Inflation
A retired couple has just purchased
an annuity that pays $2,000 each month. With today's prices,
the annuity, along with other financial resources, provides a
comfortable retirement income. The policy will pay the same amount
every month until both husband and wife die. An annuity seems
like a good idea because it is safe, but the couple worries about
inflation. Say they live for another 20 years. The payment
will still be $2,000 a month, but how much will that money buy
then? We answer this question near the end of this lesson.
Inflation is the gradual increase of prices over
a period of time. In the United States, prices as measured
by the Consumer Price Index (CPI) have risen in
every year since 1956. The link below opens a chart showing
the CPI from 1967 to 2005. An index value shows the level of
prices relative to the base year of 1983 where the index has
the value of 100. To illustrate the affect of inflation, a person
who went to work in 1967 with an annual salary of $12,000 would
have to earn almost $70,000 in 2005 to have the same buying power. During that time the general level of prices has
risen by a factor of 5.78.
The following links have charts and data on inflation
in the United States.


Consumer
Price Index Data



The inflation rate in the United States
has been relatively low since 1967 with the maximum yeartoyear
rate of increase somewhat below 14%. The rate in 2005 was about
3.36%. Other countries have seen higher inflation. The following
gives cases of hyperinflation.
1922 Germany 5000%
1985 Bolivia >10,000%
1989 Argentina 3100%
1990 Peru 7500%
1993 Brazil 2100%
1993 Ukraine 5000%
Because a rate of 100% means that prices double in one year,
the 5000% rate in Germany means that prices increased by a factor
of 51 in one year. In Germany during hyperinflation, people would
rush out to spend the day's wages as fast as possible, knowing
that only a few hours' inflation would deprive those wages
of most of its purchasing power.
The following web link has
charts and data on inflation in the US.


U.S.
Department of Labor ~ Consumer Price Indexes 


Inflation makes it difficult to make financial
decisions or even talk about relative prices at different
points in time. This lesson provides quantitative tools that
help with both of these problems.


Goals 



Use the CPI to translate the
general price levels between two points in time.

Given the prices of a commodity
at two points in time, compute the average annual
escalation rate for the commodity. Use the
geometric mean for the calculation.

Express a cash flow with real
or actual dollars. Translate between the two.

Given either the real or
market MARR value, compute the other.

Do economic analyses by hand for simple projects.

Use the Economics addin to
do economic analyses for complex projects and
for comparisons.




Text 



Causes and
Effects 

Click the icon to view an
introduction to the causes and effects of inflation.


Expressing Cash
Flows 

Inflation makes it difficult to
compare prices at different times. The cost of gasoline, tuition,
medical expenses and other things a person or corporation might
buy, typically increases with time in terms of dollars. Everyone
knows, however, that a dollar today does not have the same value
as a dollar in times past. Saying that the cost of something
is greater than at some previous time may be true, but it is
meaningless unless the effect of inflation is considered. This
is partially accomplished by expressing costs in real dollars.
The money that we earn or spend in everyday commerce
is measured in actual dollars.
These dollars change with time with respect to the amounts that
can be purchased with the same number of dollars because of inflation.
When we express a price in terms of the dollars of a specified
base year, the price is expressed in real dollars with
respect to the base year. We translate between real and actual
dollars using the general rate of inflation, usually measured
by the CPI. The translation is not perfect because prices change
because of other factors besides inflation, but the comparisons
are more meaningful when they are done in real rather than actual
dollars. The QuickTime lecture tries to explain this.




The formulas below show how to translate between
real and actual dollars for individual values and cash flows.
The formulas assume that the base year for the real dollars is
the present. Thus, we say that the real values are expressed in
year0 dollars. We use f as
the general inflation rate. Note that the formulas resemble the
present worth and future worth equivalence factors. When used here
we are not moving money around, but changing the valuation of
money.
It should be emphasized that only actual dollars are used in
economic transactions. We carry actual dollars in our pockets,
receive them as salary, and use them to pay bills. All the prices
we see at stores and in advertisements are expressed in actual
dollars. A real dollar
is not real in the sense that it exists. It is a numerical measure
that attempts to remove the inflationary effects from an estimate
of a cost or revenue. 

MARR 

Our economic evaluations in earlier
lessons have centered upon the MARR, or minimum acceptable rate
of return. When inflation is present, cash flows can be expressed
in real or actual dollars. There are two different MARR values
that are appropriate to compute the present worth of the two
kinds of cash flows. The real MARR
is used for a cash flow expressed in real dollars. The market MARR
is used for cash flows expressed in actual dollars.
One might call the latter the actual MARR, but the term market is
appropriate since we observe market interest rates in
everyday commerce.
Again there are formulas for translating from one kind of MARR
to the other. These are given below.


Estimating
Future Cash Flows 

Inflation
introduces some complexities for estimating the cash flow for
a project. We recognize three kinds of estimates. The cash flow
is first estimated using the prices at the time of the estimation;
we call these today's prices. The cash flow may consist of several
components. For instance, it might include revenue
as well as the costs of labor, capital expenses and various kinds
of materials. The cash flows associated with different
components may change at different rates. In the following we
call the inflation rate associated with a specific component
the escalation
rate for
that component.
We estimate the cost or revenue for a component
using today's prices. These are the prices we pay today and might
be found in current catalogs. For an analysis, we must project
these prices into the future. We do that by escalating the estimate.
The escalated values are in actual dollars.
When there are several components to the cash flow,
we sum over the components to find the actual dollar cash flow
in each period.
These cash flow values may in turn be expressed
in real dollars by deflating the individual values by the general
inflation rate.
Formulas for estimating escalation rates are in
the linked document.


Economic Analysis 

The economic analysis
of a project requires either the actual or the real cash flow.
There are two methods for finding the NPW, and they both lead
to the same value. Either find the NPW of the actualdollar cash
flow with the market MARR, or find the NPW of the realdollar cash
flow with the real MARR. The QuickTime lecture below describes
several steps for economic analyses with inflation. For simplicity
the lecture only uses one cash flow component and one escalation
rate.


Economic
Analysis with Inflation 


When
there are several components, the relevant formulas are summarized on the page in the next link.


Economic
Analysis Formulas



The following general rule summarizes the important
result of this section.

When the cash flow is in actual dollars
use the market MARR to find the NPW. When the cash flow is
in real dollars use the real MARR to find the NPW. The NPW
values computed with the two methods are the same.


In many cases it is difficult to estimate escalation
rates so analysts may assume that the components of the cash flow
escalate at the same rate as general inflation. When this is
true, the analysis is very much simplified by the following rule.

When
the escalation rates of all cash flow components are
the same as the general inflation rate, the estimated
cash flow is the same as the real cash flow. Use the
real MARR to find the NPW.


The NAW is a uniform series expressed in real or
actual dollars. The NAW is computed by multiplying the NPW by
the A/P factor. If the factor uses the real MARR as the interest
rate, the result is the realdollar NAW.
If the factor uses the market MARR as the interest rate, the
result is the actualdollar NAW.
When comparing alternative solutions, it is better to use the realdollar
NAW. When the annual worth represents a payment in actual
dollars, such as payments on a loan, it is better to use the actualdollar NAW.
The IRR is the interest rate that makes the NPW
equal to zero. If the realdollar cash flow is used for the evaluation,
the result is the real IRR. If the actualdollar cash
flow is used for the evaluation, the result is the actual or market IRR.
When used for decision making, comparing
the real IRR
to the real MARR, leads to the same results as comparing
the market IRR
to the market MARR. 

The
Economics Addin 


The Economics
addin allows individual escalation rates for
each component. It computes the NPW, both real and actual
NAW and IRR values. It also computes actual and real
cash flows. 

The Economics addin is easy
to use and it should be handy for homework and computer based
exams. For a review of the addin basics without audio, click
on the QuickTime icon.


Economics
addin with Inflation 


Click the Excel icon for more extensive instructions at
the ORMM site.
To illustrate the use of the addin consider the
following example. A businessman is considering the purchase
of an asset that has an initial cost of $2,000. The asset promises
an annual return of $600. Its operating cost is $100 the first
year, $150 the second, and increases by $50 in each subsequent
year. The salvage value for the asset in 10 years is $400. These
values are estimated in today's prices. The cash flow diagram is below.
To analyze the project with the Economics addin,
check the Inflation box in the Add Project dialog.
Click the browser icon below to open a window with the Excel
worksheet created by the dialog. The figure shows the project
after we have added data. The data describes our assumptions
about inflation and escalation rates. We are assuming a general
inflation rate of 6%. Escalation rates for the components of
the investment and cash flow items are entered as differences
from the general inflation rate, or as incremental
inflation rates. Here we see that the initial cost
line has an incremental inflation rate of 4%. This means that
the initial cost is escalating at a rate of 6% + 4% = 10%. Because
the initial cost is expended at time 0, inflation has no effect
on this value. The salvage value will, however, escalate at the
10% rate. Instead of being $400, as estimated in today's prices,
the salvage will increase in actual dollars at a rate of 10%
per year. The factor value for the row reflects both the 20%
salvage estimate and the 10% price escalation.




For our example, we assume that the returns for
the project escalate at a rate of 7%, that is, 1% greater than
general inflation. Since this is a uniform series when estimated
in today's prices, the return measured in actual dollars will
increase with time. The return in one year when measured in
actual dollars is equal to (1.07) times the value in the previous
year. The uniform series representing operating cost is growing
at a 4% rate, that is 2% less than general inflation. We assume
that the gradient component is constant in actual dollars, so
the escalation rate is 0 and the incremental inflation rate is
6%. The factors computed by the addin and shown in the factor column
of the form adjust the cash flows for the inflationary effects.
The NPW values are computed in the rightmost column.
The results of the analysis are computed at the
upper right of the form. With the assumed parameters, the project
has the NPW of $740.94, shown in cell L30. The positive value
indicates that the project returns more than the MARR. There
are two kinds of Uniform Worth. The first, in cell L31, is the
NAW computed using the real MARR. This value is the uniform equivalent
expressed in real dollars. The second, in cell L32, is the NAW
computed using the market MARR. This value is the uniform equivalent
expressed in actual dollars. Cell L33 holds the NPW for the study
period. For the example, the study period is the same as the life,
so this value is the same as L30. Cell L34 holds the IRR of the
project computed using the real cash flows, while L35 is the
IRR computed using the actual cash flows. Both exceed their respective
MARR values.
Although the table above shows six measures for
the worth of the project, they all lead to the same decision. They
all indicate that the project is acceptable. For simple investments,
the measures always give the same results. For nonsimple investments
where there are multiple values for the IRR, use of the RIC rather
that the IRR resolves the ambiguity. We provide all these measures
because they are useful in different contexts. Most decision
makers probably prefer the Actual IRR as a measure because they
are familiar with rates of return and most rates are expressed
as market rates.
The Show Cash Flow command provides both
actual and real cash flows. The payback period is based on the
cumulative real cash flow.


Comparisons 

To compare two or more alternatives with the
same lives, compare their NPW values as described in an earlier
lesson. The only complication introduced by inflation is in the
computation of the individual NPW values.
When comparing alternatives by the NAW method,
only the real NAW is relevant.

When
comparing alternatives with the NAW method, it is most
reasonable to compare their real NAW values.


To compare mutually exclusive alternatives with
the ROR method, use incremental analysis.
The incremental method can be performed with either real or actual
cash flows. With real cash flows the decision to accept or reject
uses the real MARR.
With actual cash flows, the decision to accept or reject uses
the market MARR.

When
comparing alternatives with the ROR method, the IRR
values computed for incremental investments depend
on whether the cash flows are expressed in real or
actual dollars.


The addin has a Compare Projects command that
explicitly compares two or more projects when inflation is present.
Click the browser icon below to open a window showing the two
alternatives used for an example. They are similar to the example
described earlier, but the second has greater first cost and
no salvage value. The assumed escalation rates are also different.




Click the browser icon below to open a window showing the Dynamic comparison
created by the Compare Projects command. The comparison
form allows the user to adjust the real MARR used for
the comparison. It is found in cell M4 for this example. This
cell is linked by formula to the real MARR values of the two
alternatives. We have used Infl_B as the challenger and Infl_A
as the defender, because Infl_B has the greater initial investment.
The extra investment yields a real return of 15.4% and it is
certainly justified when the real MARR is 10%. The cash flow
of the comparison shows the difference between the two alternatives.
It is more difficult to compare alternatives with
different lives, because the least common multiple of the lives
involves one or more likeforlike replacements. The availability
of similar replacements is questionable when inflation is present.
In this course we will not tackle comparisons with different
lives when inflation is included in the problem statement. 

We started this lecture with the
question:
An annuity payment
is $2,000 a month. How much will the payment
be worth in 20 years?

To compute the result, assume an inflation rate
of 3% a year, a number that reflects recent rates.
You should answer:
In real dollars the payment
is worth:

In 20 years the purchasing power of the payment is reduced
to almost half of its current value.


Summary 



Problems 


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