The assumption is that we take from our account only the money we need to pay our expenses and taxes; the rest is left in the account to grow for future years.
Let’s go through a few examples.
We have $1,000,000 in our account, annual expenses of $50,000, and inflation of 3%. To simplify things, I’ll assume that we pay all of our expenses at the end of the year (we’ll charge everything on our credit card throughout the year).
Our nominal, after-tax, required rate of return (excluding inflation) is $50,000 ÷ $1,000,000 = 5%.
First, we’ll assume no taxes.
In this case, our total rate of return is 5% + 3% = 8%. Here’s what happens:
-
During year 1 our account earns $80,000 (= $1,000,000 × 8%), growing to $1,080,000.
-
At the end of year 1 we take out $50,000 to pay our bills, leaving $1,030,000 (= $1,000,000 × 1.03) in our account.
-
During year 2 our account earns $82,400 (= $1,030,000 × 8%), growing to $1,112,400.
-
At the end of year 2 we take out $51,500 (= $50,000 × 1.03), leaving $1,060,090 (= $1,030,000 × 1.03) in our account.
And so on, every year.
Now, assume that our account is taxable, and our marginal tax rate is 30%. Because the account is taxable, we have to pay taxes on everything our account earns, whether we take it out (to pay expenses) or leave it in. Our total, pre-tax required rate of return is (5% + 3%) ÷ (1 - 0.30) = 11.4286% Here’s what happens:
-
During year 1 our account earns $114,286 (= $1,000,000 × 11.4286%), growing to $1,114,286.
-
At the end of year 1 we pay $34,286 (= $114,286 × 30%) in taxes, leaving $1,080,000 in our account.
-
At the end of year 1 we take out $50,000 to pay our bills, leaving $1,030,000 (= $1,000,000 × 1.03) in our account.
-
During year 2 our account earns $117,714 (= $1,030,000 × 11.4286%), growing to $1,147,714.
-
At the end of year 2 we pay $35,314 (= $117,714 × 30%) in taxes, leaving $1,112,400 in our account.
-
At the end of year 2 we take out $51,500 (= $50,000 × 1.03), leaving $1,060,090 (= $1,030,000 × 1.03) in our account.
And so on, every year.
Now, assume that our account is nontaxable, and our marginal tax rate is 30%. Because the account is nontaxable, we have to pay taxes only on the amount we take out (to pay expenses); we pay no taxes on the gains we leave in the account. Our total, pre-tax required rate of return is (5% ÷ (1 - 0.30)) + 3% = 10.1429% Here’s what happens:
-
During year 1 our account earns $101,429 (= $1,000,000 × 10.1429%), growing to $1,101,429.
-
At the end of year 1 we take out $71,429 to pay our bills and taxes, leaving $1,030,000 (= $1,000,000 × 1.03) in our account.
-
At the end of year 1 we pay $21,429 (= $71,429 × 30%) in taxes, leaving $50,000 to pay our bills.
-
During year 2 our account earns $104,471 (= $1,030,000 × 10.1429%), growing to $1,134,471.
-
At the end of year 2 we take out $73,571 to pay our bills and taxes, leaving $1,060,900 (= $1,030,000 × 1.03) in our account.
-
At the end of year 2 we pay $22,071 (= $73,571 × 30%) in taxes, leaving $51,500 to pay our bills.
And so on, every year.
Note that at the end of each year we have the same amount in the account no matter whether the account is taxable or not, and that end-of-year amount grows by the inflation rate every year.
I hope that I made this clear.