Engineering economy introduction Lec#02.ppt

Cash flows, inflows, out flows

1. Introduction
HM-202
NFC Institute of Engineering & Technological Training, Multan
Engineering Economics

2. Recap.
Definitions
I.Engineering
II.Engineering Economy
III.Alternatives
IV.First cost, useful life, salvage value.
V.Tangible & Intangible Factors.
VI.Inflation, Depreciation.

3. Topics of the Day.
•Cash flows
•Time value of money.
•Interest rate & ROR.
•Equivalence.
•Types of interest

5. Cash Flows
•Inflows (Revenues)
•Outflows (Costs)
•Without cash flow estimates over a stated
time period, no engineering economy
study can be conducted.

6. Time Value of Money
•The change in the amount of money over
a given time period is called the time value
of money; it is the most important concept
in engineering economy.
•Money makes money…. “If Invested”

7. TVM
•The idea that money available at the
present time is worth more than the same
amount in the future, due to its potential
earning capacity.
•Any amount of money is worth more the
sooner it is received. Also referred to as
"present discounted value

8. TVM
•For example, assuming a 5% interest
rate, $100 invested today will be
worth $105 in one year ($100
multiplied by 1.05). Conversely, $100
received one year from now is only
worth $95.24 today ($100 divided by
1.05), assuming a 5% interest rate

9. Interest rate & Rate of return

10. Interest Rate and Rate of
Return
•Interest is the difference between an ending
amount of money and the beginning amount
•If the difference is zero or negative, there is no
interest.
•There are always two perspectives to an amount of
interest
–Interest paid
–Interest earned
•Interest is paid when a person or organization
borrows money (obtained a loan) and repays a
larger amount.

11. •Interest is earned when a person or
organization saves, invests, or lent money
and obtains a return of larger amount.
•The computations and numerical values
are essentially the same for both
perspectives.

12. Interest Paid
•Interest = amount owed now – original amount
•When interest paid over a specific time unit is expressed as a %age
of the original amount (principal), the result is called interest rate.
•The time unit of the rate is called Interest period.
•The most common interest period used to state an interest rate is 1
year. (but can be 6 months, 1 month and so on)
•Normally stated 8.5% means over an interest period of 1-year.
100
amount original
unit timeper interest
(%) rateInterest X

13. Notations
•Notation
– I = the interest amount is $
– i = the interest rate (% / interest period)
– N = No. of interest periods (1 Normally)

14. Example 1.3
Given
You borrow $10,000 for one full year
Must pay back $10,700 at the end of one year
Determine
Interest amount = ?
Interest rate paid = ?

15. Examples
•Items which are not easily expressed in
terms of dollars are called:
A) Indirect costs B) Variable costs C) Intangible costs D) Legal issues
•Interest that is calculated using only the
principal is called:
• A) Simple interest B) Effective interest C) Add-on interest D)
Compound interest

16. Examples
•If $1000 is borrowed at 10% per year
simple interest, the total amount due at the
end of five years is nearest to:
A) $1,100 B) $1,250 C) $1,500 D) $1,611
•The amount of money five years ago that
is equivalent to $1000 now at 10% per
year compound interest is nearest to:
A) $621 B) $667 C) $1,500 D) $1,611

17. Example 1.4
•FME plans to borrow Rs. 200,000 from a bank
for 1 year at 9% interest for new equipment
–Compute the interest and the total amount due after 1
year.

18. •When the interest rate is 10% per year, all
of the following are equivalent to $5,000
now except:
A) $4,545 one year ago.
B) $5,500 one year hence.
C) $4,021 two years ago.
D) $6,050 two years hence.

19. Interest Earned
•Interest = total amount now – original amount
•Interest paid over a specific period of time is expressed
as a %age of the original amount and is called Rate of
Return (ROR).
•ROR is also called the Return on Investment (ROI).
100
amount original
unit timeper interest
(%)Return of Rate X

20. Example 1.5
•Calculate the amount deposited 1 year
ago to have $1000 now at an interest rate
of 5% per year.
•Calculate the amount of interest earned
during the time period.

21. Example
•A person borrows Rs. 1000 from bank and must
pay a total of 1100 after one year.
•Calculate the amount of interest and interest rate.
Interest = amount owed now – original amount
100
amount original
unit timeper interest
(%) rateInterest X
Formulae for use in problem:

22. Economic Equivalence

23. Equivalence

24. Economic Equivalence
•The time value of money and the interest
rate help develop the concept of economic
equivalence.
•$100 today = $106 after one year, if the
interest rate is 6%
•$100 today = $94.34 before one year, of
the interest rate is 6%

25. Simple and Compound Interest
•The terms interest period, and interest rate
are useful in calculating equivalent sums
of money for one interest period in the
past and one period in the future.
•But for more than one interest period, the
terms simple and compound interest
become important.

26. Simple Interest
•Simple interest is calculated using the principal only.
•Interest = (Principal) (number of periods) (interest rate)
where the interest rate in this case is in decimals

27. Example 1.7

28. Compound Interest
•The interest accrued for each interest period is calculated on the principal
plus the total amount of interest accumulated in all previous periods.
•Compound interest mean interest on top of interest.
•Interest=(Principal + all accrued interest) (interest rate)
•Total due after a number of years = P(1+i)
n
Interest rate in
this case is in
decimals

29. Example 1.8
•If an engineer borrows $1000 from the company credit
union at 5% per year compound interest, compute the total
amount due after 3 years.