92
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)
(
)
1
1
−
+
n
i
i
Capital Recovery
to A given P
(A/P, i%, n)
(
)
(
)
1
1
1
−
+
+
n
n
i
i
i
Uniform Series
Compound Amount
to F given A
(F/A, i%, n)
(
)
i
i n 1
1
−
+
Uniform Series
Present Worth
to P given A
(P/A, i%, n)
(
)
(
)n
n
i
i
i
+
−
+
1
1
1
Uniform Gradient
Present Worth
to P given G
(P/G, i%, n)
(
)
(
)
(
)n
n
n
i
i
n
i
i
i
+
−
+
−
+
1
1
1
1
2
Uniform Gradient †
Future Worth
to F given G
(F/G, i%, n)
(
)
i
n
i
i n
−
−
+
2
1
1
Uniform Gradient
Uniform Series
to A given G
(A/G, i%, n)
(
)
1
1
1
−
+
−
n
i
n
i
NOMENCLATURE AND DEFINITIONS
A ..........Uniform amount per interest period
B ..........Benefit
BV ........Book Value
C ..........Cost
d ...........Combined 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)
NON-ANNUAL COMPOUNDING
1
1
−
⎟
⎠
⎞
⎜
⎝
⎛ +
=
m
e
m
r
i
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