Modeling a Wealth Tax
Paul Graham uses simple compound interest calculations to model the long-term impact of a wealth tax on startup founders. Assuming a founder holds stock for 60 years, he computes the share taken by the government at various tax rates (0.1% to 5%) and with a $50 million exemption threshold. The key finding: because a wealth tax is applied annually to the same asset, its compounding effect means even a 2% tax consumes about two-thirds of a successful founder's stock over a lifetime. The article also explores sensitivity to initial valuation and growth rates, noting that actual effects may be worse due to dividend taxes. Relevant for readers interested in the trade-offs between wealth taxation and entrepreneurial incentives.
August 2020Some politicians are proposing to introduce wealth taxes in addition to income and capital gains taxes. Let's try modeling the effects of various levels of wealth tax to see what they would mean in practice for a startup founder.
2020年8月。一些政客提议在所得税和资本利得税之外引入财富税。我们不妨尝试对不同财富税税率的影响进行建模，以了解它们对初创公司创始人实际意味着什么。
Suppose you start a successful startup in your twenties, and then live for another 60 years. How much of your stock will a wealth tax consume?
If the wealth tax applies to all your assets, it's easy to calculate its effect. A wealth tax of 1% means you get to keep 99% of your stock each year. After 60 years the proportion of stock you'll have left will be .99^60, or .547. So a straight 1% wealth tax means the government will over the course of your life take 45% of your stock.
(Losing shares does not, obviously, mean becoming net poorer unless the value per share is increasing by less than the wealth tax rate.)
Here's how much stock the government would take over 60 years at various levels of wealth tax:
wealth tax | government takes 0.1% | 6% 0.5% | 26% 1.0% | 45% 2.0% | 70% 3.0% | 84% 4.0% | 91% 5.0% | 95%
假设你二十多岁时创办了一家成功的初创公司，然后又活了60年。财富税会消耗你多少股票？
如果财富税适用于你的所有资产，那么计算其效果很简单。1%的财富税意味着你每年能保留99%的股票。60年后，你剩余的股票比例将是0.99^60，即0.547。因此，1%的纯财富税意味着政府在你一生中将拿走你45%的股票。
（显然，损失股票并不等同于净财富减少，除非每股价值的增长幅度低于财富税率。）
以下是60年间不同财富税率下政府拿走的股票比例：
财富税率 | 政府拿走比例 0.1% | 6% 0.5% | 26% 1.0% | 45% 2.0% | 70% 3.0% | 84% 4.0% | 91% 5.0% | 95%
A wealth tax will usually have a threshold at which it starts. How much difference would a high threshold make? To model that, we need to make some assumptions about the initial value of your stock and the growth rate.
Suppose your stock is initially worth $2 million, and the company's trajectory is as follows: the value of your stock grows 3x for 2 years, then 2x for 2 years, then 50% for 2 years, after which you just get a typical public company growth rate, which we'll call 8%. [1]
Suppose the wealth tax threshold is $50 million. How much stock does the government take now?
wealth tax | government takes 0.1% | 5% 0.5% | 23% 1.0% | 41% 2.0% | 65% 3.0% | 79% 4.0% | 88% 5.0% | 93%
财富税通常设有一个起征门槛。高门槛会带来多大的差异？为了建模，我们需要对你的股票初始价值和增长率做一些假设。
假设你的股票初始价值为200万美元，公司的发展轨迹如下：股票价值在头两年增长3倍，接着两年增长2倍，再两年增长50%，之后你只获得典型上市公司的增长率，我们设为8%。[1]
假设财富税的门槛是5000万美元。现在政府会拿走多少股票？
财富税率 | 政府拿走比例 0.1% | 5% 0.5% | 23% 1.0% | 41% 2.0% | 65% 3.0% | 79% 4.0% | 88% 5.0% | 93%
It may at first seem surprising that such apparently small tax rates produce such dramatic effects. A 2% wealth tax with a $50 million threshold takes about two thirds of a successful founder's stock.
The reason wealth taxes have such dramatic effects is that they're applied over and over to the same money. Income tax happens every year, but only to that year's income. Whereas if you live for 60 years after acquiring some asset, a wealth tax will tax that same asset 60 times. A wealth tax compounds.
乍一看可能会惊讶，如此看似微小的税率竟然产生如此巨大的影响。2%的财富税加上5000万美元的门槛，会拿走成功创始人约三分之二的股票。
财富税产生如此巨大影响的原因是，它们被反复应用于同一笔钱。所得税每年都发生，但只针对当年的收入。而如果你在获得某项资产后活了60年，财富税将对同一资产征税60次。财富税具有复利效应。
[1] In practice, eventually some of this 8% would come in the form of dividends, which are taxed as income at issue, so this model actually represents the most optimistic case for the founder.
[1] 实践中，这8%的增长最终会有一部分以股息形式出现，而股息在发放时会被作为收入征税，因此这个模型实际上是对创始人最乐观的情况。