CFA CFA level 3 CFA level 3 CFA level 3 CFA level 3 CFA volume 2 finquiz item set answers, study session 4, reading 9

Question ID: 12504 Correct Answer: A The after-tax market values and after-tax weights for the $200,000 portfolio is calculated after deducting 40% taxes from the TDA account.. Question

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CFA Level III Item-set - Solution

Study Session 4 June 2018

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FinQuiz Level III 2018 – Item-sets Solution

Reading 9: Taxes and Private Wealth Management in a Global Context

1 Question ID: 12500

Correct Answer: C

Larson’s marginal tax rate is 46% as the portfolio’s income is above $45,000 but below

$70,000 Her next $1 of income would be taxed at 46%

Correct Answer: B

Larson’s tax liability at the end of the year would be $15,650 + 0.46 ($65,000 – $45,000) =

$24,850 Thus the average tax liability would be approximately 38% ($24,850/$65,000)

The formula for calculating the expected after-tax accumulation after a period of n years is as follows:

FVIFTAXABLE = (1 + r*) n (1 – T*) + T* − (1 – B)tcg

Prior to calculating this value, it is necessary to calculate r*

The after-tax annual return (r*) earned on Larson’s portfolio at the end of the year is

calculated as follows:

r* = r(1 – piti - pdtd – pcgtcg)

= 7.5% [1 – (0.2 × 0.14) – (0.5 × 0.14) – (0.15 × 0.12)]

= 6.63%

The effective capital gains tax rate on Larson’s portfolio is calculated as follows:

T* = tcg(1 – pi – pd – pcg)/ (1 – piti - pdtd – pcgtcg)

= 0.12 (1 – 0.2 – 0.5 – 0.15)/ [1 – (0.2 × 0.14) – (0.5 × 0.14) – (0.15 × 0.12)]

= 0.02036 or 2.036%

FVIFTAXABLE = $500,000 [(1 + 6.63%) 20 (1 – 2.036%) + 2.036% − (1 – 1)(12%)]

= $1,778,759.95 ≈ $1,780,000

The accrual equivalent after-tax return on Larson’s portfolio is calculated as follows:

$500,000 (1 + RAE) 20 = $1,778,759.95

RAE = 0.0655096 or ≈ 6.55%

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Correct Answer: A

The after-tax market values and after-tax weights for the $200,000 portfolio is calculated after deducting 40% taxes from the TDA account

Market Value ($)

Pre-Tax Market Weights (%)

After-Tax Market Value ($)

After-Tax Weights (%)

*60,000 (1 – 0.4) = $36,000

Amongst the three regimes (Heavy Interest Tax, Common Progressive, Light Capital Gain Tax), the Light Capital Gain tax regime is a progressive tax regime taxing dividends and interest income at ordinary rates and capital gains at favorable rates

The effective capital gains tax rate can be found using the following formula:

ࡱ࡯ࡳ = ࡯ࡳ (૚ିࡼ`ାࡼ ࡼ )

૚ି(ࡼ ࢀ ାࡼ ࢀାࡼ ࢀ )

૚ିሺ૙.૚૙×૙.૜૙ା૙.૜૙×૙.૛૙ା૙.૜૛×૙.૚૙ሻ

૙.ૡૠૡ

= 3.189%

First, we will calculate the effective tax rate for Harris’ portfolio using the following

formula:

ா஼ீ = ஼ீ (ଵି௉`ା௉ ௉ )

ଵି(௉ ் ା௉ ்ା௉ ் )

ଵିሺ଴.ଵ଴×଴.ଷ଴ା଴.ଷ଴×଴.ଶ଴ା଴.ଷଶ×଴.ଵ଴ሻ

଴.଼଻଼

= 3.189%

Now we can calculate the return after realized taxes using the following equation

Value in 10 years = $500,000 (1 + R୅ୖ୘)ଵ଴(1–T୉େୋ) + T୉େୋ–(1–B) Tେୋ

$1,503,400 = $500,000 (1 + R୅ୖ୘)ଵ଴(1–0.03189) + 0.03189– (1–0.75) 0.10

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Solving the above equation we get,

஺ோ் = 12%

A heavy dividend tax regime has a progressive income tax structure It has a favorable

treatment for interest income and capital gains

A light capital gain tax regime has a progressive income tax structure and a favorable treatment for capital gains

A flat and heavy regime has a flat income tax structure and a favorable treatment for interest income

Anderson’s first statement is correct Accrual taxes are paid periodically The tax drag

increases as the time horizon increases and as the investment return increases Return and investment horizon have a multiplicative effect on the tax drag associated with future

accumulations The impact of return is greater for long investment horizons, and the

impact of investment horizon is greater for higher returns

Anderson’s second statement is incorrect The proportion of investment growth consumed

by wealth based taxes decreases as return increases

Using the tax rate of 30% given in option C we can perform the following calculations:

The after tax value of the TDA account is $170,000(1– 0.30) = $119,000

The after-tax value of the tax-exempt account is $70,000

The total after-tax value of the portfolio is $189,000

Stocks represent 37% of the portfolio whereas bonds represent 63% of the portfolio

Alternatively, the tax rate can be calculated as follows:

37% x X = $70,000

X = $189,000

Where X = After tax portfolio value

$189,000 – $70,000 = $119,000

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$119,000 = $170,000(1 – tax rate)

Tax rate = 30%

Smith is incorrect in agreeing with Anderson’s first statement Tax savings realized in a

given tax year from the tax loss harvesting overstate the true gain Selling a security at a

loss and reinvesting the proceeds in a similar security effectively resets the cost basis to the lower market value, potentially increasing future tax liabilities In other words, taxes saved now may be simply postponed

Smith is incorrect in disagreeing with Anderson’s second statement The efficient frontier

of portfolios should ideally be viewed on an after-tax basis Furthermore, because the tax status of an investment depends on the type of account it is in, the same asset could appear on the efficient frontier in both taxable and non-taxable form

The capital gains on Jones’ portfolio were A$1,500,000 × 0.25 = $375,000

If losses are not realized, capital gain tax will be A$112,500 (A$375,000 × 30%)

The same year, unrealized capital losses were A$100,000 – A$70,000 = A$30,000

If these securities are sold in 2010 and the capital losses are realized, the capital gain will reduce to A$345,000 (A$375,000 – A$30,000) The new capital gain tax is:

A$345,000 × 30% = A$103,500

Tax savings = A$112,500 – A$103,500 = A$9,000

Harvesting losses is not an optimal strategy when the investor currently faces a relatively low tax environment and will face higher taxes in subsequent periods In this scenario, the best strategy will be to defer harvesting losses

A is incorrect Tax loss harvesting has more value when securities have potentially high volatility

B is incorrect Cumulative tax alphas from tax loss harvesting will increase over time

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The after-tax value of the TDA account is 0.6 × A$5,000,000 × (1 – 0.4) = A$1,800,000 After-tax value of the tax-exempt account = A$5,000,000 × 0.4

= A$2,000,000

Total after-tax value of the portfolio = A$1,800,000 + A$2,000,000

= A$3,800,000

Stock represents A$2,000,000/A$3,800,000 = 52.6% of the total after-tax value

Bonds represent A$1,800,000/A$3,800,000 = 47.4% of the total after-tax value

In a deferred capital gain taxation environment, the future value of an accumulation equals:

FV = (1 + r)n(1 – tcg)+ tcg

The future accumulation of Po’s portfolio in a deferred capital gain taxation environment is: 250,000[(1 + 0.08)15(1 – 0.25) + 0.25] = A$657,281.71

In an annual taxation environment, the future value of an accumulation equals:

FV = [1 + r(1 – ti)]n

The future accumulation of Po’s portfolio in an annual taxation environment is:

250,000[(1 + 0.08(1 – 0.25)]15 = A$599,139.55

The deferred capital gain environment accumulates to A$657,281.71/A$599,139.55 = 1.097 times the amount accumulated in an annual taxation environment

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Comment 1 is incorrect In a deferred capital gains environment, tax drags remain constant regardless of the time horizon This is because, according to the formula for calculating the future value accumulation, in such an environment, after-tax investment gain is equal to the pre-tax investment gain multiplied by one minus the tax rate

Comment 2 is incorrect The advantages of tax deferral can be offset or eliminated if

securities taxed on an accrual-basis have greater risk-adjusted returns That is, the greater the risk-adjusted returns on assets taxed on an accrual basis, the lower the relative

accumulations Therefore, the greater the future value of the accumulation in an annual taxation environment, the greater the chances that the advantages of tax deferral may be lost

A$80,000 of Po’s income will generate taxes of A$17,550 The remaining A$70,000

(A$150,000 – A$80,000) will generate taxes of A$25,900 (A$70,000 × 0.37) The average tax rate is equal to (A$17,550 + A$25,900)/A$150,000 = 28.97%

Marginal tax rate is the Tax rate paid on highest dollar of income, that is, 37% here The marginal tax rate exceeds the average tax rate by 8.03% (37% – 28.97%)

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