NO.PZ2023010410000025
问题如下：
Adrian and Olivia Barksdale live in Australia with their 16-year- old twins. Adrian, 47,
works in a highly cyclical industry as an engineering manager at a bauxite
mine. Olivia, 46, is an accountant. The Barksdales are saving for their
retirement and college funding for both children. Adrian’s annual salary is A$190,000; Olivia’s annual salary is A$85,000. The family’s living expenses are currently A$95,000
per year. Both Adrian and Olivia plan to work 18 more years, and they depend on
their combined income and savings to fund their goals. The Barksdales’ new financial adviser, Duncan Smith,
recommends an appropriate disability insurance policy to cover Adrian, given
his large salary. Because he has a highly specialized job, Adrian is willing to
pay for the most comprehensive policy available. Smith is also concerned about
the Barksdales’ existing life insurance coverage. Currently, the Barksdales have a
term life policy insuring Adrian with a death benefit of A$100,000. Smith
assesses the family’s insurance needs in the event Adrian were to die this year. To do
so, Smith uses the needs analysis method based on the financial data presented
in Exhibit 1 and the following assumptions:
■ The discount rate is 6.0%, and the tax
rate is 30%.
■ Salary and living expenses grow at 3.5%
annually.
■ Salary and living expenses occur at the
beginning of each year.
■ The following assumptions apply in the
event of Adrian’s death:
● Olivia will continue to work until
retirement;
● Family living expenses will decline by
$30,000 per year;
● Olivia’s projected living expense will be $50,000 per year for 44 years;
and
● The children’s projected living expenses will be $15,000 per year for 6 years.
Based on the given assumptions and the data in Exhibit 1, the
additional amount of life insurance coverage needed is closest to:
选项：
解释：
The additional
amount of life insurance coverage needed is calculated as the difference
between the family’s total financial needs and total capital available.
Total financial
needs are calculated as follows.
Capital needs are
determined as the present value of an annuity due: growth rate = 3.5%, discount
rate = 6.0%. Growth of payments is incorporated by adjusting the discount rate
to account for the growth rate of earnings. As long as the discount rate is
larger than the growth rate, the adjusted rate i can be calculated as follows:
[(1 + Discount rate)/(1 + Growth rate)] -1, or i = (1.06/1.035) -1 = 2.42%.
The present value
of Olivia’s living expenses is calculated as follows:
PMT = -$50,000; i
= 2.42%, n = 44. Set for payments at beginning of year. PV = $1,377,175.
The present value
of the children’s living expenses is calculated as follows:
PMT = -15,000; i =
2.42%, n = 6. Set for payments at beginning of year. PV= $84,848.
The present value
of Olivia’s income is calculated as follows:
PMT = -$85,000 × (1-Tax rate); PMT = $85,000 × 0.70 = 59,500; i = 2.42%, n = 18. Set
for payments at beginning of year. PV = –$880,756.
Total capital
needs are calculated as follows:
$1,377,175 +
$84,848 - $880,756 = $581,267. Adding this amount to total cash needs of
$750,000 results in total financial needs of $1,331,267.
The total capital
available is calculated as follows.
The additional
life insurance need is calculated as follows.
我的计算结果如下：
Salary and living expenses grow at 3.5% annually and discount rate is 6%. The the adjusted discount rate is:
1.06 / 1.035 - 1 = 2.415459%.
The after tax salary of Olivia is 59,500. The present value is: $881,063.16
The Olivia's living expense: 1,378,257.46
The living expense of children is: 84,857.35
The additional life insurance is: 1,000,000 + 881,063.16 - 750,000 - 1,378,257.46 - 84,857.35 = -332,051
