Engineering Orientation
Engineering Economics
Engineering Economics
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Value and Interest
Cost of Money
Simple and Compound Interest
Cash Flow Diagrams
Cash Flow Patterns
Equivalence of Cash Flow Patterns
Value and Interest
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“Value” is not synonymous with
“amount”. For a fixed amount of money,
the value may change over time.
The difference between the anticipated
amount in the future and its current value
is called interest.
At an annual interest rate of 10% what is
the value now of the expectation of
receiving $1 in one year?
Terms and formulae
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P or PV Principal is the amount borrowed
N # of pay periods
r Interest rate per period
F or FV, Future worth, value in the future of
what you have to payback
Formulae:
•
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Simple interest = P(1 + Nr) ( = $137,500)
Compound interest = P(1 + r)N ( = $143,563)
Pay periods
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Calculate FV
Assume your loan is compounded
quarterly, monthly or daily instead of
yearly.
Student loan of $25,000 at 8% for
• Annually for two years,
• Quarterly for two years and
• Daily for two years
Pay periods
Yearly n=1
PV
r
n*N
FV
25000
8%
2
($29,160.00)
Quarterly n=4
PV
25000
r/n
2%
n*N
8
FV
($29,291.48)
FV  PV (1  r / n) nN
Dayly n=365
PV
r/n
n*N
FV
25000
0.0219%
730
($29,337.26)
Study Examples
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Compute the effective annual interest
rate ie equivalent to 8% nominal annual
interest compounded continuously.
Calculate the FV
FV  PV (1  r / n)
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In the limit
nN
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 PV 1  r / n 
FV  PVe

n N
rN
Example
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What amount must be paid in two years
to settle a current debt of $1,000 if the
interest rate is 6% Annually?
Cash Flow Diagrams
Cash Flow Patterns
Example
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A new widget twister, with a life of six years, would save $2,000
in production costs each year. Using a 12% interest rate,
determine the highest price that could be justified for the
machine. Although the savings occur continuously throughout
each year, follow the usual practice of lumping all amounts at
the ends of years.
Example

A new widget twister, with a life of six years, would save $2,000
in production costs each year. Using a 12% interest rate,
determine the highest price that could be justified for the
machine. Although the savings occur continuously throughout
each year, follow the usual practice of lumping all amounts at
the ends of years.
PV
FV
A
n
i
-8,222.81
2,000.00
6.00
12.00
Example
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How soon does money double if it is
invested at 8% interest?
Example
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Compute the annual equivalent
maintenance costs over a 5-year life of a
laser printer that is warranted for two
years and has estimated maintenance
costs of $100 annually. Use i = 10%.
Engineering Economics






Value and Interest
Cost of Money
Simple and Compound Interest
Cash Flow Diagrams
Cash Flow Patterns
Equivalence of Cash Flow Patterns