Index numbers

ACCA F2 - Management Accounting


Index number is the measure of changes in value/(points) of commercial quantities (e.g. price, quantity, volume) in consideration to base period (current, previous, past) value expressed in 100 points. The change can be presented in two forms. The first is the increase or decrease in points (absolute value) in relation to base period point of 100. (e.g. 110-100)The second is the increase or decrease in percent points (relative value) in relation to base period point of 100. (e.g. 110/100) Price index is the change in price of a product (a basket of products) in relation to the base period. Index derived is often used as an independent variable in regression analysis.

Simple Index: This method presents change in values in relation to base period. The choice of base period determines the periodic absolute magnitude (PAM) but periodic proportional magnitudes (PPM)  remains unaffected by the choice. E.g.

Year	Average price	base year 2013	base year 2014	Link / Chain
2012	16	100	64	-
2013	20	125	80	125
2014	25	156.25	100	125
PAM (013/014)		156.25-125 = 31.25	100 - 80 = 20
PPM (013/014)		156.25/125 = 1.25	100/80 = 1.25

Linked or Chain based Index:  Link relative series express the value of the series in each period as percent of the value in the immediately preceding period. E.g. Check table above.

Weighted Aggregate: The method of weighted aggregates for compiling a price index simply compares the cost of the typical quantities consumed at the prices of a given period with the corresponding cost in the base period. For working example click the link on "Price and Quantity Indexes".

Weighted Average: The method of weighted average utilizes the percent relatives of the prices for the item in the schedule. For working example click the link on "Price and Quantity Index".

Quantity index is the change in quantity of basket in relation to the base period. Volume index is the change in volume of basket (especially for liquids and gas substances) in relation to the base period.

Laspeyres and Paasche indices: For full details, formulas and visuals check the article - "Laspeyres and Paasche indices”

Synopsis:

Laspeyers index of 1 means that, as the nominator is the same as the denominator, an individual can afford the same basket of goods in the current period as he did in the base period.

A Paasche index of 1 means that the consumer could have afforded the same bundle of goods in the base period as they can now.

Key - Laspeyers indes is always greater than Paasche. 

Price and Quantity Index

Laspeyres and Paasche indices