ENGINEERING ECONOMICS BASIC CONCEPTS

1
ENGINEERING ECONOMICSBASIC CONCEPTS

• TERMINOLOGY AND CASH-FLOW DIAGRAMS

2
TERMINOLOGY

• ENGINEERING ECONOMICS - Collection of
  mathematical techniques used to develop rational
  approaches to evaluating economic consequences of
  actions

3
TYPICAL PROBLEMS

• Personal
• Should I borrow money to pay off the credit card
  ?
• Should I buy or lease the new car ?
• Should I pay down my home mortgage or invest
  elsewhere forgoing the income tax write off ?

4
TYPICAL PROBLEMS

• Corporations and Businesses
• Are the savings resulting from an investment in a
  new machine adequate ?
• Should the required new space be built or
• leased ?
• Which process should be used for the product ?

5
TYPICAL PROBLEMS

• Public Institutions
• How much tax revenue is needed to pay off the
  school bonds ?
• How much will it cost to build and perpetually
  maintain a memorial ?
• Do the benefits outweigh the cost for another
  bridge crossing the river ?

6
TERMINOLOGY

• INTEREST - MANIFESTATION OF THE TIME VALUE OF
  MONEY. THE AMOUNT PAID TO USE MONEY.
• INVESTMENT
• INTEREST VALUE NOW - ORIGINAL AMOUNT
• LOAN
• INTEREST TOTAL OWED NOW - ORIGINAL AMOUNT

7
TERMINOLOGY

• INTEREST RATE - INTEREST PER TIME UNIT

8
TERMINOLOGY

• SIMPLE INTEREST - Interest calculated considering
  the principle only.
• I P i P i P i
  ...
• COMPOUND INTEREST - Interest calculated
  considering the principle and interest previously
  earned.
• I P i (P P i) i (P P i P i2 ) i
  ...

9
EXAMPLE 1.1

• Payment for a 3 year 1000 loan with 14 interest
  per year.
• Simple Interest
  Compound Interest
• 1st yr 1000(0.14) 140 1000(0.14)
  140
• 2ed yr 1000(0.14) 140 1140(0.14)
  159.60
• 3ed yr 1000(0.14) 140 1299.60(0.14)
  181.94
• Interest .......420
  Interest .......481.54

10
NOTATION

• P VALUE AT PRESENT TIME
• F VALUE AT A FUTURE TIME
• A VALUE OF CONSECUTIVE, EQUAL, END OF PERIOD
  PAYMENTS

11
NOTATION

• n Number of interest periods
• i interest rate per period

12
CASH FLOW DIAGRAMS
CASH FLOW
A
A
A
1
2
3
TIME ( PERIODS )
F
FUTURE VALUE, F, OF THREE EQUAL
PAYMENTS OF SIZE A
13
EXAMPLE 1.2
You have the option of investing 1000 at 7
simple interest or 6 compound interest, both for
three years. Which would you choose?
14
EXAMPLE 1.2
OPTION 1 - INTEREST 3 ( 1000 ) .07 210
OPTION 2 - INTEREST 1st year 1000 (.06) 60
2ed year 1060(.06) 63.60 3ed year
1123.60 (.06)67.38 TOTAL
INTEREST 197.76
CHOOSE OPTION ONE
15
EXAMPLE 1.3
DRAW THE CASH FLOW DIAGRAM FOR THE FOLLOWING
SITUATION. WHAT 5 YEAR EQUIVALENT ANNUAL PAYMENT
STARTING ONE YEAR FROM NOW IS EQUIVALENT TO A
DRAW OF 5000 NOW, 20,000 AFTER YEAR THREE AND
10,000 AFTER YEAR FOUR. INTEREST IS 10 PER
YEAR.
16
EXAMPLE 1.3
A
A
A
A
A
1
2
3
4
5
10000
5000
20000
17
EXAMPLE 1.3

• IN ORDER TO FIND THE VALUE OF A THE TOTAL VALUE
  OF THE POSITIVE CASH FLOWS WILL BE EQUATED TO THE
  NEGATIVE CASH FLOWS AT YEAR 5.

18
EXAMPLE 1.3

• POSITIVE CASH FLOWS -
• First Year Equivalent at year 5 - A (10.1)4
• Second Year - A
  (10.1)3
• Third Year -
  A (10.1)2
• Fourth Year -
  A (10.1)
• Fifth Year -
  A
• A 1.464 1.331 1.210 1.100
  1.0 A (6.105)

19
EXAMPLE 1.3

• NEGATIVE CASH FLOWS -
• 5000 (10.1)5 8,053
• 20,000 (10.1)2 24,200
• 10,000 (10.1) 11,000
• TOTAL 43,253
• A (6.105) 43,253
• A 7085

20
TERMINOLOGY

• RATE OF RETURN, ROR - THE INTEREST RATE EARNED ON
  AN INVESTMENT OVER ITS LIFE
• IF P IS INVESTED OVER n PERIODS AT WHICH TIME IT
  HAS A VALUE OF F

21
TERMINOLOGY

• MINIMUM ATTRACTIVE RATE OF RETURN, MARR
• MARR IS THE CUT OFF VALUE IN ROR BELOW WHICH
  INVESTMENT ALTERNATIVES ARE IGNORED