Time value of money for print economics .pdf

Standard notations in EC analysis
• A standard notation has been adopted for all
factors. It is always in the general form (X/Y ,
i, n)
– The letter X represents what is sought,
– The letter Y represents what is given.
• For example, F/P means find F when given P
• The i is the interest rate in percent, and n
represents the number of periods involved.
– Thus, (F/P,6%,20) represents the factor that is used
to calculate the future amount F accumulated in 20
periods if the interest rate is 6% per period.

1. Engineering Economy
“how time affects money”
IE-4198
Bereket Bezabih
[email protected]
Hydraulic and Water Resources
Engineering
2014
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2. TIME VALUE OF MONEY
Lecture 2
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3. Standard notations in EC analysis
•The time value of money is accounted for by
using factors in standard notation
•The future value of money F after n years of
interest period at i compound interest rate of
the current amount P is
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4. Standard notations in EC analysis
•Generally, the term in the bracket is referred to
as a factor and is only the function of interest
rate i and number of periods, n


•If we reverse the problem and determine the P
value for some future F value, the equation and
factor become
Single payment compound amount ,SPCAF or in
short F/P factor
Single payment present
worth factor, P/F factor
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5. 5
Standard notations in EC analysis

6. Standard notations in EC analysis
•A standard notation has been adopted for all
factors. It is always in the general form (X/Y ,
i, n)
–The letter X represents what is sought,
–The letter Y represents what is given.
•For example, F/P means find F when given P
•The i is the interest rate in percent, and n
represents the number of periods involved.
–Thus, (F/P,6%,20) represents the factor that is used
to calculate the future amount F accumulated in 20
periods if the interest rate is 6% per period.
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7. Single Payment Formula and factors
•If one has single payments at times different
from the start or the end, these payments can
be transferred to one of these positions on the
cash flow to calculate the other.
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8. 8
Single Payment Formula and factors

9. Single Payment Formula and factors
•Example 1
–An engineer received a bonus of $12,000 that he
will invest now. He wants to calculate the
equivalent value after 24 years, when he plans to
use all the resulting money as the down payment
on an island vacation home.
–Assume a rate of return of 8% per year for each of
the 24 years. Find the amount he can pay down
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10. Single Payment Formula and factors
•Exercise 1
–Hewlett-Packard has completed a study indicating
that $50,000 in reduced maintenance this year (i.e.,
year zero) on one processing line resulted from
improved wireless monitoring technology.
•a. If Hewlett-Packard considers these types of savings
worth 20% per year, find the equivalent value of this
result after 5 years.
•b. If the $50,000 maintenance savings occurs now, find
its equivalent value 3 years earlier with interest at 20%
per year.
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11. Uniform Serious Formula and
factors
•There are four uniform series formula that
involve A, where A means that:
–The cash flow occurs in consecutive interest
periods, and
–The cash flow amount is the same in each period.
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12. 12
Uniform Serious Formula and
factors

13. Uniform Serious Formula and
factors
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14. Uniform Serious Formula and
factors
•Example 2
–How much money must an electrical contractor
deposit every year in her savings account starting 1
year from now at 5.5% per year in order to
accumulate $6000 seven years from now?
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15. Arithmetic Gradient Formula
•An arithmetic gradient is one wherein the cash
flow changes (increases or decreases) by the
same amount in each period




•The present formula for Arithmetic cash flow
is
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16. Arithmetic Gradient Formula
•The equivalent uniform series AG is given by
arithmetic gradient uniform gradient factor
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17. Geometric Gradient Formula
•A geometric gradient series is a cash flow
series that either increases or decreases by a
constant percentage each period. The uniform
change is called the rate of change.
–g = constant rate of change , in decimal form, by
which cash flow values increase or decrease from
one period to the next. The gradient g can be +ve
or -ve
–A1= initial cash flow in year 1 of the geometric
series
–Pg= present worth of the entire geometric gradient
series, including the initial amount A1
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18. Geometric Gradient Formula
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