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Engineering Economics
Civil Engineering (BSCE 01)
Ateneo de Davao University
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ENGINEERING ECONOMICS
Engineering Economy
- the discipline concerned with the economic
aspect of engineering. It involves the systematic
evaluation with the economic merits of proposed
solutions to the engineering problems.
- To be economically acceptable (i., affordable),
solutions to engineering problem must
demonstrate a positive balance of long-term
benefits over long term cost.
Engineering Economics
- the application of economic techniques to the
evaluation of design and engineering
alternatives.
- The role of engineering economics is to assess
the appropriateness of a given project, estimate
its value, and justify it from an engineering
standpoint.
COST CONCEPTS FOR DECISION MAKING
Ease of Traceability
Direct Costs
- costs that can be reasonably measured and
allocated to a specific output or work activity.
o Examples are labor and material costs.
Indirect Costs
- those that are difficult to attribute or allocate to a
specific output or work activity.
o Examples are the costs of common tools,
general supplies, and equipment
maintenance.
Cost Behavior
Fixed Costs
- are those unaffected by changes in activity level
over a feasible range of operations for the
capacity or capability available.
o Examples are insurance and taxes on
facilities, general management and
administrative salaries, license fees, and
interest costs on borrowed capital.
Variable Costs
- are those associated with an operation that vary
in total with the quantity of output or other
measures of activity level.
o Examples are the costs of material and
labor used in a product or service.
Semi-Variable Costs
- The fixed portion is the minimum amount, and
when it goes beyond that, one will be charged
with the variable.
Based on Transaction
Cash Costs
- are that involving payment of cash.
Book Costs/Noncash Costs
- costs that do not involve a cash payment, but
rather represent the recovery of past
expenditures over a fixed period.
o Example is the depreciation charged.
Relevance to Decision Making
Standard Costs
- are representative costs per unit of output that are
established in advance of actual production or
service delivery.
Overhead Costs
- consists of plant operating costs that are not
direct labor or direct material costs. Examples are
electricity, general repairs, property taxes and
supervision.
Incremental Costs
- the additional cost (or revenue) that results from
increasing the output of the system by one or
more units.
Sunk Costs
- is one that has occurred in the past and has no
relevance to estimates of future costs and
revenues related to an alternative course of
action.
Opportunity Costs
- is incurred because of the use of limited
resources such that the opportunity to use those
resources to monetary advantage in an
alternative use is foregone.
Life-Cycle Costs
- refers to a summation of all the costs, both
recurring and nonrecurring, related to product,
structure system, or services during its life span.
o Investment Costs
▪ is the capital required for most of
the activities in the acquisition
phase.
o Working Capital
▪ refers to the funds required for
current assets that are needed
for the startup and support of
operational activities.
o Operational and Maintenance Cost
▪ includes many of the recurring
annual expense items
associated with the operation
phase of the life cycle.
o Disposal Cost
▪ includes those nonrecurring
costs of shutting down the
operation and the retirement and
disposal of assets at the end of
the life cycle. These costs will be
offset in some instances by
receipts from the sale of assets
with remaining value.
Other Costs
Recurring Costs
- are those that are repetitive and occur when an
organization produces similar goods or services
on a continuing basis.
Nonrecurring Costs
- are those which are not repetitive even though the
total expenditure may become cumulative over a
relatively short period of time.
Illustrative Problem A
Illustrative Problem B
Illustrative Problem C
PRESENT ECONOMY STUDIES
- when alternatives for accomplishing a specific
task are being compared over one year or less
and the influence of time on money can be
ignored
Selection of Material
TIME AND MONEY RELATIONSHIP
INTEREST AND THE TIME VALUE OF MONEY
Money
medium of exchange
unit of account
power over time
Interest Rate
- the percentage of borrowed money that is paid to
the lender on some time basis
- justified from a lender’s perspective in view of:
o opportunity cost
o risk of lending
CASH FLOW DIAGRAM
- is the stream of monetary values – costs and
benefits – resulting from a project investment.
- Cash flow diagram is a graphical representation
of cash flows drawn in a time scale. It has three
elements:
o Horizontal Line
▪ represents time with progression
of time moving from left to right.
▪ The period labels can be applied
to intervals of time rather than to
point on the time scale.
▪ A time interval is divided into an
appropriate number of equal
periods.
o Arrows
▪ represent cash flow and are
place at the specified period.
▪ If distinctions are needed to be
made, downward arrows
represent cash outflows
(expenditures, disbursements)
and upward arrows represents
cash inflows (income).
o Depends on the person’s viewpoint
▪ Unless otherwise indicated, all
such cash flows are considered
to occur at the end of their
respective periods. The following
symbols nomenclatures will be
used:
▪ P = Present sum of money
▪ F = Future sum of money
▪ N = Number of interest periods
▪ i = interest rate per period
SIMPLE INTEREST
- When the total interest earned is linearly
proportional to the amount of the loan (principal),
the number of the interest rate per interest
periods for which the principal is committed, and
the interest rate per interest period, the interest is
said to be simple.
- Is calculated using the principal only, ignoring any
interest that had been accrued in preceding
periods. In practice, simple interest is paid on
short term loans in which the time of the loan is
measured in days
𝑰 = 𝑷𝒏ⅈ
The future worth is equal to:
F = P + I
F = P + Pni
𝑭 = 𝑷 (𝟏 + 𝒏ⅈ)
Where:
I = Interest
P = Principal or Present Worth
n = number of interest periods
i = rate of interest per interest period
F = accumulated amount or future
Types of Simple Interest
- Ordinary Simple Interest (OSI)
o Based on one banker’s year which is
equivalent to 300 days or 30 days in one
month.
o is computed based on 1 2 months of 30
days a year.
𝑶𝑺𝑰 = 𝑷𝒏ⅈ
- Exact Simple Interest (ESI)
o Based in the exact number of days which
is 365 days in ordinary year or 366 days
for leap year.
o is based on the exact number of days in
year, 365 days for an ordinary year and
366 days for a leap year.
o 1 interest period = 365 or 366 days
𝑬𝑺𝑰 = 𝑷
𝒏
𝟑𝟔𝟓
(ⅈ), 𝑓𝑜𝑟 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑦𝑒𝑎𝑟
𝑬𝑺𝑰 = 𝑷
𝒏
𝟑𝟔𝟔
(
ⅈ
)
, 𝑓𝑜𝑟 𝑙𝑒𝑎𝑝 𝑦𝑒𝑎𝑟
Illustrative Problem (Simple Interest)
COMPOUND INTEREST
- Whenever the interest charge for any interest
period is based on the remaining principal
amount plus any accumulated interest charges
up to the beginning of that period the interest is
said to be compounded.
- Interest on top of interest.
Derivation of Formula
Compound Interest Formula:
𝑭 = 𝑷 (𝟏 + ⅈ)
𝒏
Where:
( 1 + 𝑖)
𝑛
= single payment compound amount
factor
= can be written as F/P, i%, n
▪ Read as “F given P at per cent in
n interest period.”
𝑷 = 𝑭 (𝟏 + ⅈ)
−𝒏
Where:
( 1 + 𝑖)
−𝑛
= single payment present worth factor
= can be written as P/F, i%, n
▪ Read as “P given F at i percent
in n interest periods.”
Illustrative Problem (Compound Interest)
Rate of Interest
- is defined as the amount earned by one unit of
principal during a unit of time
- Nominal Rate of Interest
o specifies the rate of interest and a
number of interest periods in one year.
o “indicative” rate per annum and the
number of interest periods in one year
ⅈ =
𝒓
𝒎
Where:
i = rate of interest per interest period
r = nominal interest rate
m = number of compounding periods
per year
𝒏 = 𝑻𝒎
Where:
n = number of interest periods
T = number of years
m = number of compounding periods
per year
𝑭 = 𝑷 (𝟏 + ⅈ)
𝒏
*Applying 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑇𝑚
𝑭 = 𝑷 (𝟏 +
𝒓
𝒎
)
𝒎𝒏
Illustrative Problem (Compound Interest: Nominal)
- Effective Rate of Interest
o quotes the actual rate of interest on the
principal for one year
▪ EIR are always expressed on an
annual basis.
o Effective is equal to nominal if
compounded annually
o Effective is greater if there are more
than one interest period in one year
TIME AND MONEY RELATIONSHIP
Economic Equivalence
- Established when there is a difference between
future payment/s and a present sum of money
- Considers the comparison of alternative options,
or proposals, by reducing them to an equivalent
basis, depending on:
o Interest Rate
o Amounts of Money Involved
o Timing of the affected monetary receipts
and/or expenditures
o Manner in which the interest or profit on
invested capital is paid and in which the
initial capital is recovered
- An equation of value by setting the sum of the
values on a certain comparison or focal date
- There is equilibrium at a chosen focal point
(inflows = outflows)
CASH FLOW
Illustrative Problem A
Illustrative Problem B
Illustrative Problem C
Illustrative Problem D
ANNUITY
- a series of equal payments made at equal
intervals of time. Financial activities like
installment payments, monthly rentals, life-
insurance premium, monthly retirement benefits,
are familiar examples of annuity.
TYPES OF ANNUITIES
- Ordinary Annuity
o series of uniform cash flows where the
first amount of the series occurs at the
end of the first period and every
succeeding cash flow occurs at the end
of each period.
o one where the payments are made at the
end of each period.
a. Finding Present Equivalent Value given a
series of uniform equal receipts
o P = A (P/A, i%, n)
o Uniform series present worth factor in []
𝑷 = 𝑨 [
𝟏 −
(
𝟏 + ⅈ
)
−𝒏
ⅈ
]
Illustrative Problem (Annuity: Finding P)
b. Finding Future Equivalent Value given a
series of uniform equal receipts
o F = A (F/A, i%, n)
o Uniform series compound amount factor
in []
𝑭 = 𝑨
[
(
𝟏 + ⅈ
)
𝒏
− 𝟏
ⅈ
]
Illustrative Problem (Annuity: Finding F)
Illustrative Problem (Annuity: Finding F)
c. Finding amount A of a uniform series, given
the equivalent present value
o A = P (A/P, i%, n)
o Capital recovery factor in []
𝑨 = 𝑷 [
ⅈ(𝟏 + ⅈ)
𝒏
(𝟏 + ⅈ)
𝒏
− 𝟏
]
d. Finding amount A of a uniform series when
given the equivalent future value
o A = F (A/F. i%, n)
o Sinking fund factor in []
𝑨 = 𝑭 [
ⅈ
(
𝟏 + ⅈ
)
𝒏
− 𝟏
]
Illustrative Problem (Annuity A)
Illustrative Problem (Annuity B)
- Deferred Annuity
o is one where the first payment is made
several periods after the beginning of
the annuity.
o where the first cash flow of the series is
not at the end of the lot period, or it is
deferred for some time
Illustrative Problem (Annuity Due B)
d. Perpetuity
o an annuity in which the payments
continue indefinitely.
o a series of uniform cash flows where they
extend for a long time or forever.
o P = A (P/A, i%, ∞)
𝑷 = 𝑨 [
𝟏 − (𝟏 + ⅈ)
−∞
ⅈ
] =
𝑨
ⅈ
Illustrative Problem (Perpetuity A)
Illustrative Problem (Perpetuity B)
Illustrative Problem (Perpetuity C)
TIME AND MONEY RELATIONSHIP
GRADIENT SERIES
- The series of cash flow where the amounts
change every period
UNIFORM ARITHMETIC GRADIENT
- In certain cases, economic analysis problems
involve receipts or disbursement that increase or
decrease by a uniform amount each period.
- For example, maintenance and repair expenses
on specific equipment or property may increase
by a relatively constant amount each period. This
is known as a uniform arithmetic gradient.
- Solving for P:
𝑷 = 𝑷
𝑨
+ 𝑷
′′
Where:
𝑃
𝐴
= 𝐴 [
1 − ( 1 + 𝑖)
−𝑛
𝑖
]
𝑃
′′
=
𝐺
𝑖
[
1 −
(
1 + 𝑖
)
−𝑛
𝑖
−
𝑛
(
1 + 𝑖
)
𝑛
]
Thus,
𝑷 = 𝑨 [
𝟏 −
(
𝟏 + ⅈ
)
−𝒏
ⅈ
] +
𝑮
ⅈ
[
𝟏 −
(
𝟏 + ⅈ
)
−𝒏
ⅈ
−
𝒏
(
𝟏 + ⅈ
)
𝒏
]
Illustrative Problem (UAG A)
Illustrative Problem (UAG B)
- Solving for F
𝑭 = 𝑭
𝑨
+ 𝑭
′′
Where:
𝐹
𝐴
= 𝐴 [
(
1 + 𝑖
)
𝑛
− 1
𝑖
]
𝐹
′′
=
𝐺
𝑖
[
( 1 + 𝑖)
𝑛
− 1
𝑖
− 𝑛]
Thus,
𝑭 = 𝑨 [
(
𝟏 + ⅈ
)
𝒏
− 𝟏
ⅈ
] +
𝑮
ⅈ
[
(
𝟏 + ⅈ
)
𝒏
− 𝟏
ⅈ
− 𝒏]
Illustrative Problem (UAG C)
Alternative Solution:
Engineering Economics
Course: Civil Engineering (BSCE 01)
University: Ateneo de Davao University
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