127 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 −+n
i
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
in11 −+
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
in
−
−+
2
11
Uniform Gradient
Uniform Series to A given G (A/G,i%,n)
( )
11
1
−+
−n
i
n
i
NOMENCLATURE AND DEFINITIONS
A .......... Uniform amount per interest period
B .......... Benefit
BV ........ Book value
C .......... Cost
d........... Inflation adjusted interest rate per interest period
Dj ......... Depreciation in year j
F .......... Future worth, value, or amount
f ........... General inflation rate per interest period
G .......... Uniform gradient amount per interest period
i ........... Interest rate per interest period
ie .......... Annual effective interest rate
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
im
r
11
e
m
=+ -
bl
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 just 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.
