The document discusses the concepts of engineering economics and time value of money. It provides an overview of why engineering economics is important for engineers when making design decisions. The document also covers key concepts in time value of money, including present value, future value, and formulas for calculating things like lump sums, cash flows, and annuities under different conditions.

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Engineering Economics (2+0)
Fundamentals of Engineering Economics-2
And
Time value of Money
Instructor:
Prof. Dr. Attaullah Shah
Lecture # 2
Department of Civil Engineering
City University of Science and IT Peshawar

3. Engineering Economics
 It deals with the concepts and techniques of analysis useful in
evaluating the worth of systems, products, and services in relation to
their costs
 Engineering economics deals with the methods that enable one to take
economic decisions towards minimizing costs and/or maximizing
benefits to business organizations.
 It is used to answer many different questions
 Which Engineering projects are worthwhile?
 Has the mining or petroleum engineer shown that the mineral or
oil deposits is worth developing?
 Which engineering projects should have a higher priority?
 Has the industrial engineer shown which factory improvement
projects should be funded with the available dollars?
 How should the engineering project be designed?
 Has civil or mechanical engineer chosen the best thickness for
insulation?

4. Why Engineering Economy is Important
to Engineers
 Engineers design and create
 Designing involves economic decisions
 Engineers must be able to incorporate economic analysis into
their creative efforts
 Often engineers must select and implement from multiple
alternatives
 Understanding and applying time value of money, economic
equivalence, and cost estimation are vital for engineers
 A proper economic analysis for selection and execution is a
fundamental task of engineering

5. General Steps for Decision Making Processes
1. Understand the problem – define
objectives
2. Collect relevant information
3. Define the set of feasible
alternatives
4. Identify the criteria for decision
making
5. Evaluate the alternatives and apply
sensitivity analysis
6. Select the “best” alternative
7. Implement the alternative and
monitor results

6. Time Value of Money
 What is money?
 Money is any set of assets used to buy goods and services, and has
three key characteristics.
 First, money is a medium of exchange: it offers buyers and
sellers a mutually recognized means of payment for exchanging
goods and services.
 Second, money is a unit of account, or a yardstick for
measuring the value of goods and services to sellers and buyers.
 Third, money is a store of value: it can be reliably saved, stored
and predictably used once retrieved. Other desirable features of
money are that it should have a stable value and be difficult to
counterfeit.

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What is The Time Value of
Money?
 A dollar received today is worth more than a
dollar received tomorrow
 This is because a dollar received today can be
invested to earn interest
 The amount of interest earned depends on the rate
of return that can be earned on the investment
 Time value of money quantifies the value of a
dollar through time

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Uses of Time Value of Money
 Time Value of Money, or TVM, is a concept that is
used in all aspects of finance including:
 Bond valuation
 Stock valuation
 Accept/reject decisions for project management
 Financial analysis of firms
 And many others!

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Formulas
 Common formulas that are used in TVM calculations:*
 Present value of a lump sum:
PV = FV / (1+i)n
 Future value of a lump sum:
FV = PV * (1+i)n
Present value of a cash flow stream:
PV = S [FV / (1+i)n]

10. Equal-Payment Series Compound Amount
 To determine Future worth “F” of equal payments “A”
made at equal interval of times and compounded at the
interest rate:
 F =
 Example: A person who is now 35 years old is planning for his retired
life. He plans to invest an equal sum of Rs. 10,000 at the end of every
year for he next 25 years starting from the end of the next year. The
bank gives 20% interest rate, compounded annually. Find the maturity
value of his account when he is 60 years old.
 A = Rs. 10,000, n = 25 years., i = 20% , F = ?

11. Equal-Payment Series Sinking Fund
 To find the equivalent amount A to be deposited at the
end of each markup period for n periods to realize the
future value F.
 A Company has to replace its equipment after 15 year at the cost of
Rs. 500,000. If it plans to deposit an equal amount in the bank for
15 years at markup rate of 18%, what is the annual payment?
 F = 500,000 n = 15 , i = 18% Find A=?


12. Equal-Payment Series Present Worth Amount
 To determine the present worth of equal instalment paid
for period n at interest rate i and compounded annually.
 A company wants to set up a reserve which will help the company
to have an annual equivalent amount of Rs. 10,00,000 for the next
20 years towards its employees welfare measures. The reserve is
assumed to grow at the rate of 15% annually. Find the single-
payment that must be made now as the reserve amount.
 A = Rs. 10,00,000, i = 15%, n = 20 years, P = ?

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Types of TVM Calculations
 There are many types of TVM calculations
 The basic types will be covered in this review module
and include:
 Present value of a lump sum
 Future value of a lump sum
 Present and future value of cash flow streams
 Present and future value of annuities
 Keep in mind that these forms can, should, and will be
used in combination to solve more complex TVM
problems

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Basic Rules
 The following are simple rules that you should always use no matter
what type of TVM problem you are trying to solve:
1. Stop and think: Make sure you understand what the problem is
asking. You will get the wrong answer if you are answering the
wrong question.
2. Draw a representative timeline and label the cash flows and time
periods appropriately.
3. Write out the complete formula using symbols first and then
substitute the actual numbers to solve.
4. Check your answers using a calculator.
 While these may seem like trivial and time consuming tasks, they will
significantly increase your understanding of the material and your
accuracy rate.

15. Class Assignments- Practice Problems
 A person deposits a sum of Rs. 1,00,000 in a bank for his son’s education who
will be admitted to a professional course after 6 years. The bank pays 15%
interest rate, compounded annually. Find the future amount of the deposited
money at the time of admitting his son in the professional course.
 A person needs a sum of Rs. 2,00,000 for his daughter’s marriage which will
take place 15 years from now. Find the amount of money that he should deposit
now in a bank if the bank gives 18% interest, compounded annually.
 5. A person who is just 30 years old is planning for his retired life. He plans to
invest an equal sum of Rs. 10,000 at the end of every year for the next 30 years
starting from the end of next year. The bank gives 15% interest rate,
compounded annually. Find the maturity value of his account when he is 60
years old.
 A company is planning to expand its business after 5 years from now. The
expected money required for the expansion programme is Rs. 5,00,00,000. The
company can invest Rs. 50,00,000 at the end of every year for the next five
years. If the assured rate of return of investment is 18% for the company, check
whether the accumulated sum in the account would be sufficient to meet the
fund for the expansion programme. If not, find the difference in amounts for
which the company should make some other arrangement after 5 years.

16.  A financial institution introduces a plan to pay a sum of Rs.
15,00,000 after 10 years at the rate of 18%, compounded annually.
Find the annual equivalent amount that a person should invest at the
end of every year for the next 10 years to receive Rs. 15,00,000 after
10 years from the institution.
 A company wants to set-up a reserve which will help it to have an
annual equivalent amount of Rs. 15,00,000 for the next 20 years
towards its employees welfare measures. The reserve is assumed to
grow at the rate of 15% annually. Find the single-payment that must
be made as the reserve amount now.
 Toyota company recently advertised its car for a down payment of
Rs. 1,500,000. Alternatively, the car can be taken home by customers
without making any payment, but they have to pay an equal yearly
amount of Rs. 250,000 for 15 years at an interest rate of 18%,
compounded annually. Suggest the best alternative to the customers.