1. The document discusses the time value of money concept in engineering economy and introduces related terminology and formulas.
2. Key points covered include equivalence of money over time with interest, definitions of interest rate and rate of return, and explanations of simple and compound interest.
3. Standard notation for interest factors is presented, including the general form of (X/Y,i%,n) to represent various interest factors. Cash flow diagrams and the symbols P, F, and A are also explained.
How value of money changes with time; factors affecting the change; economic equivalence; relationship between present amount, future amount, interest rate and time period, annuity are discussed.
How value of money changes with time; factors affecting the change; economic equivalence; relationship between present amount, future amount, interest rate and time period, annuity are discussed.
Engineering economic importance & applicationabdus sobhan
Application of engineering or mathematical analysis and synthesis to decision making in economics.
The knowledge and techniques concerned with evaluating the worth of commodities and services relative to their cost.
Analysis of the economics of engineering alternativesThis course has to do with money and success.
Most of us want some measure of success in life.
For better or for worse, money (and economics) has a lot to do with success.
Whether should an organization replace it's assets or not depends on replacement analysis. terms like useful life, EUAC, economic life, ownership life, physical life are explained.
This presentation discusses the following topics:
What is Engineering Economics?
Why Engineering Economics?
Scope of Engineering Economics
Example of Engineering Economics
Rational Decision-Making Process
Engineering Economics Decision
Role of Engineers in Business
Types of Business Organizations
Engineering economic importance & applicationabdus sobhan
Application of engineering or mathematical analysis and synthesis to decision making in economics.
The knowledge and techniques concerned with evaluating the worth of commodities and services relative to their cost.
Analysis of the economics of engineering alternativesThis course has to do with money and success.
Most of us want some measure of success in life.
For better or for worse, money (and economics) has a lot to do with success.
Whether should an organization replace it's assets or not depends on replacement analysis. terms like useful life, EUAC, economic life, ownership life, physical life are explained.
This presentation discusses the following topics:
What is Engineering Economics?
Why Engineering Economics?
Scope of Engineering Economics
Example of Engineering Economics
Rational Decision-Making Process
Engineering Economics Decision
Role of Engineers in Business
Types of Business Organizations
1031191EE 200 Engineering Economics 2Time Value o.docxaulasnilda
10/31/19
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EE 200: Engineering Economics 2
Time Value of Money
2
2
136 ENGINEERING ECONOMICS
ENGINEERING ECONOMICS
Factor Name Converts Symbol Formula
Single Payment
Compound Amount to F given P (F/P, i%, n) (1 + i)
n
Single Payment
Present Worth to P given F (P/F, i%, n) (1 + i)
–n
Uniform Series
Sinking Fund to A given F (A/F, i%, n) ( ) 11 + ni
i
Capital Recovery to A given P (A/P, i%, n)
( )
( ) 11
1
+
+
n
n
i
ii
Uniform Series
Compound Amount to F given A (F/A, i%, n)
( )
i
i n 11 +
Uniform Series
Present Worth to P given A (P/A, i%, n)
( )
( )n
n
ii
i
+
+
1
11
Uniform Gradient
Present Worth to P given G (P/G, i%, n)
( )
( ) ( )nn
n
ii
n
ii
i
++
+
11
11
2
Uniform Gradient †
Future Worth to F given G (F/G, i%, n)
( )
i
n
i
i n+
2
11
Uniform Gradient
Uniform Series to A given G (A/G, i%, n) ( ) 11
1
+ ni
n
i
NOMENCLATURE AND DEFINITIONS
A �������������Uniform amount per interest period
B �������������Benefit
BV �����������Book value
C �������������Cost
d��������������In ation ad usted interest rate per interest period
Dj ������������Depreciation in year j
EV �����������Expected value
F �������������Future worth, value, or amount
f �������������� eneral in ation rate per interest period
G �������������Uniform gradient amount per interest period
i ��������������Interest rate per interest period
ie �������������Annual effective interest rate
MARR ����Minimum acceptable/attractive rate of return
m �������������Number of compounding periods per year
n��������������Number of compounding periods; or the expected
life of an asset
P �������������Present worth, value, or amount
r ��������������Nominal annual interest rate
Sn ������������Expected salvage value in year n
Subscripts
j ����������� at time j
n����������� at time n
†����������� F/G = (F/A – n)/i = (F/A) × (A/G)
Risk
Risk is the chance of an outcome other than what is planned to
occur or expected in the analysis�
NON-ANNUAL COMPOUNDING
i m
r1 1e
m
= + -b l
BREAK-EVEN ANALYSIS
By altering the value of any one of the variables in a situation,
holding all of the other values constant, it is possible to find a
value for that variable that makes the two alternatives equally
economical� This value is the break-even point�
Break-even analysis is used to describe the percentage of
capacity of operation for a manufacturing plant at which
income will ust cover expenses.
The payback period is the period of time required for the profit
or other benefits of an investment to equal the cost of the
investment�
Time Value of Money Relating Future and
Present Worth Shows Unreasonable Costs
3
𝐹 is Future Worth 𝑃 is Present Worth 𝑛 is the number of compounding periods
𝐴 is Uniform Amount per interest period (Payment) 𝑖 is the interest rate per period
3
10/31/19
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College Costs Have Historically Increased Faster
than Inflation: Compound Interest Model
• Umich: Total Annual Cost
o 1980: $3,500
o 2020: $30,0