CHAPTER 2: THE GENERAL
CONCEPTS ON
ENGINEERING ECONOMICS
1
A SHORT INTRODUCTION TO A
CASH FLOW STATEMENT
Definition: a financial statement showing
information on cash inflows and outflows
occurring during the fiscal year.
 It is prepared for either a enterprise wide basis or
a specific investment project basis.
 Other types of the financial statements are a
balance sheet, an income statement, and a
statement of changes in owner’s equity.

2
Types of the Financial Statements
-
balance sheet
income profit/loss(PL) statement
cash flow statement
statement of changes in owner’ equity
Cash flow Basis
10 million won(cash outflow)
Depositor
Tong_Il Bank
11million won(cash inflow)
3
Cash Flow Statement prepared with
MS_Excel
4
An investment project for
purchasing the equipment
Ex 2.1]
(Unit: 000 won)
90,000
90,000
90,000
90,000
90,000
0
1
2
3
4
(unit: 000 won)
-300,000
year
Year
Net Cash Flows
0
-300,000
1
90,000
2
90,000
3
90,000
4
90,000
5
90,000
5
5
An investment project for
purchasing the equipment
- Evaluation Techniques
(1)
(2)
(3)
(4)
Ex) NPV using MS-Excel
net present value: NPV
annual equivalent worth: AE
net future value: NFV
internal rate of return: IRR
=NPV(D1,D5:D9)+D4
6
What Is Interest?
We pay interest only when we borrow money. Borrowing is a matter of obtaining
purchasing power that we have not yet earned. Borrowers want money now
though they currently have no valuable service to offer in exchange for it. They
persuade lenders to provide them with money bow by promising to pay later. Then
enter a mutually agreed-upon contract. The ratio between what is given back later
and what is obtained now determined the interest rate
Interest is thus the price that people pay to obtain resources now rather than
wait until they have earned the purchasing power with which to buy the resources.
The best way to think about interest is to view it as the premium paid to obtain
current command of resources. It surely is not the price of money.
Current resources are generally more valuable than future resources because
having resources now usually expands one’s opportunity. Present command of
resources will often enable us to do things that cause our earning capacity to
increase over time, so that we will have more resources at some future date than
we would otherwise have had. When we see such a prospect, we want to borrow.
And we are willing to pay, if we have to, a premium-interest-as long as the interest
is less than what we expect to gain as a result of borrowing
7
THE TYPES OF INTEREST
1. A SIMPLE INTEREST
2. A COMPOUND INTEREST
8
• A Simple Interest Calculation
Interest is applied to the initial principal only
I  (iP ) N
F  P  I  P(1  iN )
9
• A Compound Interest Calculation
Interest is applied to the total amount accumulated by
so far.
F1  P  Pi  P(1  i)
F2  P(1  i )  i[ P(1  i )]  P(1  i )(1  i )  P(1  i) 2
F3  P(1  i ) 2  i[ P (1  i ) 2 ]  P (1  i )3
F  P(1  i ) N
10
A Simple Interest
(unit: 000 won)
• P = principal
• i = interest rate
• N = a number of
interest periods
• Ex 2.2]:
P = 200milliomn
won
i = 6%
N = 3 years
N
Balance
at the
Interest
beginning
0
Balance
at the
ending
200,000
1
200,000
12,000
212,000
2
212,000
12,000
224,000
3
224,000
12,000
236,000
11
A Compounding Interest
(unit: 000 won)
• Ex 2.3]:
P = 200 million won
i = 6%
N = 3 years
N
Balance
at the
interest
beginning
0
Balance
at the
ending
200,000
1
200,000
12,000
212,000
2
212,000
12,720
224,720
3
224,720
13,483.
2
238,203.2
12
The Fundamental of EE
F  P(1  i)
N
13
A COMPARISON OF A SIMPLE AND
COMPOUND INTEREST
 A white


man bought Manhattan Island for $24 in 1626
Given: P=$24 i=8% N=383years
Simple: F =24(1+0.08×383) = $759.4

Compound: F =24(1+0.08)383 = $151trillion 883.1billion
14
WHO IS THE WEALTHIEST IN THE
WORLD?
Rothschild Family
Given:
P: $600 million in 1840
i: 8%
N: 169 years
F=6*(1+0.08)169=$267trillion 156.7billion(the value as of 2009
Bill Gates: $57 bl in 2008
Warren Buffett: $50 bl in 2008
15
THE FUTURE VALUE OF THE
INVESTMENT PROJECT FOR THE
EQUIPMENT PURCHASE
Ex 2.5]
Given: cash flows for each year, i=12%, N=5 years
(unit: 000 won)
N
C.F.
Future Value
Factor
F. V.
0
-300,000
(1+0.12)5=1.762
-528,703
1
90,000
(1+0.12)4=1.574
141,617
2
90,000
(1+0.12)3=1.405
126,444
3
90,000
(1+0.12)2=1.254
112,896
4
90,000
(1+0.12)1=1.120
100,800
5
90,000
(1+0.12)0=1.000
90,000
Total
43,054
16
Inflation ?
 The value of Money
Earning Power
Purchasing power
 Earning Power
Investment Opportunities
 Purchasing Power
Decrease in purchasing power (inflation)
Increase in purchasing power (deflation
17
Calculate Inflation Rate
- Calculate the inflation rate by dividing the
difference between the previous and current
year’s price by the previous year’s price.
 The price index changes every 5 years in Korea
Ex) calculate the inflation rate with the price of a sports
footwear
Given] 100,000 won in 2008
110,000 won in 2009
Find] f
Sol.]
11  10
f 
 0.1  10%
10
18
A Type of Interest Rates Based on
the Inflation Concept
 Market
Interest Rate (i): It is an interest rate
for which the inflation and deflation effects are
reflected.
 Inflation_Free Interest Rate(i’): it is an
interest rate for which the inflation and deflation
effects are completely removed
 Fisher’s Equation: The Relationship among the
interest and inflation (deflation)rates
(1  i )  (1  i ')(1  f )
i  i ' f  i ' f
19
A Type of Cash Flows Based on The
Inflation Effect
 Actual
Cash Flow(An): It is a cash flows for
which the inflation and deflation effects are
reflected.
 Constan Cash flow(A’n): It is a cash flows for
which the inflation and deflation effects are
not reflected.
A.C.F
M.I.R(i)
C.C.F
Inflation_Free. I.R(i’)
20
A Nominal and Real Rate of Return on
Investment
Ex 2.6]
Given] P=100million won, I=8 million won, f=5.5%
Find] A Nominal ROR(r) and A Real ROR(r’)
Sol]
-
No min al ROR
r
800
 0.08  8%
100, 000
- Re al ROR(r ')  Fisher ' s Equation(i  r , i '  r ')
r  r ' f  r ' f
0.08  r ' 0.055  0.055r '
r'
(r  f ) 0.08  0.055

 0.0237  2.37%
i f
(1  0.055)
21
An Economic Evaluation Based on The
Constant Cash Flow
Ex 2.7]
Given] Cash flows, inflation rate(f)=5.4%, market interest rate(i)=10%
i  i' f  i' f , i' 
n
(i  f ) 0.1  0.054

 0.04364  4.364%
i f
(1  0.054)
C. C. F
(unit: 000 won)
Compounding
Factor(i=4.364%)
F. V.
0
-300,000 (1+0.4364)5=1.238
1
90,000 (1+0.4364)4=1.186
2
90,000 (1+0.4364)3=1.137
102,304
3
90,000 (1+0.4364)2=1.089
98,027
4
90,000 (1+0.4364)1=1.044
93,928
5
90,000 (1+0.4364)0=1.000
90,000
total
-371,428
106,769
(단위: 천원)
119,600
22
An Economic Evaluation Based on A
Actual Cash Flow
♦Step 1: convert the constant cash flows to the actual
cash flows
(unit: 000 won)
n
C. C. F
Inflation Factor
A. C. F.
0
-300,000 (1+0.054)0=1.000
-300,000
1
90,000 (1+0.054)1=1.054
94,860
2
90,000 (1+0.054)2=1.111
99,982
3
90,000 (1+0.054)3=1.171
105,381
4
90,000 (1+0.054)4=1.234
111,072
5
90,000 (1+0.054)5=1.301
117,070
23
Inflation Rate=5.4%, Market Interest Rate=10%
An Economic Evaluation Based on A
Actual Cash Flow
♦ step 2: calculate the future value of each actual cash flow
using the market interest rate
(unit: ooo won)
n
A. C. F.
Compounding
Interest Factor
F. V.
0
-300,000
(1+0.1)5=1.611
-483,153
1
94,860
(1+0.1)4=1.464
138,885
2
99,982
(1+0.1)3=1.331
133,076
3
105,381
(1+0.1)2=1.210
127,511
4
111,072
(1+0.1)1=1.100
122,179
5
117,070
(1+0.1)0=1.000
117,070
Total
155,568
Inflation Rate=5.4%, Market Interest Rate=10%
24
Depreciation
The Characteristics of the Fixed Asset: its value decreases as
time goes on
Definition: decrease in the value of the fixed assets
A Depreciation Cost: the amount of decrease in the value of the
fixed assets over the specific period of time
Ex: The worth of 15million won for an automobile
n
15,000
10,000
8,000
6,000
5,000
4,000
Deprecia
tion
5,000
2,000
2,000
1,000
1,000
(unit: thousand won
Depreciation
0
1
2
3
4
5
Market
value
25
THE FACTORS CONSIDERED
WITH DEPRECIATION
A Depreciable Life
A Salvage Value
A Depreciation Method
Cost Basis
26
THE CONDITIONS FOR A
DEPRECIABLE ASSETS
The fixed assets must be used longer than one year with the
limited time.
They must be used for production, not for sale.
Their value must decreases over the time due to erosion,
worn out, and so on.
Considering the three conditions, land can not be a depreciable
asset.
27
The Reason Why Considering A
Depreciation Cost
Managerial
Expense:
A depreciation cost
decreases
a
taxable
income
and finally results
in taxes
Revenue-Expense:
(COGS)
( Depreciation)
(Operating)
Taxable Income
- Taxes
Net Income
28
Depreciation Methods
-
Straight-Line Depreciation Method: SL)
 The value of the fixed assets decreases by the same amount of money per year
 Equation
I S
D
N
where,
I: a cost basis
N: a depreciable life
S: a salvage value at the end of the depreciable life
- Declining-Balance Method: DB)
: The value of the fixed assets decreases by the same rate of mony per year
29
Calculate the Depreciation Cost Using
the SL Method
Ex 2.8]
 Given: cost basis(I)=300 million won, depreciable life(N)=5 years,
salvage value(S)=50M won, depreciation method= SL
 Sol.:
n도
D
I  S 300, 000  50, 000

 50Mwon
N
3
depreciation
0
(unit: ooo won)
Book value
300,000
1
50,000
250,000
2
50,000
200,000
3
50,000
150,000
4
50,000
100,000
5
50,000
50,000
30
Taxable Income and Taxes
Item
Revenue
Expenses:
Cost of Goods Sold
Depreciation
Operating Cost
Taxable Income
Corporate Taxes
Net Income
31
Calculate A Corporate Tax
Ex 2.9]
Given] Taxable Income=350M won, Corporate Tax Rate
Sol.]
Taxable
Income
Tax Rate
Tax
100,000
13%
13,000
250,000
25%
62,500
Total
75,500
32
Appraisal Techniques
- Those which do not consider interest


payback period: PB
accounting rate of return: ARR
- Those which consider interest




net present value: NPV
net future value: NFV
annual equivalent worth: AE
internal rate of return: IRR
33
Payback Period
 Definition
Time to completely recover the initial investment cost with the cash flows
generated by the underlying project.
Method:
Point in time which equates the initial investment cost
with the accumulated cash flow
 수Mathematical Expression:
n
CF0   CFt
t 1
Where
t: time at which a cash flow occurs
CF0: the initial investment cost incurred at time= “0”
CFt: a cash flows occurring at time = “t”
34
Determine The Payback Period of The
Project for Purchasing The Tooling
Equipment
Ex 2.10]
(unit: 000 won)
n
Cash Flow
Acc. C. F.
0
-300,000
-300,000
1
90,000
-210,000
2
90,000
-120,000
3
90,000
-30,000
4
90,000
60,000
5
90,000
150,000
PB=3~4 years
= 3 1 years
3
300,000(initial cost)=90,000(C. F. for the 1st year)+ 90,000(C.F. for the 2nd year)
+ 90,000(C.F. for the 3rd year) +
(300,000  270,000)
90,000
35
An Accounting Rate of Return
 This technique does not consider interest like the PB
 This technique depends on a net(accounting) income instead
of a cash flow
 Mathematical Expression
After - Tax Average Net Income
ARR 
Initial Investment Cost
36
Calculate The Accounting Rate of
Return
Ex 2.11]
n
(unit: 000 won)
Net Income for Each
Alternative
The After-Tax Average Accounting
Profit for Alt. “A”
 1,000  100  900  100  100  400
 80
5
A
B
C
D
0
-1,000
-1,000
-1,000
-1,000
1
100
0
100
200
The ARR for Alt. “A”
2
900
0
200
300
ARRA 
3
100
300
300
500
4
-100
700
400
500
5
-400
1,300
1,250
600
26%
25%
ARR
-8%

After - Tax Average Pr ofit 80

 8%
Initial Cost
1,000
22%
37
Net Present Value
 Definition: It is a technique which allows us to convert the value of
all cash flows occurring at any time to the value of the cash flows at
time=0 using an interest rate given and subtract the sum of the
present value of the cash outflows from that of the cash inflows.
Decision Rule: if NPV(i)> 0, accept, if NPV(i)<0, reject
*minimum attractive rate of rate: MARR
Cash inflow
0
1
2
Cash outflow
3
4
5
NPV
PW(i)
PW(i) > 0
0
PW(i)
38
NPV for the Tooling Equipment Project
Ex 2.12] Make an investment decision based on the NPV
Given] cash flows for the tooling equipment, MARR=15%
n
C.F.
0
(unit: 000 won)
Discounting Factor
(MARR=15%)
PV
-300,000
(1+0.15)0=1.000
-300,000
1
90,000
(1+0.15)-1=0.870
78,260
2
90,000
(1+0.15)-2=0.756
68,052
3
90,000
(1+0.15)-3=0.658
59,176
4
90,000
(1+0.15)-4=0.572
51,458
5
90,000
(1+0.15)-5=0.497
44,746
Total
1,692
Since NPV(15%)=1.692M won>0 , it is desirable for a company to undertake the project.
39
Net Future Value
(unit: 000 won)
Given: Cash Flows
MARR (i)
 Find: To find the
future value at the
end of the project
life

24,400
27,340
55,760
0
1
2
3
75,000
Project Life
40
Calculate the NFV of the Equipment Project
Ex 2.13] Make an investment decision based on the NFV
Given] Cash Flow, MARR=15%
n
C.F.
0
(unit: 000 won)
Compounding Factor
(MARR=15%)
Future Value
-300,000
(1+0.15)5=2.011
-603,407
1
90,000
(1+0.15)4=1.749
157,410
2
90,000
(1+0.15)3=1.521
136,879
3
90,000
(1+0.15)2=1.323
119,025
4
90,000
(1+0.15)1=1.150
103,500
5
90,000
(1+0.15)0=1.000
90,000
Total
3,407
Since NFV(15%)=3.407M won>0 , it is economically better for a firm to undertake the
project. It is noted that NPV(15%)=NFV(15%)(1+MARR)-N=3,407(1+0.15)-5=1,694
41
Rate of Return
 Def. 1: The term of ROR is defined as an interest rate earned on unpaid
balance of an installment loan.
Def. 2: The term of ROR is the break-even interest rate, i*, which makes the
sum of the present value of the cash inflows equal that of the cash
outflows.
Mathematical Relationship:
PW (i* )  PW (i* )C. I nf l ow  PW (i* )C. Out f l ow
0
Def. 3: The term of Return on invested capital is defined as an interest rate
earned on the unrecovered balance of the initial investment cost by the
end of the project life and makes the unrecovered balance zero at the
end of the project life. This rate is generally coined as an internal rate
of return , IRR.
42
Calculate the IRR
Ex 2.14] Make an investment decision based on the IRR criteria
Given] Cash Flows, MARR=15%
Sol.]
1) Calculate the IRR using MS-Excel
NPV (i * )  300,000 

90,000 90,000 90,000


(1  i * ) (1  i * ) 2 (1  i * )3
90,000 90,000

0
(1  i * ) 4 (1  i * )5
43
Calculate the IRR
2) Calculate the IRR using Mathematica 7.0
44
Calculate the IRR
3) Calculate the IRR using the computer program
45
A Project Evaluation and Uncertainty
 The Characteristics of the Real Investment Project
(a) Uncertainty (b) irreversibility (c) the flexibility of the investment time
 The reason for why uncertainty exists in the investment project
: all the benefits and costs happen in the future time
46
What-if framework
Wait-see framework
A Variety of the Techniques Dealing
with Uncertainty
1) Sensitivity Analysis
2) Scenario analysis
3) Break-even point analysis
4) Decision tree analysis
5) Probabilistic approach
6) ROV etc.
47
Sensitivity Analysis
-Def.: It is the techniques which allows us to see what will happen at the final variable of
interest(ex. NPV) when one of the variables changes.
Step 1
Evaluate the economic value using the base scenario
Step 2
Indentify changes in the economic value by varying the
value of the variable selected by a constant rate
step 3
Take the same procedure for the remaining variable as
in step 2
Step 4
Draw a graph for the varied economic values
48
A COST OF CAPITAL FOR THE
PROJECT
 The NPV profile for the project corresponding to the varying interest rate
(unit: 000 won)
n
Cash flow
0
-300,000
1
90,000
2
90,000
3
90,000
4
90,000
5
90,000
IRR=15.0268%
total
49
WEIGHTED AVERAGE COST OF CAPITAL
(WACC)



Capital =equity + debt
A cost of capital must reflect the cost of debt and equity
WACC: The WACC is calculated as following
WACC 
단, T: total capital,
tm: marginal tax rate,
D
E
(rd )(1  t m )  (re )
T
T
D: total debt
rd: cost of debt
E: total equity
re: cost of equity
50
CALCULATE THE WACC
Ex 2.14]
Given] Total capital(T)=300M won, total debt(D)=100M won,
Total equity(E)=200M won, Marginal tax rate(tm)=25%, cost of
debt(rd)=6%, cost of equity(re)=12%
Sol.]
D
E
(rd )(1  t m )  (re )
T
T
1
2
 (0.06)(1  0.25)  (0.12)
3
3
 0.095
WACC 
51