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
选项:
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.
1.the distributions from Patel’s portfolio are expected to can be sufficient to cover the expected shortfall between his retirement needs and his anticipated income.
2.His anticipated income include pension payments of EUR50,000 per year and business income of EUR120,000 per year ,total anticipated income is EUR 170,000.Patel estimates will require EUR200,000 per year during retirement,so the shortfall is EUR 30,000.
the distributions from Patel’s portfolio is EUR 480,000 per year,which is calculated as follows:
40millionx{[1+2%x(1-40%)]-1}=EUR 480,000
the distributions of EUR 480000 is larger than the shortfall of EUR 30,000.