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TRANSCRIPT
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Chapter 13
Inflation and Its Impact on Project
Cash Flows
Meaning and Measureof Inflation
EquivalenceCalculations underInflation
Effects of Inflation onProject Cash Flows
Rate of Return Analysisunder Inflation
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Inflation and Economic Analysis
What is inflation?
How do we measure inflation?
How do we incorporate the effect of inflationin economic analysis?
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What is Inflation?
Value of Money
Earning Power
Purchasing Power
Earning Power
Purchasing 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 Macsin year 1990.
You can only buy 40 BigMacs in year 2001.
$2.00 / unit $2.50 / unit25%
Price change
due toinflation
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 purchase63.69 gallons of
unleaded gasoline
a year ago.
You can now purchase80 gallons of unleaded
gas.
$1.57 / gallon $1.25 / gallon
Price 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 800Mens 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 pricechange, compiled monthly by the BLS, U.S. Department of Labor
Consumer Price Index: a statistical measure of change, overtime, of the prices of goods and services in major expendituregroupssuch as food, housing, apparel, transportation, and medicalcaretypically purchased by urban consumers
Average Inflation Rate (f): a single rate that accounts for theeffect of varying yearly inflation rates over a period of several years.
General Inflation Rate ( ): the average inflation ratecalculated based on the CPI for all items in the market basket.
f_
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Measuring Inflation
Consumer Price Index (CPI): the CPIcompares 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 designatedas the base period.
Market basket
Base Period (1967) 2001$100 $512.9
CPI for 2001 = 512.9
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Selected Price Indexes
Year
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 72.7 116.4 135.21998 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 thefollowing equivalence equation.
$100 ( 1+f) = $112.32
f= 5.98%
2
$100
$112.32
0 1
2
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Average Inflation Rate
Item1967 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 6.88Mens 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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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 rates
and the average inflation rate over 3 years?
Solution
Inflation 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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Conversion
from Constant to Actual Dollars
A A f A F P f nn nn
n' ( ) ' ( / , , )_ _
1
$1,000 (1 + 0.08)
= $1,260
3
Constant
Dollars
n
f
3
8%_
$1,000
3Actual
Dollars
$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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0
1 2 3 4 5
0
1 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
$250,0
00(1+0.0
5)0
$100,000(1+0.0
5)
$110,0
00(1+0.0
5)2
$120,0
00
(1+0.0
5)3
$130,0
00(1+0.0
5)4
$120
,000(1+0.0
5)5
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Conversion
from Actual to Constant Dollars
A A f A P F f nn nn
n' ( ) ( / , , )_ _
1
Constant
Dollars $1,260 (1 + 0.08)= $1,000
-3
n
f
3
8%_
$1,000
3Actual
Dollars
$1,260
3
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Conversion from Actual to Constant
Dollars
End of
period
Cash Flow
in Actual $
Conversion
atf = 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 Method
Adjusted-discount method
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Inflation Terminology - III
Inflation-free Interest Rate (i): an estimate of thetrue earning power of money when the inflation
effects have been removed (also known as realinterest rate).
Market interest rate (i): interest rate which takes
into account the combined effects of the earningvalue of capital and any anticipated changes inpurchasing 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 theevaluation of many long-termpublic 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 Dollars
Multiplied by
Discounting Factor
Equivalent
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
16,2955 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
Present
Worth
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
n
n
n
n n
( )
( ) ( ) ( ' )
( ) ( )( ' )
' '
1
1 1 1
1 1 1
1
P
A
f
in
n
n
n
( )
( ' )
1
1
A
f i
n
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
$32,000$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
Present
Worth
%5.15fifii
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Equivalence Calculation with Composite
Cash Flow Elements
Age College expenses
(in todays 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 solveforC:
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 indollars ofdeclining values;
taxable income is overstated,
resulting in higher taxes
Note: Depreciation expenses are based on historical costs and
always expressed in actual dollars
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Item Effects of Inflation
Salvage value Inflated salvage value
combined with book valuesbased 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 ofdecreased 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 workingcapital increases in an
inflationary environment.
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Item Effects of Inflation
Rate of Return
and NPW
Unless revenues are
sufficiently increased to keeppace 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 0.2
Contract $ 23500 Market interest rate 0.26
Investment 15000 Income tax rate 0.4
Income Statement 0 1 2 3 4 5
Inflation rate
Revenues $23,500 $23,500 $23,500 $23,500 $23,500
Expenses:
O&M 8% $14,040 $15,163 $16,376 $17,686 $19,101
Depreciation $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 $1,414
Net Income $3,876 $2,122 $2,546 $2,451 $2,121
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Cash Flow Statement 0 1 2 3 4 5
Inflation rate
Operating Activities:
Net Income $2,122 $2,546 $2,451 $2,121
Depreciation $3,876 $4,800 $2,880 $1,728 $864
Investment Activities: $3,000
Investment $15,000
Salvage 5% $1,276
Gains Tax $181
Net cash flow (actual$) $15,000 $6,876 $6,922 $5,426 $4,179 $4,442
Net 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 $1,399
Net 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
01
2
3
4
-$30,00013,570
15,860
13,358
13,626
-$30,00012,336
13,108
10,036
9,307
IRR 31.34% 19.40%i
i
f'
.
.
.40%
_
1
1 1
1 0 3134
1 0 101
19Not correct IRR
f_
10%
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Summary
The Consumer Price Index (CPI) is a statisticalmeasure of change, over time, of the prices ofgoods and services in major expenditure groupssuch as food, housing, apparel, transportation, and
medical caretypically purchased by urbanconsumers.
Inflation is the term used to describe a decline inpurchasing 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 averageinflation rate based on the CPI. An annual general
inflation rate ( ) can be calculated using thefollowing equation:
Specific, individual commodities do not alwaysreflect the general inflation rate in their pricechanges. We can calculate an average inflationrate for a specific commodity (j) if we have anindex (that is, a record of historical costs) for thatcommodity.
f
fCPI CPI
CPIn
n n
n
1
1
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Economics
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Project cash flows may be stated in one of twoforms
Actual dollars (An): Dollars that reflect theinflation or deflation rate.
Constant dollars (An): Year 0 dollars
Interest rates for project evaluation may be statedin one of two forms:
Market interest rate (i): A rate which combinesthe effects of interest and inflation; used with
actual dollar analysisInflation-free interest rate (i): A rate fromwhich 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 methodtwo steps:
1. Convert actual dollars by deflating with thegeneral inflation rate of
2. Calculate the PW of constant dollars bydiscounting at i
Adjusted-discount methodone step
1. Compute the market interest rate.
2. Use the market interest rate directly to find thepresent value.
f