Managing Ind. Portfolios / Taxes & PWM - R10/11

Question 1

What are the objectives and constraints for individuals?

Answer 1

RRTTLLTU

• Risk
• Return
• Taxes
• Time horizon
• Legal/regulatory
• Liquidity
• Trusts
• Unique circumstances

Question 2

How to calculate

1. after-tax real required return
2. pre-tax real required return
3. nominal pre-tax return

Answer 2

1. after-tax real required return =
   
   • after-tax liquidity needs / asset base
2. pre-tax real required return
   
   • after-tax real return / (1 - tax rate)
3. nominal pre-tax return
   
   • pre-tax required return + inflation
   • (1 + pre-tax required return)(1 + inflation)

Question 3

Can you describe some common tax regimes?

Answer 3

• Common Progressive
• Heavy Dividend Tax
• Heavy Capital Gain Tax
• Heavy Interest Tax
• Light Capital Tax
• Flat and Light
• Flat and Heavy

Common progressive is most common (favourable treatment for interest income, dividends, and capital gains), followed by light capital tax (favourable treatment of capital gains only).

Question 4

Name the 3 primary categories of taxes.

Answer 4

1. Income taxes
2. Wealth Taxes
3. Consumption Taxes

Question 5

Accrual Tax

What is the formula for the future value interest factor after investment income tax (FVIF_IT)?

Answer 5

FVIF_IT = [1 + R(1-T_I)]^N

Where:

R = before-tax investment return

T_I = annual tax rate on investment income

N = # investment periods

FVIF_IT is a time value of money factor that shows the future after-tax value of each unit of currency for N periods earning a return of R.

Question 6

Describe the 3 important relationships surrounding (accrual) tax drag.

Answer 6

Tax drag % > tax rate

investment horizon increases => tax drag $ & % increases

investment return increases => tax drag $ & % increases

Question 7

Using T_CG as the tax rate on capital gains, the after-tax future value interest factor for deferred capital gains (FVIF_CGT) is:

Answer 7

FVIF_CGT = [1+R)^N(1-T_CG)+T_CG]

[1+R)^N(1-T_CG) calculates the after-tax future value of the investment account, including the initial investment. Assuming the initial investment is made from after-tax dollars and is, thus, not subject to further taxation, we add T_CG to add back that tax.

Question 8

Describe the 3 important relationships surrounding tax drag when applied on a deferred basis.

Answer 8

Tax drag % = tax rate

As investment horizon increases => Tax drag unchanged

As investment return increases => tax drag unchanged

Additionally, as either/both horizon and return increases, the value of the tax deferral increases (think RRSPs).

Question 9

Can you calculate the FVIF_{CGT,MV=/=basis}? Recall that we are adjusting the cost basis

Answer 9

FVIF_{CGT,MV=/=basis} = [(1+R)^N(1-T_CG)]+T_CGB

Where B = Basis

Question 10

What is the future value interest factor after the wealth-based tax (FVIF_WT)?

T_W = Wealth-based tax rate

Answer 10

FVIF_WT = [(1 + R)(1 - T_W)]^N

Be mindful that as a wealth tax, it applies to both principal and investment return (ie, total account value)

Question 11

What are the three primary relationships for tax drag on wealth-based tax?

Answer 11

Tax drag % > tax rate

As investment horizon increases => tax drag $ & % increase

As investment return increases => tax drag $ increases, while tax drag % decreases

Question 12

Use the following notation:

P_I = proportion of total return from interest

P_D = proportion of total return from dividends

P_CG = proportion of total return from realized capital gains

Calculate:

Realized Tax Rate

R_ART (annual return after realized taxes)

Answer 12

Realized Tax Rate = (P_IT_I + P_DT_D + P_CGT_CG)

R_ART = R(1-realized tax rate) = R[1-(P_IT_I + P_DT_D + P_CGT_CG)]

Question 13

Deferred Tax rates will be greater as less accrual tax is paid annually.

How do you calculate T_ECG?

(T_ECG = Effective capital gains tax rate)

Answer 13

T_ECG = T_CG * [[1-(P_I + P_D + P_CG)] / [1-(P_IT_I + P_DT_D + P_CGT_CG)]

or otherwise

T_CG*[ 1-(P_I+P_D+P_CG) / (1-realized tax rate)

Question 14

An accrual equivalent after-tax return is the annual return that produces the same terminal value as the taxable portfolio

R_AE = ?

Answer 14

R_AE = (FV_T / PV)^1/N-1

where FV_T = the taxable future value