Let’s say we have annual income of EUR 120,000 per year for 10 years. There is no growth/decline rate.
Inflation is 5% per year.
Which is the correct method to calculate the real value of the EUR 120,000 in 10 years?
Method 2.
Thanks @S2000magician, it’s really weird because CFAI used Method 1 in one of their solution keys. Thanks anyway!
I know that they do.
I have no idea why. It makes no sense.
Yeah I also find that strange, since I also have seen CFAI use Method 1 numerous times.
My understanding of the difference is that Method 1 seems to account for inflation by converting the return to a real rate, meanwhile Method 2 seems to account for inflation by converting the discount rate to a nominal rate.
I am curious when to assume one versus the other, or if for exam purposes we should just assume Method 2, since that is the “correct” method according to S2000.
Well, it depends.
The standard way to present annual inflation data by statistics institutions is YoY (year-over-year), which is calculated as P0 * (1+infl1) = P1, where " infl1 " is the annual inflation rate for that year, and “P” the price index of each point in time (beggning of year and end of year). So how would you calculate P2? It would be:
P1 * (1+infl2) = P2
If you repeat the calculation for 10 years it becomes P0 * (1+infl1) * (1+infl2) * … * (1+infl10) = P10
so the general inflationary compound factor becomes (1+infl)^10. As you are told to calculate the real value of money at year 10 you use 1 / (1+infl)^10.
You would use method 1 if you were told the annual inflation rate is calculated as a variation of P0 in each year, so probably the inflation rate would rise steadily as P0 becomes smaller and smaller compared to each Pi (base effect). This is why statistics institutions don’t use this method, it is confusing and less informative, also little practical as we always want to see what happenned this actual year. For example, as FED inflation target be 2% each year (compounded, YoY), under method 1 we would see inflation 2% at year 1, but for year 2 would be 2.12%, for year 3 would be 2.24%, and so on. Rising for ever.
However, under method 2 we lose in sight the real effect of compound inflation. As it is common nowadays that people cheers up inflation is going down from 8% to 3%! but in fact we still seeing rising prices… and the compound effect of real value loss of our money is like 25% since just 2020. Method 1 would have let see that effect much harder than method 2.
Perhaps CFA book question used inflation rate under method 1? Would need to see the wording.
there’s a minus sign in his method 1.
It may be as simple as approximating
\frac{1}{1+r}\approx 1-r with an error {\mathcal O}(r^2)
Indeed CFAI used Method 1 in one of the questions…