Di · 2021年10月06日

对unrealized capital gain tax的计算有疑问

NO.PZ2021090804000006

问题如下：

Johnson is a tax adviser who provides tax awareness advice to private clients. One of Johnson’s clients is Lily.

Lily asks Johnson to evaluate Mutual Fund A, which has an embedded gain of 10% of the ending portfolio value. Lily asks Johnsonto calculate a post-liquidation return over the most recent three-year period. Mutual Fund A exhibited after-tax returns of 9.0% in Year 1, 5% in Year 2, and 8% in Year 3, and capital gains are taxed at a 25% rate.

The annualized after-tax post-liquidation return calculated by Johnson is closest to:

选项：

21.1%

B.5.62%.

6.59%

解释：

C is correct.

The annualized after-tax post-liquidation return is calculated as follows.

First, calculate the ending portfolio value. Given Fund A’s after-tax returns over the past three years, the ending portfolio value is calculated as

Final after-tax portfolio value = (1 + 0.09) × (1 + 0.05) × (1 + 0.08) = 1.236.

The after-tax returns compounded in this way account for the tax on distributions and realized capital gains but do not account for any unrealized capital gains. The assumed tax liability from capital gains at liquidation is 2.5% of the final value, which is the product of the 10% embedded gain and the 25% capital gains tax rate. The portfolio value net of the unrealized gains tax liability is given by subtracting the assumed tax liability from capital gains at liquidation from the final after-tax portfolio value:

Portfolio value net of the unrealized gains tax liability = 1.236 − 0.025 = 1.211.

Second, calculate the annualized post-liquidation return as follows:

1.211^1/3− 1=6.59%

年化税后清算后回报计算如下。

首先，计算期末投资组合价值。鉴于基金 A 过去三年的税后回报，期末投资组合价值计算为

最终的税后投资组合价值 = (1 + 0.09) × (1 + 0.05) × (1 + 0.08) = 1.236。

以这种方式复利的税后回报计算了分配税和已实现的资本收益，但不考虑任何unrealized capital gains。清算时资本收益的假定纳税义务为最终价值的 2.5%，这是 10% 的内含收益和 25% 的资本收益税率的乘积。通过从最终税后投资组合价值中减去清算时的资本收益中的假定税负，得出 The portfolio value net of the unrealized gains tax liability：

1.236 − 0.025 = 1.211。

其次，计算年化清算后回报如下：

1.211^1/3 − 1=6.59%

题目中说有10% embeded gain tax on final value of the portfolio. Final value of the portfolio = 1.236, 这样的话CG tax=1.236*10%*25%=0.0309. 跟答案中的不一样，想请问上述计算的问题在哪里？谢谢

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5 个答案

已采纳答案

王暄_品职助教 · 2021年10月09日

请问为什么直接减去10%*25%?这两个相乘只是一个税率呀？为什么不乘以final value 1.236得到一个tax的值？

10%为Capital gain return，25%是针对这部分return所收取的税率，所以两个相乘得到的不是税率，而是【unrealized capital gain所缴纳税收的值】。

而Mutual fund A，题干中已经说了，这几个return是after-tax的，所以不用再乘以税率：

Mutual Fund A exhibited after-tax returns of 9.0% in Year 1, 5% in Year 2, and 8% in Year 3, 所以1.236中仅仅是没有减去【unrealized capital gain所缴纳税收的值】，所以要从1.236中减去，得到最终账户净值。