Can't reconcile dividend taxation problem

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Kelly
Posts: 255
Joined: Sun Nov 18, 2012 7:39 am

Can't reconcile dividend taxation problem

Post by Kelly » Mon Aug 28, 2017 8:38 am

Hi all

I'm trying to reconcile two computations concerning the difference in ending balance of two investments. Each returns only a 2% dividend yield that is taxed either annually (investment A) or all once at the end of 3 compound periods (investment B). I'm trying to measure the loss of growth on A's annual tax bill. The table below shows A. It can also be calculated as 105.187=1.017^3, where 1.7 is the dividend after paying the 15% tax.

Code: Select all

SOY	EOY	GAIN	TAX	BASIS	periods	Compounded tax
100.000	102.000	2.000	0.300	101.700	3	0.018
101.700	103.734	2.034	0.305	103.429	2	0.012
103.429	105.497	2.069	0.310	105.187	1	0.006
						0.037
Investment B pays the tax at the end: 100 x (1.02^3) = 106.128. 100 + (0.85 x 6.128) = 105.2027. The difference between the two ending values is 0.15= 105.2027 - 105.187.

I would think that the difference would be attributed to the loss of growth on the annual tax bill of investment A. To prove this to myself, I broke out the tax bill and compounded it at the full 2%. So, the 0.30 tax in year one would grow to 0.18= .30 - (.30 x (1.02^3)). These total 0.37 (last column), not the expected 0.15.

I'm either thinking about this wrong or I've got a timing issue. Any insight?

Many thanks for any insight!

Kelly

Kelly
Posts: 255
Joined: Sun Nov 18, 2012 7:39 am

Re: Can't reconcile dividend taxation problem

Post by Kelly » Mon Aug 28, 2017 8:41 am

Sorry, forgot to mention 15% dividend tax rate.

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#Cruncher
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Re: Can't reconcile dividend taxation problem

Post by #Cruncher » Mon Aug 28, 2017 11:54 am

Kelly wrote:
Mon Aug 28, 2017 8:38 am
I would think that the difference would be attributed to the loss of growth on the annual tax bill of investment A.
That's correct; but remember that the extra growth on the annual tax would itself be subject to tax at the end of the 3rd year. Your comparison is also off because you incorrectly include the third year dividend tax and because you misplace the decimal point a couple of times. Here is the extra due to tax deferral calculated on the total amounts:

Code: Select all

106.1208000 = pretax grows to            = 100 * 1.02 ^ 3
  0.9181200 = tax                        = 6.1208 * 15%
-----------
105.2026800 = grows to after tax
105.1871913 = grows to if taxed annually = 100 * 1.017 ^ 3
-----------
  0.0154887 = extra due to tax deferral
And here is the same extra amount calculated based on growing the first and second year's tax:

Code: Select all

  0.3000000 = tax first year            = 15% * (100   * 1.02 - 100)
  0.3051000 = tax second year           = 15% * (101.7 * 1.02 - 101.7)

  0.3121200 = 1st year tax grows to     = 0.3000 * 1.02 ^ 2
  0.3112020 = 2nd year tax grows to     = 0.3051 * 1.02
-----------
  0.6233220 = total
  0.6051000 = basis                     = 0.3000 + 0.3051
-----------
  0.0182220 = pretax gain
  0.0154887 = extra due to tax deferral = 0.018222 * 85%

Kelly
Posts: 255
Joined: Sun Nov 18, 2012 7:39 am

Re: Can't reconcile dividend taxation problem

Post by Kelly » Tue Aug 29, 2017 8:57 am

Numbercruncher,

You certainly live up to your name! Thank you. I was chasing my tail on this one for some time. Probably took you 2 mins. I owe you a beer next time I'm in NYC.

Kelly :sharebeer

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