Transcript Chapter 13 Inflation and Its Impact on Project Cash Flows

Chapter 13
Inflation 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 Power
Investment Opportunity
• Purchasing Power
Decrease in purchasing power (inflation)
Increase in purchasing Power (deflation)
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Purchasing Power
$100
$100
1990
1990
You could buy 50 Big Macs
in year 1990.
$2.00 / unit
2001
You can only buy 40 Big
Macs in year 2001.
25%
Price change
due to
inflation
$2.50 / unit
The $100 in year 2001 has only $80
worth purchasing power of 1990
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$100
-2
-1
$100
0
1
-2
0
1
You can now purchase
80 gallons of unleaded
gas.
You could purchase
63.69 gallons of
unleaded gasoline
a year ago.
$1.57 / gallon
-1
20.38%
$1.25 / gallon
Price change due to
deflation
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Price Increase Due to Inflation
Item
1967 Price
Consumer price index (CPI)
2000 Price
% Increase
100
512.9
413
$114.31
$943.97
726
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
294.00
3,960.00
1,247
Monthly housing expense
Monthly automobile expense
Annual public college tuition
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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 (f):
the average inflation rate
calculated based on the CPI for all items in the market basket.
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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 Indexes
Year
New CPI
Base Period 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.
0
2
$100 ( 1+ f) = $112.32
f = 5.98%
$112.32
1
2
$100
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Average Inflation Rate
1967 Price
Item
Consumer price index (CPI)
Monthly housing expense
Monthly automobile expense
2000 Price
100
Average Inflation
Rate
512.9
5.07%
$114.31 $943.97
6.61
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
294.00 3,960.00
8.19
Annual public college tuition
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General Inflation Rate (f)
Average inflation rate based on the CPI
_
CPI n  CPI 0 (1  f ) n ,
_
CPI n
f 
CPI 0
1/ n
1
_
where f  The genreal inflation rate,
CPI n  The consumer price index at the end period n,
CPI 0  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 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 (
$629,500 1/ 3
)  1  0.0769  7.69%
$504,000
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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
_
_
An  A' n (1  f )  A' n ( F / P, f , n)
n
n3
$1,000
$1,260
_
f  8%
3
3
Constant
Dollars
3
$1,000 (1 + 0.08)
= $1,260
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Actual
Dollars
15
Conversion from Constant to Actual
Dollars
Period
0
Net Cash Flow in
Constant $
-$250,000
Conversion Cash Flow in
Factor
Actual $
(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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$100,000
$110,000
$120,000 $130,000
$120,000
0
4
$121,275
$120,000(1+0.05)3
Years
(a) Constant dollars
5
$120,000(1+0.05)5
3
$130,000(1+0.05)4
2
$110,000(1+0.05)2
$250,000(1+0.05)0
$250,000
$100,000(1+0.05)
1
$138,915 $158,016
$153,154
$105,000
0
1
2
3
4
5
Years
(b) Actual dollars
$250,000
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Conversion
from Actual to Constant Dollars
_
n
_
A' n  An (1  f )  An ( P / F, f , n)
n3
$1,000
$1,260
_
f  8%
3
3
Constant
Dollars
-3
$1,260 (1 + 0.08)
= $1,000
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Actual
Dollars
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Conversion from Actual to Constant
Dollars
End of
period
0
Cash Flow
in Actual $
Conversion Cash Flow in
Loss in
at f = 5%
Constant $ Purchasing
Power
-$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
Market Interest rate (i)
Inflation-free interest rate (i’)
2.
Types of Cash Flow
In Constant Dollars
In Actual Dollars
3.
Types of Analysis Method
Constant Dollar Analysis
Actual Dollar Analysis
Deflation Method
Adjusted-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 inflationadjusted 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:
- Step 2:
Bring all cash flows to have
common purchasing power.
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
0
-$75,000
1
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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Cash Flows in
Constant Dollars
-$75.000
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Step 2:
Convert Constant dollars to Equivalent
Present Worth
n
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
16,295
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
n=0
Actual
Dollars
Constant
Dollars
Present
Worth
n=1
-$75,000
-$75,000
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
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Adjusted-Discount Method
Pn 
An
(1  f ) n
Pn 
(1  i ' ) n
An
An

n
(1  i )
(1  f ) n (1  i' )
Step 1
n
(1  i )  (1  i )(1  i' )
Step 2
An

(1  f ) n (1  i ') n

An
(1  i ) n
 1  i'  f  i' f
An
(1  f ) (1  i' )
n
n
i  i ' f  i ' f
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Adjusted-Discounted Method
i  i'  f  i' f
 0.10  0.05  ( 0.10 )( 0.05)
 15.5%
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
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Adjusted-discount method
$58,000
$35,700
$32,000
$32,800
$29,000
0
1
2
3
4
5
- $75,000
$27,706
$26,761
$21,288
$16,295
$28,218
$45,268
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Adjusted Discount Method: Example 13.7
Converting actual dollars to present worth dollars by
applying the market interest rate
n=0
Actual
Dollars
n=1
-$75,000
n=2
n=3
n=4
n=5
$32,000 $35,700 $32,800 $29,000 $58,000
i  i  f  if  15.5%
Present
Worth
$28,218
-$75,000
$27,706
$26,761 $21,288
$16,295
$45,268
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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.
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
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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
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Effects of Inflation on Project Cash
Flows
Item
Depreciation
expense
Effects of Inflation
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 and
always expressed in actual dollars
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Item
Salvage value
Effects of Inflation
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
Working capital
requirement
Effects of Inflation
Known as working capital
drain, the cost of working
capital increases in an
inflationary environment.
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Item
Rate of Return
and NPW
Effects of Inflation
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
Salvage
Contract $
Investment
Income Statement
13000
1000
23500
15000
0
1
General Inflation rate
Inflation-free interest
Market interest rate
Income tax rate
2
3
4
0.05
0.2
0.26
0.4
5
Inflation rate
Revenues
Expenses:
O&M
Depreciation
Taxable Income
Income taxes (40% )
Net Income
$23,500 $23,500 $23,500 $23,500 $23,500
8%
$14,040
$3,000
$6,460
$2,584
$3,876
$15,163
$4,800
$3,537
$1,415
$2,122
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$16,376
$2,880
$4,244
$1,697
$2,546
$17,686
$1,728
$4,086
$1,634
$2,451
$19,101
$864
$3,535
$1,414
$2,121
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Cash Flow Statement
0
Inflation rate
Operating Activities:
Net Income
Depreciation
Investment Activities:
Investment
$15,000
Salvage
5%
Gains Tax
Net cash flow (actual$)
$15,000
Net cash flow (constant $)
$15,000
Equ. Present worth
$15,000
Net present worth
$587
1
2
3
4
5
$3,876
$3,876
$3,000
$3,000
$2,122
$4,800
$2,546
$2,880
$2,451
$1,728
$2,121
$864
$4,179
$3,438
$1,658
$1,276
$181
$4,442
$3,480
$1,399
$6,876
$6,549
$5,457
$6,922
$6,279
$4,360
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$5,426
$4,687
$2,713
40
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 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
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%
Not correct IRR
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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 ( f ) can be calculated using the
following equation:
CPI n  CPI n1
fn
CPI n 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.
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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 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
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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
f
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.
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