Unit 2- Value Engineering and Time Value of Money

Prepared by
Dr. Vignesh V
Department of Structural Engineering
Sanjivani College of Engineering, Kopargaon.
EEST241-ENGINEERING ECONOMICS
UNIT II VALUE
ENGINEERING
Make or buy decision, Value engineering – Function, aims, value engineering procedure.
Interest formulae and their applications –Time value of money, Single payment
compound amount factor, Single payment present worth factor, Equal payment series
sinking fund factor, Equal payment series payment Present worth factor equal payment
series capital recovery factor- Uniform gradient series annual equivalent factor, Effective
interest rate, Examples in all the methods.
2.1 INTRODUCTION – Make or buy
In the process of carrying out business activities of an organization, a component/product
can be made within the organization or bought from a subcontractor. Each decision
involves its own costs.
So, in a given situation, the organization should evaluate each of the above make or buy
alternatives and then select the alternative which results in the lowest cost. This is an
important decision since it affects the productivity of the organization.
In the long run, the make or buy decision is not static. The make option of a
component/product may be economical today; but after some time, it may turn out to be
uneconomical to make the same.
Thus, the make or buy decision should be reviewed periodically, say, every 1 to 3 years.
This is mainly to cope with the changes in the level of competition and various other
environmental factors.
Make or Buy Decisions - is a determination whether to produce a component part
internally or to buy it from an outside supplier. The Organization should evaluate the costs
and benefits of manufacturing a product or product component against purchasing it and
then select the alternative which results in the lower cost.

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2.1.1 CRITERIA FOR MAKE OR BUY
Criteria for make
The following are the criteria for make:
The finished product can be made cheaper by the firm than by outside suppliers.
The finished product is being manufactured only by a limited number of outside
firmswhich are unable to meet the demand.
The part has an importance for the firm and requires extremely close quality control.
The part can be manufactured with the firm’s existing facilities and similar to other
itemsin which the company has manufacturing experience.
Criteria for buy
The following are the criteria for buy:
Requires high investments on facilities which are already available at supplier’s
plant. The company does not have facilities to make it and there are more
profitableopportunities for investing company’s capital.
Existing facilities of the company can be used more economically to make other
parts. The skill of personnel employed by the company is not readily adaptable
to make thepart.
Patent or other legal barriers prevent the company for making the
part.Demand for the part is either temporary or seasonal.
2.1.2 APPROACHES FOR MAKE OR BUY DECISION
Types of analysis followed in make or buy decision are as follows:
1. Simple cost analysis
2. Economic analysis
3. Break-even analysis
2.2INTRODUCTION- value analysis
Value analysis is one of the major techniques of cost reduction and cost prevention. It is a
disciplined approach that ensures necessary functions for minimum cost without
sacrificing quality, reliability, performance, and appearance. According to the Society of
American Value Engineers (SAVE), Value Analysis is the systematic application of
recognized techniques which identify the function of a product or service, establish a
monetary value for the function and provide the necessary function reliably at the lowest
overall cost.
It is an organized approach to identify unnecessary costs associated with any product,

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material part, component, system or service by analyzing the function and eliminating such
costs without impairing the quality, functional reliability, or the capacity of the product to
give service.
2.2.1 WHEN TO APPLY VALUE ANALYSIS
One can definitely expect very good results by initiating a VA programme if one or more of
thefollowing symptoms are present:
1. Company’s products show decline in sales.
2. Company’s prices are higher than those of its competitors.
3. Raw materials cost has grown disproportionate to the volume of production.
4. New designs are being introduced.
5. The cost of manufacture is rising disproportionate to the volume of production.
6. Rate of return on investment has a falling trend.
7. Inability of the firm to meet its delivery commitments.
2.2.2 Value Analysis vs. Value Engineering
Often the terms value analysis and value engineering are used synonymously. Though the
philosophy underlying the two is same, i.e. identification of unnecessary cost, yet they are
different. The difference lies in the time and the stage at which the techniques are applied.
Value analysis is the application of a set of techniques to an existing product with a view to
improve its value. It is thus a remedial process.
Value engineering is the application of exactly the same set of techniques to a new product
at the design stage, project concept or preliminary design when no hardware exists to
ensure that bad features are not added. Value engineering, therefore, is a preventive
process.
2.2.3 Value
The term ‘value’ is used in different ways and, consequently, has different meanings. The
designer equates the value with reliability; a purchase person with price paid for the item;
a production person with what it costs to manufacture and a sales person with what the
customer iswilling to pay.
Value, in value investigation, refers to “economic value”, which itself can be divided into
four
types: cost value, exchange value, use value, and esteem value.
Cost value: It is the summation of the labor, material, overhead and all other elements of
cost required to produce an item or provide a service compared to a base.

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Exchange value: It is the measure of all the properties, qualities and features of the
product, which make the product possible of being traded for another product or for
money.
In a conventional sense, exchange value refers to the price that a purchaser will offer for
the product, the price being dependent upon satisfaction (value) which he derives from the
product. Value derived from the product consists of two parts “use value” and “esteem
value”.
Esteem value: It involves the qualities and appearance of a product (like a TV set), which
attractpersons and create in them a desire to possess the product.
Therefore, esteem value is the price paid by the buyer or the cost incurred by the
manufacturer beyond the use value.
Use value: It is known as the function value.
The use value is equal to the value of the functions performed. Therefore, it is the price paid
by the buyer (buyer’s view), or the cost incurred by the manufacturer (manufacturer’s
view) in order to ensure that the product performs its intended functions efficiently. The
use value is the fundamental form of economic value. An item without “use value” can have
neither “exchange value” nor “esteem value”.
2.2.4 Applications
The various application areas of value engineering are machine tool industries, industries
makingaccessories for machine tools, auto industries, import substitutes, etc
2.2.5 Performance
The performance of a product is the measure of functional features and properties that
make itsuitable for a specific purpose. Appropriate performance requires that
(a) The product reliably accomplishes the intended use of work or service requirement
(functional requirements)
(b) The product provide protection against accident, harmful effects on body and
danger tohuman life (safety requirements)
(c) The product give trouble-free service cover during its specified life span (reliability
requirements)
(d) Service and maintenance work can be carried out on the product with ease and with
simpletools (maintainability requirements)
(e) Appearance of the product creates an impression on the buyer and induces in him or
her thedesire to own the product (appearance requirements).
Performance and cost must be interwoven. Desired performance at the least cost should be
achieved by selecting appropriate materials and manufacturing operations, which is the
measure of value. Therefore, the value of the product is the ratio of performance (utility) to
cost. Thus,

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Value = Performance (utility) / Cost
Value can be increased by increasing the utility for the same cost or by decreasing the cost
for the same utility. Satisfactory performance at lesser cost through identification and
developmentof low cost alternatives is the philosophy of Value analysis.
2.3 FUNCTION
Function is the purpose for which the product is made. Identification of the basic functions
and determination of the cost currently being spent on them are the two major
considerations of valueanalysis.
Function identifies the characteristics which make the
product/component/part/item/device to work or sell. “Work functions” lend performance
value while “sell functions” provide esteem value.
Verbs like “support”, “hold”, “transmit”, “prevent”, “protect”, “exhibits”, “control”, etc., are
used to describe work functions, while “attract”, enhance”, “improve”, “create”, etc., are
used to describe “sell” functions. For example, in a “bus driver cabin”, the functional
analysis of some ofthe parts are given in Table
Component of study
Functional
analysis
Verb Noun Steering
Wheel Control Direction Gear box
Change Speed Brake
system
Stop
Vehicle Wiper Clear Water
Horn Make Sound
Side mirror Show Side traffic
2.3.1 Classification of the functions
Rarely do all functions assume equal importance. Usually, some functions are more
importantthan others. Functions can be classified into the following three categories:
1. Primary function
2. Secondary function
3. Tertiary function
1. Primary functions are the basic functions for which the product is specially designed to
achieve. Primary functions, therefore, are the most essential functions whose non-
performance would make the product worthless, e.g. a photo frame exhibits photographs, a
chair supports weight, a fluorescent tube gives light.

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2. Secondary functions are those which, if not in-built, would not prevent the device from
performing its primary functions, e.g., arms of a chair provide support for hands. Secondary
functions are usually related to convenience. The product can still work and fulfill its
intended objective even if these functions are not inbuilt and yet they may be necessary to
sell the product.
3. Tertiary functions are usually related to esteem appearance. For example, Sun mica top
of a table gives esteem appearance for the table.
2.4 Objectives of value engineering/value analysis
Increased profits – With the cost reduction of a product, the profits of an organization
increased. This results in time reduction. It also ensures greater returns on invested capital.
The competitive position of company also improves.
Improved product Design – With the modification in design, the customer will get a new
and more acceptable product.
Efficiency – It increases the efficiency of employees as it motivates them to come forward
with their creative ideas. It also makes contributions to improve human factors such as
creativity, team work and positive attitude among employees. The team approach also
improves the decision making.
Time consideration – A product has value for the customer if it is available to him on time.
Sotime element has great importance in value engineering. It may have no value if it arrives
later.
Improvement in quality – This results in improvement in quality, reliability, performance
andmaintainability of a product.
2.4.1 Aim / objectivesof value engineering/value analysis
The aims of value engineering are as follows:
1. Simplify the product.
2. Improves quality of the product.
3. Promotes standardization and production of quality products are economically achieved
4. Use (new) cheaper and better materials.
5. Modify and improve product design.
6. Improve organizational efficiency.
7. Develop logical approach to solve problems
8. Use efficient processes.
9. Reduce the product cost.
10. Increase the utility of the product by economical means.

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11. Save money or increase the profits.
12. Ensures greater returns on investment.
The value content of each piece of a product is assessed using the following questions:
1. Does its use contribute to value?
2. Is its cost proportionate to its usefulness?
3. Does it need all its features?
These three questions pertain to the function of the part which may decide the
elimination ofparts.
Is there anything better for the intended
use?Can company or vendor standard be
used?
Can a usable part be made by a lower-cost method?
Is it made with the proper tooling, considering
volume?Does the part yield suitable profit?
Can another vendor furnish the same at a lower cost?
2.4.2 Advantages
The advantages of value engineering are as follows:
1. It is a much faster cost reduction technique.
2. It is a less expensive technique.
3. It reduces production costs and adds value to sales income of the product.
2.5 VALUE ANALYSIS PROCEDURE
Some of the most important phases that can be implemented in value analysis procedure
are asfollows:
1. The Orientation Phase
2. The Information phase
3. Functional phase
4. Creation phase
5. Evaluation phase
6. Investigation phase
7. The Recommendation and Implementation phase.
1. The Orientation Phase:
In this phase the project for study is identified and selected. It is advisable to chose/select a
specific problem which is manageable e.g. it would be inadvisable to apply value analysis
on a whole car. The fuel injection system or clutch system may be a specific problem.
Likewise do not work on problem as a whole but break it into elements and study each

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element separately. Constitute a team consisting of experts of various fields/departments
such as from design, Sales purchase and accounts etc. this phase can be represented as:
Identify and select .......................The project to be studied.
Establish.................................................. Priorities.
Plan.................................................................A specific project.
Constitute ...............................................A team.
Prepare .....................................................Terms of reference for the selected project.
Fix........................................................................Responsibility for data collection.
When we speak of a team, the emphasis is on team work which signifies the subordination
or personal preferences to group consensus.
2. Information phase:
Normally this phase consists of following three portions:
(i) Collection of facts:
This is probably the most tough task and all efforts should be made to collect all the
relevant information rather facts. These may relate to specifications; drawings parts,
names of suppliers, manufacturing methods use, used methods of purchase followed and
annual requirements of various items/materials etc. It should be ensured that information
collected is based on facts only.
(ii) Determination of costs:
For each element being studied complete and accurate cost must be obtained. Considerable
importance should be given to the accuracy of these costs since these would form basis for
value analysis. The direct costs (e.g. labor, materials) for each of the assemblies,
subassemblies and parts of the project as well indirect cost (e.g. cost of indirect labor,
Materials, jigs & fixtures, packing materials etc.) should be taken into consideration.
(iii) Fixation of costs of specifications and requirements:
It has been observed that specifications and requirements are simply statements of the
desired results to be incorporated in the final product. Thus it is desirable to segregate the
specifications and actual requirement by analysis of the facts.
It is often found that over designing at the start of product development is a common
phenomenon. So it is essential to find out what s it that is really required. Thus
requirements should not be based on imposed specifications but oasis should be facts.
3. Function Phase:
The objectives of this phase are

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To decide the area of analysis and the functions that it actually performs; because if
the value of an item/product is to be determined it is essential to determine its use
orfunction.
To relate these functions to the cost and worth of providing them; since the
term
functions in “Value Analysis” means that which makes the product work or sell.
From the above, two important relations can be determined and these reveals the
importance of function.One is the relationship between value and function. Another
relationship is between work and sell.Here, the word “work” directly relates to “value” and
the word “sell” relates between value & function.
The rules of conation definitions are:
All the functions should be accomplished in two words-a-verb and a noun.
All the functions must be categorized into two levels of importance basis of primary
andsecondary etc.
Basic are those which serve the primary purpose and secondary are those which serve
other purposes not directly accomplishing the basic but supporting it.
As per first rule the objective is to identify simply and unambiguously the tasks to be
carried out by the product/item under consideration. It is preferable if it is done in two
words i.e. a verb and a noun e.g. the various functions of a bulb are-gives light, removes
darkness, illuminates space. Increase visibility etc.
The work and sell functions are expressed by different categories of verbs and nouns: e.g.
for work functions we use action verbs (like support, create, enclose and insulate etc.)
and measurable nouns (like weight, current, density, force and voltage etc.) which establish
quantitative statements. For expressing sell functions; passive verbs (like increase,
decrease, improve etc.) and non measurable nouns (like beauty, convenience, style form
and features etc.) which establish qualitative statements.
After having defined the functions, the next step is to establish the worth of each basic
function.The objective of evaluating functional relationship is to:
Determine which the poor value functions are and whether the value analysis
effortshould be continued.
Obtain a reference point from which the cost of alternatives can be compared.
Formulate a target cost, to provide a psychological incentive to discourage a
prematurerelaxation of the value analysis effort.

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In this way establish descending order of importance of the functions with relative
value ofimportance.
4. Creation Phase:
In value analysis as in method study a persistent critical examination of facts is extremely
important. Creative phase objective is to produce ideas and to formulate alternative ways
for accomplishing the essential functions and improving the value of the problem under
consideration.
This effort starts as soon as enough information has been collected, reviewed and
understood.The first step is to ask and answer questions like:
WHAT (What is
achieved)WHY (Why is it
essential)
HOW (How it is achieved?) Why that way?
WHERE (Where does it take place?) Why
there?WHEN (When is it done?) Why then?
WHO (Who does it?) Why that man?
Creative problem solving techniques are utilized to discover alternatives that will provide
essential or required functions at the lowest possible cost. Consider whether the function
can be eliminated whether it can be achieved in simpler way or it can be combined or
integrated with any other Isolate items/ components that contribute nothing to the use
function e.g. consider if the inspection can be eliminated or whether SOC can be replaced by
100% inspection or whether the tolerances are realistic or if the reduced surface finish is
acceptable.
Similarly as are materials concerned consider if.
Cheaper components/parts can be purchased from outside market instead of making.
Whether alternative cheaper materials can be used.If the design changes can reduce
the material used.If the dimensions can be reduced.
If a new design can reduce the number of components used.
If redesign will combine two or more functions or will eliminate any
component/part orfunction.
If with redesign excess material, scrap or number of rejects will be reduced.
Thus creativity may be defined as the process of combining already existing elements
intosomething that is new as far as creator is concerned for the purpose of solving

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problems.
The followings are the simple steps in creative thinking:
(A) Identification of the problem:
Ask what is the problem
List out the objectives of the
problem.Define the situation of the
problem.
Try to develop the challenges.
Define the problem in various ways and from several angles and then try to identify
theteal problem.
(B) Determination of the Facts:
Make all observations.
List out the elements of the problem.
Ask creative question such as what, when how, where, why and
who.Determine what is good regarding the problem,
Do not make assumptions.
Do not assume No without basis or beware of “automatic” No.
(C) Idea Determination:
Apply brain storming.
Use fertile imagination and do not judge the
situation.Incubate your ideas.
(D) Determination of Solution:
Evaluate your ail ideas.
Make a fair comparison.
Determine inter
relationshipsAnticipate
objections if any.
Determine and develop place and time for appropriate action.

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5. Evaluation Phase:
The objectives of evaluation phase are:
To select for further analysis the most promising of the ideas generated during
thecreative phase.
To subject the ideas to a preliminary screening to identify those which satisfy the
following criteria?
Will the idea work?
Is it cheaper than present
design?Is it feasible to
implement?
Will it satisfy the user requirements?
If the answer to any of the above is “no” can it be modified or combined with another
togive a yes answer.
To find out which is the most suitable proposal and obtain its cost?
The generation of a quantity of ideas does not accomplish anything until these ideas are put
to use. Before these can be utilized continued creativity must be applied. This may be done
on a single idea or a combination of ideas.
Now the estimated cost is to be determined on all ideas i.e. what will be the potential cost of
utilizing the ideas (under consideration) and what are the resultant savings implied. After
that an assessment of good and bad features of taking the lowest cost idea or group of ideas
should be made. Attempts should be made to by refinement of an idea and again evaluating
it for the purpose of minimization of bad features.
When such rough solutions along with their estimated costs are established, they are
compared to determine which one will provide the greatest possibility of attaining the
value- level target. Now the selection of ideas which are to be carried through further
development is made. The combined creative ideas that have been refined to basically
workable solutions and have greatest possible return on further investment are subjected
to “investigation phase” techniques.
6. Investigation Phase:
The objectives of this phase are:
To bring partially developed or selected untried ideas to fruitarian and to find out
theirfeasibility and limitation.
To prepare a work plan for converting the selected ideas into tangible proposals.

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In this phase, further refining of the selected ideas is made to convert them into workable
and salable solutions. Use company and industrial standards because within a standard
lies a tried and tested solution to a problem. This type of solution is utilized if it also the
lowest total cost approaches.
Adopt the following procedure:
(i) Consul specialists and vendors:
These people must always be consulted because of their specialized knowledge. They can
pinpoint problems in their specialized field and bring new information to effect the
solution of the problem.
(ii) Utilized specialty products, processes and procedures:
The use of these in many cases provide a lower cost way of providing the function or
functions These need evaluation and are utilized when they accomplish a lower total cost
than would standard products, processes and procedures.
7. Recommendation and Implementation Phase:
The objectives of this phase are:
To prepare and submit the planned proposals along with benefits and limitation
to themanagement.
To review submitted proposals if not acceptable to the management.
The recommendation phase and its included techniques are the culmination and warp up
of all the previous efforts exerted throughout the job plan. Upon these techniques and their
diligent fulfillment hinges success or failure of all the foregoing work. In this phase the
selected alternative is presented to the decision maker.
The selected proposal should contain an accurate description of the change as accurate
cost, whether estimate or factual must be presented as part of the final recommendation so
as to support the validity of the savings potential calculation.
The final recommendation need not in fact should contain all the data accumulated but
shouldhowever contain sufficient data for the decision maker to select the course of action to
be taken. After the recommendations have been carefully accepted, the implementation
phase should becarefully monitored and followed up by the value analysis team. It may be
noted that most of thevalue analysis projects collapse primarily due to the resistance to
change by the actual users.INTEREST FORMULAS AND APPLICATIONS
2.7.1 INTRODUCTION
Interest rate is the rental value of money. It represents the growth of capital perunit period.

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The period may be a month, a quarter, semiannual or a year. Aninterest rate 15%
compounded annually means that for every hundred rupeesinvested now, an amount of Rs.
15 will be added tothe account at the end ofthe first year. So, the total amount at the end of
the first year will be Rs. 115.At the end of the second year, again 15% of Rs. 115, i.e. Rs.
17.25 will be addedto the account. Hence the total amount at the end of the second year
will beRs. 132.25. The process will continue thus till the specified number of years.
TIME VALUE OF MONEY
If an investor invests a sum of Rs. 100 in a fixed deposit for five years with aninterest
rate of15% compounded annually, the accumulated amount at the endof every year will be
as shown in Table.
The formula to find the future worth in the third
column isF = P (1 + i)n
Where P = principal amount invested at time 0,
F = future amount
i = interest rate compounded
annually,n = period of deposit.
The maturity value at the end of the fifth year is Rs. 201.14. This means thatthe amount
Rs.
201.14 at the end of the fifth year is equivalent to Rs. 100.00at time 0 (i.e. at present).
This isdiagrammatically shown in Fig. Thisexplanation assumes that the inflation is at zero
percentage.

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Alternatively, the above concept may be discussed as follows: If we wantRs. 100.00 at the
end ofthe nth year, what is the amount that we should depositnow at a given interest rate,
say 15%? A detailed working is shown in Table 3.2
From Table 3.2, it is clear that if we want Rs. 100 at the end of the fifthyear, we should now
deposit an amount of Rs. 49.72. Similarly, if we wantRs. 100.00 at the end of the 10th year,
we should now deposit an amount ofRs. 24.72.
Also, this concept can be stated as follows:A person has received a prize from a finance
company during the recentfestival contest. But the prize will be given in either of the
following two modes:
1. Spot payment of Rs. 24.72 or
2. Rs. 100 after 10 years from now (this is based on 15% interest ratecompounded
annually).
If the prize winner has no better choice that can yield more than 15%interest rate
compounded annually, and if 15% compounded annually is thecommon interest rate paid
in all the finance companies, then it makes nodifference whether he receives Rs. 24.72 now
or Rs. 100 after 10 years.
On the other hand, let us assume that the prize winner has his own businesswherein he can
get a yield of 24% interest rate (more than 15%) compoundedannually, it is better for him
to receive the prize money of Rs. 24.72 at presentand utilize it in his business. If this option
is followed, the equivalent amountfor Rs. 24.72 at the end of the 10th year is Rs. 212.45.
This example clearlydemonstrates the time value of money.
2.7.2 FORMULA
While making investment decisions, computations will be done in many ways. To simplify
all these computations, it is extremely important to know how to use interest formulas
more effectively. Before discussing the effective application of the interest formulas for
investment- decision making, the various interest formulas are presented first.

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Interest rate can be classified into simple interest rate and compound interest rate.
In simple interest, the interest is calculated, based on the initial deposit for every interest
period. In this case, calculation of interest on interest is not applicable.
In compound interest, the interest for the current period is computed based on the amount
(principal plus interest up to the end of the previous period) at the beginning of the
current period.
The notations which are used in various interest formulae are as follows:
P = principal amount
n = No. of interest periods
i = interest rate (It may be compounded monthly, quarterly, semiannually or
annually)F = future amount at the end of year n
A = equal amount deposited at the end of every interest period
G = uniform amount which will be added/subtracted period after period to/ from the
amount ofdeposit A1 at the end of period 1
Single-Payment Compound Amount
Here, the objective is to find the single future sum (F) of the initial payment (P) made at
time 0after n periods at an interest rate i compounded every period.The cash flow diagram
of this situation is shown in Fig.
The formula to obtain the single-payment compound amount is
F = P(1 + i)n = P(F/P, i, n)
Where(F/P, i, n) is called as single-payment compound amount factor.
Single-Payment Present Worth Amount
Here, the objective is to find the present worth amount (P) of a single future sum(F)
which will be received after n periods at an interest rate of i compounded at the end of
every interest period.The corresponding cash flow diagram is shown in Fig.

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The formula to obtain the present worth is
P = = F(P/F, i, n)
Where (P/F, i, n) is termed as single-payment present worth factor.
Equal-Payment Series Compound Amount
In this type of investment mode, the objective is to find the future worth of n equal
payments which are made at the end of every interest period till the end of the nth interest
period at an interest rate of i compounded at the end of each interest period. The
corresponding cash flow diagram is shown in Fig.
In Fig, A = equal amount deposited at the end of each interest
periodn = No. of interest periods
i = rate of interest
F = single future
amountThe formula to
get F is
F =A = A(F/A, i, n)
Where (F/A, i, n) is termed as equal-payment series compound amount factor.
Equal-Payment Series Sinking Fund
In this type of investment mode, the objective is to find the equivalent amount (A) that
should be deposited at the end of every interest period for n interest periods to realize a
future sum (F) at the end of the nth interest period at an interest rate of i. The
In Fig. A = equal amount to be deposited at the end of each interest
periodn = No. of interest periods

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i = rate of interest
F = single future amount at the end of the nth
periodThe formula to get F is
A = F = F (A/F, i, n)
Where (A/F, i, n) is called as equal-payment series sinking fund factor.
Equal-Payment Series Present Worth Amount
The objective of this mode of investment is to find the present worth of an equal payment
made at the end of every interest period for n interest periods at an interest rate of i
compounded at the end of every interest period. The corresponding cash flow diagram is
shown in Fig.
Here, P = present worth
A = annual equivalent
paymenti = interest rate
n = No. of interest
periodsThe formula to compute
P is
P = A = A (P/A, i, n)
Where (P/A, i, n) is called equal-payment series present worth factor.
Equal-Payment Series Capital Recovery Amount
The objective of this mode of investment is to find the annual equivalent amount (A) which
is to be recovered at the end of every interest period for n interest periods for a loan (P)
which is sanctioned now at an interest rate of I compounded at the end of every interest
period.
In Fig P = present worth (loan amount)
A = annual equivalent payment (recovery

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amount)i = interest rate
n = No. of interest periods
The formula to compute P is as follows:
A = P = P(A/P, i, n)
Where,
(A/P, i, n) is called equal-payment series capital recovery factor.
Uniform Gradient Series Annual Equivalent Amount
The objective of this mode of investment is to find the annual equivalent amount of a series
with an amount A1 at the end of the first year and with an equal increment (G) at the end of
each of the following n – 1 years with an interest rate i compounded annually. The
The formula to compute A under this situation is
A = A1 + G
Where(A/G, i, n) is called uniform gradient series factor.
Effective Interest Rate
Let i be the nominal interest rate compounded annually. But, in practice, the compounding
may occur less than a year. For example, compounding may be monthly, quarterly, or semi-
annually. Compounding monthly means that the interest is computed at the end of every
month. There are 12 interest periods in a year if the interest is compounded monthly.
Under such situations, the formula to compute the effective interest rate, which is
compounded annually, is
Effective interest rate, R = (1 + i/ C )C− 1
Where, i = the nominal interest rate
C = the number of interest periods in a year.
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Unit 2- Value Engineering and Time Value of Money

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Unit 2- Value Engineering and Time Value of Money