Restating earnings in today's dollars?

CFA Level III
#1

Couple quick questions:

1.) To convert a historical dollar figure to today’s dollars, why isn’t the coversion process:

–> earnings x (1+inflation rate)^n

– Instead it is Earnings x [CPI(now) / CPI(prior)]. Doesn’t the ladder, which is how the book teaches, ignore compounding?

2.) The result gives you “the value in today’s dollars”. Does this mean that the value is in today’s real terms or nominal terms? I’d think nominal because you are including the impact of inflation, no? Or is that once adjusted for inflation, today’s dollars now indeed represent today’s value in real terms?

When you generally hear people drawing comparison’s between someone’s wealth 100 years ago and someone today, is this how they convert the numbers to make an apples-to-apples comparison ?

Thanks all!

#2

CPINow/CPIThen -> is the way that the variation in inflation is accounted for. The basket of items you bought in 1990 had a CPI of say 150. Now the same basket costs say 225. So it is 1.5 times as expensive - and that is strictly the inflation portion.

Different periods have a different CPI # associated with them.

Your assumption is that the inflation rate is a constant when you do earnings x (1+inflation rate)^n - which may not be the case.

#3

So is the result in real or nominal terms (would you say that is today’s dollars in real terms)?

Thank you

#4

It includes Inflation effect - so it should be nominal I think.

the earlier earnings you started out with (before you applied the factor of CPINow/CPIThen) would have been the real earnings.

#5

Let’s do the first one first:

If inflation is 3%, and you need to find the value of $100 in two years, then:

100 x (1.03)^2 = 106.09.

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And if you do the second one:

If the CPI in 2001 was $100, and

The CPI in 2002 was $103, and

The CPI in 2003 was $106.09, then:

106.09/100 = 106.09= 1.0609

1.0609 - 1 = 6.09% over two years.

1.0609 ^ .5 = 1.03

1.03 - 1 = 3% inflation.

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As you can see, these two are mathematically the same. The second does not ignore compounding–the asset prices are compounding with time.

#6

Thanks, Green. I had that inclination but didn’t run out the math. Makes sense.

CPK, I have to think it is the nominal dollar amount, but they tend to refer to the amount in today’s terms as being in “today’s real terms” - so it makes me wonder.