Chapter 4

Equivalence Calculations under

Inflation

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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, housing, apparel,
transportation, and medical care—typically
purchased by urban consumers.
The CPI compares the cost of a sample “market
basket” of goods and services in a specific period
with the cost of the same market basket in an
earlier reference period.
This reference period is designated as the base
period.

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• Inflation : a decline in purchasing power
evidenced in an economic environment of rising
prices.

• Deflation : an increase in purchasing power

evidenced by falling prices.

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• The general inflation rate is an average
inflation rate based on the CPI.

_
CPI n = CPI 0 (1 + f ) n ,
_ 1/ n
CPI n
f = −1
CPI 0
_
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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•

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•

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•

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• Adjusted‐discount method(use the market
interest rate, j)

• where

• Alternatively, just use the market interest rate to

find the net present worth.

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 EXAMPLE 4.1 Calculating an Average
Inflation Rate

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 EXAMPLE 4.1 (continued) Calculating an
Average Inflation Rate

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 EXAMPLE 4.2 Developing Specific Inflation
Rate for Baseball Tickets

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 EXAMPLE 4.3 Conversion from Constant to
Actual Dollars

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 EXAMPLE 4.4 Comparing Prize Monies
Earned at Different Points in Time

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 EXAMPLE 4.4 (continued) Comparing
Prize Monies Earned at Different Points in
Time

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 EXAMPLE 4.4 (continued) Comparing
Prize Monies Earned at Different Points in
Time

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 EXAMPLE 4.5 (continued) How Much
Does It Cost to Go to College?

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 EXAMPLE 4.5 (continued) How Much
Does It Cost to Go to College?

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 EXAMPLE 4.5 (continued) How Much
Does It Cost to Go to College?

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 EXAMPLE 4.5 (continued) How Much
Does It Cost to Go to College?

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 EXAMPLE 4.6 Equivalence Calculations
under Inflation—Constant- and Actual-Dollar
Analysis

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 Method One : Constant Dollar Analysis

EXAMPLE 4.6 (continued) Equivalence

Calculations under Inflation—Constant- and
Actual-Dollar Analysis

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 EXAMPLE 4.6 (continued) Equivalence
Calculations under Inflation—Constant- and
Actual-Dollar Analysis

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 EXAMPLE 4.6 (continued) Equivalence
Calculations under Inflation—Constant- and
Actual-Dollar Analysis

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 Method two : Actual Dollar Analysis

EXAMPLE 4.6 (continued) Equivalence

Calculations under Inflation—Constant- and
Actual-Dollar Analysis

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 EXAMPLE 4.6 (continued) Equivalence
Calculations under Inflation—Constant- and
Actual-Dollar Analysis

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 EXAMPLE 4.7 Equivalence Calculations
with Composite Cash Flow Elements

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 EXAMPLE 4.7 (continued) Equivalence
Calculations with Composite Cash Flow
Elements

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 EXAMPLE 4.7 (continued) Equivalence
Calculations with Composite Cash Flow
Elements

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 EXAMPLE 4.7 (continued) Equivalence
Calculations with Composite Cash Flow
Elements

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 EXAMPLE 4.7 (continued) Equivalence
Calculations with Composite Cash Flow
Elements

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Figure 4.6 Establishing a college fund under an inflationary economy for a five‐year‐old child by making 48 quarterly
deposits

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 TABLE 4.5 Required Quarterly Savings at
Varying Interest Rates and Inflation Rates

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:Constant dollar and actual dollars

Convert from actual dollar to Constant dollar: discount using inflation rate, f.

Convert from constant dollars to actual dollars: compound using inflation rate,
f.

Use market interest rate ,i, for equivalence calculations in actual dollar
cashflows

Use inflation free interest rate, f’, for equivalence calculations in actual dollar
cashflows

//meet.google.com/jnm-imvz-gco

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4.3 The following data indicate the price indices of lumber (price index
for the base period (1982–1984 = 100) during the last 10 years

(a) If the base period (price index = 100) is reset to the year 2001,
compute the inflation rate for lumber between 2001 and 2009.
(b) If the past trend is expected to continue, how would you estimate the
price of lumber in 2014?

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4.15 A series of four annual constant-dollar payments beginning with
$50,000 at the end of the first year is growing at the rate of 8% per year.
Assume that the base year is the current year ( n = 0). If the market
interest rate is 16% per year and the general inflation rate ( f ) is 10% per
year, find the present worth of this series of payments, based on
(a) constant-dollar analysis.
(b) actual-dollar analysis.

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4.24 A man is planning to retire in 20 years. He can deposit money for
his retirement at 8% compounded monthly. It is estimated that the future
general inflation ( f ) rate will be 3% compounded annually. What deposit
must be made each month until the man retires so that he can make
annual withdrawals of $20,000, in terms of today’s dollars, over the 15
years following his retirement? (Assume that his first withdrawal occurs
at the end of the first six months after his retirement.)

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4.26 A couple wants to save for their daughter’s college expense. The
daughter will enter college eight years from now, and she will need
$50,000, $51,000, $52,000 and $53,000 in actual dollars for four school
years. Assume that these college payments will be made at the beginning
of each school year. The future general inflation rate is estimated to be 7%
per year, and the annual inflation-free interest
rate is 6%.
(a) What is the market interest rate to use in the analysis?
(b) What is the equal amount, in actual dollars, the couple must save each
year until their daughter goes to college?

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4.27 A father wants to save for his eight‐year‐old son’s college expenses. The son
will enter college 10 years from now. An annual amount of $40,000 in constant
dollars will be required to support the son’s college expenses for four years.
Assume that these college payments will be made at the beginning of each school
year. The future general inflation rate is estimated to be 6% per year, and the
market interest rate on the savings account will average 8% compounded annually.
(a) What is the amount of the son’s freshman‐year expense in terms of actual
dollars?
(b) What is the equivalent single‐sum amount at the present time for these college
expenses?
(c) What is the equal amount, in actual dollars, the father must save each year until
his son goes to college?

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