Ch 4: Equivalence calculations under inflation
Inflation: decrease in purchasing power
– Measure of inflation
– Actual versus constant dollars
– Equivalence calculations under inflation
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Purchasing power: Big Mac
$100
$100
1990
1990
You could buy 50 Big
Macs in year 1990.
$2.00 / unit
2003
You can only buy 40 Big
Macs in year 2003.
25%
$2.50 / unit
price change
due to inflation
The $100 in year 2003 has only $80
worth purchasing power of 1990
Purchasing power: gasoline
$100
-2
-1
0
$100
1
-2
You could purchase 33 gal of
unleaded gas 5 months ago
$3.05 / gallon
Price change
due to deflation
-15.7%
-1
0
1
You can now purchase 40
gal of unleaded gas.
$2.50 / gallon
Purchasing power: gasoline
$100
-2
-1
$100
0
1
-2
But 2 yr ago you could purchase
48 gal of unleaded gas
$2.10 / gallon
Price change
due to inflation
-1
0
1
You can now purchase 40
gal of unleaded gas.
+19.0%
$2.50 / gallon
Purchasing power: gasoline
In inflation
adjusted dollars
the price of gas
has declined
since 1918
Inflation vocabulary
Producer Price Index: a statistical measure of industrial price
change, compiled monthly by the BLS, U.S. Dept of Labor
Consumer Price Index: a statistical measure of change, over
time, of the prices of goods & services in major
expenditure groups – such as food, housing, apparel,
transportation & medical care – typically purchased by
urban consumers
Average inflation rate: 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
Measuring inflation
Consumer Price Index (CPI)
The CPI compares the cost of a sample “market
basket” of goods & services in a specific period
relative to the cost of the same “market basket” in
an earlier reference period, or “base period”.
base period
(1982-84)
$100
Dec 2005
$198.60
CPI for Dec 2005 = 198.6
Selected price indexes
Average inflation rate (f)
Example
Base price = $100 (year 0)
Inflation rate (yr 1) = 4%
Inflation rate (yr 2) = 8%
Average inflation rate over 2 years?
1. Find the actual inflated price at the end of year 2
$100 ( 1 + 0.04) ( 1 + 0.08) = $112.32
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
Example 4.1 Average inflation rate
Item
Consumer price index (CPI)
2003 Price
2000 Price
Average Inflation
Rate (%)
$184.20
$171.20
2.47
0.37
0.33
6.44
Homeowners insurance
603.00
500.00
7.56
Private college tuition and fees
18,273
15,518
5.60
1.65
1.56
1.89
12.00
10.50
4.55
Car (Toyota Camry)
22,000
21,000
1.56
Natural gas (MBTU)
5.67
3.17
21.38
148.66
132.44
3.92
47.97
36.97
9.07
Postage
Gasoline
Haircut
Baseball tickets
Cable TV
General inflation rate,⎯ f
Average inflation rate based on the CPI
CPIn = CPI0(1 +⎯ f)n
⎯f=
(−−)
CPIn
1/n
CPI0
⎯f = general inflation rate
CPIn = CPI at the end period, n
CPI0 = CPI for the base period
Example 4.2: Yearly & average inflation rates
Year
Cost
0
$504,000
1
538,000
2
577,000
3
629,500
What are the annual inflation rates &
the average inflation rate over 3 years?
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
Inflation vocabulary
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: Estimates of future cash flows for year
n in constant purchasing power, independent of the
passage of time (or base period).
Conversion from constant to actual dollars
_
_
An = A' n (1 + f ) ↔ A' n ( F / P, f , n)
$1,000
n
n=3
⎯ f = 8%
3
Constant
dollars
$1,000 (1 + 0.08)3 = $1,260
$1,260
3
Actual
dollars
Example 4.3 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
$100,000
$110,000
$120,000 $130,000
$120,000
Constant dollars
0
$121,275
5
$120,000(1+0.05)5
4
$130,000(1+0.05)4
3
$120,000(1+0.05)3
2
$110,000(1+0.05)2
$250,000(1+0.05)0
$250,00
0
$100,000(1+0.05)
1
$138,915 $158,016
$153,154
$105,000
Actual dollars
0
1
$250,000
2
3
4
5
Conversion from actual to constant dollars
_
−n
_
A' n = An (1 + f ) ↔ An ( P / F, f , n)
$1,000
n=3
⎯ f = 8%
3
Constant
dollars
$1,260 (1 + 0.08)-3 = $1,000
$1,260
3
Actual
dollars
Example 4.4 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
Practice problem - How to compare the
winning prizes at two different points in time
Jack Nicklaus won his
first Master Tournament
in 1963. The prize was
$20,000.
Phil Mickelson won his
first Master Tournament
in 2004. The prize
amount was $1.17M.
Consumer Price Index
91.7
100
561.23
2004
1963
1967
What is the worth of $1.17M in terms of
purchasing power in 1963?
91.7
561.23
100
2004
1963
1967
Average inflation rate = 4.525%
$1.17M in 2004 would have a purchasing power of
$190,616 in 1963
At what inflation-free interest rate would Jack need to invest his
prize money in 1963 at for it to grow to match Phil’s 2004 prize?
$20,000
0
1963
$190,616
P = $190,616(P / F,5.65%,41)
= $20,000
0
1963
41
2004