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.
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