09年CFA III 上午第一题 求教高手 face, university, employee, company, ffffff

forest_hu

去年3级的题，求税前return，答案里是最后加inflation的，就是先算real 的税后return，除以1－T，然后加inflation

我怎么觉得是 real税后return先加inflation再除以1—T呀，求教高手了

晕

 

原文

Patricia and Alexander Tracy, both age 59, are residents of Canada. They have twin sons who
will enter a four-year university program in one year. Patricia is a long-time employee of a
telecommunications company. Alexander is a self-employed sales consultant.
Alexander’s annual income is now steady after years of extreme highs and lows. The Tracys
have built an investment portfolio through saving in Alexander’s high income years. The
Tracys’ current annual income is equal to their total expenses; as a result, they cannot add to
savings currently. They expect that both their expenses and income will grow at the inflation
rate. All medical costs, now and in the future, are fully covered through government programs.
The Tracys worry about whether they have saved enough for retirement, and whether they will
be able to maintain the real value of their portfolio. Inflation is expected to average 4% for the
foreseeable future.
The Tracys have approached Darren Briscoe to help them analyze their investment strategy and
retirement choices. The Tracys disagree about the appropriate investment strategy. Patricia
prefers not losing money over making a high return. This is partly a result of continuing regret
for a loss experienced in an equity mutual fund several years ago. Alexander’s history of making
frequent changes in their portfolio greatly annoyed Patricia. She thinks Alexander focused only
on potential return and paid little attention to risk.
The Tracys currently have all their assets in inflation-indexed, short-term bonds that are expected
to continue to earn a return that would match the inflation rate after taxes. After retirement, they
are willing to consider changing their investment strategy if necessary to maintain their lifestyle.
The Tracys are eligible to retire next year at age 60. If they do, Patricia will receive annual
payments from her company’s defined-benefit pension plan and both Patricia and Alexander will
receive payments from the Canadian government pension plan. Alexander does not participate
in any company or individual retirement plan. Briscoe has compiled financial data and market
expectations for the Tracys’ retirement, shown in Exhibit 1. Currently, Briscoe estimates that the
Tracys’ investment portfolio will grow to 1,100,000 Canadian dollars (CAD) by their retirement
date next year.

Exhibit 1
Financial Data and Market Expectations
Patricia and Alexander Tracy
Retirement at Age 60
(2010)
Expected annual expenses CAD 125,000
Annual pension income (after-tax)
Patricia’s company plan CAD 40,000
Combined government pension CAD 40,000
Total annual pension income CAD 80,000
Expected annual inflation 4.0%
Expected annual after-tax portfolio return 4.0%
Pension income from both Patricia’s company plan and the government pension plan is fully
indexed for inflation. Briscoe expects a tax rate of 20% to apply to the Tracys’ withdrawals from
the investment account. The Tracys expect to earn no employment income after retirement. The
Tracys’ residence is not considered part of their investable assets.
The Tracys have the option to delay retirement until age 65. The Tracys intend to retire together,
whether it is in 2010 at age 60 or in 2015 at age 65.
Briscoe determines that if the Tracys retire at age 60, their risk tolerance is below average. If
they retire at age 60, they plan to pay off their mortgage and associated taxes by withdrawing
CAD 100,000 from their portfolio upon retirement.
Another consideration for the Tracys relates to funding university expenses for their sons. If the
Tracys retire at age 60, each son will receive a scholarship available to retiree families from
Patricia’s company that will cover all university costs.
If the Tracys retire at age 65, all pension income would increase and would almost meet their
annual spending needs. If they retire at age 65, the Tracys would pay all university expenses
from their investment portfolio through an arrangement with the university. The arrangement,
covering both sons, would require the Tracys to make a single payment of CAD 200,000 at age
60.

 

答案

Return Calculations are:
Retire Next Year at
Age 60
Cash Flows
Inflows
Patricia’s company pension CAD 40,000
Combined government pension 40,000
Total Inflows 80,000
Outflows
Estimated expenses 125,000
After-tax net income needed (45,000)
Pretax net income needed (using 20% tax rate) (56,250)
Investable Assets
Estimated investment portfolio in one year 1,100,000
Mortgage payoff (100,000)
Investment portfolio upon retirement 1,000,000
Required Return Calculation
Pretax income need divided by investable assets 5.625%
Plus expected inflation 4.000%
Required Pretax Nominal Return (arithmetic) 9.625%
Required Pretax Nominal Return (geometric) 9.850%
[(1.05625 × 1.04) – 1 = .0985 = 9.850%] OR [(1.0563 × 1.04) – 1 = 9.86%]