Private Wealth: Tax Deferred Account and Deferred Capital Gain

CFA Level III Portfolio Management
#1

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

#2

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.

#3

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)

#4

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.

#5

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

L3 - tax deferred account question
#6

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

#7

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

#8

@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!

#9

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

#10

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?