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问一道题：NO.PZ2018091705000028 [ CFA III ]

问题如下：

Allen is an investment manager, who recently recruited a new customer, Jack. Jack invested $2,000,000 in a portfolio for 20 years that promises to offer an annual return of 8% before tax. The costs basis is 1,500,000. The ratio of interest, dividends, realized capital gains, unrealized capital gains to earnings and related tax rates are shown in the following table.

Calculate the post-tax value of the investment after 20 years later.

选项：

$6,203,347

$6,609,332

$6,053,347

解释：

C is correct.

考点：Blend Taxing Environments

解析：这道题考法非常常规。对于Blend Taxing，我们首先还是要计算其 $R_{ART}$ 以及 $T_{ECG}$

${l}R_{ART}=R\times\lbrack1-(P_I\times T_I+P_D\times T_D+P_{CG}\times T_{CG})\rbrack\\=0.08\times{\lbrack1-{(0.3\times0.4+0.35\times0.2+0.150.3\times)}\rbrack}=6.12\%$

${l}T_{ECG}=\frac{\lbrack1-(P_I+P_D+P_{CG})\rbrack\times T_{CG}}{1-(P_IT_I+P_DT_D+P_{CG}T_{CG})}\\=\frac{\lbrack1-(0.30+0.35+0.15)\rbrack\times0.3}{\lbrack1-{(0.3\times0.4+0.35\times0.2+0.15\times0.3)}\rbrack}=7.843\%$

接下来直接套用Blend Taxing的公式，题目明确说明costs basis等于1,500,000，那么B=1,500,000/2,000,000=0.75。

${l}FVIF_T={(1+R_{ART})}^N-{\lbrack{(1+R_{ART})}^N-1\rbrack}T_{ECG}-{(1-B)}T_{CG}\\FV=2,000,000{\{{(1+6.12\%)}^{20}-{\lbrack{(1+6.12\%)}^{20}-1\rbrack}7.843\%-{(1-0.75)}30\%\}}\\=6,053,347$

请教下下标art，ecg是什么的缩写呢？

问一道题：NO.PZ2018091705000028 [ CFA III ]

2 个答案

2

1

671

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