CHAPTER 3 - Educators

84 CHAPTER 3/COST-ESTIMATION TECHNIQUES
(typically, 100). A composite index is created by averaging the ratios of selected
item costs in a particular year to the cost of the same items in a reference year.
The developer of an index can assign different weights to the items in the index
according to their contribution to total cost. For example, a general weighted index
is given by
Īn = W1(Cn1/Ck1) + W2(Cn2/Ck2) +···+WM(CnM/CkM)
W1 + W2 +···+WM
where M = total number of items in the index (1 ≤ m ≤ M);
Cnm = unit cost (or price) of the mth item in year n;
Ckm = unit cost (or price) of the mth item in year k;
Wm = weight assigned to the mth item;
Īk = composite index value in year k.
× Īk, (3-2)
The weights W1, W2, ..., WM can sum to any positive number, but typically sum
to 1.00 or 100. Almost any combination of labor, material, products, services, and
so on can be used for a composite cost or price index.
EXAMPLE 3-4 Weighted Index for Gasoline Cost
Based on the following data, develop a weighted index for the price of a gallon
of gasoline in 2006, when 1992 is the reference year having an index value
of 99.2. The weight placed on regular unleaded gasoline is three times that of
either premium or unleaded plus, because roughly three times as much regular
unleaded is sold compared with premium or unleaded plus.
Price (Cents/Gal) in Year
1992 1996 2006
Premium 114 138 240
Unleaded plus 103 127 230
Regular unleaded 93 117 221
Solution
In this example, k is 1992 and n is 2006. From Equation (3-2), the value of Ī2006 is
(1)(240/114) + (1)(230/103) + (3)(221/93)
× 99.2 = 227.5.
1 + 1 + 3
Now, if the index in 2008, for example, is estimated to be 253, it is a simple matter
to determine the corresponding 2008 prices of gasoline from Ī2006 = 227.5:
253
Premium: 240 cents/gal = 267 cents/gal,
227.5