Chapter 1. INTRODUCTION TO
ENGINEERING ECONOMICS
Engineering Economic Analysis Procedure
Engineering - “is the profession in which a knowledge
of the mathematical and natural sciences gained by
study, experience, and practical is applied with
judgment to develop ways to utilize, economically, the
materials and forces of nature for the benefit of
mankind.”
Engineering Economy - involves the systematic
evaluation of the economic merits of proposed solutions
to engineering problems.
- to be economically acceptable (i.e., affordable),
solutions to engineering problems must demonstrate a
positive balance of long-term benefits over long term
costs
FUNDAMENTAL PRINCIPLES OF
ENGINEERING ECONOMY
1. Develop the alternatives
2. Focus on the differences
3. Use a consistent viewpoint -the prospective
outcomes of the alternatives, economic and other, should
be consistently developed from a defined viewpoint
(perspective).
4. Use a common unit of measure - Using a common
unit of measurement to enumerate as many of the
prospective outcomes as possible will simplify the
analysis of the alternatives
5. Consider all relevant criteria – the decision process
should consider both the outcomes enumerated in the
monetary unit and those expressed in some other unit of
measurement or made explicit in a descriptive manner.
6. Make risk and uncertainty explicit - Risk and
uncertainty are inherent in estimating the future
outcomes of the alternatives and should be recognized in
their analysis and comparison
7. Revisit your decisions
Engineering Economy and the Design Process
•
•
An engineering economy study is accomplished
using a structured procedure and mathematical
modeling techniques.
The economic results are then used in a decision
situation that normally includes other
engineering knowledge and input.
> Consumer goods and services - are those products or
services that are directly used by people to satisfy their
wants.
> Producer goods and services - are used to produce
consumer goods and services or other producer goods.
> Necessities - are those products or services that are
required to support human life and activities, that will
purchased in somewhat the same quantity even though
the price varies considerably.
> Luxuries - are those products or services that are
desired by humans and will be purchased if money is
available after the required necessities have been
obtained
> Demand - the quantity of a certain commodity that is
bought at a certain price at a given place and time(High
Price – Low Demand, Low Price – High Demand)
> Elastic demand - occurs when a decrease in selling
price result in a greater than proportionate increase in
sales.
> Inelastic demand - occurs when a decrease in the
selling price produces a less than proportionate increase
in sales.
> Unitary elasticity - of demand occurs when the
mathematical product of volume and price is constant.
> Perfect competition - occurs in a situation where a
commodity or service is supplied by a number of
vendors and there is nothing to prevent additional
vendors entering the market.
> Monopoly - the opposite of perfect competition. A
perfect monopoly exists when a unique product or
service is available from a single vendor and that vendor
can prevent the entry of all others into the market.
> Oligopoly - exists when there are so few suppliers of a
product or service that action by one will almost
inevitably result in similar action by the others.
> Supply - the quantity of a certain commodity that is
offered for sale at a certain price at a given place and
time ( High Supply – Low Price, Low Supply – High
Price)
> Fixed costs - are those unaffected by changes in
activity level over a feasible range of operations for the
capacity or capability available.
> Direct costs - are costs that can be reasonably
measured and allocated to a specific output or work
activity. The labor and material costs directly associated
with a product, service or construction activity are direct
costs.
> Indirect costs - are costs that are difficult to allocate to
a specific output or work activity. Normally, they are
costs allocated through a selected formula to the outputs
or work activities.
Chapter 2: TIME VALUE OF MONEY
> Capital - refers to wealth in the form of money or
other assets owned by a person or organization that can
be used for a particular purpose such as starting a
company or investing.
Types of Capital
1. Equity Capital- owned by individuals who have
invested their money or property in a business project or
venture in the hope of receiving a profit.
2. Borrowed Capital – obtained from lenders for
investment, with a promise to repay the principal amount
and interest on a specific date.
3. Human Capital
4. Social Capital
5. Natural Capital
Cash Flow Diagram
> Overhead costs- consists of plant operating costs that
are not direct labor or direct material costs.
> Standard costs - are planned costs per unit of output
that are established in advanced of actual production or
service delivery.
> Cash costs - involves payment of cash. Are estimated
from the perspective established for the analysis and are
the future expenses incurred for the alternatives being
analyzed.
> Book costs - are costs that do not involve cash
payments but rather represent the recovery of past
expenditures over a fixed period of time. Example:
depreciation charged for the used assets
> Sunk costs - is one that has occured 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
related to a product, structure, system, or service during
its life span.
Elements:
1. Horizontal line. Represents the time with progression
of time moving from left to right (i.e. month, year).
2. Arrows. Represents cash flows.
↑ = receipts (positive cash flow or cash inflow i.e
income)
↓ = disbursements (negative cash flow or cash outflow
i.e expenses)
3. Depends on the person’s viewpoint.
Borrower’s viewpoint
Lender’s viewpoint
1. Single Cash Flows- simplest case involves the
equivalence of a single present amount (P)and its future
worth (F).
2. Equal Uniform Series- transactions arranged as a
series of equal cash flows at regular intervals.
DISCOUNT – discount in simple terms is the interest
deducted in advance. It is the difference between the
amount a borrower receives in cash (present worth) and
the amount he pays in the future (future worth).
Discount = Future Worth – Present Worth
D=F–P
3. Linear Gradient Series- cash flow that increase or
decrease by uniform amount each periods.
4. Geometric Gradient Series- cash flows that increase
or decrease by a fixed percentage.
5. Irregular Series – consists of cash flow that change
with no pattern.
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Interest- the amount of money paid for the use of
borrowed capital or income produced by money which
has been loaned.
SINGLE CASH FLOW
Simple Interest – the interest on a loan that is based
only on the principal. Usually used for short-term loans
where the period is measured in days rather than years.
I = Pin
F = P + I = P + Pin
F = P(1+in)
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 worth
Ordinary Simple Interest - interest is computed on the
basis of 12 months of 30 days each which is equivalent
to 360 days a year. In this case, the value of n that is
used in the preceding formulas may be computed as:
n= d/360; where d is the number of days the principal
was invested
EXACT SIMPLE INTEREST – interest is computed
based on the exact number of days in a given year which
is 365 days for a normal year and 366 days during a leap
year (which occurs every 4 years, or if it is a century
year, it must be divided by 400). Note that during leap
years, February has 29 days and 28 days only during a
normal year. In this case, the value of n that is used in
the preceding formulas may be computed as:
n= d/365 for a normal year
N= d/366 for a leap year
Rate of discount is the discount on one unit of principal
for one unit of time.
d = 1 – (1 + i)-1 ; d=i/(1+i) ; d= (F-P)/F
i = d/(1-d) ; i= (F-P)/P
Where: d = rate of discount
i = rate of interest for the same period
Compound Interest- -interest which is based on the
principal plus the previous accumulated interest. It may
also be defined as ‘interest on top of interest.” This is
usually used in commercial practice especially for longer
periods.
Computing for present and future value;
F = P(1+i)n
P = F(1+i)-n
Where: F = future amount of money
P = present worth or principal
i = rate of interest per interest period
n = number of interest periods
(1+i)n = single payment compound amount factor
(1+i)-n = single payment present worth factor
Rate of Interest - -the cost of borrowing money or the
amount earned by a unit principal per unit time.
TYPES OF RATES OF INTEREST
Nominal Rate Of Interest – is the basic annual rate of
interest. It specifies the rate of interest and the number of
interest periods in one year.
i= r/m
Where: i = rate of interest per interest period
r = nominal rate of interest
m = number of compounding periods per year
EFFECTIVE RATE OF INTEREST – is the actual or
the exact rate of interest earned on the principal during a
one-year period.
ERi = (1+i)m – 1
Where: ERi = effective rate of interest
Compounding period occur in one year
Annually
m= 1
Semi-annually
m= 2
Quarterly
m= 4
Bi-monthly
m= 6
Monthly
m= 12
Semi-monthly
m= 24
Weekly
m= 52
Daily
m= 365
Continuously
m= ∞
Deferred Annuity - this type of annuity is one where
the first payment is made several periods after the
beginning of the annuity.
Continuous Compounding - based on the assumption
that cash payments occur once per year but
compounding is continuous throughout the year.
F = P(e)rn
Annuities - a series of equal payments occurring at
equal interval of time.
TYPES OF ANNUITIES
Ordinary Annuity – this type of annuity is one where
the payments are made at the end of each period
beginning from the first period.
Annuity Due - The annuity due is when payments are
made at the beginning of the payment period.
Finding F when A is given: Finding P when A is
given:
F = A[
(𝟏+𝒊)𝒏−𝟏
𝒊
]
P= A[
𝟏−(𝟏+𝒊)−𝒏
𝒊
]
Where: F = future worth of an annuity
A = a series of periodic, equal amounts of money
P = present worth of an annuity
i = interest rate per interest period
n = number of interest periods
Perpetuity - is an annuity where the payment period
extends forever, which means that the periodic payments
continue indefinitely.
*The annuity amount A, can be determine from
these two formulas:
𝑨=𝑷 [
𝒊
]
𝟏 − (𝟏 + 𝒊)−𝒏
The factor in the bracket is called capital
recovery factor and can be designated by the
symbol (A/P, i, n).
𝒊
𝑨 = 𝑭 [(𝟏+𝒊)𝒏 −𝟏]
The factor in the bracket is called sinking
fund factor and can be designated by the symbol
(A/P, I, n).
Annuity with Continuous Compounding
Gradient Series - series of cash flows where the
amounts change every period.
Geometric Gradient Series - A geometric gradient is
when the periodic payment increases or decreases by a
constant percentage.
Types of Gradient Series
1. Arithmetic Gradient Series
2. Geometric Gradient Series
Arithmetic Gradient Series An arithmetic gradient cash flow is one wherein the
cash flow changes (increase or decreases) by the same
amount in each cash flow period. The amount of
increase or decrease is called gradient.
Capitalized Cost (CC) - this is one of the most important
applications of perpetuity. The capitalized cost of any
property is the sum of its first cost and the present
worth of all costs for replacement, operation, and
maintenance for a long period or forever.
Amortization - is any mode of paying debt, the
principal and the interest included, usually by a series of
uniform amount every period.
Amortization schedule- a table showing the payments
throughout the total interest period
Chapter 3: DEPRECIATION AND
DEPLETION
Depreciation- is an allowable expense in general
accounting purposes and income tax accounting
purposes. But it differs categorically from other
conventional expenses because depreciation charge does
not occur any out flow of business fund.