How to Calculate a Cost of Living Index

Definition:

A Cost Of Living Index (COLI) is a price index that measures the relative cost of living over time. It is an index that measures differences in the price of goods and services.

A COLI measures changes over time in the amount that consumers need to spend to reach a certain level or standard of living. COLI is typically a number, where the Base Index is 100.

A Consumer Price Index (CPI) on the other hand is a measure of the average change over time in the prices paid by consumers. CPI is typically a percentage change compared to the previous period. An increase in CPI is called inflation, while a decrease is called deflation. Both the COLI and the CPI use a market basket of consumer goods and services.

A COLI is also used to measure the price of the same quantities and types of goods and services in different geographic locations. The COLI used in this way shows the difference in living costs between different locations.

An international COLI measures the differences in the local currency price of the same quantities and types of goods and services in different countries converted to a single currency. This shows the difference in relative living costs between international cities. The cost of living difference between locations indicates the amount that consumers need to spend to maintain a certain level or standard of living.

Amongst other uses, COLI's are used by organizations and individuals in the calculation of expatriate salary and cost of living allowances in order to ensure consistent salary purchasing power between the home and host country.

Next we will discuss how to calculate a COLI between 2 locations applicable to expatriate employees.

Methodology:
For consistency the goods and services are grouped into similar/related basket groups.

For accuracy the exact quantity and type of each of the goods and services within each basket are defined. Using these definitions, the prices of the same quantities and types of goods and services in each geographic location is obtained from at least 3 different suppliers representative of those that would typically be used by expatriates.

When calculating the cost of living between 2 locations the difference in the aggregate cost of all the selected basket groups are examined in each location using the average reported price in each location for the same quantity of each item. The basket groups are weighted according to Expatriate expenditure norms.

For example the following 13 basket groups have the following weighting which represents expatriate expenditure norms (the 13 basket groups do not count equally):

' Alcohol & Tobacco (Weight 2.0%)
' Clothing (Weight 2.5%)
' Communication (Weight 2.0%)
' Education (Weight 5.0%)
' Furniture & Appliances (Weight 5.0%)
' Groceries (Weight 16.5%)
' Healthcare (Weight 5.0%)
' Household (Weight 30.0%)
' Miscellaneous (Weight 3.0%)
' Personal Care (Weight 3.0%)
' Recreation and Culture (Weight 6.0%)
' Restaurants, Meals Out and Hotels (Weight 2.0%)
' Transport (Weight 18.0%)

Prices for the defined quantities and types of goods and services in each location per basket are gathered on a quarterly basis and the resulting index is updated for each of the above baskets. These indexes are then used to calculate the COLI between any 2 locations. The COLI is the relative differential in the local cost of the basket groups and the ruling exchange rate between the 2 selected locations.

When comparing the cost of living between different locations the objective is to calculate the difference in the cost of living expressed as an index using one of the locations as the Base. Typically the home location is referred to as the Base Location (Index = 100).

Practical Example:

Take for example a company headquartered in Location A with overseas operations in Location B and C. They send employees on 2 to 3 year assignments from time to time to Location B and C and need a set of COLI's using Location A as the Base City in order to calculate assignment salary and cost of living allowances.

In our example Location A has an index of 92, Location B has an index of 129, and Location C has an index of 75.

Using our example, you want to know what the COLI is for Location B and C using Location A as the Base Location:

' Location A COLI = (Location A / Location A) X 100 = (92 / 92) X 100 = 100
' Location B COLI = (Location B / Location A) X 100 = (129 / 92) X 100 = 140.2
' Location C COLI = (Location C / Location A) X 100 = (75 / 92) X 100 = 81.5

The COLI indicates the difference in the cost of living between the locations. In the above example the COLI of 140.2 means that Location B is 1.402 times more expensive than Location A. In this example the COLI is positive (higher). This would mean that a person who moves from Location A to Location B would need to earn 40.2% more, to have the same standard of living in Location B as they have currently in Location A.

Location C on the other hand has a COLI of 81.5. This means that Location C is 0.815 times less expensive than Location A. In this example the COLI is negative (lower). This would mean that a person who moves from Location A to Location C could earn 18.5% less and have the same standard of living in Location C as they have currently in Location A.

Applying a cost of living index to a salary calculation:

The COLI values are useful in calculating an appropriate salary in another location. A calculator such as a Salary Purchasing Power Parity Calculator (SPPP) calculates an appropriate salary using the COLI, exchange rate and hardship difference.

The salary used in the calculator is gross or net salary. We advise using net (after tax) salary. This will result in a net salary result in the new location, which would then be grossed up for tax and any other statutory deductions in the new location. The calculator will then apply the following formula based on the selections in the calculator:

Salary X Cost of living Index Differential X Exchange Rate X Hardship Differential = Calculated Salary in new location

Applying the formula to our earlier example with a salary of $100,000 in Location A, sent on assignment to Location B, with an increase in hardship of 10% and paid in US Dollars:

' Location B COLI = 140.2
' Location C COLI = 81.5

Salary Calculation = $100,000 X 1.402 X 1 X 1.1 = $154,220

This means that an employee earning a salary of $100,000 in Location A, requires a salary of $154,220 in Location B to compensate for a 40.2% higher cost of living and a 10% higher level of hardship.

Steven is Chief Instigator at Xpatulator.com a website that provides cost of living index information and calculates what you need to earn to compensate for cost of living, hardship, and exchange rate differences.