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(c) 2001 Contemporary Engineering Economics
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Chapter 13Inflation and Its Impact on Project
Cash Flows
• Meaning and Measure of Inflation
• Equivalence Calculations under Inflation
• Effects of Inflation on Project Cash Flows
• Rate of Return Analysis under Inflation
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Inflation and Economic Analysis
• What is inflation?
• How do we measure inflation?
• How do we incorporate the effect of inflation in economic analysis?
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What is Inflation?
• Value of Money
• Earning Power
• Purchasing Power
Earning PowerPurchasing power
Investment Opportunity
Decrease in purchasing power (inflation)Increase in purchasing Power (deflation)
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Purchasing Power
1990
$100
1990 2001
$100
You could buy 50 Big Macs in year 1990.
You can only buy 40 Big Macs in year 2001.
$2.00 / unit $2.50 / unit25% Price change due to inflation
The $100 in year 2001 has only $80 worth purchasing power of 1990
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-2 -1 0 1
$100
-2 -1 0 1
$100
You could purchase 63.69 gallons of unleaded gasoline a year ago.
You can now purchase 80 gallons of unleaded gas.
$1.57 / gallon $1.25 / gallonPrice change due to
deflation
20.38%
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Price Increase Due to Inflation
Item 1967 Price 2000 Price % Increase
Consumer price index (CPI) 100 512.9 413
Monthly housing expense $114.31 $943.97 726
Monthly automobile expense 82.69 471.38 470
Loaf of bread .22 1.84 736
Pound of hamburger .39 2.98 564
Pound of coffee .59 4.10 595
Candy bar .10 0.90 800
Men’s dress shirt 5.00 39.00 680
Postage (first-class) 0.05 0.33 660
Annual public college tuition 294.00 3,960.00 1,247
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Inflation Terminology - I
• Producer Price Index: a statistical measure of industrial price change, compiled monthly by the BLS, 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 rate that accounts for the effect of varying yearly inflation rates over a period of several years.
• General Inflation Rate ( ): the average inflation rate calculated based on the CPI for all items in the market basket.f
_
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Measuring Inflation
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.
Market basket
Base Period (1967) 2001
$100 $512.9
CPI for 2001 = 512.9
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Selected Price IndexesYear
Base Period
New CPI
1982-84
Old CPI
1967
Gasoline
1982
Steel
1982
Passenger Car
1982
1991 135.2 405.1 66.9 110.6 124.2
1992 139.5 417.9 65.6 107.1 127.3
1993 144.0 461.2 67.9 106.7 129.8
1994 147.4 441.4 59.5 111.9 133.3
1995 152.2 455.0 67.7 121.7 134.0
1996 156.6 468.2 76.4 114.9 135.2
1997 160.2 479.7 72.7 116.4 135.2
1998 162.5 487.1 54.0 115.4 132.2
1999 166.2 497.8 64.4 105.3 121.4
2000 171.2 512.9 92.6 109.8 133.4
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Average Inflation Rate (f)Fact:
Base Price = $100 (year 0)Inflation rate (year 1) = 4%Inflation rate (year 2) = 8%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) = $112.32f = 5.98%
2
$100
$112.32
0 1
2
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Average Inflation Rate
Item 1967 Price 2000 Price Average Inflation Rate
Consumer price index (CPI) 100 512.9 5.07%
Monthly housing expense $114.31 $943.97 6.61
Monthly automobile expense 82.69 471.38 5.42
Loaf of bread 0.22 1.84 6.64
Pound of hamburger 0.39 2.98 6.36
Pound of coffee 0.59 4.10 6.05
Candy bar 0.10 0.90 6.88
Men’s dress shirt 5.00 39.00 6.42
Postage (first-class) 0.05 0.33 5.89
Annual public college tuition 294.00 3,960.00 8.19
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General Inflation Rate (f)
Average inflation rate based on the CPI
CPI CPI f
fCPI
CPI
f
CPI n
CPI
nn
nn
n
0
0
1
0
1
1
( ) ,_
_ /
_
where The genreal inflation rate,
The consumer price index at the end period ,
The consumer price index for the base period.
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Example 13.2: Yearly and Average Inflation Rates
Year Cost
0 $504,000
1 538,000
2 577,000
3 629,500
What are the annual inflation ratesand the average inflation rate over 3 years?
SolutionInflation rate during year 1 (f1): ($538,400 - $504,000) / $504,000 = 6.83%.Inflation rate during year 2 (f2): ($577,000 - $538,400) / $538,400 = 7.17 %.Inflation rate during year 3 (f3): ($629,500 - $577,000) / $577,000 = 9.10%.The average inflation rate over 3 years is
f ($629,
$504,) . ./500
0001 0 0769 7 69%1 3
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Inflation Terminology – II
• Actual Dollars (An ): Estimates of future cash flows for year n that take into account any anticipated 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).
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Conversion from Constant to Actual Dollars
A A f A F P f nn nn
n ' ( ) ' ( / , , )_ _
1
$1,000 (1 + 0.08)= $1,260
3ConstantDollars
n
f
3
8%_
$1,000
3ActualDollars
$1,260
3
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Conversion from Constant to Actual Dollars
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
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01 2 3 4 5
01 2 3 4 5
$250,000
$105,000$121,275 $138,915 $158,016
$153,154
Years(b) Actual dollars
$250,000
$100,000$110,000
$120,000 $130,000
$120,000
Years(a) Constant dollars
$250
,000
(1+
0.05
)0
$100
,000
(1+
0.05
)
$110
,000
(1+
0.05
)2
$120
,000
(1+
0.05
)3
$130
,000
(1+
0.05
)4
$120
,000
(1+
0.05
)5
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Conversion from Actual to Constant Dollars
A A f A P F f nn nn
n' ( ) ( / , , )_ _
1
ConstantDollars $1,260 (1 + 0.08)
= $1,000
-3
n
f
3
8%_
$1,000
3ActualDollars
$1,260
3
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Conversion from Actual to Constant Dollars
End of period
Cash Flow in Actual $
Conversion at f = 5%
Cash Flow in Constant $
Loss in Purchasing
Power
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
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Equivalence Calculation Under Inflation
1. Types of Interest Rate
2. Types of Cash Flow
3. Types of Analysis Method
Market Interest rate (i)Inflation-free interest rate (i’)
In Constant DollarsIn Actual Dollars
Constant Dollar AnalysisActual Dollar Analysis
Deflation MethodAdjusted-discount method
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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): 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).
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Inflation and Cash Flow Analysis
•Constant Dollar analysis
- Estimate all future cash flows in constant dollars.- Use i’ as an interest rate to find equivalent worth.
•Actual Dollar Analysis
- Estimate all future cash flows in actual dollars.- Use i as an interest rate to find equivalent worth.
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Constant Dollar Analysis
• In the absence of inflation, all economic analyses up to this point is, in fact, constant dollar analysis.
• Constant dollar analysis is common in the evaluation of many long-term public projects, because government do no pay income taxes.
• For private sector, income taxes are levied based on taxable income in actual dollars, actual dollar analysis is more common.
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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.
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Step 1: Convert actual dollars to Constant
dollars
n Cash Flows in Actual Dollars
Multiplied by Deflation Factor
Cash Flows in Constant Dollars
0 -$75,000 1 -$75.000
1 32,000 (1+0.05)-1 30,476
2 35,700 (1+0.05)-2 32,381
3 32,800 (1+0.05)-3 28,334
4 29,000 (1+0.05)-4 23,858
5 58,000 (1+0.05)-5 45,445
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Step 2:Convert Constant dollars to Equivalent
Present Worthn Cash Flows in
Constant DollarsMultiplied by
Discounting FactorEquivalent
Present Worth
0 -$75,000 1 -$75,000
1 30,476 (1+0.05)-1 27,706
2 32,381 (1+0.05)-2 26,761
3 28,334 (1+0.05)-3 21,288
4 23,858 (1+0.05)-4 16,295
5 45,445 (1+0.05)-5 28,218
$45,268
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Deflation Method (Example 13.6):Converting actual dollars to constant dollars and then to
equivalent present worth
-$75,000 $30,476 $32,381 $28,334 $23,858 $45,455
-$75,000 $32,000 $35,700 $32,800 $29,000 $58,000
-$75,000
$27,706$26,761$21,288$16,295
$28,218
$45,268
Actual Dollars
Constant Dollars
PresentWorth
n = 0 n = 1 n = 2 n = 3 n = 4 n = 5
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Adjusted-Discount Method
PA
i
A
i
A
f i
i i i
i f i f
nn
n
nn
n
n n
( )
( ) ( ) ( ' )
( ) ( )( ' )
' '
1
1 1 1
1 1 1
1
P
Afin
nn
n
( )( ' )11
A
f in
n n( ) ( ' )1 1
A
f i
n
n n( ) ( ' )1 1 i i f i f ' '
Step 1
Step 2
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Adjusted-Discounted Method
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
i i f i f
' '
. . ( . )( . )
.
0 10 0 05 0 10 0 05
15 5%
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Adjusted-discount method
0
1 2 3 4 5
- $75,000$27,706$26,761$21,288$16,295$28,218
$45,268
= $
32,0
00 (
P/F
, 15
.5%
, 1)
= $
35,7
00 (
P/F
, 15
.5%
, 2)
= $
32,8
00 (
P/F
, 15
.5%
, 3)
= $
29,0
0 0 (
P/F
, 15.
5%, 4
)
= $
58,0
00 (
P/F
, 15.
5%, 5
)
$32,000$35,700
$32,800$29,000
$58,000
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Adjusted Discount Method: Example 13.7Converting actual dollars to present worth dollars by
applying the market interest rate
n = 0 n = 1 n = 2 n = 3 n = 4 n = 5
-$75,000 $32,000 $35,700 $32,800 $29,000 $58,000
Actual Dollars
-$75,000
$27,706$26,761$21,288$16,295
$28,218
$45,268
PresentWorth
%5.15 fifii
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Equivalence Calculation with Composite Cash Flow Elements
Age College expenses
(in today’s dollars)
College expenses
(in 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
Approach: Convert any cash flow elements in constant dollars into actual dollars. Then use the market interest rate to find the equivalent present value.
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V1 = C(F/A, 2%, 48)
V2 = $229,211
Let V1 = V2 and solvefor C:
C = $2,888.48
Required Quarterly Contributions to College Funds
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Effects of Inflation on Project Cash Flows
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
Note: Depreciation expenses are based on historical costs andalways expressed in actual dollars
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Item Effects of Inflation
Salvage value Inflated salvage value combined with book values based on historical costs results in higher taxable gains.
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Item Effects of Inflation
Loan repayments Borrowers repay historical loan amounts with dollars of decreased purchasing power, reducing the debt-financing cost.
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Item Effects of Inflation
Working capital requirement
Known as working capital drain, the cost of working capital increases in an inflationary environment.
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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.
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Excel Example of an after-tax cash flow analysis including differential inflation (Example 13.14)
INPUT: O&M Cost 13000 General Inflation rate 0.05Salvage 1000 Inflation-free interest 0.2Contract $ 23500 Market interest rate 0.26Investment 15000 Income tax rate 0.4
Income Statement 0 1 2 3 4 5Inflation rate
Revenues $23,500 $23,500 $23,500 $23,500 $23,500Expenses:
O&M 8% $14,040 $15,163 $16,376 $17,686 $19,101Depreciation $3,000 $4,800 $2,880 $1,728 $864
Taxable Income $6,460 $3,537 $4,244 $4,086 $3,535Income taxes (40%) $2,584 $1,415 $1,697 $1,634 $1,414Net Income $3,876 $2,122 $2,546 $2,451 $2,121
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Cash Flow Statement 0 1 2 3 4 5Inflation rate
Operating Activities:Net Income $2,122 $2,546 $2,451 $2,121
Depreciation $3,876 $4,800 $2,880 $1,728 $864Investment Activities: $3,000
Investment $15,000Salvage 5% $1,276
Gains Tax $181Net cash flow (actual$) $15,000 $6,876 $6,922 $5,426 $4,179 $4,442Net cash flow (constant $) $15,000 $6,549 $6,279 $4,687 $3,438 $3,480Equ. Present worth $15,000 $5,457 $4,360 $2,713 $1,658 $1,399Net present worth $587
$3,876$3,000
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Rate of Return Analysis under Inflation
• Principle:True (real) rate of return should be based on constant dollars.
• If the rate of return is computed based on actual dollars, the real rate of return can be calculated as:
n
Net cash flows in actual dollars
Net cash flows in constant dollars
0
1
2
3
4
-$30,000
13,570
15,860
13,358
13,626
-$30,000
12,336
13,108
10,036
9,307
IRR 31.34% 19.40%
ii
f'
.
..40%
_
1
11
1 0 3134
1 0 101
19Not correct IRR
f_
10%
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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.
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• The general inflation rate (f) is an average inflation rate based on the CPI. An annual general inflation rate ( ) can be calculated using the following equation:
• 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.
f
fCPI CPI
CPInn n
n
1
1
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• Project cash flows may be stated in one of two forms
Actual dollars (An): Dollars that reflect the inflation or deflation rate.
Constant dollars (A’n): Year 0 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 analysisInflation-free interest rate (i’): A rate from which the effects of inflation have been removed; this rate is used with constant dollar analysis
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• To calculate the present worth of actual dollars, we can use a two-step or a one-step process:Deflation method—two steps:1. Convert actual dollars by deflating with the general inflation rate of
2. Calculate the PW of 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.
f