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努力做个学霸Sam · 2020年10月21日

问一道题：NO.PZ2018091705000024 [ CFA III ]

  1. CFA III
  2. 个人IPS

问题如下：

Allen is an investment manager, who recently recruited a new customer, Polly. Polly invested $100,000 in an asset for 20 years that promises to offer an annual capital gain of 8%, which are deferred capital gains. The investment account is expected to be taxed 15% when capital gains are realized. Assume at beginning of the investment period, the investment has a cost basis of $80,000, Calculate the post-tax value of the investment after 20 years later.

选项：

A.

$411,181.36

B.

$372,756.35

C.

$ 408,181.36

解释：

C is correct.

考点：Deferred Capital Gain Tax

解析：首先，我们计算一下B = 80,000/100,000=0.8

接着我们运用税基基础不等于1时候的Deferred Capital Gain Tax计算，即

lFV=PV[(1+R)N−[(1+R)N−B]×TCG]100,000[(1+8%)20−[(1+0.08)20−0.8]×15%]=408,181.36{l}FV=PV{\lbrack{{(1+R)}^N-\lbrack{(1+R)}^N-B\rbrack\times T_{CG}}\rbrack}\\100,000{\lbrack{(1+8\%)}^{20}-{\lbrack{(1+0.08)}^{20}-0.8\rbrack}\times15\%\rbrack}=408,181.36

请问这里为什么不能用:(1+8%)*20✘(1-15%)-(1–80/100)✘15%呢？我这里有点混乱了，我这个做法错在哪里呢？

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1 个答案

王暄_品职助教 · 2020年10月22日

嗨，爱思考的PZer你好：


首先，Tcg=15%，这是资本利得所要交的税，也就增值的那部分的资本应该要扣15%的税

你这个式子上来就错了：（1+8%）^20*(1-15%)，这等于说是对20年后，账户的全部金额扣税了


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NO.PZ2018091705000024 Allen is investment manager, who recently recruitea new customer, Polly. Polly investe$100,000 in asset for 20 years thpromises to offer annucapitgain of 8%, whiare ferrecapitgains. The investment account is expecteto taxe15% when capitgains are realize Assume beginning of the investment perio the investment ha cost basis of $80,000, Calculate the post-tvalue of the investment after 20 years later. $411,181.36 $372,756.35 $ 408,181.36 C is correct. 考点ferreCapitGain T解析首先，我们计算一下B = 80,000/100,000=0.8 接着我们运用税基基础不等于1时候的ferreCapitGain Tax计算，即 lFV=PV[(1+R)N−[(1+R)N−B]×TCG]100,000[(1+8%)20−[(1+0.08)20−0.8]×15%]=408,181.36{l}FV=PV{\lbrack{{(1+R)}^N-\lbrack{(1+R)}^N-B\rbrack\times T_{CG}}\rbrack}\\100,000{\lbrack{(1+8\%)}^{20}-{\lbrack{(1+0.08)}^{20}-0.8\rbrack}\times15\%\rbrack}=408,181.36lFV=PV[(1+R)N−[(1+R)N−B]×TCG​]100,000[(1+8%)20−[(1+0.08)20−0.8]×15%]=408,181.36 可否这样计算(1+8%)^20-[(1+8%)^20-1]*0.15-(1-0.8)*0.15 上面这个是blentaxing里稅基不是1的算法，为什么两个地方不一样？

2021-11-03 21:37 2 · 回答

为什么得出B,为什么-0.8？

2019-12-10 07:33 2 · 回答