I'd make two suggestions.1. You will be hard pressed to actually...

I'd make two suggestions.

1. You will be hard pressed to actually pay 47% tax.
There is a difference between the brackets used during the taxable income calculation and the actual amount of tax you pay.
Otherwise the calculation would have been as easy as 47% * income.
Instead progressive tax tables are used as illlustrated below and tax is paid on total taxable income amount.
The amount of tax payable divided by taxable income determines your effective tax rate, which will be much lower than your marginal rate.
You would have to earn 1.5M to crack 45% effective rate.

2. Come up with a sweet math formula that will determine the CAGR required depending on the effective tax rate.
Like you did for the post about options the other day?

For example
An investor with and income of 120,000 has an effective tax rate of 26.56%.
What CAGR does a trader need to get ahead vs 50% CGT vs hold over 10yrs?

Income of 200K is 32.33%
Income of 80K is 22.58%

This ignores some of the offsets that are available to some people.
A different tax rate will change the outcome.

I've done this in a spreadsheet somewhere but not with a single neat formula, if you even can.

	Tax bracket	Marginal Rate	Fixed Amount	Medicare Rate
1	18201	19.00%	0	0.00%
2	45001	32.50%	5092	2.00%
3	120001	37.00%	29467	2.00%
4	180001	45.00%	51667	2.00%
5
6
7	Taxable income	Marginal Tax Rate	Fixed Amount	Variable Amount	Medicare Rate	Medicare Amount	Tax Payable	Effective Tax Rate
8	40,000.00	19.00%	0.00	4,142.00	0.00%	0.00	4,142.00	10.36%
9	80,000.00	32.50%	5,092.00	11,375.00	2.00%	1,600.00	18,067.00	22.58%
10	120,000.00	32.50%	5,092.00	24,375.00	2.00%	2,400.00	31,867.00	26.56%
11	160,000.00	37.00%	29,467.00	14,800.00	2.00%	3,200.00	47,467.00	29.67%
12	200,000.00	45.00%	51,667.00	9,000.00	2.00%	4,000.00	64,667.00	32.33%
13	240,000.00	45.00%	51,667.00	27,000.00	2.00%	4,800.00	83,467.00	34.78%
14	280,000.00	45.00%	51,667.00	45,000.00	2.00%	5,600.00	102,267.00	36.52%
15	320,000.00	45.00%	51,667.00	63,000.00	2.00%	6,400.00	121,067.00	37.83%
16	360,000.00	45.00%	51,667.00	81,000.00	2.00%	7,200.00	139,867.00	38.85%
17	400,000.00	45.00%	51,667.00	99,000.00	2.00%	8,000.00	158,667.00	39.67%
18	440,000.00	45.00%	51,667.00	117,000.00	2.00%	8,800.00	177,467.00	40.33%
19	480,000.00	45.00%	51,667.00	135,000.00	2.00%	9,600.00	196,267.00	40.89%
20	520,000.00	45.00%	51,667.00	153,000.00	2.00%	10,400.00	215,067.00	41.36%
21	560,000.00	45.00%	51,667.00	171,000.00	2.00%	11,200.00	233,867.00	41.76%
22	600,000.00	45.00%	51,667.00	189,000.00	2.00%	12,000.00	252,667.00	42.11%

Of course I could have made an error, so feel free to point it out