NO.PZ202410180200002401
问题如下：
Determine whether the distributions from Patel’s portfolio are expected to be sufficient to cover the expected shortfall between his retirement needs and his anticipated income
解释：
The solution below shows that the expected distributions of EUR48,000 are greater than the expected shortfall of EUR30,000. Thus, the distributions are expected to be more than sufficient to help Patel meet his annual income needs in retirement. The expected shortfall between Patel's retirement needs and his anticipated income is equal to EUR30,000 (=200,000—50,000 - 120,000). The expected after-tax distributions from his portfolio are EUR48,000, as shown below:
FVA=B{[1+r(1-tx)]^T}-1=4,000,000{[1+0.02(1-0.40)]}=48,000
The current value of the portfolio or basis, B, is EUR4,000,000. The before-tax return, r, is the 2% yield from dividends and interest. The tax rate, tx ， is 40%, and Tequals 1 to reflect the annual cash distributions to augment the shortfall. Note that this return ignores the after-tax return from capital appreciation, which would add to the excess of after-tax earnings over annual income needs.
The expected shortfall between Patel’s retirement needs and his expected income is EUR 30k ( 200k-120k-50k)
The distributions from his portfolio is
EUR 4000k *(2%*60%)=EUR 48k>EUR 30k
So the distributions is sufficient to cover the shortfall.