Engineering Economic Analysis

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452 INFLATION ANDPRICECHANGE

For example, consider the LCI for the year 1980. We calculate the LCI as follows.

LCI year 1980=([(0.15 - 0.06)/0.06] x 100) + 100= 250

As mentioned, engineering economists are often in the business of using cost indexes to ~

project future cash flows. As such, our first job is to use a cost index to calculate annual

cost increases for the items tracked by the index. To calculate theyear-to-yearpercentage

increase (orinflation)of prices tracked by an index, one can use Equation 14-3.

Annual percentage increase,n=([Index(n)-Index(n -1) ]/Index(n -1» x 100% (14-3)

To illustrate the use of this equation, let us look at the percent change from 1977 to

1978 for the LCI just given..

Annual percentage increase (1978)=[250- 216]/216 x 100%=15.74%

For 1978the price of mailing a first-classletter increased by 15.74%over the previous year.

This is the value tabulated in Table 14-1.

An engineering economist often wants to know how a particular cost quantity changes

over time. Often we are interestedin calculatingtheaveragerate of price increase or inflation

in some quantity,such as the cost of postage, over a period of time. For instance, one might

want to know the average yearly increase in postal prices from 1970 to 2003. How do we

calculate this quantity? Can we use Equation 14-2? If we were to use Equation 14-2 to

calculate the percent change from 1970 to 2003, we would obtain the following:

% Increase (1971 to 1991)=(617 - 100)/100 x 100%=517%.

But how do we use this calculation to obtain the average rate of increase over those

years? Should we divide 517% by 33 years (517/33=15.67%)? Of course not! As was

establishedin earlier chapters,the conceptofcompoundingpreclud~ssuch a simpledivision.

To do so would be to treat the interest rate as simple interest-where compoundingis not in

effect. So the question remains: How do we calculate anequivalentaverage rate of increase

in postage rates over a period of time? Let us start by thinking about the LCI. We have

a number (index value) of 100 in year 1970 and another number, 617, in year 2003, and

we want to know the interest rate that relates these two numbers. If we think of the index

numbers as cash flows,it is easy to see that we have a simple internal rate of return problem.

Given this approach, let us calculate theaverage rate of increasein postage rates for the

years under consideration.

P=100 F= (^617) n=33 years i=?
UsingF= P(1+i)n 617 = 100(1+i)33 i= (617/100)1/33- 1 i = 0.0567'= 5.7%
In the same way, we can use a cost index to calculate the average rate of increase over
any period of years. Understanding of how costs have behaved historically should provide
insight into how they may behave in the future.