CFA Institute 2017 Level III Mock - AM Portion Q 6-A

CFA Level III Portfolio Management
#1

This question threw me through a loop. Please put my mind at ease.

_ Highlights are as follows: _

  1. Fiona, 35, is a just retired former tennis player.

  2. Fiona receives a pension during her retirement. $375K annually, pre-tax, in coming year. In future years, annual pension payment indexed to 1.25% per year inflation. Pension is taxes 33%

  3. T-12 living expenses are $400K. These are expected to grow at inflation every year forward.

  4. Current investment portfolio is $5.2M. Next week going to buy real estate for $450K (exclude from Inv.Port.) and will also receive $1.1M bonus that will immediately be invested in Inv. Port.

  5. This bonus and all investment returns are taxed 33%.

  6. Fiona wants Inv. port. to fund any expenses not covered by pension, while maintaining its real value over time.

Q: What is (Determine) Fiona’s nominal after-tax required rate of return for the coming year?

_ CFA Answer: _

  1. Inflows: Fiona’s pension after-tax: $375K * (1-0.33) = +$251,250

  2. Outflows: Living Expenses, inflation-adjusted: $400K * 1.0125 = ($405,000)

  3. Annual Deficit/Cash Need: ($251.25 - 405.0) = ($153,750)

  4. Total Asset Base: Portfolio $5.2M + $737K Bonus {$1.1M (1-0.33)} - $450K Re. Purchase = $5,487,000

  5. Real After Tax Req. Return = Cash Need/Total Asset Base (153,750/5,487,000) = 2.8%

  6. Nominal After-Tax Req. Return ( Arithmetic Answer) = Real Return + Inflation = 2.8% + 1.25% = 4.05%

or

6. Nominal After-Tax Req. Return (Geometric Answer) = (1+Real Return)*(1 + Inflation) - 1 = (1.028*1.0125) - 1 = 4.09%

Still following me? Good.

Now my issue is this: “The bonus and all investment returns are taxes 33%”.

Wouldn’t the current portfolio need a pre-tax return of $153,750 / (1 - 0.33) = $229,477?

This $229,477 would then be realized and taxed [$229,477 * (1 - 0.33)] such that after-tax = $153,750

I suppose it is terminology, but I think of " nominal after-tax required rate of return" as being the rate of return necessary/required _t o fund the _ nominal cash need/deficit amount of $153,750 after-taxes have been paid.

Thus $229,477/$5,487,000 = 4.1822%

4.1822%% + 1.25% Inflation = 5.4322% = nominal after-tax required rate of return

Now that I’ve typed this out, I suppose the CFA Institute would consider 4.1822% to be the real pre-tax required rate of return and 2.8% to be the real after-tax required rate of return(?).

But what benefit would knowing the minimum required return after taxes be? As obviously your investment goal would need to be a return of 5.4322% to be able to fund the living expense deficit/cash need and maintain real value of portfolio after inflation.

Maybe I’ve wandered down a CFA rabbit hole and gotten lost…

Thanks all & god speed (good luck June 23rd).