E - ENGINEERING ECONOMICS problems and solutions.pptx

1. Engineering Economics
• Engineering Economics – is the study of the cost
factors involved in engineering projects, and
using the results of such study in employing the
most efficient cost-saving techniques without
affecting the safety and soundness of the project
2

2. Definitions
• Investment – is the sum total of first cost (fixed
capital) and working capital which is being put
up in a project with the aim of getting a profit.
• Fixed Capital – is a part of the investment which
is required to acquire or set up the business.
• Working Capital – is the amount of money set
aside as part of the investment to keep the
project or business continuously operating.
3

2. Definitions (cont..)
• Demand – is the quantity of a certain commodity that is
bought at a certain price at a given place and time.
• Supply – is the quantity of a certain commodity that is offered
for sale at certain price at a given place.
• Perfect Competition – is a business condition in which a
product or service is supplied by a number of vendors and
there is no restriction against additional vendors entering the
market.
• Monopoly – is a business condition in which as unique
product or service is available from only one supplier and that
supplier can prevent the entry of all others into the market.
• Oligopoly – is a condition in which there are so few suppliers
of a product or service that action by one will almost result in
similar action by the others.
4

2. Definitions (cont..)
• Law of Supply and Demand - “Under
conditions of perfect competition, the price of a
product will be such that supply and demand are
equal.”
• Law of Diminishing Returns – “When the use of
one of the factors of production is limited, either
in increasing cost or by absolute quantity, a
point will be reached beyond which an increase
in the variable factors will result in a less than
proportionate increase output.”
5

3. Interest
• Interest – is the money paid for the use of
borrowed money.
6

4. Simple Interest
• Simple interest – is the interest paid on the
principal (money lent) only.
•
•
• Where:
• F = future value
• P = present value
• n = number of interest period
• i = interest rate per period
• I = interest
7
Pni
I 
 
ni
P
Pni
P
I
P
F 




 1

4. Simple Interest (cont..)
• Two Types of Simple Interest
• 4.1 Ordinary simple interest , 1 year = 360 days
• 4.2 Exact simple interest, 1 year = 365 or 366
days
•
8

5. Compound Interest
• Compound interest – is the interest which is
calculated not only on the initial principal but
also the accumulated interest of prior periods.
•
• Single payment compound amount factor =
•
9
 n
i
P
F 
 1
   n
i
n
i
P
F 
 1
%,
,
 
n
i
P
F
P
F %,
,


5. Compound Interest (cont..)
• Single payment present worth factor =
•
• Where:
• P = present value
• n = number of interest period
10
    n
i
n
i
F
P 

 1
,
,
 
n
i
F
P
F
P %,
,


6. Cash Flow Diagram
• Cash flow diagram – is a graphical
representation of cash flows drawn on a time
scale.
11

7. Discount
• Discount – is the difference between the future
worth and the present worth of a unit.
• Discount,
• Rate of discount,
12
P
F
D 

F
P
F
d



8. Nominal and Effective Rate of
Interest
• Nominal interest rates – is the cost of borrowed
money which specifies the rate of interest and
the number of interest periods.
• Effective interest rates – is the actual rate of
interest on the capital and is equal to the
nominal rate if compounded annually. Effective
interest rate is greater than nominal interest
rates.
13

8. Nominal and Effective Rate of
Interest (cont..)
• Let in = nominal interest rate or annual percentage
rate
• m = number of sub periods per year
• Effective interest rate =
• Where:
• m = 2 for semi-annually
• m = 4 for quarterly
• m = 12 for monthly
• m = 6 for bi-monthly
• m = 360 for daily
14
1
1 








m
n
m
i
i

9. Continuously Compounding
Interest Rate
•
• Where:
• P = principal or present value
• r = continuously compounding interest rate
• t = number of interest periods
15
rt
Pe
F 

10. Annuity
• Annuity – is a series of equal payments
occurring at equal intervals of time.
• Amortization – is a payment of debt by
installment usually by equal amounts and at
equal intervals of time.
16

10.1 Applications of annuity
• 10.1.1 Installment purchase.
• 10.1.2 Amortization of loan.
• 10.1.3 Depreciation
• 10.1.4 Payment of insurance premiums.
17

10.2 Types of annuity
• 10.2.1 Ordinary Annuity – payments occur at
the end of each period.
• 10.2.2 Annuity Due – payments occur at the
beginning of each period.
• 10.2.3 Deferred Annuity – first payment
occurs later than at the end of the first period.
• 10.2.4 Perpetuity – an annuity that continues
indefinitely.
18

11. Ordinary Annuity (cont..)
• Uniform series compound amount factor =
•
• Uniform series sinking fund factor =
•
• Capital recovery factor =
•
20
   
i
i
n
i
A
F
n
1
1 


%,
,
 
n
i
A
F
A
F %,
,

 
  1
1 

 n
i
i
n
i
F
A %,
,
 
n
i
F
A
F
A %,
,

   
  1
1
1



 n
n
i
i
i
n
i
P
A %,
,
 
n
i
P
A
P
A %,
,


11. Ordinary Annuity (cont..)
• Uniform series present worth factor =
•
• Where:
• F = future value of the periodic payments at the end
of n periods.
• P = present value of the periodic payments
• A = Annuity or periodic payments
• n = number of periodic payments
21
   
 n
n
i
i
i
n
i
A
P




1
1
1
%,
,
 
n
i
A
P
A
P %,
,


12. Annuity Due (cont..)
23
 
4
%,
,i
A
P
A
A
P 

 
5
%,
,i
P
F
P
F 
 5
1 i
P
F 


13. Deferred Annuity (cont..)
25
  
3
%,
,
5
%,
, i
F
P
i
A
P
A
P 
 
8
%,
,i
P
F
P
F 
 8
1 i
P
F 


14. Perpetuity
•
• Where:
• P = present value of the perpetuity
• A = Annuity or periodic payments
26
i
A
P 

15. Arithmetic Gradient
• Arithmetic-gradient present worth factor =
• Arithmetic-gradient future worth factor =
• Arithmetic-gradient uniform-series factor =
27
   
   n
n
n
i
i
n
i
i
i
n
i
G
P






1
1
1
1
2
%,
,
   
i
n
i
i
n
i
G
F
n



 2
1
1
%,
,
 
  1
1
1
%,
,



 n
i
n
i
n
i
G
A

15. Arithmetic Gradient (cont..)
•
28

15. Arithmetic Gradient (cont..)
•
• Where:
• AG = Equivalent annual amount of gradient
series.
29
 
n
i
G
P
G
PG %,
,

 
n
i
G
A
G
AG %,
,

   
n
i
G
F
G
n
i
P
F
P
F G
G %,
,
%,
, 


16. Geometric Gradient (cont..)
31































i
g
i
n
A
i
g
g
i
i
g
A
P
n
g
1
1
1
1
1
1
 
n
i
P
F
P
F g
g %,
,


17. Depreciation
• Depreciation – is the decrease in value of a
physical property due to the passage of time.
Depreciation of a property is an example of
capitalization.
32

17.1 Types of Depreciation
• 17.1.1 Physical depreciation – is a type of
depreciation caused by the lessening of the
physical ability of the property to produce
results, such as physical damage, wear and tear.
• 17.1.2 Functional depreciation – is a type of
depreciation caused by the lessening in the
demand for which the property is designed to
render, such as obsolescence and inadequacy.
33

17.2 Purposes of Depreciation
• 17.2.1 To provide for the recovery of capital
invested in the property.
• 17.2.2 To enable the cost of depreciation to be
charged to the cost of producing the products
turned out by the property.
34

17.3 Depreciation Terms
• First Cost (FC) – is the total amount invested on the
property until the property is put into operation.
• Economic Life (n) – is the length of time at which a
property can be operated at a profit.
• Valuation (Appraisal) – is the process of
determining the value or worth of a physical
property for specific reasons.
• Value – is the present worth of all the future profits
that are to be received through ownership of the
property.
35

17.4 Classification of Values
• Market value – is the price that will be paid by a
willing buyer to a willing seller for a property
where each has equal advantage and is under no
compulsion to buy or sell.
• Book value (BV) – is the worth of a property as
shown in the accounting records of an
enterprise.
• Salvage or resale value (SV) – is the price of a
property when sold second-hand; also called
trade-in value.
36

17.4Classification of Values (cont..)
• Scrap value (SV) – is the price of a property
when sold for junk.
• Fair value – is the worth of a property as
determined by a disinterested party which is fair
to both seller and buyer.
• Use value – is the worth of property as an
operating unit.
• Face or par value (F) – is the amount that
appears on the bond which is the price at which
the bond is first bought.
37

18. Methods of Computing
Depreciation
38

18.1 Straight Line Method
• Straight line method – is a method of computing
depreciation in which the depreciation has the
same value each year.
• Annual Depreciation =
• Book Value for m years.
•
39
n
SV
FC
d







 


n
SV
FC
m
FC
BV

18.1 Straight Line Method
• Depreciation rate (d) – is the annual rate for
reducing the value of a property using
depreciation method.
• Depreciation rate =
40
Cost
First
on
Depreciati
Annual

18.2 Sinking Fund Method
• Sinking fund method – is a method of
computing depreciation in which the initial
depreciation is low.
• Where:
• i = interest rate or worth of money
41
   
i
i
SV
FC
n
i
A
F
SV
FC
d n
1
1
%,
, 






18.2Sinking Fund Method (cont..)
42
 







 



i
i
d
FC
BV
n
1
1

18.3Sum-of-the-Years-Digits (SOYD)
Methods
• SOYD – is a method of computing depreciation
in which the digits from year 1 to year n are
added and the depreciation in a certain year
decreases by a constant amount each year.
43
 
2
1



n
n
SOYD
T
 
SV
FC
T
k
n
dk 





 


1
 
SV
FC
T
n
d 







1

18.3Sum-of-the-Years-Digits (SOYD)
Methods (cont..)
• Etc.
•
44
 
SV
FC
T
n
d 





 

1
2
 
SV
FC
T
n
d 





 

2
3
 
m
d
d
d
d
FC
BV 




 3
2
1

18.4 Declining Balance Method
• (Also called Diminishing Balance Method,
Matheson Method, Constant-Percentage or
Constant Ratio Method).
45
 n
r
FC
SV 
 1
   1
1 

 k
k r
FC
r
d
 
FC
r
d 
1
  
r
FC
r
d 
 1
2
  2
3 1 r
FC
r
d 


18.4 Declining Balance Method
• Etc.
•
46
 m
r
FC
BV 
 1

18.5Double Declining Balance Method
• Double declining balance method – is a method
of computing depreciation in which the
depreciation of salvage and the book value never
stops decreasing. Double declining balance is
dependent on accumulated depreciation.
47
L
L
FC
SV 







2
1

(cont..)
• Etc.
48
 
1
2
1
2









k
L
FC
L
dk
 
FC
L
d
2
1 
  







L
FC
L
d
2
1
2
2
 
2
3
2
1
2








L
FC
L
d

(cont..)
Book Value for m years.
49
m
L
FC
BV 







2
1

18.6Service Output or Production Units
Method
• Service output method – is a method of
computing depreciation in which depreciation is
calculated based on the total production
produced per year.
• Depreciation per unit,
50
capacity
units
of
No
SV
FC
d
.



18.7Working Hours or Machine Hours
Method
• Depreciation per hr,
51
capacity
hours
of
No
SV
FC
d
.



19. Depletion
• Depletion - is the decrease in value of property
due to the gradual extraction of its contents,
such as mining properties, oil wells, timber
lands and other consumable resources.
52

19. Depletion (cont..)
• Two Methods of Depletion
• 19.1 Cost Depletion – is based on the level
of activity or usage, not time, as in depreciation.
It may be applied to most types of natural
resources.
• Cost depletion factor for year t is the ratio of the
first cost of the resource to the estimated
number of units recoverable.
53
capacity
resource
t
cos
first
pt 

• The annual depletion charge is pt times the
year’s usage or volume. The total cost depletion
cannot exceed the first cost of the resource. If
the capacity of the property is reestimated some
year in the future, a new cost depletion factor is
determined based upon the undepleted amount
and the new capacity estimate.
54

• 19.2 Percentage Depletion – is a special
consideration given for natural resources. A
constant, stated percentage of the resource’s gross
income may be depleted each year provided it does
not exceed 50% of the company’s taxable income.
For oil and gas property, the limit is 100% of taxable
income. The annual depletion amount is calculates
as
• Percentage depletion amount = percentage x gross
income from property
• Using percentage depletion, total depletion
charges may exceed first cost with no limitation.
55

20. Capital Recovery (Factors of
Annual Cost)
• 20.1 Using Sinking Fund Method
• Capital Recovery = Annual Depreciation +
Interest on Capital
• Interest on Capital =
56
 
i
i
SV
FC
n
1
1 


 
FC
i

20. Capital Recovery (Factors of
Annual Cost) – (cont..)
• 20.2 Using Straight Line Method
• Capital Recovery = Annual Depreciation +
Average Interest
•
• Interest on Capital =
57
n
SV
FC 
   
SV
i
SV
FC
n
n
i







 1
2

21. Capitalized Cost
• Capitalized Cost – is the sum of the first cost and
the present worth of all cost of replacement,
operation, and maintenance for a long time.
• Methods of Computing Capitalized Cost
• 21.1 For perpetual life.
• Capitalized Cost =
58
i
OM
FC 

21. Capitalized Cost (cont..)
• 21.2 For life n.
• Capitalized Cost =
• Where:
• OM = annual operation and maintenance cost.
59
  1
1 



 n
i
SV
FC
i
OM
FC

22. Break-Even Analysis
• Break-even analysis – is a method of
determining the income to equal the expenses or
the costs of two alternatives are equal.
• Break-even point – is the value of a certain
variable for which the costs of two alternatives
are equal.
60

22. Break-Even Analysis (cont..)
•
61

22. Break-Even Analysis (cont..)
• Income = Expenses
•
• Where:
• x = no. of units produced and sold
• P = selling price per unit
• M = material cost per unit
• L = labor cost per unit
• V = variable cost per unit
• FC = first cost
62
        FC
x
V
x
L
x
M
x
P 




23. Business Organizations
• Types of Business Organizations (Forms of
Business or Company Ownership)
• 23.1 Individual Ownership or Single
Proprietorship - Is also termed as sole
proprietorship and is the type of ownership in
business where individual exercises and enjoy
rights in their own interest. The owner has the
total control of the business and makes all
decisions.
63

23. Business Organizations (cont..)
• 23.2 Partnership – is also termed as general
partnership and is an association of two or more
individuals for the purpose of operating a business
as co-owners of a profit.
• 23.3 Corporation – is an artificial being created
by operation of law, having the right of succession
and the powers, attributes, and properties expressly
authorized by law or incident to its existence. It is an
association of not less than five but not more than
15, all of legal age.
64

• Private corporation – are those formed for some
private purpose or benefits.
• Public corporation – are those formed or organized
for the government.
• Semi-public corporation – are those formed that is
partly government and partly a private individual.
• Quasi-public corporation – are those formed for
public utilities and contracts, involving public duties
but which are organized for profit.
• Non-profit organization – are those formed for
community service and religious activities, but
organized for non-profit.
65

• Four Classes of Persons Composing a Corporation
• 23.3.1 Corporators – are those who compose the
corporation.
• 23.3.2 Incorporators – are those corporators
originally (5-15) forming and composing the
corporation.
• 23.3.3 Stockholders – are owners of shares of
stock.
• 23.3.4 Members – are corporators of corporation
who has no capital stock.
66

• Stock – a certificate of owners corporation
• a. Common stock – a residual owners of a
corporation.
• b. Preferred stock – which entitles the holder
thereof to certain preferences over the holder of
common stock.
67

24. Contract
• Contract – is a legally binding agreement to
exchange services.
• 24.1 Four Basic Requirements in a Contract
• 24.1.1 There must be a clear, specific and definite
offer with no room for misunderstanding.
• 24.1.2 There must be some form of conditional
future payments.
• 24.1.3 There must be an acceptance of the
contract and the agreement must be voluntary.
• 24.1.4 Both parties must have legal capacity and
the purpose must be legal.
68

24. Contract (cont..)
• 24.2 Breach of contract – it occurs when one
party fails to satisfy all obligations of the
contract.
• 24.3 Negligence – is an action, whether
willful or unwillful, which is taken without
proper care for safety, resulting to property
damages or injury to persons.
• 24.4 Torts – a civil wrong committed by one
person causing damage to another person or his
property, emotional well-being, or reputation.
69

25. Bond
• Bond – a certificate of indebtedness of a
corporation usually for a period of not less than
10 years and guaranteed by a mortgage on
certain assets of the corporation or the
subsidiaries.
• 25.1 Types of bonds
• 25.1.1 Mortgage bonds – a type of bond in
which the security behind are the assets of the
corporation.
70

25. Bond (cont..)
• 25.1.2 Collateral bonds – a type of bond in
which the security behind are the assets of a well
known subsidiary.
• 25.1.3 Debenture bonds – a type of bond in
which there is no security behind except a
promise to pay.
71

25.2 Bond Value
• Where:
• P = value of bond n periods before maturity
• F = face or par value of the bond
• Fr = periodic dividend
• n = number of periods
• R = redeemable value (usually equal to face
or par value)
• i = investment rate
72
   
n
i
F
P
R
n
i
A
P
Fr
P %,
,
%,
, 


26. Basic Investment Studies
• 26.1 Rate of return – usually stated in
percent per year and is an effective annual
interest rate.
•
• 26.2 Payout period – is the length of time
the investment can be recovered.
73
Investment
Total
rofit
P
Net
turn
Re
of
Rate 
Flow
Cash
Annual
Net
Value
Salvage
Investment
Total
Period
Payout



27. Selection of Alternatives
• 27.1 Present Economy
• This involves selection of alternatives in which
interest or time value of money is not a factor.
Studies usually involve the selection between
alternative designs, materials, or methods.
• 27.2 Rate of Return
• Rate of return – is usually stated in percent per
year and is an effective annual interest rate. The
alternative which gives a higher rate of return on
investment is then the favorable choice.
74

27. Selection of Alternatives (cont..)
• 27.3 Payout Period
• Payout period – this usually expressed in years
and is the length of time for the net annual profit
to equal the initial investment.
• 27.4 Annual Cost
• Annual Cost = Depreciation + Interest on
Capital + Operation and Maintenance + Other
out-of-pocket Expenses
• The alternative with a lower annual cost is then
the more economical alternative.
75

27. Selection of Alternatives (cont..)
• 27.5 Present Worth
• Present Worth - is applicable when the
alternatives involve future expenses whose
present value can be easily determined.
• 27.6 Future Worth
• Future Worth – is applicable when the
alternatives involve expenses whose future
worth is more suitable basis of comparison.
•
76

28. Replacement Studies
• Replacement studies – is an application of
selection of alternatives in which the alternatives
are to replace the old equipment with a new one
or to continue using the old equipment.
• 28.1 Rate of Return
77
quired
Re
Capital
Additional
placement
Re
By
Incurred
Savings
turn
Re
of
Rate 

28. Replacement Studies (cont..)
• 28.2 Annual Cost
• Annual Cost = Depreciation + Interest on
Capital + Operation and Maintenance + Other
out-of-pocket Expenses
• In computing depreciation and interest of the
old equipment in either method, actual present
realizable values and not historical values should
be used.
78

29. Benefit-to-Cost Ratio in Public
Projects
• Benefit-to-Cost Ratio – is commonly used in
public project evaluations where present worth
of all benefits is divided by the present worth of
all costs.
79

Projects
•
80

Projects
• Where:
• FC = first cost
• SV = salvage value at the end of life
• n = useful life
• OM = annual operation and maintenance cost
• i = interest rate or worth of money
• B = annual benefits, that is, the annual worth of
benefits incurred because of the existence of the
project.
81

Projects
• C = annual equivalent of the cost
•
• Benefit-to-Cost Ratio
•
• B/C should be greater than 1 for the project to be
justifiable.
82
   
n
i
F
A
SV
n
i
P
A
FC
C %,
,
%,
, 

C
OM
B
C
B



30. Economic Order Quantity
• Economic order quantity (E O Q) – is the order
quantity which minimized the inventory cost per
unit time. An assumption of the basic (E O Q) with
no shortages: “There is no upper bound on the
quantity ordered.”
•
• Where:
• a = the constant depletion rate (items per unit time)
• k = the fixed cost per order, Pesos
• h = the inventory storage cost (Pesos per item per
unit time)
83
h
ak
Q
O
E
2


31. Principles of Accounting
• 31.1 Bookkeeping System
• Bookkeeping system – is used to record all
financial transactions of the company. All
transactions are recorded in a journal then
categorized and posted in a ledger. A ledger is
classified into asset, liability and owner’s equity.
84

31. Principles of Accounting (cont..)
• 31.2 Balancing System
• Balancing system – where balancing the book
means maintaining the equality of the basic
accounting equation:
• Assets = Liability + Owner’s Equity
• Double entry bookkeeping system - is a balancing
system by maintaining the equality by entering each
transaction into two ledger accounts. All
transactions are either debits or credits. For liability
and owner’s equity, credit increases the account and
debt decreases the account.
85

• 31.3 Cash System
• Cash system – is the simplest form of bookkeeping
system and transactions recorded into the journals
are the present cash and expenses.
• 31.4 Financial Statements
• Financial statements – the process of determining
the success or failure of the company. Financial
statements are usually evaluated by accountants,
business management and stockholders.
86

• 31.4.1 Two Types of Financial Statements
• 31.4.1.1 Balance sheet – is the presentation of
the basic accounting equation.
• 31.4.1.2 Profit and loss statement – is the
presentation of income source and expenses.
This is also known as statement of income and
retained earnings. Examples of income or
revenue are sales, interest, etc. and for expenses
are salaries, supplies, utilities, etc.
87

• 31.4.2 Terms used in the Balance Sheets
• 31.4.2.1 Current assets – also known as liquid
assets and defined as cash and other assets that
can be converted quickly into cash such as
accounts receivable and merchandise.
• 31.4.2.2 Fixed assets – are properties that will
not be converted into cash or difficult to convert
into cash such as buildings, land, machinery,
equipment and fixtures.
88

• 31.4.2.3 Current liabilities – are liabilities
which will due within a short period, usually a
year such as accounts payable and accrued
expenses.
• 31.4.2.4 Long-term liabilities – are liabilities
that are not payable within a short period of
time such as notes payable and mortgage.
89

• 31.4.3 Terms used in the Financial Statements
• 31.4.3.1 Current ratio – an index of short term
paying ability.
•
• 31.4.3.2 Acid-test ratio – also known as quick
ratio and defined as measure of short-term
paying ability.
90
s
Liabilitie
Current
Assets
Current
Ratio
Current 
s
Liabilitie
Current
Assets
Quick
Ratio
Test
Acid 


• 31.4.3.3 Receivable turn-over – measures the
speed of collections of accounts receivables.
•
• 31.4.3.4 Gross margin – gross profit as a
percentage of sales.
•
91
ceivables
Re
Average
Credit
on
Sales
Net
Turnover
ceivable
Re 
Sales
Net
ofit
Pr
Gross
in
arg
M
Gross 

• 31.4.3.5 Profit margin ratio – percentage of
sales that is net income.
•
• 31.4.3.6 Return on investment ratio – percent
return on the investment.
92
Sales
Net
Tax
Before
Income
Net
Ratio
in
arg
M
ofit
Pr 
Equity
s
Owner
Income
Net
Investment
on
turn
Re
'


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