# Private Wealth: Tax Deferred Account and Deferred Capital Gain

Hi guys,

I’m going trough different providers and sometimes I’m confused on TDA and Deferred Capital Gain

My understanding is the following:

• FV TDA = (1+r)n x (1-t)
• FV CG = (1+r)n x (1-t) + txB

Also in the 2020 mock of the CFA Q5B they apply the second formula on a tax deferred, without any other additional info…can someone clarify?

Thanks

The second formula is for circumstances when the asset is purchased at a different price than what the price is when the assessment is done. For example, suppose you are calculating this when the stock in question is priced at \$100, except that you bought it four months ago at a price of \$75. Your B will then be 75/100 = 0.75.

Hi! Not sure about it…that’s the point.

The curriculum clearly defines Taxable Account, TDA and TEA: only in the taxable accounts the second formula applies, for my understanding.

Question 14 in Reading 29 shows how to move from a taxable to a TDA either for bond or for capital gain equities. Equity are taxed as deferred capital gain in the taxable account (Formula 2), but when held in TDA Formula 1 applies (same asset, same return, same cost basis etc)

The last sentence on Q14 implies that the cost basis = 1. The formula thus converges to (1+r)n * (1-tx) + tx for deferred capital gain. As of why the 2020 mock chooses the second one (deferred capital gain with cost basis) for TDA, however, I shall have to check. I am doing the 2020 mock today and hopefully I’ll get to figure out why that’s the case. The only circumstance that comes to mind on why that formula is appropriate for a TDA is that one transfers asset with embedded unrealized capital gain into the TDA, which then carries some cost basis <1. However, with all the errors in the 2020 mock, I would not be surprised if this is purely an error.

Please look again to Q14 compared to Q15: same assumptions but different formulas for Kaplan and Forest, the only difference is where the assets are located:

Kaplan Q14: Equity in TDA and Formula 1 applies
Forest Q15: Equity in TA and Formula 2 applies

so it seems like TDA if not mentioned has 0 cost basis because of pre tax contribution, but if mentioned cost basis you gotta deduce that part out of capital gain calculation

Do you mean cost basis of 1? If so, then yes.

@ste79

When the cost basis is different from 1, I found it better to compute it without the formula.

Example:

PV = 100
Cost basis = 75
Rate = 8
N = 10
Tax rate = 30%

a) FV= 100 x (1.08)^10 = 215.89

b) Subtract cost basis = 215.89 - 75 = 140.89 (this is the capital gains subject to taxes)

c) Compute capital gains after taxes = 140.90 x (1 - 0.30) = 98.63

d) Add back cost basis = 75 + 98.63 = 173.63

Hope it helps!

Thanks to all…but again look at the two questions that I have mentioned. For me some provider does not clarify well in the questions, inclusive in the mock 2020

Try to put formulas apart a little while for this one:

Tax deferred: pay 40% tax rate at withdraw. Value subject to taxes is entire final value (initial investment + capital gains)

Taxable: pay taxes every year*

• except in case of stocks. If hold on taxable account, stocks will be in a tax deferred regime, but only on capital gains

Question 14 - Kaplan

a) Allocated 50,000 to tax deferred with 7% return and deferred 40% tax rate:

• 50,000 x 1.07^20 = 193,484
• After taxes = 193,484 * (1-0.40) = 116,090

b) Allocated 50,000 to taxable with 4% return and annual 40% tax rate:

After tax return: 4% * (1-0.40) = 2.40%

• 50,000 x 1.024^20 = 80,347

A + B = 80.347 + 116,090 = 196,437

Question 15 - Everest

a) Allocated 50,000 to tax deferred with 4% return and 40% deferred tax rate:

• 50,000 x 1.04^20 = 109,556
• After taxes = 109,556 * (1-0.40) = 65,733

b) Allocated 50,000 to taxable with 7% return and 20% deferred capital gains tax rate:

• 50,000 x (1,07)^20 = 193,484
• subtract cost basis = 193,484 - 50,000 = 143,484
• compute capital gains after taxes = 143,484 x (1-0.2) = 114,787
• add back cost basis = 114,787 + 50,000 = 164,787

A + B = 164,787 + 65,733 = 230,520

Does it make sense now?