Taxes and Private Wealth Management in a Global Context

Question 1

10.b: Determine the effects of different types of taxes and tax regimes on future wealth accumulation

Answer 1

the future value interest factor after
investment income tax (FVIFIT) is: = (1+R(1-t))^N

Compounding of accrual (annual) taxes makes their effect stated as a percentage of total gain greater than the tax rate.

The gain lost to taxes, stated as a currency or
as a percentage, is referred to as tax drag.

• Increasing investment horizon increases tax drag in both currency and percentage terms.
• Increasing return on investment increases tax drag in both currency and percentage terms.

Question 2

10.d: Explain how investment return and investment horizon affect the
tax impact associated with an investment.

Answer 2

1. Tax drag%> tax rate.
2. As investment horizon increases ==> tax drag $ and tax drag % increase.
3. As investment return increases ==> tax drag$ and tax drag% increase.

FVIFcGT = (1 + R)^N *(1-Tcg) + Tcg

Question 3

1 O.d: Explain how investment return and investment horizon affect the tax impact associated with an investment.

Answer 3

Wealth-Based Taxes vs. Accrual Taxes

As with accrual taxes, tax drag$ and tax drag % increase with investment horizon.

Unlike accrual taxes, when investment return increases, tax drag % decreases.

The realized tax rate is nothing more than the weighted- average tax rate paid by the investor.

realized tax rate= (Pi Ti+ Pd Td+ Pcg Tcg)

RART = R(l-realized tax rate)= R[l-(PiTi+Pd Td +PcgTcg)]

annual return after realized taxes ( ART)

effective capital gains tax rate (TECG)= Tcg( 1-(Pi+Pd+Pcg)/[l-(PiTi+Pd Td +PcgTcg)]

FVIFr = [(1 +Rart)^t *(1-Tecg)+ Tecg -(1-B)Tcg)

Question 4

1 O.c: Calculate accrual equivalent tax rates and after-tax returns.

Answer 4

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

Rae = (FVt/PV)^1/n -1

Accrual equivalent tax rate ( T AF.) is the tax rate that makes the pre-tax return (R) equal to the accrual equivalent after-tax return (RAF.)

an accrual equivalent tax rate = Rae = R(1-Tae)

Question 5

1 O.e: Discuss the tax profiles of different types of investment accounts and explain their impact on after-tax returns and future accumulations.

Answer 5

FVIFtda = (1 + R)N (1-TN) 
FVIFtea = (1 + R)N (1-To)

R  = before-tax return on the account 
TN = tax rate in effect at the time of withdrawal

any funds contributed to a tax-exempt
account are first subject to the current income tax,

T0

Question 6

10.f: Explain how taxes affect investment risk.