engineering econimics

1. ENGINEERIN
G
ECONOMICS

2. DEFINITION
• Engineering is the profession in which knowledge of the mathematical and natural
sciences gained by study experience and practice is applied with judgment to
develop ways to utilize economically the material and forces of nature for the
benefit of mankind.
• Economics - social science that focuses on the production, distribution, and
consumption of goods and services, and analyzes the choices that
individuals, businesses, governments, and nations make to allocate
resources.
• Engineering economics is the application of economic principles and calculations
to engineering projects. It is important to all fields of engineering because no
matter how technically sound an engineering project is, it will fail if it is not
economically feasible.
• In summary, Engineering Economics refers to those aspects of economics and its
tools of analysis most relevant to the Engineer’s decision making process

3. The 7 principles of Engineering Economics /
The Engineering Process
• USE COMMON UNITS OF MEASUREMENT
• Using a common unit of measurement to analyze the perspective
outcome will make easier the analysis and comparison of alternatives
• USE ALL RELEVANT CRITERIA
• The decision maker will normally select the alternatives that will best
serve the long terms interest of the owner
• MAKE UNCERTAINTY VERY EXPLICIT
• Risk and uncertainty are inherent in estimating the future outcomes of
the alternatives and should be recognized
• REVISIT/REVIEW YOUR DECISION
• A good decision making process can result in a decision that has an
undesirable outcomes

4. The 7 principles of Engineering Economics /
The Engineering Process
• DEVELOP THE ALTERNATVES
• Define the PROBLEM! Then the choice (decision) is among alternatives.
• The alternatives needed to be identified and then defined for subsequent
analysis
• two or more Alternatives
• FOCUS ON THE DIFFERENCES
• Only the differences in the future outcomes of the alternatives are
important
• Outcomes that are common can be disregarded
• HOLD SAME POINT OF VIEW
• The perspective outcomes of the alternatives should be consistently
developed from a defined view point

5. COST CONCEPTS TERMINOLOGIES
• Cost
• any amount that is paid for a service or a thing.
•Fixed cost
• cost that is constant, unaffected by any changes in the
activity.
•Variable cost
• cost that is affected by the changes in the activity.
•Incremental cost
• additional cost resulting from increasing output of the
system by one or more units.

6. Money-Time Relationships and Equivalence
Simple Interest
• Simple Interest – define as the interest on a loan or principal that is based only on the
original amount of the loan or principal. This means that the interest grows on a linear
function over a period of time. Usually use on short period of time, usually days or weeks.

7. COST CONCEPTS TERMINOLOGIES
• Direct cost
• cost that is allocated to a specific work activity.
• Indirect cost
• cost that is changing when a work activity is also changing.
• Standard cost
• cost per unit output.
• Cash cost
• cost that is paid through cash
• Non-cash / book cost
• cost that does not involve cost
• Sunk cost
• cost, sometimes called a retrospective cost, refers to an investment already incurred that can't be recovered.

8. Money-Time Relationships and Equivalence
Simple Interest
• Ordinary Simple Interest – base on one banker's year. A banker year is
composed of 12 months of 30 days each which is equivalent to a total of 360
days in a year. The value of t (period) that is used in the preceding formulas
may be calculated by the following formula:
𝑡 =
𝑑
360
d = number of days the principal was invested
• Exact Simple Interest – based on the exact number of days in a given year. A
normal year has 365 days while a leap year has 366 days.
𝑡 =
𝑑
365
for normal year
𝑡 =
𝑑
366
for leap year

9. Money-Time Relationships and Equivalence
Discount
Types of Discounts
• Discounts are offered while we purchase an item from a seller or a manufacturer.
There are three types of discounts:
• Trade Discount - This type of discount is offered by the distributor to the
retailer and not to the end customer. A distributor is one who holds huge
quantities of a product and offers it at a reduced price to a retailer, who
runs a unit or a shop selling the product. This type of discount is offered
to sell the product easily.
• Quantity Discount - If a customer buys a product in large numbers, then
quantity discounts are offered. This type of discount is offered to tempt
the customers to buy a product in large quantities.
• Promotional Discount - Promotional discounts are offered when a new
product is to be promoted or if a stock clearance is to be done. This is
usually advertised as offering something extra for buying a certain
number of items. For example, 'Buy 2 Get 1 Free' is a common example of
a promotional discount.

10. Money-Time Relationships and Equivalence
Discount
• Discount - reduction in the price of goods or services offered by shopkeepers at the marked price. This
percentage of the rebate is usually offered to increase the sales or clear the old stock of goods. The List
price or Marked price is the price of an article as declared by the seller or the manufacturer, without any
reduction in price. Selling price is the actual price at which an article is sold after any reduction or discounts
in the list price. "Off", "Reduction" are some common terms used to describe discounts. It should be noted
that discount is always calculated on the Marked price (List price) of the article. The formula to calculate
discount is:

11. Money-Time Relationships and Equivalence
Discount Rate
• When the price of an article is reduced and sold it means a
discount has been offered. When the price reduced is expressed as
a percentage, it is called a discount percentage or the discount
rate. The formula to calculate the discount rate is:
Discount = Future worth – Present worth
d = 1 -
1
1+𝑖
i =
𝑑
1−𝑑
Discount (%) = (List price - Selling Price)/ List Price × 100

12. Compound Interest
• Defined as the interest of loan or principal which is based not only on the
original amount of the loan or principal but the amount of the loan or
principal plus the previous accumulated interest. This means that aside from
the principal, the interest now earns interest as well.
• The future amount of the principal is derived by the following tabulation:
Period Principal Interest Total Amount
1 P Pi P ( 1 + i )
2 P (1 + i ) P (1 + i )i P (1 + i )2
3 P (1 + i )2 P (1 + i )2i P (1 + i )3
n P (1 + i )n

13. Compound Interest
• Future amount, F:
• F = P (1 + i )n
• Present Worth, P:
• P =
𝐹
(1 + i )n
0 1 4
3
2 n
F
P
Cash Flow
0 1 4
3
2 n
F
P
Cash Flow
Where:
P = Principal
i = interest per period (in decimals)
n = number of interest periods
(1 + i )n = single payment compound amount
factor
Where:
1
(1 + i )n = single payment present worth factor

14. Problem Solving
• If P1000 accumulates to P1500 when invested at a simple interest for 3
years, what is the rate of interest?
• You loan from a loan firm an amount of P100,000 with a rate of simple
interest of 20% but the interest was deducted from the loan at the time the
money was borrowed. If at the end of one year , you have to pay the full
amount of P100,000, what is the actual rate of interest?
• If you borrowed P10,000 from a bank with 18% interest per annum, what is
the total amount to be repaid at the end of one year?
• A price tag of P1200 is payable in 60 days but if paid within 30 days it will
have a 3% discount. Find the rate of interest.
• A man borrowed P2000 from a bank and promise to pay the amount for one
year. He received only the amount of P1920 after the bank collected an
advance interest of P80.00. What was the rate of discount and the rate of
interest that the bank collected in advance?

15. Problem Solving
• It is a practice of almost all banks in the Philippines that when they grant loan, the
interest for one year is automatically deducted from the principal amount upon
release of money to a borrower. Let us therefore assume that the you applied for a
loan with a bank and the P80,000 was approved at an interest rate of 14% of
which P11,200 was deducted and you were given only P68,800 as a check. Since
you have to pay P80,000 after a year, what then will be the effective interest rate?
• A businessman wishes to earn 7% on his capital after payment of taxes. If the
income from an available investment will be taxed at an average rate of 42%, what
minimum rate of return, before payment of taxes, must the investment offer to be
justified?
• A deposit of P110,000 was made for 31 days. The net interest after deducting 20%
withholding tax is P890.36. Find the rate of return annually.
• A man borrowed P20,000 from a local commercial bank which has a simple
interest of 16% but the interest is to be deducted from the loan at the time that
the money was borrowed and the loan is payable at the end of one year. How
much is the actual interest rate.
• Karen borrowed money from a bank. She receives P1340.00 from the bank and
promised to pay P1500.00 at the end of 9 months. Determine the corresponding
discount rate or often referred to as the “banker’s account”.

16. Problem Solving
• Determine the exact simple interest on P5000 invested for the period from
January 15, 1996 to October 12, 1996, if the interest rate is 18%.
• The exact simple interest of P5000 invested from June 21, 1995 to December
25, 1995 is P100. What is the rate of interest?
• The amount of P20000 was deposited in a bank earning an interest of 6.5%
per annum. Determine the total amount of the principal at the end of 7 years
if the principal and interest were not withdrawn during this period.