Inflation and
Cost Indices
Introduction
• Simply put, inflation is an increase in the
amount of money necessary to obtain the
same amount of product or service before
the inflated price was present.
• Inflation occurs because the value of
currency has changed.
• As a result, it takes more money to buy
fewer goods.
General Price Inflation Rate
• It is a measure of the average change in
the purchasing power of a dollar during a
specified period of time.
• In engineering economic analysis, this rate
is projected for a future time interval and
usually is expressed as an effective
annual rate.
• It is symbolized by f.
Inflation Calculations
Future dollars Current dollars 1 f N
• Current dollars
– today’s dollars, constant-value dollars, real
dollars (R$)
• Future dollars
– Then-current dollars, nominal dollars, inflated
dollars, actual dollars (A$)
• It is always possible to state future inflated
amounts in terms of current dollars by
using the above equation.
Rates in Inflation Calculations
• Real or inflation-free interest rate (ir)
– This is the rate at which interest is earned when
the effects of changes in the value of currency
have been removed.
• Combined/actual/inflated/market rate (ic or im)
– This is the interest rate in the marketplace, the
rate we hear about and commonly quoted every
day.
– It is a combination of the real interest rate (ir) and
the inflation rate (f), and thus changes with
inflation.
Rates in Inflation Calculations
• Inflation rate (f)
– This is a measure of the rate of change in
the value of currency.
• MARR
– A company’s MARR, when adjusted for
inflation, is correctly referred to as an
inflation-adjusted MARR.
Inflation Calculations Example
Year PW at Year 0 Future Inflation Future
(i = 10%) Cost (R$) (4%) Cost (A$)
0 5,000 5,000 0 5,000
1 4,545 5,000 0.04(5,000) 5,000(1.04)
= 200 = 5,200
2 4,132 5,000 0.04(5,200) 5,000(1.04)2
= 208 = 5,408
3 3,757 5,000 0.04(5,408) 5,000(1.04)3
= 216 = 5,624
4 3,415 5,000 0.04(5,624) 5,000(1.04)4
= 225 = 5,849
Inflation Calculations
For our purposes, the following convention is
used:
A$ - this refers to “actual” dollars
- this amount accounts for both inflation
and interest
R$ - this refers to “real” dollars
- this amount accounts for interest only
- this is usually expressed in terms of
year 0 (EOY 0) “buying power”
Inflation Calculations
To adjust the interest formulas to account for
inflation:
1 1
PF
N
(1 i r ) (1 f ) N
1
F
(1 i r )N (1 f )N
1
F
(1 i r f i r f )N
1
F
(1 i c ) N
Inflation Calculations
The expression ic is the combined interest
rate and is defined as
ic ir f irf
Where ir = real interest rate
f = inflation rate
ic = combined interest rate
Inflation Calculations
Alternate formula:
(1 i c ) (1 i r )(1 f )
i c (1 i r )(1 f ) 1
Inflation Calculations
For example, at a real interest rate of 10% per
year and an inflation rate of 4% per year,
the combined interest rate is:
ic = 0.10 + 0.04 + 0.10(0.04)
= 0.144
Inflation Calculations
For example, at a real interest rate of 10% per
year and an inflation rate of 4% per year,
the combined interest rate is:
Alternate solution:
ic = (1 + ir)(1 + f) – 1
ic = (1 + 0.10)(1 + 0.04) – 1
= 0.144
Which i to use?
Interest Rate
(MARR)
Analysis in Real / ir
EOY 0 Amount
(R$)
Analysis in Actual ic
Amount (A$)
A more general inflation formula
k b
( A$)k (R$)(1 f )
where k = any time period (e.g. year)
b = base time period
A$ = actual dollars of any time period k
R$ = real dollars of constant purchasing
power as of any base time
period, b
A more general inflation formula
k b
( A$)k (R$)(1 f )
• The base or reference time period, b, is used
to define the constant purchasing power of
real dollars.
• In practice, the base time period is set to time
zero (i.e., the present).
• However, b can be any designated point in
time.
Remember…
Inflation is treated computationally like an
interest rate, but the inflation rate makes
the cost of the same product or service
increase over time due to the decreased
value of money.
Remember…
PW of a future amount with
inflation and interest both
considered:
N
P F(1 ic )
Remember…
Future amount to cover a current
amount with both inflation and
interest accounted for:
N
F P(1 ic )
Remember…
Future value of a present amount
with the same buying power (i.e.,
with interest, but no inflation):
N
F P(1 ir )
Remember…
Future amount to cover a current
amount with no interest (i.e., only
inflation is considered):
N
F P (1 f )
Remember…
At the base time period, the actual
amount is equivalent to the real
amount:
A$ = R$
That is, the purchasing power of an
actual dollar and a real dollar is the
same in the base time period.
Cost Indices
• A cost index is a ratio of the cost of something
today to its cost at some time in the past.
• One such index is the Consumer Price Index
(CPI), which shows the relationship between
present and past costs for many things that
“typical” consumers buy.
• In the Philippines, the National Statistical
Coordination Board publishes CPI data:
http://www.nscb.gov.ph/secstat/d_price.asp
http://www.nscb.gov.ph/ru5/technotes/cpi.html
Cost Indices
Many indices are periodically published, such
as:
– Engineering News Record construction
index
– Marshall and Stevens cost index
– Statistical Abstract of the United States
– Producer Prices and Price Indexes
– Consumer Price Index Detailed Report
Cost Index
The general equation for updating costs
through the use of any cost index over a
period from time t = 0 (base) to another time
is
Ct C0
It I0
where Ct = estimated cost at present time t
C0 = cost at previous time t0
It = index value at time t
I0 = index value at time 0
Cost-Capacity Equation
• A cost-capacity equation relates the cost of
a component, system, or plant to its
capacity.
• One common cost-capacity equation is:
x
Q2
C2 C1
Q
1
where C1 = cost at capacity Q1
C2 = cost at capacity Q2
x = empirical exponent
Differential Price Inflation
• The variation between the general price
inflation rate and the best estimate of
future price changes for specific goods
and services is called differential price
inflation (or deflation).
• It is caused by factors such as
technological improvements, regulatory
requirements, restriction in supply, an
increase in demand, etc.
Differential Price Inflation
Let ej’ = differential price inflation (or
deflation rate)
= the % of price change above or
below the general price
inflation rate, for good or
service j
ej = total price escalation (or de-
escalation) rate
= the total rate (%) of price
change during a time period, for
good or service j
Differential Price Inflation
'
1 e j (1 e j )(1 f )
' 1 ej
ej 1
1 f
Modeling Price Changes with
Geometric Gradients
(1 E)N
D N
1
(1 i )
PE
Ei
Modeling Price Changes with
Geometric Gradients
What “E” What interest
(geometric rate) to rate (or MARR)
use in the geometric to use?
gradient PE formula?
A$ ej ic
Analysis
R$ ej ’ ir
Analysis
Because of general price inflation
in the economy, the purchasing
power of the dollar shrinks with
the passage of time. If the
average general price inflation
rate is expected to be 8% per
year into the foreseeable future,
how many years will it take for the
dollar’s purchasing power to be
one-half of what it is now?
Annual expenses for two alternatives are as follows:
EOY Alternative A Alternative B
(Actual $) (Real $)
1 -$120,000 -$100,000
2 -$132,000 -$110,000
3 -$148,000 -$120,000
4 -$160,000 -$130,000
If the average general price inflation rate is 6% per
year and the real interest rate is 9% per year, which
alternative has the least negative equivalent worth in
the base time period (EOY 0)?
A recent engineering graduate has received the
annual salaries shown in the following table
over the past four years. During this time, the
CPI has performed as indicated. Determine
the engineer’s annual salaries in year 0
dollars using the CPI as the indicator of
general price inflation.
EOY Salary (A$) CPI
1 $34,000 7.1%
2 $36,200 5.4%
3 $38,800 8.9%
4 $41,500 11.2%
A reactor vessel cost $375,000 ten years
ago. The reactor had the capacity of
producing 500 pounds of product per
hour. Today, it is desired to build a
vessel of 1,000 pounds per hour
capacity. With a general price inflation
rate of 5% per year and assuming a
cost-capacity factor to reflect economies
of scale to be 0.75, what is the
approximate cost of the new reactor
now?
The operating budget estimate for an
engineering staff for the year 1999 is
$1,780,000. The actual budget expenditures
for the previous two years, as well as
estimates for the next two years, are as
shown. These are actual dollar amounts.
Management, however, also wants annual
budget amounts for these years expressed
using a constant dollar perspective. The
1999 fiscal year is to be used for this
purpose. The estimated annual general price
inflation rate is 5.6%. What are the annual
constant (real) dollar budget amounts?
(continued at next slide)
Fiscal Year Budget Budget
(A$) (R$)
1997 $1,615,000 ?
1998 $1,728,000 ?
1999 $1,780,000 ?
2000 $1,858,300 ?
2001 $1,912,200 ?
An investor established an individual savings account in
1991 that involves a series of 20 deposits: F
1992 1993 1994 2011
1991
$2,000/year
The account is expected to compound at an average interest
rate of 12% per year through the year 2011. General
price inflation is expected to average 6% per year during
this time.
(a) What is the FW of the savings account at EOY 2011?
(b) What is the FW of the savings account in 1991 (base
time period) spending power?
A gas-fired heating unit is expected to meet an
annual demand for thermal energy of 500
million BTU, and the unit is 80% efficient.
Assume that each 1,000 cubic feet of
natural gas, if burned at 100% efficiency,
can deliver 1,000,000 BTU. Suppose
further that natural gas is now selling for
$2.50 per 1,000 cubic feet. What is the PW
of fuel cost for this heating unit over a 12-
year period if natural gas prices are
expected to escalate at an average rate of
10% per year? The firm’s MARR ( = ic) is
18% per year.
A small heat pump, including the duct system,
now costs $2,500 to purchase and install. It has
a useful life of 15 years and incurs annual
maintenance expenses of $100 per year in real
(year 0) dollars over its useful life. A
compressor replacement is required at the end
of the 8th year at a cost of $580 in real dollars.
Annual electricity cost is $680 based on present
prices. Electricity prices are expected to
escalate at an annual rate of 10%. All other
costs are expected to escalate at 6%, which is
the projected general price inflation rate.
(continued at next slide)
The firm’s MARR, which includes an
allowance for general price inflation, is
15% per year. No market value is
expected from the heat pump at the end
of 15 years.
(a) What is the AW, expressed in actual
dollars, of owning and operating the heat
pump?
(b) What is the AW, expressed in real
dollars, of owning and operating the heat
pump?
An electric utility company is trying to decide
whether to switch from oil to coal at one of
its power generation sites. After much
investigation, the problem has been
reduced to the following trade-offs:
Oil Coal
Cost to retrofit boilers to
burn coal N/A ?
Annual fuel expense
(year 0 dollars) -$25M -$17M
Escalation rate 10%/year 6%/year
Life of plant
25 years 25 years
(continued at next slide)
Determine the cost of retrofitting the boilers
(to burn coal) that could be justified at
this generating station. The utility’s real
MARR is 3% per year, and the general
price inflation rate in the economy will
average 6% per year over the next 25
years.
(a) Solve using an actual dollar analysis.
(b) Solve using a real dollar analysis.