Here are the formulas for calculating critical thresholds for the NAT -- as given from the original white paper:
Let's say ROR is the BEFORE TAX rate of return an entity can typically

get from its assets including capital gains as well as profits. Let's

say ITR is the income tax rate and ATR is the government debt rate

and therefore would be the hypothetical asset tax rate. Let's say

the entity owns net assets with a market value totaling MV.

For simplicity, let's ignore the standard exemption and assume

that the capital gains tax rate is the same as the income

tax rate:

The income I = ROR*MV

Income tax IT = I*ITR

After income tax income AITI = I-IT

After income tax rate of return AITROR = AITI/MV

Asset tax AT = MV*ATR

After asset tax income AATI = I-AT

After asset tax rate of return AATROR = AATI/MV

Now we can ask:

What how efficient does a business currently have to be in order

to prefer the NAT over the current tax system?

This is the same as asking:

At what values of ROR is AATI>AITI?

First let's set AATI=AITI:

I-AT = I-IT ; Substituting for AATI and AITI

I-MV*ATR = I-I*ITR ; Substituting for AT and IT

MV*ROR-MV*ATR = MV*ROR-MV*ROR*ITR ; Substituting for I

ROR-ATR = ROR-ROR*ITR ; Dividing by MV

1-ATR/ROR = 1-ITR ; Dividing by ROR

ATR/ROR = ITR ; Subtracting 1

ROR = ATR/ITR ; Solving for ROR

So if your BEFORE tax rate of return on net assets is greater than

the hypothetical asset tax rate divided by the income tax rate,

you want the NAT. If it is less, you want the present system.

In terms of current AFTER INCOME TAX rates of return, this translates to:

AITROR = AITI/MV ; Definition of AITROR

AITROR = (I-IT)/MV ; Substituting for AITI

AITROR = (I-I*ITR)/MV ; Substituting for IT

AITROR = (ROR*MV-ROR*MV*ITR)/MV ; Substituting for I

AITROR = ROR-ROR*ITR ; Simplifying

AITROR = (ATR/ITR-ITR*ATR/ITR) ; Substituting for ROR

AITROR = ATR/ITR-ATR ; Simplifying

AITROR = ATR*(1/ITR-1) ; Collecting ATR

So under current conditions (approximately)

Setting ATR = .06 ; Interest on national debt is about 6%

Setting ITR = .28 ; Income tax is about .28% (ignoring social

security)

AITROR = .06*(1/.28-1)

AITROR = .154

In other words, if our current after tax (ignoring social security tax)

income (including capital gains) is more than 15.4% of our net assets,

we benefit from the NAT. We'll call the AITROR at which we prefer

the NAT over the current tax system the "Critical AITROR". For each

Critical AITROR there is an implied "Critical AITI" which is simply

the level of after tax income one must be making under the current

income tax system, in order to prefer the NAT.

If we factor in the standard exemption (E) as well (still ignoring

social security tax relief) the Critical AITROR is given by the formula:

Critical AITROR = (1/ITR-1)*(1-E/MV)*ATR

The Critical AITI is given by:

Critical AITI = MV * Critical AITROR

Now,

Setting E = $100,000:

Critical AITROR = (1/.28-1)*(1-$100,000/MV)*.06

For various values of MV (market value of net assets), then the

Critical AITROR's (still ignoring social security tax relief) are:

MV Critical AITROR Critical AITI/YEAR

$0 - $100,000 0% $0

$150,000 5.1% $7650

$200,000 7.7% $15,400

$300,000 10.3% $31,200

$500,000 12.32% $61,600

$1,000,000 13.77% $137,700

These are the figures that are most relevant to wealthy retirees

and other individuals who pay no social security.

The most regressive of all taxes, Social Security payroll tax, is

at 15.3% of your income (I) up to $53,400 (split 7.65% for you and

your employer half and half). Taking this into account, for

incomes (I) up to $53,400, ITR is close to 40%, so adjusting

for social security, the critical AITROR without the exemption

is only 9%. With the exemption the formula is:

Critical AITROR = (1/.40-1)*(1-$100,000/MV)*.06

This formula is a good approximation for MV's up to approximately

$500,000. As MV values rise beyond $500,000, the Critical AITROR

factor of .40 decays, approaching .28.

For each level of net asset ownership, there is a critical after

income tax income (AITI) above which we prefer the NAT over the

current tax system. This critical AITI is simply the critical

after income tax rate of return one one's assets, multiplied

by one's assets.

Taking into account social security tax relief under the NAT, as

well as the $100,000 standard household exemption on net assets,

the critical AITI levels needed to prefer the NAT are:

For various values of MV (market value of net assets), the

levels of income we need to prefer the NAT over the current

tax system are approximately:

MV Critical AITROR Critical AITI/YEAR

$0 - $100,000 0% $0

$150,000 3% $4500

$200,000 4.5% $9000

$300,000 6% $18,000

$500,000 7.2% $36,000

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