What is your number?

The answer in the movie “Wall Street: Money Never Sleeps” was
more; however, the goal “more” only works when you have enough. Here we
estimate how much investment capital is needed and never have to work again.

The standard financial advice follows the 4% rule. This rule
states that one can annually withdraw 4% of the investment principal and the
money will last 30+ years. For example, if one has total balance B = $600k of
invested equity, one can annually withdraw E = 0.04·$600k=$24k for expenses E. This
4% is adjusted annually for inflation. For example, with annual inflation of
3%, the next years withdrawal can be 1.03·$24k = $24.7k.

The inverse relation between expenses E and investment
balance B is B = E/0.04 = 25·E. Thus, if we know our annual expenses, we need
to multiply this number by 25 to reach the goal of financial independence. This
should be your savings goal. After you reach this number, you can always try to
get “more” if you so choose ;) The 4% rule is summarized in Equation (1) below:

Alternatively, we can calculate the number using monthly
expenses

In summary, the steps for finding your number are:

1. Find out your monthly expenses E_{month}.

2. Calculate the needed balance B of invested equity using
Equation (2).

Table 1 shows a couple of examples to illustrate this
process.

#### Table1: Calculation of financial goal

Calculation of financial goal

A link for an editable spreadsheet for the above analysis is below:

https://spreadsheets.google.com/spreadsheet/ccc?key=0AlyBMfBlh5aodGN5amJ1OVV4TE9SWmZzVzFFME8xR0E&hl=en_US

F

The critical part of the process is accurate assessment of
monthly expenses. One way to approach this is to take your current expenses as
the starting point – something you should know although surprisingly many are
ignorant of! Next, deduct any expenses are that will be lowered (for example, mortgage
paid in full). Finally, deduct any additional income such as social security
(if you believe it will be around when you are eligible!). This is income that your investments should generate.

Finally, we note that the 4% rule corresponds to the
historical inflation adjusted total return for the stock market. As such, there
is not much margin for error in using this rule especially if the investments
need to last over 30 years. Given that the dividend yield is historically low and the corresponding total future return is likely lower than the historical average, it
may be prudent to use a smaller withdrawal rate such as 3% which results in a
higher savings goal of 400 times the monthly expenses.