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.
Next, Smith discusses the advantages and disadvantages of annuities. The Barksdales are interested in purchasing an annuity that offers the following characteristics: a payout that begins at retirement,the ability to invest in a menu of investment options, and a payout that continues as long as either Olivia or Adrian is living.
Olivia’s mother, Sarah Brown, is also a client of Smith. She is age 75 and retired, and she needs a known income stream to assist her with current and future expenses.
Brown’s parents both lived longer than average, and she is concerned about outliving her assets. Smith recommends an annuity. The Barksdales also worry about longevity risk given their family history and healthy lifestyle. Both spouses want an annuity for their later years (beginning in 40 years) that will ensure the greatest supplemental, level income stream relative to the cost. The Barksdales are willing to forgo the right to cash out the policy. Smith turns to a discussion about the Barksdales’ investment portfolio and how total economic wealth (human capital plus financial capital) might a₤ect asset allocation decisions. The Barksdales’ human capital is valued at $2.9 million and estimated to be 35% equity-like. Smith determines that an overall target allocation of 40% equity is appropriate for the Barksdales’ total assets on the economic balance sheet. Smith makes two recommendations regarding the Barksdales’ investment portfolio.
Recommendation 1: The portfolio should have lower risk than a portfolio for similar investors in the same lifestyle stage.
Recommendation 2: The portfolio should underweight securities having a high correlation with bauxite demand.
Based on the given assumptions and the data in Exhibit 1, the additional amount of life insurance coverage needed is closest to:
选项：
A. A$0.
B. A$331,267.
C. A$2,078,101.
解释：
B is correct.
The additional amount of life insurance coverage needed is calculated as the di₤erence 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%.
题中说到每年的expense会减少3万这个条件不用嘛？
