130477是怎么计算得出的？

问题如下：

James and Wendy Chang, both age 58, plan to retire in nine years. James is a human resource manager for a large US company with a defined contribution (DC) pension plan to which he regularly contributes. Wendy is a freelance computer programmer who works out of a home-based office. She contributes to a private DC plan. Both expect to start receiving Social Security income benefits when they retire at age 67. Their long- term goal is for a comfortable retirement and to provide an inheritance for their two children. The Changs believe they will need to maintain, in real terms, their current level of spending of $100,000 when they retire.

The Changs meet with their financial adviser, Lucie Timan, to discuss the risks to their retirement lifestyle goal. She estimates their Social Security benefit amounts at age 67. In her estimation calculations, Timan assumes a 25% tax rate and a 3% inflation rate. Based on his estimates, the Changs will have total annual pretax retirement income, including Social Security benefits, of $194,500 when they retire at age 67. The Changs tell Timan that they plan to use their DC plans’ balances at age 67 to buy an immediate fixed annuity with no inflation adjustment.

Discuss how each of the following risk factors could affect the Changs’ projected retirement income:

i. inflation risk

ii. loss of employment

iii. poor investment returns

选项：

解释：

Part i: The Changs are in a good position to maintain their current lifestyle in retirement. Their total annual pretax retirement income of $194,500 will leave them with after- tax income of about $145,875 (given the assumption of a 25% tax rate). This expected after- tax income exceeds the expected nominal level of spending in their retirement year of $130,477 (given the assumption of a 3% inflation rate and nine years until retirement). One particular risk that could affect the Changs’ projected retirement income, however, is that inflation may reduce the purchasing power of their after- tax income over time. This risk is of particular concern given the expectation that the retirement plan balances are expected to be used to purchase an annuity with no inflation adjustment. Thus, purchasing the fixed annuity with no inflation adjustment should be reconsidered.

Part ii: Another risk factor that could adversely affect the Changs’ projected retirement income is the potential loss of employment. If James were to lose his job or Wendy’s freelance work were to decrease unexpectedly, and they were unable to obtain comparable levels of compensation, their projected retirement income would likely be lower.

Part iii: A third risk factor that could affect the Changs’ projected retirement income is poor investment returns. Lower returns resulting from poor market conditions in the equity and bond markets would adversely impact the Changs’ pension fund balances at retirement and likely result in lower retirement income.

第一部分：Chang 一家在退休后仍能保持目前的生活方式。他们每年 194,500 美元的税前退休总收入将使他们的税后收入约为 145,875 美元（假设税率为 25%）。这一预期的税后收入超过了他们退休年度 130,477 美元的预期名义支出水平（假设通货膨胀率为 3%，离退休还有 9 年）。然而，一个可能影响 Chang 夫妇预计退休收入的特殊风险是，随着时间的推移，通货膨胀可能会降低他们税后收入的购买力。鉴于预期退休计划余额将用于购买没有通货膨胀调整的年金，这种风险尤其令人担忧。因此，应该重新考虑购买没有通货膨胀调整的固定年金。

第二部分：另一个可能对 Chang 的预计退休收入产生不利影响的风险因素是潜在的失业。如果詹姆斯失业或温蒂的自由职业意外减少，他们无法获得可比水平的补偿，他们预计的退休收入可能会更低。

第三部分：可能影响 Chang 一家预计退休收入的第三个风险因素是投资回报不佳。由于股票和债券市场的市场状况不佳而导致的较低回报将对Chang退休时的养老基金结余产生不利影响，并可能导致退休收入减少。