Option A | |||
cgt = capital gain tax rate, % | 15.0% | ||
d = annual dividend rate, % | 2.0% | ||
g = annual growth excluding dividends, % | 5.0% | ||
n = years invested, yr | 30 | ||
P = principal invested, $ | $600,000 | ||
t = tax rate on dividends, % | 15.0% | ||
e = tax-adjusted annual growth, % | 6.70% | ||
ecgt = tax-adjusted cap. gain tax rate, % | 11.194% | ||
F = Future, after tax, value | $3,795,594 |
Option B | |||
cgt = capital gain tax rate, % | 0.0% | ||
d = annual dividend rate, % | 2.0% | ||
g = annual growth excluding dividends, % | 3.30% | ||
n = years invested, yr | 30 | ||
P = principal invested, $ | $600,000 | ||
t = tax rate on dividends, % | 0.0% | ||
e = tax-adjusted annual growth, % | 5.30% | ||
ecgt = tax-adjusted cap. gain tax rate, % | 0.0% | ||
F = Future, after tax, value | $2,824,895 |
Wow that is incredibly helpful. It goes to show the real drag costs can be. Almost a million dollar difference despite the tax free option.
I don't suppose you can share your calculations? I want to run scenario A with a 0.6 MER.
Either way that is eye opening
What is the calculation for subtracting the MER from the total? I didn't quite understand that part.
What is the calculation for subtracting the MER from the total? I didn't quite understand that part.
Yes, it is good to define TLAs (Three Letter Acronyms) when using them because people may assume the TLAs mean different things.
I'll assume MER here is Management Expense Ratio as described in https://en.wikipedia.org/wiki/Expense_ratio.
Ignoring taxes, an investment compounded annually increases by (1 + i)^n, where i = annual investment return and n = number of years. E.g., after 30 years at 2%/yr, the investment would be worth 1.02^30 = 1.81 times as much as the original amount.
Instead of saying "...increases by (1 + i)^n" we can say "...changes by (1 + x)^n". Here, n is still years but x can be positive (as in the investment return above) or negative (e.g., a MER). An investment earning no return but subject to a 2% MER for 30 years would be worth only 0.98^30 = 55% of the original amount.
An investment earning 2%/year and subject to a 2% MER, after any number of years, would be worth (1 + 0.02 - 0.02)^n = 1^n = exactly the original amount.
In other words, the MER gets subtracted from the raw investment return to determine an effective investment return. Does that make sense?
As long as we're actually writing down equations, let's do it correctly.
An investment that earns 2% a year before expenses and costs 2% in management fees doesn't mean you have
(1 + 0.02 - 0.02)^n = 1^n.
It's actually
((1+0.2)*(1-.02))^n = 0.9996^n.
So you're actually very slowly losing money.
As long as we're actually writing down equations, let's do it correctly.
An investment that earns 2% a year before expenses and costs 2% in management fees doesn't mean you have
(1 + 0.02 - 0.02)^n = 1^n.
It's actually
((1+0.2)*(1-.02))^n = 0.9996^n.
So you're actually very slowly losing money.
Although, it depends on the definition of "correctly." :) And we'll ignore typos. ;)
If either or both 2% numbers are good to 1 significant figure, (1 + 0.02) * (1 - 0.02) still equals 1.
But yes, if the 2% growth is based on the year's starting amount, while the 2% MER is based on the year end amount after the 2% increase has occurred, the change is indeed as johnny847 implied.
This is similar to the difference between real (ignoring inflation) and nominal (including inflation) growth. See http://www.investopedia.com/terms/n/nominalinterestrate.asp.
I'm not sure what typo you're talking about.That would be the difference between 0.02 and 0.2.
And the order of growth vs when the expenses happen doesn't matter at all, because multiplication is commutative. The 2% fee could be taken at the beginning of the year and you'd still have the same result.You are correct that multiplication is commutative, so 1.02 * 0.98 is the same as 0.98 * 1.02. But the underlying details of how the investment grows and how the MER is charged do matter. E.g., if the 2% fee is taken at the end of the year but based on the value at the beginning of the year it really would be a (1 + .02 - .02) situation.
Finally there's is only one definition of correct. It means 100% accurate. Now we can say something is close enough, or approximately true, or within the margin of error if we're lacking significant figures in the numbers (which I don't know why we would, expense ratios are typically written out to two decimal places, and we're not talking about single digit basis point expense ratios here), but your formula is still not correct. I purposely point out this error because while it does not lead to any significant difference in this case, there are other real world cases where it actually can amount to a significant difference.Yup.
I'm not sure what typo you're talking about.That would be the difference between 0.02 and 0.2.
QuoteAnd the order of growth vs when the expenses happen doesn't matter at all, because multiplication is commutative. The 2% fee could be taken at the beginning of the year and you'd still have the same result.You are correct that multiplication is commutative, so 1.02 * 0.98 is the same as 0.98 * 1.02. But the underlying details of how the investment grows and how the MER is charged do matter. E.g., if the 2% fee is taken at the end of the year but based on the value at the beginning of the year it really would be a (1 + .02 - .02) situation.
Prospectus Gross Expense Ratio - Gross Expense Ratio represents the total gross expenses divided by the fund's average net assets. In some instances, a mutual fund might "waive" a portion of its costs. Some fee waivers have an expiration date; other waivers are in place indefinitely. If the gross expense ratio is not equal to the net expense ratio, the gross expense ratio portrays the fund's expenses had the fund not waived a portion, or all, of its fees. Thus, to some degree, it is an indication of fee contracts.https://www.bogleheads.org/wiki/Expense_ratios (https://www.bogleheads.org/wiki/Expense_ratios)
QuoteFinally there's is only one definition of correct. It means 100% accurate. Now we can say something is close enough, or approximately true, or within the margin of error if we're lacking significant figures in the numbers (which I don't know why we would, expense ratios are typically written out to two decimal places, and we're not talking about single digit basis point expense ratios here), but your formula is still not correct. I purposely point out this error because while it does not lead to any significant difference in this case, there are other real world cases where it actually can amount to a significant difference.Yup.
There is still something to be said, when explaining new concepts, for keeping things simple and "correct enough". E.g, one can get a long way in physics by assuming F=MA instead of the details as described in https://en.wikipedia.org/wiki/Relativistic_mechanics.
That's not how expense ratios are calculated.While it may not be true in that case, there are other real world cases (e.g., the AUM fee my mother pays to her adviser) where it is calculated differently.
Yes there's something to be said for good enough, but there should be a disclaimer along the lines of "this is close enough for this situation, but you should keep in mind this assumption can start to break apart when ...."Yes, sometimes that is appropriate. Gets tiresome if one would do that for every possible post. YMMV.
That's not how expense ratios are calculated.While it may not be true in that case, there are other real world cases (e.g., the AUM fee my mother pays to her adviser) where it is calculated differently.
Guess we'll have to agree to disagree.QuoteYes there's something to be said for good enough, but there should be a disclaimer along the lines of "this is close enough for this situation, but you should keep in mind this assumption can start to break apart when ...."Yes, sometimes that is appropriate. Gets tiresome if one would do that for every possible post. YMMV.
Sure, but I wasn't talking about the AUM fee you mother pays to her adviser.
Guess we'll have to agree to disagree.
Actually, one more twist on this scenario.
How would these two situations compare once the retiree was ready for the withdrawal/retirement phase? Assuming the same tax situation as in the above.
Since the person in the tax free situation does not pay any capital gains, etc, would they not come out ahead?