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sliang · 2024年11月08日

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NO.PZ202410180200002402

问题如下:

Determine whether Patel should sell half of his securities portfolio to buy the vacation home.

选项:

解释:

To determine whether Patel should sell the securities, an analysis can be done to compare the expected after-tax value of the home purchase and the expected after-tax value of the securities portfolio at the end of the 10-year time horizon. To avoid additional complexity, the analysis may initially avoid considering the cash distributions of the securities portfolio. If half of the securities portfolio (i.e., EUR2,000,000) is sold, then Patel will realize a capital gain of EURl,500,000 (i.e., half of the capital gain of the full portfolio). Thus, the tax on the sale of the securities will be EUR300,000 (=20% x 1,500,000), and Patel will have EURl, 700,000 (=2,000,000 - 300,000) to buy the house. Alternatively, Patel could choose to forego buying the vacation home and maintain his securities portfolio for another 10 years (i.e., continue to invest EUR2,000,000). For both alternatives, use the following equation to calculate the after-tax values:

FVAcgb=B [(1 + r)^T(1—tcg) + tcg (B)]

For the vacation home purchase alternative, the basis (B) is equal to EURl, 700,000 and the expected pretax rate of return r is equal to 8%. If the vacation home is foregone and the portfolio is fully reinvested, the basis is equal to EUR2,000,000 and the expected pretax rate of return is equal to 6.5%. In both cases, the time horizon (1) is 10 years and the capital gains tax rate (tcg) is 20%. After-tax value of vacation home = 1,700,000 [(1 + 0.08) 10 (1—0.20) + 0.20 (l,700,000/1,700,000)] = 3,276,138

After-tax value of reinvesting = 2,000,000 [(1 + 0.065)^ 10 (1—0.20) + 0.20 (2,000,000/2,000,000)] = 3,403,420 Thus, although the pretax investment return on the securities portfolio is lower than the pretax return on the vacation, the higher-value solution on an after-tax basis is to keep the securities portfolio in place. This is because a return can be earned on the capital gains tax amount that would have to be paid if the securities were liquidated. Patel should consider an alternative source of funding for the vacation home.

请问这个 investment value = 3,403,420是怎么算出来的呀?可以再详细的讲一下么?

3 个答案
已采纳答案

费费_品职助教 · 2024年11月08日

嗨,爱思考的PZer你好:


同学你好

1.如果他卖掉一半的组合,他可以得到 2,000,000-(4,000,000-1,000,000)*20%=1,700,000

2.如果他用这些钱去买房子,那么10年后房子的价值是

1700,000*【(1+8%)^10-[(1+8%)^10-1]*20%】=3,276,138

3.如果他没有卖掉组合,那么2,000,000的价值在10年之后是

2,000,000*【(1+6.5%)^10-[(1+6.5%)^10-1]*20%】=3,403,420

所以不应该卖组合

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

sliang · 2024年11月09日

组合的这个计算,只算了capital gain的收益,为什么不把2% dividend的收益也放进去呀?题目里给了这个 条件呀 - “portfolio primarily contains dividend-paying stocks and interest-bearing bonds, and the yield on the portfolio is 2%. Both stock dividend and bond interest are taxed annually at a rate of 40%”

sliang · 2024年11月09日

1. 不明白为什么是1,700,000? 一半组合是2,000,000,cost是500,000,那么卖掉一半组合到手的钱是 = 2,000,000 - (2,000,000-500,000)*20%= 1,200,000。请问你的税基为什么要用(4M-1M)算呀?这个是整个组合的税基 3. 一半组合在10年后卖掉的话,你的计算中税基是2M, 请问这里要用0.5M作为税基算capital gain么?

费费_品职助教 · 2024年11月10日

嗨,从没放弃的小努力你好:


Tcg=(2000,000-500,000)*20%=300,000 这样和同学思路是一致的。

这里哈,用0.5做税基也是可以的,税基在计算税的时候来考虑即可。

在我之前的公式中税基是题目给的1,000,000:税收=0.5*(4,000,000-1,000,000)*20%,其实整体思路是一样的

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努力的时光都是限量版,加油!

费费_品职助教 · 2024年11月10日

嗨,爱思考的PZer你好:


同学你好

1.整个组合现在的价值是4,000,000,Basis是1,000,000,如果全部卖掉的话可以实现capital gain是=4,000,000-1,000,000=3,000,00。但现在只卖出组合的一半是2,000,000.所以卖掉之后确认的capital gain也是一半,即3,000,000/2=1,500,000.对这部分要征收20%的税,因此实际到手的资金=2,000,000-1500,000*20%=1700,000

2.这里需要注意,卖出一半是指卖出组合现值的一半,不考虑税的话可以到手2000,000。而basis是在计算对CG征税的时候才用到。除了用上面的计算逻辑,也可以:Tcg=(2000,000-500,000)*20%=300,000 这样和同学思路是一致的。

3.在不考虑利息和分红的情况下,投资组合的价值已经超过房子的了,这一点已经可以帮助投资者判断是否应该卖组合来买房子,所以不需要再计算分红和利息的部分。 如果这里算出来组合的价值小于房子,那么确实应该再考虑到分红和利息

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加油吧,让我们一起遇见更好的自己!

sliang · 2024年11月10日

谢谢老师。请问这一问你有回答么?“一半组合在10年后卖掉的话,你公式的计算中税基是2M, 请问这里要用0.5M作为税基算capital gain么? ”

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NO.PZ202410180200002402 问题如下 termine whether Patel shoulsell half of his securities portfolio to buy the vacation home. To termine whether Patel shoulsell the securities, analysis cne to compare the expecteafter-tvalue of the home purchase anthe expecteafter-tvalue of the securities portfolio the enof the 10-yetime horizon. To avoiaitioncomplexity, the analysis minitially avoiconsiring the cash stributions of the securities portfolio. If half of the securities portfolio (i.e., EUR2,000,000) is sol then Patel will realize a capitgain of EURl,500,000 (i.e., half of the capitgain of the full portfolio). Thus, the ton the sale of the securities will EUR300,000 (=20% x 1,500,000), anPatel will have EURl, 700,000 (=2,000,000 - 300,000) to buy the house. Alternatively, Patel coulchoose to forego buying the vacation home anmaintain his securities portfolio for another 10 years (i.e., continue to invest EUR2,000,000). For both alternatives, use the following equation to calculate the after-tvalues:FVAcgb=B [(1 + r)^T(1—tcg) + t(B)]For the vacation home purchase alternative, the basis (is equto EURl, 700,000 anthe expectepretrate of return r is equto 8%. If the vacation home is foregone anthe portfolio is fully reinveste the basis is equto EUR2,000,000 anthe expectepretrate of return is equto 6.5%. In both cases, the time horizon (1) is 10 years anthe capitgains trate (tcg) is 20%. After-tvalue of vacation home = 1,700,000 [(1 + 0.08) 10 (1—0.20) + 0.20 (l,700,000/1,700,000)] = 3,276,138After-tvalue of reinvesting = 2,000,000 [(1 + 0.065)^ 10 (1—0.20) + 0.20 (2,000,000/2,000,000)] = 3,403,420 Thus, although the pretinvestment return on the securities portfolio is lower ththe pretreturn on the vacation, the higher-value solution on after-tbasis is to keep the securities portfolio in place. This is because a return cearneon the capitgains tamount thwoulhave to paiif the securities were liquite Patel shoulconsir alternative sourof funng for the vacation home. 红线部分的数据代表了什么,没看懂

2024-10-25 10:04 1 · 回答