales departments and sales agencies (except where these
agencies actually handle the goods), window displays, and displays and demonstration of all
kinds.”
It should be noted that transportation should not be construed as increasing the demand, as it
apparently appears. This is because the transportation does not really increase the demand; it
merely enables the producer to meet the demand of the consumer which is already there
whether the transport cost is incurred by the producer or by the consumer himself.
Likewise, a high site rent for a shop in a well-located area will increase the sales of the firm but
cannot be considered as a part of selling costs, since in this the firm is meeting the given or
existing demand for the product more accurately or exactly and not altering the demand for the
product.
By paying a high rent for a shop or a factory building in the well-located area, the producer is
merely adapting the product or himself more exactly to the given demand and not altering the
demand or adapting his customers.
Therefore, Chamberlin while drawing the distinction between production costs and selling costs
writes that those costs which are “made to adapt the product to the demand are costs of
production; those made to adapt the demand to the product are costs of selling.”
It should, however, be noted that the distinction between production costs and selling costs
cannot always be sharply made and there are cases where it cannot be said whether product is
being adapted to meet the given demand, or the demand is being adapted to sell the product.
For instance, it is difficult to say whether the extra cost on attractive packaging is production
cost or selling cost. However, as far as advertisement expenditure is concerned, there is little
doubt about its being a selling cost, since purpose of advertisement is to increase or create the
demand for the product.
Thus Chamberlin’s distinction is quite applicable so far as advertisement expenditure is
concerned. Because advertising expenditure is the most important and dominant form of
selling costs, we in our analysis below shall use them interchangeably and discuss the various
questions concerning selling costs by taking the case of advertisement expenditure.
What is the difference between cash inflow & cash out flow?