Terminal value after tax

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patso

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My solution below is wrong. The correct answer is $2,535,582, could someone point me in the right direction re what im doing wrong?? Please reply WITHOUT those long tax formulas… I don’t intend to learn them –just simple logic please.
Question:
$1m portfolio that generates a return of 14%. The portfolio has a cost basis of $0.75m. Tax rate on realised gains is 25%, tax rate on interest is 30% and tax rate on dividends is 35%. The portfolio return is composed of 15% interest, 35% dividends and 40% realised gains. Returns proportions continue for 10 years. WHAT IS THE BALANCE OF THE PORTIFOLIO AT THE END OF 10 YEARS.
Here is my solution (which is incorrect):
Taxes on Interest, dividends, realised capital gains are: 14 x 0.15 x 0.30 + 14 x 0.35 x 0.35+ 14 x 0.4 x 0.15 = 3.75%
After tax return = 14% - 3.75% = 10.26%
FV = (1+0.1026)^10 = $2,654,501
Capital gains on portfolio =($2,654,501 - $750,000)x 0.25 = $476,125
Net portfolio after 10 years is: = $2,654,501 - $476,125 = $2,178,375
 
Im not sure what’s going on but your return component only adds up to 90%… Is 10% tax exempt or something?
“The portfolio return is composed of 15% interest, 35% dividends and 40% realised gains”
Here’s how I would approach
1,000,000*(1.14^10) = 3,707,221 - 750,000 (cost base) = 2.957m profit
Realized Gain = 2.957m * 40% * -25% = net gain
Interest Gain = 2.957m * 15% * -30% = net gain
Dividends Gain = 2.957m *.35 * -35% = Net gain
————————————————————————–
Sum of the above + 750,000 = Ending Portfolio value after tax
I’m calculating 2.6m but im missing 10% of the return to tax.
EDIT: I’m also assuming tax is applied at the end of year-10 since it’s not provided which I think is a key difference for your calcs (growing at after-tax returns)
 
Galli wrote:
Im not sure what’s going on but your return component only adds up to 90%… Is 10% tax exempt or something?
“The portfolio return is composed of 15% interest, 35% dividends and 40% realised gains”
Here’s how I would approach
1,000,000*(1.14^10) = 3,707,221 - 750,000 (cost base) = 2.957m profit
Realized Gain = 2.957m * 40% * -25% = net gain
Interest Gain = 2.957m * 15% * -30% = net gain
Dividends Gain = 2.957m *.35 * -35% = Net gain
————————————————————————–
Sum of the above + 750,000 = Ending Portfolio value after tax
I’m calculating 2.6m but im missing 10% of the return to tax.
EDIT: I’m also assuming tax is applied at the end of year-10 since it’s not provided which I think is a key difference for your calcs (growing at after-tax returns)
Click to expand...
Hey Gali. I dont agree with your workings:
1. If you are given the interest, div, and realised gains, you assume the return difference is unrealised gains.
2. Tax on interest, div and realised gains are paid annually and hence you cant calculate your Future value @ 14$% rate (which is the tax free return”
 
patso wrote:
Galli wrote:
Im not sure what’s going on but your return component only adds up to 90%… Is 10% tax exempt or something?
“The portfolio return is composed of 15% interest, 35% dividends and 40% realised gains”
Here’s how I would approach
1,000,000*(1.14^10) = 3,707,221 - 750,000 (cost base) = 2.957m profit
Realized Gain = 2.957m * 40% * -25% = net gain
Interest Gain = 2.957m * 15% * -30% = net gain
Dividends Gain = 2.957m *.35 * -35% = Net gain
————————————————————————–
Sum of the above + 750,000 = Ending Portfolio value after tax
I’m calculating 2.6m but im missing 10% of the return to tax.
EDIT: I’m also assuming tax is applied at the end of year-10 since it’s not provided which I think is a key difference for your calcs (growing at after-tax returns)
Click to expand...
Hey Gali. I dont agree with your workings:
1. If you are given the interest, div, and realised gains, you assume the return difference is unrealised gains.
2. Tax on interest, div and realised gains are paid annually and hence you cant calculate your Future value @ 14$% rate (which is the tax free return”
Click to expand...
Did you provide the complete question? You seem to be drawing on conclusions that aren’t provided in your post.
 
Sum(PT) = 26.25%
Sum(P) = 90%
R* = R ( 1 - Sum(PT)) = 14 * ( 1 - 0.2625 ) = 10.325%
TCG* = TCG * (1-Sum(P)) / ( 1- SUM(PT)) = 0.25 * (1-.9) / (1-0.2625) = 0.0339
Factor = (1+R*)^N (1-TCG*) + TCG* - TCG(1-B)
= (1.10325)^10 * (1-0.0339) + 0.0339 - 0.25 ( 1-.75) = 2.552242
I have taken it to the max on the decimal places. and not rounded down or up anywhere
the answer seems to be if you truncate to 4 or 5 decimals at each point.
 
and to answer your questions - this is the blended tax environment related. the big formula R*, TCG* with a B thrown in.
 
Thanks CPK. I know i get the answer using the tax effective capital gains formula and i feel i understand conceptually the effective cap gains but i cant figure out why i cant get the same using a step by step “practical” process which doesnt use these formulas. Please see my proposed solution above, and could you kindly tell me what i have missed.
 
the step by step will not work because each year 90% is taxed, while 10% is not.
you need the 10% which changes year on year and add on its final value. That is missing.
 
On the contrary you can calculate the net future value without the formulas if you know what you are doing…though this may not be everyone’s cup of tea. However it may be quicker if you use the formulas above (see CPK’s comments).
Firstly you need to understand that your portfolio started from $750,000 to $ 2,654,501 (which you have rightly computed). Your workings are 80% ok but you are double charging CGT on the cost basis and missing the tax on the deferred account. The tax man will tax the uplift/gain from $750,000 to $2,654,501 – which are dividends, interest and capital gains and these are taxed accordingly. One way is to split the computations into two parts:
  1. GAIN FROM $750,000 TO $1,000,000
  2. GAIN FROM $1,000,000 TO $ 2,654,501
PART 1.
Starting with the new cumulative future value you have computed$ $2,654,501, has the tax man taken into account the tax on the gains from $750,000 to $1,000,000 yet? NO and hence you compute the tax:CGT 25% ie $1,000,000 - $750,000. You get $62,500 and deduct from $2,654,501.
PART 2
Secondly you consider if $ 2,654,501 takes into account all the relevant taxes for gains from $1,000,000 TO $ 2,654,501? Ofcourse No. Only the tax on interest, dividends and realised gains have been deducted. The tax on the deferred account is not yet taken into account. Remember your initial return was $140,000 (ie 14%) – made up of $56,000 realised gains, $21,000 interest,$49,000 dividends and $14,000 deferred gains. All other income accounts are taxed annually except deferred account. Hence your untaxed deferred gains in $2,654,501 is 14,000/ 102,550 x ($2,654,501 - $1,000,000) and then apply 25%. You will get $56.5k as tax on the untaxed deferred gain. [$102,550 is the $140,000 less tax paid on interest, dividends and realised gains.]
Therefore your net investment balance AFTER paying or accounting for all taxes = $ 2,654,501 - $62.5k - $56.5k =$2,536k.
 
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