Engineering Economy (MNG 102): A Comprehensive Guide with Exercises, Exercises of Engineering Economy

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ENGINEERING ECONOMY (MNG 102)

Prepared by :

Dr Hosny Abbas Abouzeid

Contents

1. CHAPTER ONE : Foundation Of Engineering Economy

1.1 Introduction to engineering economy(Objectives - terminology- Firm

Objectives-Kinds of market structure – Types of economic systems)

1.2 Laws of supply and demands – Balance sheet- Eng. Economy symbols - interest rate

types, cash flow diagrams) – - Exercises

1.3 Sheet 1

2 CHAPTER 2 : Single & Uniform Series and Gradient Payments

2.1 Present & future worth for single , uniform series factors ,and discrete payments

calculations – Uses of interest tables - Exercises

2.2 Present & future worth and EUAS for uniform gradient payments - Exercises

2.3 Calculation for unknown interest rate and number of years - Exercises

2.4 Solved problems – Sheet 2

3. CHAPTER 3 : Geometric Gradient payments & Single Project Evaluation Methods

3.1 Present /Future Worth calculation for Geometric Gradient payments

3.2 Single Project Evaluation Methods : Net Present Value – Internal Rate Of Return

3.3 Sheet 3

4. CHAPTER 4 : Selection Methods Between Proposed Projects

4.1 Selection methods between different alternatives of equal and different lived finite

time periods (present / future worth calculation methods)- Exercises.

4.2 Selection methods between different alternatives of infinite time periods

(capitalized cost ,and benefit/ cost ratio calculations methods) - Exercises

4.3 Sheet 4

5. CHAPTER 5 :Inflation Impact On Economic Calculation

5.1 Inflation Impact and Effects

5.2 Present/Future Worth Calculation Adjusted for Inflation- Exercises

5.3 Sheet 5

6. CHAPTER 6 : Basics of a Replacement Analysis

6.1 Introduction(Advantages &Terminologies Used of replacement analysis)

6.2 Different Approaches for comparing Defender and Challenger.

6.3 Sheet 5

7. CHAPTER 7 : Depreciation And Depletion Calculation Models

7.1 Different Depreciation Methods - switching between models- Exercises

7.2 Depletion calculations models for natural resources- Exercises

7.3 Sheet 7

8. CHAPTER 8 :Breakeven & Payback Analysis

8.1 Breakeven Analysis & applications for single and two alternatives – Exercises

8.2 Payback Analysis models & applications - Exercises

8.3 Sheet 8

become (1.1) of its original value after one year. TVM calculations can be used to

compare between different alternatives as will be explained later.

1.3.4 Interest:

Is a measure of increase between the original sum borrowed or invested and the final

amount owed or accrued as follow:

a. For invested money :

Interest = total amount accumulated – original investment

b. For borrowed money :

Interest = Present amount owed – original loan

1.3.5 Interest Rate and Rate of Return (ROR):

Defined as the ratio between the interest accrued per unit time and the original amount

expressed as percentage. In case of borrowed money , this value is called “Interest Rate”

while in case of invested money is called “ Rate of Return(ROR)”. Both value s are calculated

as follow:

Interest rate % = Interest accrued per unit time X 100% / original amount

1.3.6 Principle: Is the original investment or loan.

Example 1:

A company borrowed $100000 and repaid 110000 after one year , compute

the interest and the interest rate?

Solution:

Interest =110000-10000 = 100000 $ , Interest rate = 100000x100%/100000 =10 %

Example 2:

A company invested $100000 for one year at 15% interest. Compute the interest

gain and the amount accumulated.

Solution:

Interest = 0 .15 X 100000 = $ 15000

Total amount accumulated = 100000 + 15000 = $ 115000

1.4 The Firm

1.4.1 Definition :

A firm is an organization that employs resources to produce and sell goods and

Services using suitable technology.

1.4.2 Firm Objectives

• Firms exist to perform useful functions in society by producing and distributing

goods and services.

• Firms use society's scarce resources, provide employment, and pay taxes.
• The firm can work toward long-term sustainability or aim to produce high profit

levels in a short period of time.

• The firm perform four functions :
  • Produce product or service. - Market and sell product /service.
  • Track the accounting and financial transactions.
  • Perform basic human resources tasks such as hiring and training employees.

1.5 Types of Economic systems

E conomic Defined as is the social science that analyzes the production, distribution, and

consumption of goods and services.

The type of economy is determined by the extent of government involvement in

economic decision making. Therefore , there are 4 types of systems as follow :

1.5.1 Traditional Economic System

• Economic system is based on customs and traditions (handed down from 1

generation to another).

• Allocation of scarce resources stems from habit, or customs
• Use BARTER( مقايضة (system in trade! No money!
• No two traditional economies are the same, so it is impossible to describe typical

economic mechanisms in this type.

Examples: parts of Africa, parts of India, the original people of Australian, Eskimos

Disadvantages : Discourages new ideas - Lack of progress - Lower standard of living

1.5.2 Command (

Communism) Economy

• A central authority (government or state) controls the economy by deciding how to use

and distribute resources.

• Government decides the needs of the people, the best way to produce it and for

everyone!

• There is very little if any input from the people.
• The government regulates prices and wages; it may even determine what sorts of work

individuals do.

Example: Vietnam, North Korea, Former Soviet Union.

Advantages : Basic Needs (Education, public health, other services )cost very little.

And very little unemployment.

Disadvantages : Doesn’t meet wants – no motivation- Requires a large bureaucracy

• New and different ideas are discouraged

1.5.3 Capitalism/Market (or Free Market Economy Capitalism)

1.6.4 Oligopoly is a market structure in which :

• A small number of firms compete.
• The firms might produce almost identical products or differentiated products.
• Barriers to limit entry into the market.
• Profits are interdependent. Actions by any one firm will affect sales & profits of other

firms.

Comparison between Different kinds of Market Structure

Type of market

structure

Number

of firms

Nature of products Selling price

control

Condition of

market entry

Perfect competition Large Homogeneous Non- existent Easy

Monopolistic

competition

Large Are close substitutes Non-

existent(low)

Easy

Oligopoly Few May be homogeneous

or close substitutes

Medium or high Difficult

Monopoly One Unique product Very high Impossible

1.7 Demand – Price Relationship

1.7.1 What is Demand?

Demand for a commodity refers to the quantity of the commodity that people are

willing to purchase at a specific price per unit of time, other factors (such as price of

related goods, income, advertising, etc) being constant.

1.7.2 The Law of Demand

The law of demand states that, if all other factors remain equal, the higher the price of

a good, the lower the quantity demanded from this good.

1.7.3 Demand Curve

Demand curve is a graphical representation of price- quantity relationship. Individual

demand curve shows the highest price which an individual is willing to pay for

different quantities of the commodity.

Demand curve has a negative slope, i.e, it slopes downwards from left to right depicting

that with increase in price, quantity demanded falls and vice versa.

The factors affecting the downward sloping demand curve are :

1. Income effect- With the fall in price of a commodity, the purchasing power of

consumer increases.

2. Substitution effect - the consumers tend to substitute a commodity of high price

with other cheaper commodities.

3. Diminishing marginal utility-. When the price of commodity falls, a rational

consumer purchases more so as to equate the marginal utility and the price level.

1.8 Supply – Price Relationship

1.8.1 What is Supply?

Supply refers to the amount of a certain good producers are willing to supply when

receiving a certain price.

1.8.2 The Law of Supply

The law of supply states that the higher the price, the higher the quantity supplied. But

unlike the law of demand, the supply relationship shows an upward slope.

1.8.3 Supply Curve

Supply curve is a graphical representation of price- quantity relationship. The supply curve o

a commodity usually slopes upward. In other words, an industry will offer to sell more

quantity of a good at a higher price than at a lower one.

A, B and C are points on the supply curve. Each point on the curve reflects a direct

correlation between quantities supplied (Q) and price (P). At point B, the quantity

supplied will be Q2 and the price will be P2, and so on.

Time and Supply

Unlike the demand relationship, however, the supply relationship is a factor of time.

Time is important to supply because supplier takes time to adjust himself to a change in

the demand condition according to the nature of technical conditions of production.

1.9.2.1 Assets

It includes all resources owned by or owed to the firm or company and have two main

classes of assets : Current assets and fixed assets (sometimes called non-current or

long-term assets)

A. Current assets:

Represent shorter-lived working capital (cash, accounts receivable, etc.), which is

more easily converted to cash, usually within 1 year. It include the following:

• Cash and cash equivalents: the most liquid assets, these can include assets that

have short-term re-payments under three months.

• Marketable securities: (أوراق مالية قابلة للتداول)

Assets that the company can liquidate on short notice.

• Accounts receivable: money which customers owe the company such as deposits
• Inventory: goods available for sale, valued at the lower of the cost or market price
• Prepaid expenses: representing value that has already been paid for, such as

insurance, advertising contracts or rent.

B. Non Current Assets (Long-term assets)

Assets that the business will own beyond the next year and Include the following:

• Long-term investments: securities that will not or cannot be liquidated in the next

year

• Fixed assets: these include land, machinery, equipment, buildings and other

durable, generally capital-intensive assets, that used to produce and deliver

goods and/or services, and they are not intended for sale.

• Intangible Assets :This line item will include all of the companies intangible fixed

assets, such as patents, licenses, and secret formulas.

1.9.2.2 Liabilities

Defined as all financial obligations or money that a firm owes to outside parties such as

debts, bills ( فواتير ) , loans, bonds( سندات ودائع, ) ,etc... Liabilities have two main classes :

Current Liabilities and non-Current Liabilities.

A.Current liabilities are those that are due within one year and are listed in

order of their due date. Current liabilities accounts might include:

• Current portion of long-term debt or current debt payable
• Bank indebtedness( مديونيات البنك(
• Interest payable
• Rent, tax, utilities
• Wages payable
• Customer prepayments
• Dividends payable (أرباح مستحقة الدفع) and others.

B.Non-Current liabilities :or Long-term liabilities are due at any point after

one year and include :

• Long-term debt: outlines all the companies outstanding debt, the interest

expense and the principal repayment for every period.

• Bonds Payable سندات مستحقة : This account includes the sinking fund

amount of any bonds the company has issued.

• Pension fund liability: the money a company is required to pay into its

employees' retirement accounts

• Deferred tax liability: إلتزامات ضريبيه مؤجلة taxes that have been accrued but will

not be paid for another year.

• Mortgages رهونات عقاريه

1.9.2.3. Shareholders' Equity

Defined as all the financial value of ownership or the money attributable to a business'

owners(or shareholders). It is also known as "net assets or net worth ," since it is

equivalent to w hat’s left of the company’s assets after paying off liabilities.

It includes Share capital , stocks issued and retained earning by a firm.

A. Share Capital

This is the value of funds that shareholders have invested in the company when a

company is first formed.

B. Retained Earnings

Retained earnings are the net earnings a company either reinvests in the business

or uses to pay off debt; the rest is distributed to shareholders in the form of

dividends أرباح.

C. Preferred and common stocks سهم المفضلة والشائعةاأل

Common stock and preferred stock are the two main types of stocks that are sold by

companies and traded among investors on the open market. A preferred stock pay an

agreed-upon dividend at regular intervals. Common stocks may pay dividends depending

on how profitable the company is.

Example Of Balance Sheet For a Firm

P

1

= sum at end of year 1 = P(1+i) + 200 = 2000(1.1) +200 = 2400 L.E

P

2

= sum at end of year 2 = P 1

(1+ i ) + 200 = 2400(1.1)+200 = 2840 l..E

P3 = sum at end of year 3 = P 2 (1+ i ) + 200 = 2840(1.1) + 200 = 3324 L.E

P4= sum at end of year 4 = P 3 (1+ i ) + 200 = 3324 (1.1) + 200 = 3856.4 L.E

P

5 =

sum at end of year 5 = P 4

(1+ i ) + 200 = 3856.4(1.1) + 200 = 4444.04 L.E

Final sum at the end of the five years = 4444.04 L.E

Note:

Generally interest rates refer to compound interest unless specified otherwise.

1.11.3 Nominal , Effective Interest , and Effective annual Interest Rates

Many financial transactions require that interest be compounded often than once a

Year (e.g quarterly ,monthly , daily , etc..) In such situations ,there are three

Expressions for the interest rates as follow :

1. The nominal interest rate , r , is expressed on an annual basis.

2. The effective interest rate , ieff , is the rate that corresponding to the actual interest

Periods (m). Value of ieff is obtained dividing the nominal interest rate “r” by the

number interest periods per year “m” as follow :

ieff = r% / m (per Compounding period m).

3. The effective annual interest rate , ieffa ,and calculated as follow :

ieffa = (1 + r/m)

m

• 1

Example 6 :

A bank claims to pay interest to its depositors at rate of 6% per year compounded

quarterly. What are the nominal , effective interest rates and the effective annual

interest rates?

The nominal interest rates is r = 6% .since there are four interest periods per year (m)

then the effective interest rate is :

ieff =6%/4 = 1.5 % per quarter or quarterly.

The effective annual interest rate , ieffa , obtained as follow :

ieffa = (1 + r/m)m - 1= (1+.06/4)4 - 1 = .06136 = 6.136 %

Example 7 :

Three different bank loan rates for electric generation equipment are listed below :

Determine the effective rate on the basis of the compounding period for each rate.

(a) 9% per year , compounded quarterly (b) 9% per year , compounded monthly

(c) 4.5 % per 6 months , compounded weekly.

solution

Apply the equation ieff = r% / m to determine the effective rate per compounding

period (cp) for different compounding periods as shown in the following table :

1.12 Cash Flow Diagram :

The cash flow defined as the flow of receipts (income) and cash disbursement

(costs) which occur over a given time interval.

The cash flow diagram is simply a graphical representation of cash flows drawn

on a time scale as shown.

General Rules:

• The cash flow follows the “end – period conventions “i.e. all cash flows occur at the end of inte

period. End of period means one time period from date of transaction.

• The direction of arrows is very importa nt as “+” represents income &

“– “represents disbursements.

• All unknown values for the symbols P, A, F, n, i are represented by a question mark “?
• Time 0 represent the present time while the times 1, 2, ….. , 5 are the end of time periods 1, 2,3,

Example 1.8:

A person deposited 10000 L.E now into his account which pays 10% per year. He plans

withdraw an equal end of year amount of 2000 L.E for 5 years starting next year and closing

account by with drawing the remaining money at the of sixth year. Construct the cash f

diagram. Find the amount of exit in each of end interest periods and the remaining sum.

Solved Problems

1.1 The ABC Company deposited $100 000 in a bank account on June 15 and withdrew a

total of $115 000 exactly one year later. Compute: (a) the interest which the ABC Company

received from the $100 000 investment, and (b) the annual interest rate which the ABC

Company was paid.

1.3 Compare the interest earned from an investment of $1000 for 15 years at 10% per year

simple interest, with the amount of interest that could be earned if these funds were

invested for 15 years at 10°/o per year, compounded annually.

The simple interest is given by I = (15)(0.10)($10 00 = ) $

Compound interest = F-P = P(1+ i)

n

- P = $1000(1+0.10)

15

= $3177.25 or more than double the amount earned using simple interest.

1.4 How it would take for an investor to double his money at 10% per year compounded annually?

Actually, since the interest is compounded only at the end of each year, the investor

would have to wait 8 years.

1.5 Suppose that a man lends $1000 for four years at 12% per year simple interest. At the end of the

four years, he invests the entire amount which he then has for 10 years at 8% interest per year,

compounded annually. How much money will he have at the end of the 14-year period?

F = P(1+ n 1

x i l

)(l+ i 2

n

= $1000[1+ (4)(0.12)](1+ 0.08)

10

1.6 Suppose that the interest rate is 10% per year, compounded annually. What is the minimum

amount of money that would have to be invested for a two-year period in order to earn $300 in

interest?

I = 300 = F – P = P(1.1)^2 – P

P = 300/ (1.1^2 – 1 ) = 1428.

Higher Technological Institute Engineering economy MNG

Tenth Of Ramadan Sheet 1 _________

I. Answer The Following Questions :

1.1 Mention the Objectives and functions of a firm.

1.2 Mention the Types of Economic systems indicating for each one two of the following

terms: main characteristics - Examples - Advantage – disadvantages.

1.3 Mention the Kinds of Market structure indicating two main characteristics of each

1.4 Explain in brief the demand curve and its characteristics.

1.5 Explain in brief the supply curve and its characteristics.

1.6 Explain in brief the meaning of balance sheet and it

,

s structure using a suitable diagram.

1.7 Calculate the principle and the present value of a sum that has been deposited three years

ago to become 12000 L.E after one year from now in both cases of simple and compound

interest of 12 % per year. Calculate also the interest.

1.8 If you invest 10000 L.E now in a business venture that promises to return 14641 L.E, how

many years required to receive this return in order to make interest rat of 10 % per year

compounded yearly. On your investment?

1.9 Assume that you have been offered an investment opportunity in which you may invest $

at 7%per year simple interest for 3 years or you may invest the same $1000 at 6% per year

compound interest for 3 years. Which investment offer you accept?

1.10 Sales revenues for a lift – truck product line are estimated to be 500,000 L.E in the first year,

then decrease by 40000 L.E per year up to year 5 at interest rate of 15 % per year. Draw the

cash flow diagram, and then calculate the future worth at the end of year five.

1.11 As a result of an old loan for a bank, there remain 5 equal payments each of 10000 L.E with

interest rate of 8 % per year. The house just been sold to a new owner, who wishes to

renegotiate the loan to reduce the annual payments by increasing it’s number t o ten instead

of five years. The bank agree but with interest rate of 10 % per year. Calculate the amount of

the new annual payments and the total amounts of money received by the bank in both cases.

1.12 The costs of production in a factory is 86120 L.E in the first year , 97100 L.E in the

second year and 105630 L.E in the fourth year with interest rate of 14% per year. A tooling

investment of 12000 L.E is carried out now to reduce all production costs by 12% per year.

Calculate the present worth before and after carrying out the tooling investment. If this

investment is delayed for one year from now; Calculate the present worth of the cost of delay.

Draw the cash flow diagrams in all cases.

1.13 Calculate the present worth and the future worth of an expenditure of 17000 L.E per year for

6 years starting 3 years from now if the interest rate if 15% per year. Draw the cash flow

diagram and list the values of the engineering economy symbols used in this problem.

Calculate the equivalent annual expenditure if it starts from first year up to the end of the

interest period.

1.14 Suppose that a person invests $3000 at 10% per year, compounded annually, for

a. Market economy b. Command economy…….

C. traditional economy d. Mixed economy

2.1 5 Which of the following is an economic system in which the government and

individuals are used to decide how to use scarce resources?

a. Market economy b. Command economy

c. traditional economy d. Mixed economy…….

2.1 6 Type of economy that is based on trading and bartering?

a. Socialist b. Traditional c. Free Enterprise d. Command

2.1 7 An economic system in which private property is almost totally restricted is called ...

A. A mixed economy B. Competition C. Free enterprise

D. A centrally planned economy

III. Answer The Following Questions Using Either (√ ) OR ( χ ) Only:

3.1 Market structure refers to the competitive environment in which the buyers and

sellers of a product operate… T

3.2 A market is defined as a place where buyers go to purchase units of a commo dity …..F

3.3 Oligopoly refers to a type of market organization that is characterized by large number of

firms selling a differentiated commodity….F

3.4 Monopolistic competition is a form of market organization that combines elements of

perfect competition and monopoly……T

3.5 Monopoly is a market structure in which there is only one buyer of a product for which

there are no close substitutes….F

3.6 Oligopoly is a market structure in which there are few sellers of a product and additional

s ellers cannot easily enter the industry T…...

3.7 The demand curve shows that the demanded quantity increases with increasing the price ….F

3.8 In supply curve , the supplied quantity increases with increasing the price

3.9 The demand curve shows that the demanded quantity increases with increasing the price….F

3.10 A price ceiling imposed above the market equilibrium price will result in a shortage of the

product…. F

3.11The law of demand refers to the relationship between consumer income and the quantity

of a commodity demanded per time period…F

3.12 The substitution effect holds that an increase in the price of a commodity will cause an

individual to search for substitutes….T

3.13 The income effect holds that a decrease in the price of a commodity is, some respects, the

same as an increase in income….T

3.14 The balance sheet heading will specify a Period Of Time…..F

3.15 The balance sheet heading will specify a Point Of Time…..T

3.16 Repaid expenses are considered as one of current liabilities in the balance sheet….F

3.17 Fixed assets are considered as one of current assets in the balance sheet. …… F

3.19 Customer prepayments are considered as one of current liabilities in the balance sheet….T

3.20 Pension fund liabilities are considered as one of current liabilities in the balance sheet…..F

3.21 If current assets > current liabilities ,the then company does not has enough cash to run

the business…..F

Dr HOSNY ABBAS ABOUZEID

0 1 2 3 n- 1 n

P? i= …. %

CHAPTER 2

SINGLE PAYMENT FACTORS

2.1 Introduction

The aim of this chapter is to derive a formula for the following engineering economy

factors:

• Single – Payment Factors ( Compound Amount Factor & Present Worth Factor )
• Uniform Series Compound – Amount Factor.

2.2 Derivation of Single – Payment formulas Factors: Compound Amount (

)

& present worth (

):

In this case , it is required to get the final value “F” , in terms of given values of a

single payment “P” with compound interest rate “ i” , and after time period “ n” , as

shown in the cash flow diagram.

Since F 1 = final sum at year 1=P +P*i , F 2 =F 1 +F 1 *i , P i= …%

Then F 2

= Final sum at end of year 2 = P*(𝟏 + 𝒊)

𝟐

, 0 1 2 n=… F 3

Final sum at end of year 3 =F 2

+F

2

*i F?

= F 2 (1+i)= P*

𝟑

, So, Fn =Final sum at end of year n =P*

𝒏

=

( 𝟏 + 𝒊

)

called single payment compound amount factor

=

𝒏

called single payment present worth factor

2.3 Derivation of Uniform – Series Present Worth Factor (

):

In this case, it is required to get the present worth value P in terms of known values Of

A, i, n as shown in the cash flow diagram.

P=P 1 +P 2 +P 3 +…..= P n

= Sum of all the present worth values

𝟐

𝒏

A = …… L. E

Multiply both sides by

we get :

= A[

𝟐

𝟑

• ⋯ +

𝒏

𝒏+𝟏

]

Then,

- P=A [

𝟐

𝟑

• ⋯ +

𝒏

𝒏+𝟏

− {

𝟐

𝟑

• ⋯ +

𝒏

}]