NO.PZ202410180200002403
问题如下：
Sharfepto Zik, a private wealth manager, is meeting with a 60-year-old client, Garbanzo Patel, in order to create an IPS for Patel’s upcoming retirement in the next year. Patel estimates that he will require EUR200,000 per year, with annual increases for inflation, during retirement. Patel’s primary spending goals during retirement are to provide for his family’s needs and maintain his retirement lifestyle. His secondary goals are to fund his philanthropic activities and leave a significant inheritance to his children. During his retirement, Patel will receive union pension payments of EUR50,000 per year with annual increases for inflation. In his spare time, Patel runs a small business that provides him with an annual income of EUR120,000 and is valued at EUR1 million. He will continue running his business during retirement. Patel holds a portfolio of securities valued at approximately EUR4 million with a cost basis of EUR1 million. Patel expects an annual pretax capital gains return of 6.5% per year on his securities portfolio. The capital gains tax rate is 20%. The 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%. In the past, Patel has reinvested all these distributions back into his portfolio but anticipates that after retirement he may need to use some of the distributions to fund his expenses. Additionally, Patel plans to buy a vacation home to enjoy his early retirement years and expects to hold the home for 10 years. His budget for the vacation home is approximately EUR1.7 million. He expects an 8% annual pretax appreciation in the value of his vacation home and expects to pay capital gains tax of 20% on the sale of this vacation home. Patel is considering selling half of his securities portfolio to fund the vacation home purchase. Patel is also worried about the effects of inflation. While his pension income will adjust for inflation, he is concerned that the income from his small business is unlikely to adjust with inflation. He asks Zik to do an analysis to assess whether his income sources are expected to be sufficient in 10 years to cover the effects of inflation of 5% per year
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 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.
老师，请问这个思路是否可行？以下回答是否正确。
pension = 50k x(1+5%)^10=81.44k
business = 120k
div. = 4mx(1+2%x(1-40%))-4m=48k
expense=200kx(1+5%)^10=325.78k
income=81.44k+120k+48k=249.44k<325.78k
income cannot meet his retirement needs in 10 years
