# Engineering Economics in Canada

```Engineering Economics in Canada
Chapter 9 Inflation
9.1 Introduction
• Inflation: An increase in the average price paid for
goods and services over time.
– Results in a reduction in purchasing power.
– Value dose not equal to purchasing power.
• Deflation: A decrease in the average price paid for
goods in services over time.
– Results in an increase in purchasing power.
• Prices are likely to change over the life of an
engineering project due to inflation or deflation
• This chapter deals with how to take inflation into
account when evaluating projects
9-2
9.2 Measuring the Inflation Rate
• The inflation (deflation) rate is the
rate of increase (decrease) in
average prices of goods and
services over a specified period.
• A number of price indices are
available to measure inflation,
depending upon the type of goods or
services we are dealing with.
9-3
9.2 Measuring the Inflation Rate
• The most common price index is the Consumer
Price Index (CPI)
• The CPI is a composite price index that
measures price changes in food, shelter, medical
care, transportation, apparel, and other selected
goods and services used by average individuals
and families.
• To compute the CPI, Statistics Canada
periodically measures the cost to purchase a
standard bundle of goods and services based on
prevailing prices.
9-4
The CPI
• The current cost of the bundle of goods
and services is compared to the cost of
the same bundle in a base year.
– The current base year is 1992.
• The CPI at a particular point in time is
100 x (current \$)/(\$ in base year)
• The CPI of the base year (1992) is 100.
• The current year is measured with
respect to the base year, 1992.
9-5
Other Uses of Price Indices
• Contract Escalation
– A mining company entering a long-term
equipment purchase contract with a major
distributor wants to establish guidelines
which will govern the future prices of the
– Using the Mining, Quarrying and Ore
dressing Machinery Index, the company ties
the future price increases of equipment to
those of the index.
9-6
Other Uses of Price Indices. .(con’t)
• Tracking Selling Prices
– A pharmaceutical firm wants to
compare price changes for its
products with those of the industry as
a whole.
– Using a series of Pharmaceutical
Indexes, analysts can compare their
price trends over time with those of
the industry. In this way, they can get
a sense of their own competitiveness.
9-7
9.3 Economic Evaluation with Inflation
Actual Dollars: dollars at the time that cash flows
occur
• Their purchasing power changes due to
inflation/deflation
• Also as known as current or nominal dollars
Real Dollars: dollars of constant purchasing power
• We need a reference date called the base year
(not necessarily the present)
• Also known as constant dollars.
9-8
Actual or Real?
• Past or current data from accounting
records
• Payment from an investment, annuity,
bond, or trust
• Contractual payments
• Estimated costs or revenues
9-9
Actual and Real Dollars
• Suppose that the food plan at UVic
residence costs \$1500 now and is
expected to cost \$1530 one year from
now, based on an expectation that
prices will increase at the general
inflation rate of 2% per year.
• The real (today's) dollar cost of the plan
next year is \$1500.
• The actual dollar cost of the next year
is \$1530. (Actual: the price you pay)
9-10
Inflation Rates
• We use forecasts of inflation to estimate
how prices in a project will change over
time (usually an increase).
• We normally assume that estimates of
inflation rates over the life of a project
are available, and that all prices in a
project change at that rate, but
sometimes we have reason to believe
that some prices will change at different
rates.
9-11
9.3.1 Converting Between Real and Actual
Dollars
• If we have an estimate of the inflation rate per
period over N periods, we can convert actual
dollars in period N to real dollars.
AN = actual dollars in year N
AN is not an annuity amount
R0,N = real dollars equivalent to AN relative to yr. 0
Year 0 = the base year
f = the inflation rate per year
Assumed to be constant from year 0 to year N
9-12
9.3.1 Converting Between Real and
Actual Dollars
• The conversion from actual dollars in year N to
real dollars in year N is:
R0,N 
AN
(1  f )N
• The base year (0) is usually omitted from the
notation:
RN 
AN
(1  f )N
• This can conveniently be written and computed
with the Present Worth Factor:
RN = AN(P/F, f, N)
9-13
Example 9-1 (Important)
• The residence food plan in two years
from now is expected to be \$2050.
Inflation is expected to be 1.5% per year
for the next 2 years.
• What is the real dollar cost of a food plan
at that time (two years from now)?
9-14
• N = 2, f = 1.5%, AN= 2050
AN = (P/F, f, N)
= 2050(P/F, 1.5%, 2)
= 2050(0.97066)
= 1888.66
• The real dollar cost of the food plan two years
from now is \$1888.66.
9-15
9.4 Actual and Real Interest Rates
• Engineers must be aware of potential
changes in price levels over the life of a
project.
• If inflation is anticipated, the MARR needs
to be increased in order to avoid rejecting
good projects.
9-16
9.4.1 Effect of Inflation on the MARR
• If we expect inflation, the actual dollars
returned by a project does not reflect the
actual purchasing power of the future cash
flow.
• The purchasing power depends on the real
dollar value of the earnings
9-17
Effect of Inflation on the MARR…
• Consider the (actual) value of \$M invested for
one year at an actual interest rate i: M (1 + i)
• If the inflation rate over the next year is f, the
real value of our cash flow is: M(1+i)/(1+f)
• The real interest rate, i’, is the interest rate
that would yield the same number of real
dollars in the absence of inflation as the actual
interest rate yields in the presence of inflation:
M (1  i ' )  M (1  i ) /(1  f )
 i '  (1  i ) /(1  f )  1
9-18
Effect of Inflation on the MARR…
• An investor who wishes to get a real rate
of i’ and who expects inflation at a rate f
will require an actual interest rate of:
i = i’ + f + i’f.
Summary:
• Converting from actual to real dollars:
i’ =(1+i)/(1+f)-1
Converting from real to actual dollars:
i = i’ + f + i’f.
9-19
Example 9-2 (Very Important)
• As of today, Canada Trust offers a 4%
interest rate for a 1-year Guaranteed
Investment Certificate (GIC).
• If you require a real rate of return of 3% on
your investments and you expect inflation
to be 1.5% in the coming year, is a GIC a
good investment for you?
9-20
• First, note the GIC provides 4% actual
interest and your real MARR is 3%.
• Your actual MARR is:
i  i'  f  i' f
 0.03  0.015  (0.03)(0.015)
 0.04545, or 4.545%
• No, the GIC is not a good investment
because it provides an actual interest rate
less than your actual MARR.
9-21
•
Alternatively, we can calculate a real interest rate
for the GIC:
i' = (1 + i)/(1 + f) –1
= (1 + 0.04)/(1 + 0.015) –1
= 2.46%
•
The real interest rate is less than your real
MARR  don’t invest.
•
Comparing the real interest rate to the real
MARR also leads to the same decision to not
invest.
9-22
9.4.2 The Effect of Inflation on the
IRR (Internal Rate of Return)
• The effect of expected inflation on the actual
IRR of a project is similar to the effect of
inflation on the actual MARR.
• Say we have a project with a first cost A0 and
actual cash flows A1, A2, …, AT
• The actual IRR can be found by solving for i in:
A1
A2
AT
PW  - A0 

  
0
2
T
(1  i ) (1  i )
(1  i )
9-23
The Effect of Inflation on the IRR…
• An annual inflation rate f is expected over the T
year life of the project.
• In terms of real dollars (base year = now), the
stream of actual cash flows can be written as
(note: R0 =A0)
R0, R11  f , R2 1  f 2 , ..., RT 1  f T
• The expression which gives the actual IRR can
be rewritten as:
R11  f  R2 1  f 2
RT 1  f T
PW  R0 
+
+  +
0
2
T
(1  i )
(1+ i )
(1+ i )
9-24
The Effect of Inflation on the IRR…
• The real IRR is the rate of return obtained on
the real dollar cash flows associated with the
project. It is the solution for i’ in:
 R0 
R1
R2
RT

 ... 
0
2
T
(1  i ' ) (1  i ' )
1  i ' 
• What is the relationship between the real IRR
and the actual IRR?
IRR real  (1  IRR actual ) /(1  f )  1
or
IRR actual  IRR real  f  IRR real f
9-25
Example 9-3 (Very Important)
• Ken insulated one of his company's buildings.
The energy savings are estimated at \$15 000
annually, based on today’s energy prices,
starting one year from now.
• Inflation is expected to average 4% per year and
Ken’s actual MARR is 8%. What is the present
worth of the energy savings over the next 10
years?
9-26
• Method 1: Work with real cash flows and find the
real MARR using an estimate of f.
• Method 2: Adjust the real cash flows for inflation
(i.e. get estimates of the actual cash flows using
f) and apply the actual MARR.
9-27
• Method 1: Note that the \$15 000 savings will
increase if the cost of energy rises with inflation
 \$15 000 is a real cash flow
MARRREAL  ( 1  MARRACTUAL )/(1  f)  1
 ( 1  0.08 )/(1  0.04 )  1
 3.85%
PW(total)
= 15 000 (P/A, MARRREAL, N)
= 15 000(P/A, 3.85%, 10)
= 122 600.59
9-28
• Method 2: Adjust real to actual cash flows:
PW(Nth payment)
= 15 000(P/F, MARRACTUAL, N)(1 + f)N
= 15 000 (P/F, 8%, N)(1 + 0.04)N
e.g. For N = 4, PW = 12 898.21
PW(total) = 122 600.59
9-29
Summary
• Inflation and deflation defined
• Measuring the inflation rate
• Economic Evaluation with Inflation
– Converting between real and actual
dollars
• The Effect of Correctly Anticipated
Inflation
– The effect of inflation on the MARR
– The effect of inflation on the IRR
9-30
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