Advanced Engineering Economy
Contemporary Engineering Economics, 5th edition, © 2010
Chapter Opening
Story
How Much Will It Cost
to Send Your Child to
College in Year 2015?
A year in college cost
$17,800 in 2005.
Due to inflation, the
college expense has
been increasing at a
rate of 6.5% annually.
Then, in 2015 a year
in college would cost
about $33,413.
 College Cost Calculator
Contemporary Engineering Economics, 5th edition, © 2010
Inflation and Economic Analysis

What is inflation?
 How do we measure inflation?
 How do we incorporate the effect of inflation in
equivalence calculation?
Contemporary Engineering Economics, 5th edition, © 2010
What is
Inflation?
Definition: Inflation  Time Value of Money
Earning Power
is the rate at which
Purchasing Power
the general level of
prices and goods and  Earning Power
services is rising, and
Investment Opportunity
subsequently,
purchasing power is
 Purchasing Power
falling.
Decrease in purchasing power (inflation)
Increase in purchasing power (deflation)
Contemporary Engineering Economics, 5th edition, © 2010
Inflation - Decrease in Purchasing Power
$100
$100
1990
1990
You could buy 50 Big Macs
in year 1990 with $100
$2.00 / unit
2010
You can only buy 28.5 Big
Macs in year 2010.
75%
Price change
due to
inflation
$3.50 / unit
The $100 in year 2010 has only $57
worth purchasing power of 1990
Contemporary Engineering Economics, 5th edition, © 2010
Deflation - Increase in Purchasing Power
$100
2004
2005
$100
2006
2010
You could purchase
63.69 gallons of purified
drink water a year ago.
$1.57 / gallon
2004
2005
2006
2010
You can now purchase
80 gallons of purified
drink water.
20.38%
$1.25 / gallon
Price change due to
deflation
Contemporary Engineering Economics, 5th edition, © 2010
Inflation Terminology - I
 Producer Price Index: a statistical measure of industrial price change,
compiled monthly by the Bureau of Labor Statistics, U.S. Department of
Labor
 Consumer Price Index: a statistical measure of change, over time, of
the prices of goods and services in major expenditure groups—such as food,
housing, apparel, transportation, and medical care—typically purchased by
urban consumers
 Average Inflation Rate (f): a single average rate that accounts for
the effect of varying yearly inflation rates over a period of several years.
 General Inflation Rate (f ):
the average inflation rate calculated
based on the CPI for all items in the market basket.
Contemporary Engineering Economics, 5th edition, © 2010
Consumer
Price Index
Consumer Price Index
(CPI): the CPI compares
the cost of a sample
“market basket” of
goods and services in a
specific period relative to
the cost of the same
“market basket” in an
earlier reference period.
This reference period is
designated as the base
period.
 CPI (Old measure) – Base Period =
1967
 1967
 2010
100
649.10 (January)
 CPI (New measure) – Base Period
(1982-84)
 1982-84
 2010
100
216.68 (January)
Contemporary Engineering Economics, 5th edition, © 2010
Selected Price Indexes (Index for Base Year = 100,
Calendar Month = April)
Contemporary Engineering Economics, 5th edition, © 2010
Average Inflation Rate (f )
Fact:
Base Price = $100
(year 0)
Inflation rate (year 1)
= 4%
Inflation rate (year 2)
= 8%
Find: Average inflation rate
over 2 years?
 Step 1: Find the actual inflated price at the end
of year 2.
$100 ( 1 + 0.04) ( 1 + 0.08) = $112.32
 Step 2: Find the average inflation rate by solving
the following equivalence equation.
$100 ( 1+ f)2 = $112.32
f = 5.98%
0
$112.32
1
2
$100
Contemporary Engineering Economics, 5th edition, © 2010
Example: Average Inflation Rate
Sample Calculation for Average
Inflation rate for Gasoline:
 Average Inflation Rate
Given: P = 127.3, F = 175.3, N =
2009-2000 = 9.
Find: f
Contemporary Engineering Economics, 5th edition, © 2010
General Inflation Rate (f)
Calculation:
 Given:
Formula:
_
CPIn  CPI0 (1  f )n ,
 CPI for 2009 = 213.2,
1/ n
 CPI 
f   n  1
 CPI0 
_
_
 CPI for 2000 = 172.2
where f  The genreal inflation rate,
CPIn  The consumer price index at the end period n,
CPI0  The consumer price index for the base period.
 Find: f
 213.2 
f 
 172.2 
 2.40%
Contemporary Engineering Economics, 5th edition, © 2010
1/9
1
Example Yearly and Average Inflation Rates
 Year
 Solution:
cost data:
Year
Cost
0
$504,000
1
538,000
2
577,000
3
629,500
 Find: Yearly and Average
inflation rates
Contemporary Engineering Economics, 5th edition, © 2010
Inflation Terminology – II
 Actual Dollars (An ): Estimates of future cash
flows for year n that take into account any
anticipated future changes in amount caused by
inflationary or deflationary effects.
 Constant Dollars (An’ ): Estimates of future cash
flows for year n in constant purchasing power,
independent of the passage of time (or base
period).
Contemporary Engineering Economics, 5th edition, © 2010
Finding Actual Dollars

Conversion from Constant to Actual Dollars

General inflation rate = 5%
Period
Net Cash Flow in
Constant $
Conversion
Factor
Cash Flow in
Actual $
0
-$250,000
(1+0.05)0
-$250,000
1
100,000
(1+0.05)1
105,000
2
110,000
(1+0.05)2
121,275
3
120,000
(1+0.05)3
138,915
4
130,000
(1+0.05)4
158,016
5
120,000
(1+0.05)5
153,154
Contemporary Engineering Economics, 5th edition, © 2010
Finding Constant Dollars
 Conversion from Actual to Constant
dollars
 Example General inflation rate of 5%
End of
period
Cash Flow in
Actual $
Conversion
at f = 5%
0
-$20,000
(1+0.05)0
-$20,000
0%
1
20,000
(1+0.05)-1
-19,048
4.76
2
20,000
(1+0.05)-2
-18,141
9.30
3
20,000
(1+0.05)-3
-17,277
13.62
4
20,000
(1+0.05)-4
-16,454
17.73
Contemporary Engineering Economics, 5th edition, © 2010
Cash Flow in
Constant $
Loss in
Purchasing
Power
Equivalence Calculations under Inflation
Types of Interest Rate
Market Interest Rate (i)
Inflation-free Interest Rate (i’)
Types of Cash Flows
Estimated in Constant Dollars
Estimated in Actual Dollars
Types of Analysis Method
Constant-Dollar Analysis
Actual-Dollar Analysis
Contemporary Engineering Economics, 5th edition, © 2010
Inflation Terminology - III
 Inflation-free interest rate (i’): an estimate of the
true earning power of money when the inflation
effects have been removed (also known as real
interest rate).
 Market interest rate (i): an interest rate which takes
into account the combined effects of the earning
value of capital and any anticipated changes in
purchasing power (also known as inflation-adjusted
interest rate).
Contemporary Engineering Economics, 5th edition, © 2010
Inflation and Cash Flow Analysis
Constant Dollar analysis
 Estimate all future cash flows in constant dollars.
 Use i’ as an interest rate to find the equivalent worth.
Actual Dollar Analysis
 Estimate all future cash flows in actual dollars.
 Use i as an interest rate to find the equivalent worth.
Contemporary Engineering Economics, 5th edition, © 2010
When do we Prefer Constant Dollar
Analysis?
 In the absence of inflation, all economic analyses up
to this point is, in fact, the constant dollar analysis.
 Constant dollar analysis is common in the evaluation
of many long-term public projects, because
governments do not pay income taxes.
 For private sector, income taxes are imposed based
on the taxable income in actual dollars, so the actual
dollar analysis is more common.
Contemporary Engineering Economics, 5th edition, © 2010
Two Alternate Ways in Conducting Actual
Dollars Analysis
• Method 1: Deflation Method
- Step 1:
Bring all cash flows to have
common purchasing power.
- Step 2:
Consider the earning power.
• Method 2: Adjusted-discount Method
- Combine Steps 1 and 2 into one step.
Contemporary Engineering Economics, 5th edition, © 2010
Example: Deflation Method
Step 1: Converting Actual Dollars into
Constant Dollars
Step 2: Calculating Equivalent
Present Worth
Contemporary Engineering Economics, 5th edition, © 2010
Graphical Overview on Deflation Method (Example): Converting actual
dollars to constant dollars and then to equivalent present worth
n=0
Actual
Dollars
Constant
Dollars
Present
Worth
-$75,000
-$75,000
n=1
n=2
n=3
n=4
n=5
$32,000 $35,700 $32,800 $29,000 $58,000
$30,476
$32,381 $28,334 $23,858 $45,455
$28,218
-$75,000
$27,706
$26,761 $21,288
$16,295
$45,268
Contemporary Engineering Economics, 5th edition, © 2010
Adjusted-Discount Method – Perform
Deflation and Discounting in One Step
o Discrete Compounding
An
(1  f ) n
Pn 
(1  i ' ) n
Step 2
Step 1
Pn 
An
An

n
(1  i)n
(1  f )(1  i ')


(1  i)  (1  f )(1  i ')
An

(1  f )n (1  i ')n

 1  i ' f  i ' f
An
(1  f )(1  i ')


An
(1  i)n
i  i ' f  i ' f
n
o Continuous Compounding
i  i ' f
Contemporary Engineering Economics, 5th edition, © 2010
Example: Adjusted-Discounted Method
Given: inflation-free interest
rate = 0.10, general inflation
rate = 5%, and cash flows in
actual dollars
i  i ' f  i ' f
 0.10  0.05  (0.10)(0.05)
 15.5%
Find: i and NPW
n
Cash Flows in Actual
Dollars
Multiplied
by
Equivalent
Present Worth
0
-$75,000
1
-$75,000
1
32,000
(1+0.155)-1
27,706
2
35,700
(1+0.155)-2
26,761
3
32,800
(1+0.155)-3
21,288
4
29,000
(1+0.155)-4
16,296
5
58,000
(1+0.155)-5
28,217
$45,268
Contemporary Engineering Economics, 5th edition, © 2010
Graphical Overview on Adjusted Discount Method:
Converting actual dollars to present worth dollars by applying the market interest
rate
n=0
Actual
Dollars
-$75,000
n=1
n=2
n=3
n=4
$32,000 $35,700 $32,800 $29,000 $58,000
i  i  f  if  15.5%
Present
Worth
n=5
$28,218
-$75,000
$27,706
$26,761 $21,288
$16,295
$45,268
Contemporary Engineering Economics, 5th edition, © 2010
Mixed-Dollar Analysis – College Savings Plan Equivalence Calculation with Composite Cash Flow Elements
Approach: Convert any cash flow elements in constant dollars into actual
dollars. Then use the market interest rate to find the equivalent present
value. Assume f = 6% and i = 8% compounded quarterly.
Age
(Current Age = 5
Years Old)
Estimated College
Expenses
in Today’s Dollars
College Expenses Converted into
Equivalent Actual Dollars
18 (Freshman)
$30,000
$30,000(F/P,6%,13) = $63,988
19 (Sophomore)
30,000
30,000(F/P,6%,14) = 67,827
20 (Junior)
30,000
30,000(F/P,6%,15) = 71,897
21 (senior)
30,000
30,000(F/P,6%,16) = 76,211
Contemporary Engineering Economics, 5th edition, © 2010
Solution: Required Quarterly Contributions
to College Funds
V1 = C(F/A, 2%, 48)
V2 = $229,211
Let V1 = V2 and solve
for C:
C = $2,888.48
Contemporary Engineering Economics, 5th edition, © 2010
Effects of Inflation on Projects with
Depreciable Assets
Item
Effects of Inflation
Depreciation expense
Depreciation expense is charged to
taxable income in dollars of declining
values; taxable income is overstated,
resulting in higher taxes
Salvage value
Inflated salvage value combined with
book values based on historical costs
results in higher taxable gains.
Note: Depreciation expenses are based on historical costs and
always expressed in actual dollars
Contemporary Engineering Economics, 5th edition, © 2010
Example 11.8
Reconsider the Automated
Machining Center project
discussed earlier. What will
happen to this investment
project if

the general inflation
during the next five years
is expected to increase by
5% annually,
 sales, operating costs, and
working capital
requirements are
assumed to increase
accordingly,
 depreciation will remain
unchanged, but taxes,
profits, and thus cash flow
will be higher.
 the firm’s inflation-free
interest rate is known to
be 15%.
Determine the PW of the
project.
Contemporary Engineering Economics, 5th edition, © 2010
Solution: Excel Worksheet
Contemporary Engineering Economics, 5th edition, © 2010
Effects of Inflation on Return on
Investment
Item
Effects of Inflation
Rate of Return
and NPW
Unless revenues are sufficiently
increased to keep pace with
inflation, tax effects and/or a
working capital drain result in
lower rate of return or lower
NPW.
Contemporary Engineering Economics, 5th edition, © 2010
Example 11.11 IRR Analysis with Inflation
IRR in the absence of inflation
IRR Calculation under Inflation
Contemporary Engineering Economics, 5th edition, © 2010
Rate of Return Analysis under Inflation
_
f  10%
 Principle: True (real) rate of
return should be based on
constant dollars.
 If the rate of return is
computed based on cash
flows in actual dollars, the
real rate of return can be
calculated as:
i' 
1i
_
1
1 f
1  0.3134

1
1  0.10
 19.40%
n
Net cash
flows in
actual
dollars
0
1
2
3
4
-$30,000
13,570
15,860
13,358
13,626
IRR
31.34%
Contemporary Engineering Economics, 5th edition, © 2010
Net cash
flows in
constant
dollars
-$30,000
12,336
13,108
10,036
9,307
19.40%
Decision Criterion
 If you use 31.34% as your IRR, you should use a market
interest rate (or inflation-adjusted MARR) to make an
accept and reject decision.
 If you use 19.40% as your IRR, you should use an
inflation-free interest rate (inflation-free MARR) to make
an accept and reject decision. In our example, MARR’ =
20%.
Contemporary Engineering Economics, 5th edition, © 2010
Effects of Inflation on Working Capital
Item
Effects of Inflation
Working capital
requirement
Known as working capital drain,
the cost of working capital
increases in an inflationary
environment.
Contemporary Engineering Economics, 5th edition, © 2010
Example 11.12 Effects of Inflation on Working Capital
Contemporary Engineering Economics, 5th edition, © 2010
Summary
 The Consumer Price Index (CPI) is a statistical
measure of change, over time, of the prices of goods
and services in major expenditure groups—such as
food, housing, apparel, transportation, and medical
care—typically purchased by urban consumers.
 Inflation is the term used to describe a decline in
purchasing power evidenced in an economic
environment of rising prices.
 Deflation is the opposite: An increase in purchasing
power evidenced by falling prices.
Contemporary Engineering Economics, 5th edition, © 2010
 The general inflation rate (f) is an average inflation
rate based on the CPI. An annual general inflation
rate ( f ) can be calculated using the following
equation:
fn 
CPIn  CPIn 1
CPIn 1
 Specific, individual commodities do not always
reflect the general inflation rate in their price
changes. We can calculate an average inflation rate
for a specific commodity (j) if we have an index (that
is, a record of historical costs) for that commodity.
Contemporary Engineering Economics, 5th edition, © 2010
 Project cash flows may be stated in one of two forms
 Actual dollars (An): Dollars that reflect the inflation or
deflation in the economy.
 Constant dollars (A’n): Dollars in Year 0 purchasing
dollars.
 Interest rates for project evaluation may be stated in
one of two forms:

Market interest rate (i): A rate which combines the
effects of interest and inflation; used with actual dollar
analysis.
 Inflation-free interest rate (i’): A rate from which
the effects of inflation have been removed; this rate is
used with constant dollar analysis.
Contemporary Engineering Economics, 5th edition, © 2010
 To calculate the present worth of cash flows in actual
dollars, we can use a two-step or a one-step process:

Deflation method—two steps:
1. Convert cash flows in actual dollars by deflating
with the general inflation rate of f
2. Calculate the PW of cash flows in constant dollars
by discounting at i’
 Adjusted-discount method—one step
1. Compute the market interest rate.
2. Use the market interest rate directly to find the
present value of cash flows in actual dollars.
Contemporary Engineering Economics, 5th edition, © 2010
Contemporary Engineering Economics, 5th edition, © 2010