EQUIVALENCE CALCULATIONS
UNDER INFLATION
CHAPTER 4
Inflation and Economic Analysis
 What is inflation?
 How do we measure inflation?
 How do we incorporate (include) the effect of
inflation in equivalence calculation?
What is inflation?
 Inflation is the rate of increase in the level of prices for goods and
services, which affects the purchasing value of money.
 A loss in the purchasing power of money over time.
 The same dollar amount buys less of an item over time.
 Value of Money
Earning Power How much you currently make at your place of
employment plays a major part in your earning power.
Purchasing power The value of a currency expressed in terms of
the amount of goods or services that one unit of money can buy.
 Purchasing Power
Decrease in purchasing power (inflation)
Increase in Purchasing Power (deflation)
Purchasing Power
$100
$100
2000
2000
You could buy 50 Big Macs in
year 2000.
$2.00 / unit
2010
You can only buy 40 Big Macs in
year 2010.
25%
Price
change
due to
inflation
$2.50 / unit
Deflation
$100
-2
-1
$100
0
1
-2
You could purchase 63.69 gallons
of unleaded gas a year ago.
$1.57 / gallon
20.38%
-1
0
1
You can now purchase 80 gallons
of unleaded gas.
$1.25 / gallon
Price change due to deflation
Inflation Terminology - I

Producer Price Index (PPI): a statistical measure of wholesale
industrial price change, compiled monthly by the BLS, to
evaluate wholesale price levels in the economy.

Consumer Price Index (CPI): a statistical measure of change,
over time, of the prices of goods and services in major
expenditure groups – such as food and beverages, housing,
apparel, transportation, entertainment, medical care and
other goods and services – typically purchased by city
consumers.
Inflation Terminology - I

Average Inflation Rate ( f ): a single rate that accounts
for the effect of unstable 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.
CONSUMER PRICE INDEX
Original
Measure
Revised
Measure
Figure 4-1 Measuring inflation based on CPI
Consumer Price Indexes for 1963 and 2004
91.7
100
1963
1967
561.23
2004
Average inflation rate = 4.52%
561.23  91.70(1  f ) 41
f 
41
6.1203  1
 4.5176%
Measuring Inflation
Consumer Price Index (CPI) is a measure of the average change
over time in the price paid by city family for a set of consumer
goods and services. 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 (1982-84)
$100
2009
$179.9
CPI for 2009 = 179.9 %
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
$112.32
Step 2: Find the average inflation rate by solving the
following equivalence equation.
2
0
$100 ( 1+ f ) = $112.32
f = 5.98%
1
2
$100
Example 4.1
Calculating Average Inflation Rate
Item
(CPI) Base Period: 1982 - 84 = 100
Consumer price index (CPI)
2006 Price
2000 Price
F
P
Average Inflation
Rate (%)
$200.43
$171.20
2.66
0.39
0.33
2.82
Homeowners Insurance
617.00
500.00
3.57
Private college tuition and fees
22,218
15,518
6.16
Gasoline
2.56
1.56
8.61
Haircut
15.00
10.50
6.12
22,900
21,000
1.45
7.08
3.17
14.33
171.19
132.44
4.37
2,351.00
1,656.00
6.01
Postage
Car (Toyota Camry)
Natural gas (MBTU)
Baseball tickets
Health care (per year)
General Inflation Rate ( f )
This average inflation rate is calculated on the basis of CPI
for all items in the market basket. The market interest rate
is expected to respond to this general inflation rate. In
terms of CPI, we define the general inflation rate as
_
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.
13
Example: 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
$629,500 1/ 3
f (
)
 1  0.0769  7.69%
$504,000
ACTUAL VERSUS CONSTANT DOLLARS

Due to inflation, the purchasing power of the dollar changes
over time.

To compare dollar values of different purchasing power from
one period to another, they need to be converted to dollar
values of common purchasing power – conversion from
actual to constant dollars or from constant to actual dollars.

To introduce the effect of inflation into our economic
analysis, we need to define two inflation – related terms.
Inflation Terminology – II
The effect of inflation into economic analysis
Actual (current) 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. Usually, these
amounts are determined by applying an inflation rate to
base-year dollar estimates.
Constant (real) Dollars (A'n):
Represents constant purchasing power independent of
the passage of time. We will assume that the base year is
always time zero unless we specify otherwise.
16
Conversion from
Constant to Actual Dollars
Conversion from
Actual to Constant Dollars
_
A' n  An (1  f )
$1,000
n
_
 An ( P / F, f , n)
n3
$1,260
_
f  8%
3
3
Constant
Dollars
-3
$1,260 (1 + 0.08)
= $1,000
Actual
Dollars
Examples 4.3 & 4.4
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
Inflation Terminology - III

Inflation-free Interest Rate (
i' ): an estimate of the true
earning power of money when the inflation effects have
been removed.

This rate is known as real interest rate, and it can be
computed if the market interest rate and the inflation
rate are known.
21
Inflation Terminology - III

Market interest rate (
i ) known as the nominal interest
rate, which takes into account the combined effects of the
earning value of capital (earning power) and any anticipated
inflation or deflation (purchasing power).

Most firms use a market interest rate (also known as
inflation-adjusted required rate of return) in evaluating
their investment projects.
22
Inflation and Cash Flow Analysis
Constant Dollar analysis (A' n) (inflation free interest rate i' )
 All cash flow elements are given in constant dollars
 Compute the equivalent present worth of constant dollars
(A' n) in year n.
 In the absence of inflationary effect, we use
i' to account
the earning power of the money.
23
Inflation and Cash Flow Analysis
Actual Dollar Analysis (An) ( market interest rate i )
 All the cash flow elements are estimated in actual dollars.
 To find the equivalent present worth of this actual dollar
amount (An ) in year n.
 We use two steps to convert actual dollars into equivalent
present worth dollars.
24
Actual Dollars (An ) Analysis
Method 1: Deflation Method
Convert actual dollars into equivalent constant dollars by
discounting with the general inflation rate, a step that
removes the inflationary effect. Now we can use i' to find
the equivalent present worth.
Method 2: Adjusted-discount Method
Combine two steps into one step, which performs deflation
and discounting in one step.
Example:
Equivalence Calculation
when cash flows are
in actual dollars:
Deflation Method
n
Net Cash Flows
in Actual Dollars
0
-$75,000
1
32,000
2
35,700
3
32,800
4
29,000
5
58,000
Applied instrumentation, a small manufacturer of custom electronics to make
investment to produce sensors and control systems that have been requested by a fruit
drying company. The work would be done under a contract that would terminate in five
years. The project is expected to generate the above cash flows in actual dollars:
a) What are the equivalent constant dollars if the general inflation rate is 5% per year.
b) Compute the present worth these cash flows in constant dollars at i' = 10%
Solution: Step 1
Convert Actual dollars to Constant dollars
n
Cash Flows in
Actual Dollars
Multiplied by
Deflation
Factor 5%
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
Step 2
Convert Constant dollars to Equivalent Present Worth
n
Cash Flows in Constant
Dollars
Multiplied by
Discounting Factor
i' = 10%
Equivalent
Present Worth
0
-$75,000
1
-$75,000
1
30,476
(1+0.10)-1
27,706
2
32,381
(1+0.10)-2
26,761
3
28,334
(1+0.10)-3
21,288
4
23,858
(1+0.10)-4
16,295
5
45,445
(1+0.10)-5
28,218
$45,268
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
-$75,000
$27,706 $26,761 $21,288 $16,295 $28,218
$45,268
Adjusted-Discount Method
Perform Deflation and Discounting in One Step
Pn 
An
(1  i ) n
An
(1  f ) n
Pn 
(1  i ' ) n
Step 2
Step 1
An
 (1  f ) (1  i ') 


n
n
(1  i )  (1  f )(1  i ')
 1  i ' f  i ' f
An

(1  f ) n (1  i ' ) n


An
(1  i ) n
i  i ' f  i ' f

i  i  f  i f
An
(1  f ) (1  i ') 


n

n
_
_
i  f  i(1  f )

i 
i f

1 f
Previous Example
i  i'  f  i' f
Adjusted - Discounted  0.10  0.05  (0.10)(0.05)
Method
 15.5%
n
Cash Flows in Actual
Dollars
Multiplied
By (15.5%)
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
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
$28,217
-$75,000
$27,706
$26,761 $21,288
$16,296
$45,268
MIXED DOLLAR ANALYSIS

Consider situation that some cash flow elements are expressed in
constant (or today’s) dollars.

In this situation, we convert all cash flow elements into same dollar
units (either constant or actual).

If the cash flow elements are all converted into actual dollars, we can
use the market interest rate i in calculating the equivalence value.

If the cash flow elements are all converted into constant dollars, we
can use the inflation-free interest rate i'
Example 4.7 illustrates this situation.
Example 4.7 Equivalence Calculation
with Composite Cash Flow Elements
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
Required Quarterly Contributions to College Funds
HOMEWORK PROBLEMS
DUE DATE IS
Monday, April 18th, 2011 class time
NO LATE SUBMISSION WILL BE ACCEPTED
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12,
14,
16,
20,