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monicaaaaa · 2025年06月12日

答案

  1. CFA III
  2. 个人IPS

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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

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解释：

Patel requires EUR200,000 of real purchasing power throughout retirement. His pension income will adjust for inflation, so this amounts to EUR50,000 of real income. So, he needs EUR 150,000 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 EUR150,000 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 EUR5,113,600. 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.

  1. Patel is not able to generate his retirement needs in 10 years after accounting for the effects of inflation.
  2. his income contains pension income (annual increases for inflation), small business income and portfolio income. The retirement needs is EUR200,000 and the pension income is EUR 50,000.
  3. The after inflation adjustment income for small business is 120,000/(1+5%)^10=EUR73,669.59 
  4. The after tax and inflation adjustment income for portfolio is 4,000,000x(1.065/1.05)^10x2%x(1-40%)=55315.
  5. The total income is EUR178984.59. So the shortfall is EUR21015.41

老师，我计算small business income时在分母考虑了通胀因素，这样做可以吗

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1 个答案

费费_品职助教 · 2025年06月12日

嗨，从没放弃的小努力你好：


同学你好

这样做是正确的。

在处理通胀的时候可以用除法（原版书知识点的做法）也可以用减法（原版书答案的做法），数据结果差异不大，看同学的习惯即可

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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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