Regular Assets and First Year Accounting

Knowledge Base Tags: 

All of the reports are presented in current year real dollars and show end-of-year balances.

(This article was written in the year 2017. )

Every model assumes three important variables:

a) prior end-of-year balance,
b) inflation rate, and
c) nominal rate of return.

The prior-year balance, the inflation rate, and the nominal rate of return are entered in the program input areas. These variables are used to calculate end-of-year balance for the Regular Assets and the Retirement Accounts shown in the reports.

There are two equivalent ways of looking at this accounting:
1. Nominal rate of return for all years with all balances expressed in current year real 2017 dollars.
2. Nominal rate of return for the first year and real rate of return afterwards.

Let's begin with the first way:
This example assumes a 2016 prior end-of-year balance of $1M and a nominal return of 3% and inflation of 2%

YEAR ONE

The $1,000,000 nominal balance at the end of 2016 grows by the nominal rate of return during the 2017, i.e. $1,030,000 = 1.03 * $1,000,000, in current year dollars.
The retirement reports show an end-of-year balance of $1,030,000 assuming there are no contributions or withdrawals.
Regular asset end-of-year balance reporting.

Whereas the nominal return is $1,030,000, this $30,000 return is distributed and reported in two places for regular assets: $10,000 is reported as real return in the Total Income report, and the balance of Saving/Dis-saving + what remains is shown as the ending balance for 2017. Were there no saving or withdrawal this ending balance in the Regular Assets report would be $1,020,000, where the other $10,000 is shown in the Total Income report, hence the full $30,000 is accounted for.

YEAR TWO RETIREMENT ASSETS
The $1,030,000 nominal balance at the end of the current year (2017) grows by the nominal rate of return during the second year, i.e. $1,060,900 = 1.03 * $1,030,000, in 2018 dollars. But, these need to be reported in 2017 dollars, so we divide by inflation of 1.02 to get $1,040,098 in 2017 dollars.

YEAR THREE RETIREMENT ASSETS
The $1,060,900 nominal balance at the end of 2018 grows by the nominal rate of return during 2019, i.e. $1,092,727 = 1.03 * $1,060,900, in 2019 dollars. But, we want that reported in 2017 dollars, so we divide by inflation of 1.02^2 to get $1,050,295 in 2017 dollars.

. . . and so on for each future year.

The second way, i.e. nominal rate of return for the first year and real rate of return afterwards is as follows:

Note: that the EoY Balances in real 2017 dollars is exactly the same in both cases!

--------------
Real return is calculated in this way:

1 + nominal = (1 +real) * (1 + inflation)
So, 1 + real = (1 + nominal) / (1 + inflation). 1 + real = 1.03 /1.02 = 1.009804. Hence, the real rate of return is 0.9804%