cityboy

Basically when translating to a base year all you are doing is finding a discount factor (rate) to remove the nominal CPI growth over so many years.

For example:

earnings in year 1 are X1 and the CPI is 100. CPI in year 2 is 105 - that's 5% growth from year 1 to year 2 or X1*105/100 =X2. (this could also be written like X1*1.05 = X2) we are just growing the earnings at the expected inflation rate.

If we wanted to find out what the real price is in X2 we just need to solve for X2:

X2 / (105/100) or X2 * 100/105 = Real X1

If you add another year to this and prices are X3 and the CPI is at 120 then:

X3 * 100/120 = Real X1
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This is why it is a discount factor:

The inflation over the 2 years is: 120/100 - 1 = .20 or 20%

or similarly:
year 1 to yr 2 inflation = (105 - 100)/100 - 1= .05

year 2 to yr 3 inflation = (120 - 105)/105 - 1= .1429


total inflation compounded over yr 1 to 3 = (1.05)*(1.1429) - 1 = .20

and the average annual inflation is 1.2^1/2 = .0954 or 9.54% <--- which would be your annual discount rate for year 3 so the equation would become 120/1.0954^2 = 100 if you were to calculate in this way.

This last part is stricly for further information, and is really just a way to go into further detail on how the equation works. it's a way to modify the CPI adjustment equation to make it look like the DDM, if it doesn't make sense then don't worry, just use the stuff above the hash line.



Edited 1 time(s). Last edit at Wednesday, May 18, 2011 at 11:56AM by FinNinja.