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 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.
200,000-50,000=150,000
120000/(1+5%)^10=73,669.59
4000000* [(1+6.5%)/(1+5%)]^ 10=4,609,598.28
4,609,598.28* 2%*(1-0.4)=55,315.18
73,669.59+73,669.59=128,984.77<150,000
so Patel can't generate his retirement needs in 10 years after accounting for the effects of inflation on his small business income and his securities portfolio value，because the two source of income (128,984.77) is less than 150,000 which he needs.
老师，我感觉这题有bug，其实small business的income是每年都有，当年的不需要考虑扣减10年inflation，每年都有，又不是10年前的120000，谢谢老师
