114 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 ..........
BV ........ Book value
C .......... Cost
d........... Combined interest rate per interest period
Dj ......... Depreciation in year j
F .......... Future worth, value, or amount
f ...........
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)
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,
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.
investment.
INFLATION
f, and then they are shifted
over the time scale using the interest rate per interest period
i. Use a combined interest rate per interest period d for
computing present worth values P and Net P.
The formula for d is d = i + f + (i × f)
