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yan · 2024年10月25日

1.4个数据没看懂;2.这道题答案能否用中文解释一遍

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NO.PZ202410180200002403

问题如下:

Evaluate Patel’s ability to generate his retirement needs in 10 years after accounting for the effects of inflation on his small business income and his securities portfolio value

选项:

解释:

Patel requires EUR200,000 of real purchasing power throughout retirement. His pension income will adjust for inflation, so this amounts to EURS0,000 of real income. So, he needs EURlS0,000 of real income from his securities portfolio and his small business income. The effects of inflation on his small business income are as follows if it remains at a nominal amount of EUR120,000 per year: Real business income in 10 years = 120,000 x (1 - 0.05)^10 = 71,848 So, in 10 years, the inflation of 5% annually is expected to reduce the purchasing power of Patel's small business income to EUR71,848. Deducting this amount from EURlS0,000 gives a subtotal of EUR78,152. Can the securities portfolio provide this amount of income in 10 years? Applying the following formula to the value of the securities portfolio:

FVIF tx,inflation==[l + r (1-tx)]^T— (1 —π)^ T=[1 + 0.065 (1 — 0)] ^10— (1 — 0.05) ^10 = 1.27840

Multiplying this amount by the current portfolio value of EUR4 million gives EURS,113,600. The securities portfolio generates a 2% pretax cash distribution taxed annually at a 40% rate; thus, the after-tax distribution is 1.2% of the portfolio value. Cash distribution in real terms in 10 years = 0.012 x 5,113,600 = EUR61,363 Thus, Patel faces an income shortfall in 10 years ofEUR16,789 (= 78,152— 61,363). To cover the shortfall, Patel may have to consider liquidating small portions of his securities portfolio to generate additional cash flow each year. Of course, such reductions will cause a decline in the value of his portfolio, thus also reducing future cash distributions from the portfolio, so these would have to be considered as well.


红色划线部分的数据是哪里来的?


1.2%是从哪里来的?


5113600是从哪里来的

1 个答案

费费_品职助教 · 2024年10月28日

嗨,努力学习的PZer你好:


同学你好

1.     这道题目是让咱们评估这个人是否有能力通过【他的小企业+证券组合价值】来满足【考虑了通胀影响的退休需求】。解题思路是分别计算这两部分的数值,比较大小。

2.     【考虑了通胀影响的退休需求】:他每年需求时200,000,随通胀调整;同时养老金pension是50000也是每年随通胀调整的。所以他实际需要150,000

3.     他公司收入每年是120,000,10年后经过通胀调整=120000*(1-5%)^10=71848. 所以现在的缺口=150000-71848=78152,看他的组合能否在10年后分红和利息达到这个数值。

4.     10年后组合的价值=[4000000*(1+6.5%)/(1+5%)]^10=4609598. 每年分红率是2%,征税40%,所以第10年得到的分红(cash distribution)=4609598*(2%*(1-40%))=4609598*1.2%=55315小于78152,所以不能满足。

5.     注意:教材给的参考答案在处理通胀的时候用了简易算法,即实际利率≈名义利率-通胀率。 我们也可以按照教材给的公式,对通胀的处理用除法,除以(1+infl)^T

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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