Author Topic: Case Study - New job, New life  (Read 7462 times)

ApplePI

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Case Study - New job, New life
« on: May 14, 2015, 08:13:21 PM »
Hi, I'm Mike. I'm starting a new job in August and I'm looking to do things "right" this time.

Info:
27 years old, no debt
42,000 starting less taxes and SS, so I'm assuming I'll have roughly a 35,000 net.
Now, my ex gets 20% of that net regardless of what it is. There is no getting around these expenses. So that's 7000.
Health care is covered.

Job Income: 35,000 net. Open to taking a weekend job, but it would be low paying.
Div Income:      Just shy of 400

Expenses:
My ex: 7000 (Can't change)

Rent: 4800 (Monthly 306 for rent, 20 for comcast, 20 for garbage, other utilities vary 20 - 50)
**I do not believe any of this can go lower. With 5 of us in a house, "power conservation" is a team effort and we aren't much of one**

Auto: 1200 (Monthly Ins 76, Bi-annual oil 30, Gas will soon be VERY minimal, ~20 TOPS since I can bike to my new job)
**My new job is within biking distance. Now, unless I am way-overpaying for insurance, I do not believe I can lower this. Opinions surely welcome**

Cellphone: 600 (50ish each month.)
**It's weird, but sometimes it's like 40's and others it's 60's. I share with my brother and his wife on a family plan. I've never felt like I'm getting screwed, but perhaps I need to rethink this one? Thoughts?**

Food: 4800 (This was last year's food bill. I have a number of eating out tabs over $50 that I did not recall when first posting. I do not have it itemized, but I ate crab legs *often.* I bought starbucks (derp). I had food delivered(double derp). I'm single and have free time to cook- there is NO excuse for this.)
**This is the REAL hole in my budget. I have cut coffee cold turkey. I will steam no more crab legs. But the truth is, my day-to-day eating is still pricey because I just don't know what is inexpensive and healthy. I have read rice and beans. I could do this. Any other suggestions?**
**I can REALLY save here! HELP! What *should* I be spending on food? **

Piano lessons: 780. This likely won't change. Music adds value to my life that is worth retiring later for. If that is extremely contrary to this community, I apologize and please know that I in no way intended to offend.

So of my 35,400, I have about 16,220 left over that is not allocated to one of the above categories. I can max an IRA, contribute ~10 grand to the 403b (granted, yes this changes some numbers), and still have some free bucks to kick around. But where are my holes? What am I overlooking? How can I be *better* ?

[From my original post:]
The 403b options I get are lousy - high ERs and such. So, I guess an IRA is the way to go, but after that is maxed, I'm likely looking at taxable account, right? Answered

I have little investing experience outside of about $10,000 in AT&T stock that I bought a decade ago so that the dividend income would pay for my Starbucks for the rest of my life... It seemed like an awesome idea at the time. I net just over $100 per quarter on this, but I always spend it on coffee or other impulse dumb things.I am DONE wasting this income, but should I sell this investment off and move it around? It's currently earning almost 5% (more like 4% after taxes) on dividends alone, although the value of the shares has not gone up almost at all. I don't recall my cost basis, but it was my army enlistment bonus less taxes - somewhere north of $8,500.

I've worked hard this year eliminating all of my debt in order to get on this track and I'm ready for the next step. Any and all advice would be stellar.


« Last Edit: May 19, 2015, 09:44:48 PM by ApplePI »

MDM

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Re: Case Study - New job, New life
« Reply #1 on: May 14, 2015, 08:29:07 PM »
Now, all told, this still leaves me with about 16,600 to invest assuming I stay on budget. The 403b options I get are lousy - high ERs and such. So, I guess an IRA is the way to go, but after that is maxed, I'm likely looking at taxable account, right?
Are the 403b options lousier than paying 15% taxes? 

RichWard

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Re: Case Study - New job, New life
« Reply #2 on: May 14, 2015, 08:35:47 PM »
The one thing that stood out to me is your food bill at $4,800 per year or $400 per month.

Does this include dining out, or only groceries?

If it's only groceries, this is a huge place to cut. For about $200 per month, I'm making decent meals, eating veggies and fruits, etc, with my significant other.

Additionally, it's great you can bike to work! That's one of the biggest expenses people have. However, how are you getting to your $1,200 budget? I walk/bike to work, and typically my gas expenses are $25 per month for driving to get groceries and socializing. Where is the rest of your commuting coming from?

Good job on the housing expenses, that's pretty low even with what I'm used to in the low cost of living midwest.

I'm not sure how realistic $16,600 per year is because you're not budgeting any entertainment, household items, clothes, etc.

A second job may be a serious consideration.

Also, great job on eliminating the debt.


ApplePI

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Re: Case Study - New job, New life
« Reply #3 on: May 14, 2015, 08:48:18 PM »
Are the 403b options lousier than paying 15% taxes? 
At what percentage point does a a high ER negate the pre-tax benefit? What I mean is, if my money will be invested pretax but earn less than the money would be if invest elsewhere post tax, wouldn't the taxable account be better? Or does such a "break even point" not exist?


The one thing that stood out to me is your food bill at $4,800 per year or $400 per month.

Does this include dining out, or only groceries?

If it's only groceries, this is a huge place to cut. For about $200 per month, I'm making decent meals, eating veggies and fruits, etc, with my significant other.
My food bill is accounting for eating out, which is very VERY sparingly. Usually it's just a 2.00 beer when out with buddies, maybe my share of a pizza. I rarely eat out because I prefer my own food. I'm fully aware that I need to cut back on food at home, though. I don't have it fully itemized from last year, but I steam crab legs about twice per month - cutting that could theoretically save me $600 over a year.

Additionally, it's great you can bike to work! That's one of the biggest expenses people have. However, how are you getting to your $1,200 budget? I walk/bike to work, and typically my gas expenses are $25 per month for driving to get groceries and socializing. Where is the rest of your commuting coming from?

My gas and car usage was 2400 last year including two oil changes and two tires. I'm assuming the cost of gas will be minimal now less a few trips for fun. I will need to replace two tires this year most likely as well. I am assuming $100/ month for any possible car related expense as I have no mechanical skill myself. I would sock this money away separate from other money.




I'm not sure how realistic $16,600 per year is because you're not budgeting any entertainment, household items, clothes, etc.

A second job may be a serious consideration.

Also, great job on eliminating the debt.


A second job is not out of the realm of possibility - this one will be 7-3 with weekends off. The time will be there, though maybe not the motivation.

My numbers are coming from the personal capital app, and last year clothing and entertainment were probably wrapped up into the groceries/restaurants section since most of my clothes are from Wally World and I never categorized these purchases separately. I rarely buy new clothes, though. Household expenses are in this same category as well.

However, one expense that does not show up in that category that I forgot to mention was that I take piano lessons to the tune of $780 per year (biweekly, $30 a pop). So that puts my investable amount at up to 15,820.

« Last Edit: May 14, 2015, 09:15:46 PM by ApplePI »

MDM

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Re: Case Study - New job, New life
« Reply #4 on: May 15, 2015, 12:51:08 AM »
Are the 403b options lousier than paying 15% taxes? 
At what percentage point does a a high ER negate the pre-tax benefit? What I mean is, if my money will be invested pretax but earn less than the money would be if invest elsewhere post tax, wouldn't the taxable account be better? Or does such a "break even point" not exist?
The general case depends on tax brackets, rates of return, and time.  It has probably been done before - I vaguely recall having done it myself - but can't find it quickly so here goes.

To keep things somewhat simple, assume equal tax brackets at contribution and withdrawal.

a = ordinary tax rate, fraction.  E.g., 0.15
b = expense ratio difference, fraction.  E.g., 0.01
i = taxable investment return, fraction.  E.g., 0.05
n = number of years
P = Principal available for investment
w = tax rate on long term capital gains, fraction.  E.g., 0.15
y = fraction of investment return subject to annual tax.  E.g., 0.5 (1/2 from dividends, 1/2 from appreciation)
z = tax rate on annual investment returns, fraction.  E.g., 0.15

The equation for the 403b is straightforward because there are only ordinary taxes, those happen only once, and due to our assumption it doesn't matter whether the tax occurs at contribution or withdrawal.
403b: (1-a) * P * (1+i-b)^n  or  P * (1+i-b)^n * (1-a)  (same, whether Roth or traditional)

Taxable is messier because taxes occur at contribution, during investment growth, and at withdrawal.

Taken in pieces:
  Amount contributed = (1-a) * P
  After 1 year, before tax = (1-a) * P * (1 + i)
  Tax on the first year = (1-a)*P*i *y*z
  After 1 year, after tax = (1-a) * P * (1 + i*(1-y*z))
  After n years, before withdrawal = (1-a) * P * (1 + i*(1-y*z))^n
  Taxable amount to withdraw = (1-a) * P * (1 + i*(1-y*z))^n - (1-a)*P
  Tax on above amount = w * ((1-a) * P * (1 + i*(1-y*z))^n - (1-a)*P)

Taxable amount after withdrawal after tax = (1-a) * P * (1 + i*(1-y*z))^n - w * ((1-a) * P * (1 + i*(1-y*z))^n - (1-a)*P)

The (1-a)*P term cancels from both the IRA and taxable equations, leaving
403b - Taxable = (1+i-b)^n - (1-w) * (1+i*(1-y*z)^n - w

If the equation above is positive, 403b is better.
If the equation above is negative, Taxable is better.

Assume i = 0.05, w = 0.15, y = 0.5, z = 0.15 and look at the resulting equation as a function of b and n:
(1.05 - b)^n - 0.85 * 1.04625^n - .15

The curvature of this equation as a function of n depends on the value of b. 
If b<0.375% (=1.05 - 1.04625), it starts positive and stays positive.  In other words, if the 403b expense ratio is 0.375% or less above the taxable, 403b is always better.
If n=1, we get 0.0106875 - b.  In other words, if the 403b expense ratio is more than 1.06875% above the taxable, taxable is always better (for >1 year).
If b = 0.7%, the 403b is better for 45 years (see plot below), after which taxable would be better.  But if you retire in <45 years, you could roll the 403b over to an IRA and get a low expense ratio.

And all this is based on all the assumptions listed.  As the saying goes, YMMV.  But you could take these formulas, put them in Excel, and enter the values specific to your situation.


ApplePI

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Re: Case Study - New job, New life
« Reply #5 on: May 15, 2015, 09:36:35 AM »
It will likely take me the better part of the weekend to fully digest that response, but I really appreciate it. I never expected the answer to be so complicated!

Bracken_Joy

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Re: Case Study - New job, New life
« Reply #6 on: May 15, 2015, 10:06:09 AM »

ApplePI

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Re: Case Study - New job, New life
« Reply #7 on: May 19, 2015, 09:24:12 PM »
Okay! I ran the numbers and have determined that *some* of the funds available in my 403b and better than comparables in a taxable account, but none are better than a Vanguard IRA (I used a combination of the two equations to get the IRA -> the amount contributed is (1-a)*P like taxable, but the rest is like the 403b portion).

So here's a few dummy questions:
-Is it "silly" to have both a 403b AND a Vanguard IRA? The idea here is that the Vanguard index funds are cheaper than the 403b (even with tax considerations), but if I want other indexes which seem similar the tax-free growth of the 403b edges out the IRA up to 30ish years (some calculations were more like 45 - 50). I won't be working that long, so I would roll over well before that time.

-I know many on this website are pro-index funds, but is it okay to purchase a number of well-known, blue chip stocks, 20-30, across all sectors and hold instead of index? The reason I ask is that, while small, an index fund has an expense ratio that is higher than commissions if enough shares are purchased at once. Perhaps there is another complicated formula to determine how to play this angle, but if there is a straight up answer, please let me know.

-I need to get over my stupid comment earlier about dividend investing "not being right for me." I am attempting to better my financial situation, and I realize that justifying my poor spending of that money is counter to this plan. So, is investing in dividend specific stocks considered viable in this investing circle, or is it gimmicky? (I'm thinking about this over index funds for S&P 500; I would still hold foreign stocks, and bonds in indexes). The goal here is not to "beat" the market, but to continue having returns to invest even if the market drops a bit. Thoughts?


------

Onto my next bit: I don't feel like I provided enough breakdown in my budget before and that's because I did not properly categorize everything in Personal Capital. So after a weekend of looking, here is a better breakdown:

Job Income: 35,000 net. Open to taking a weekend job, but it would be low paying.
Div Income:      Just shy of 400

Expenses:
My ex: 7000 (Can't change)

Rent: 4800 (Monthly 306 for rent, 20 for comcast, 20 for garbaage, other utilities vary 20 - 50)
**I do not believe any of this can go lower. With 5 of us in a house, "power conservation" is a team effort and we aren't much of one**

Auto: 1200 (Monthly Ins 76, Bi-annual oil 30, Gass will soon be VERY minimal, ~20 TOPS since I can bike to my new job)
**My new job is within biking distance. Now, unless I am way-overpaying for insurance, I do not believe I can lower this. Opinions surely welcome**

Cellphone: 600 (50ish each month.)
**It's weird, but sometimes it's like 40's and others it's 60's. I share with my brother and his wife on a family plan. I've never felt like I'm getting screwed, but perhaps I need to rethink this one?**

Food: 4800 (This was last year's food bill. I have a number of eating out tabs over $50 that I did not recall when first posting. I do not have it itemized, but I ate crab legs *often.* I bought starbucks (derp). I had food delivered(double derp). I'm single and have free time - there is NO excuse for this.)
**This is the REAL hole in my budget. I have cut coffee cold turkey. I will steam no more crab legs. But the truth is, my day-to-day eating is still pricey because I just don't know what is inexpensive and healthy. I have read rice and beans. I could do this. Any other suggestions?**
**I can REALLY save here! HELP! What *should* I be spending on food? **

Piano lessons: 780. This likely won't change. Music adds value to my life that is worth retiring later for. If that is extremely contrary to this community, I apologize and please know that I in no way intended to offend.

So of my 35,400, I have about 16,220 left over that is not allocated to one of the above categories. I can max an IRA, contribute ~10 grand to the 403b (granted, yes this changes some numbers), and still have some free bucks to kick around. But where are my holes? What am I overlooking? How can I be *better* ?

MDM

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Re: Case Study - New job, New life
« Reply #8 on: May 19, 2015, 09:38:18 PM »
So here's a few dummy questions:
-Is it "silly" to have both a 403b AND a Vanguard IRA?
Not silly at all.  Many people do, to take advantage of the separate ($18K for the 403b and $5.5K for the IRA) contribution limits.

Quote
The idea here is that the Vanguard index funds are cheaper than the 403b (even with tax considerations), but if I want other indexes which seem similar the tax-free growth of the 403b edges out the IRA up to 30ish years (some calculations were more like 45 - 50).
Don't understand this part, because both a 403b and an IRA have tax free growth.

PJ

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Re: Case Study - New job, New life
« Reply #9 on: May 19, 2015, 09:45:14 PM »
Food: 4800 (This was last year's food bill. I have a number of eating out tabs over $50 that I did not recall when first posting. I do not have it itemized, but I ate crab legs *often.* I bought starbucks (derp). I had food delivered(double derp). I'm single and have free time - there is NO excuse for this.)
**This is the REAL hole in my budget. I have cut coffee cold turkey. I will steam no more crab legs. But the truth is, my day-to-day eating is still pricey because I just don't know what is inexpensive and healthy. I have read rice and beans. I could do this. Any other suggestions?**
**I can REALLY save here! HELP! What *should* I be spending on food? **

Piano lessons: 780. This likely won't change. Music adds value to my life that is worth retiring later for. If that is extremely contrary to this community, I apologize and please know that I in no way intended to offend.

So of my 35,400, I have about 16,220 left over that is not allocated to one of the above categories. I can max an IRA, contribute ~10 grand to the 403b (granted, yes this changes some numbers), and still have some free bucks to kick around. But where are my holes? What am I overlooking? How can I be *better* ?

I can help with this!  Or at least, point you in the direction of the powerful community that we have around here.  I get hungry sometimes just reading these threads.

http://forum.mrmoneymustache.com/off-topic/the-ultimate-mustachian-food-guide/

http://forum.mrmoneymustache.com/off-topic/mustachian-recipe-index/

Also, about the piano lessons, good for you!  You've got no debt, you've made choices to keep your housing and other expenses affordable.  I can't imagine anyone's going to be handing out any face punches over something that you value so highly, and that gives your life meaning.

ApplePI

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Re: Case Study - New job, New life
« Reply #10 on: May 19, 2015, 09:51:26 PM »
Don't understand this part, because both a 403b and an IRA have tax free growth.

This was based of using the above formulas - since the ROTH IRA does not have tax free investment of principal, the 403b generally beat it (depending on the fund chosen) for many years. So it seems that having these funds in the 403b until I retire and can roll over would be best. The glaring exception to this rule was the basic Vanguard S&P index fund (I believe) whose ER was so low that it nearly instantly beat the 403b. Does that make more sense?

Food: 4800 (This was last year's food bill. I have a number of eating out tabs over $50 that I did not recall when first posting. I do not have it itemized, but I ate crab legs *often.* I bought starbucks (derp). I had food delivered(double derp). I'm single and have free time - there is NO excuse for this.)
**This is the REAL hole in my budget. I have cut coffee cold turkey. I will steam no more crab legs. But the truth is, my day-to-day eating is still pricey because I just don't know what is inexpensive and healthy. I have read rice and beans. I could do this. Any other suggestions?**
**I can REALLY save here! HELP! What *should* I be spending on food? **

Piano lessons: 780. This likely won't change. Music adds value to my life that is worth retiring later for. If that is extremely contrary to this community, I apologize and please know that I in no way intended to offend.

So of my 35,400, I have about 16,220 left over that is not allocated to one of the above categories. I can max an IRA, contribute ~10 grand to the 403b (granted, yes this changes some numbers), and still have some free bucks to kick around. But where are my holes? What am I overlooking? How can I be *better* ?

I can help with this!  Or at least, point you in the direction of the powerful community that we have around here.  I get hungry sometimes just reading these threads.

http://forum.mrmoneymustache.com/off-topic/the-ultimate-mustachian-food-guide/

http://forum.mrmoneymustache.com/off-topic/mustachian-recipe-index/
Yes... and yes. This is exactly the kind of information I knew I needed. Once again, this is a lot to digest and will take time. Thank you!

Quote
Also, about the piano lessons, good for you!  You've got no debt, you've made choices to keep your housing and other expenses affordable.  I can't imagine anyone's going to be handing out any face punches over something that you value so highly, and that gives your life meaning.

That means a lot. Thanks, again.

MDM

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Re: Case Study - New job, New life
« Reply #11 on: May 19, 2015, 09:59:39 PM »
Don't understand this part, because both a 403b and an IRA have tax free growth.

This was based of using the above formulas - since the ROTH IRA does not have tax free investment of principal, the 403b generally beat it (depending on the fund chosen) for many years. So it seems that having these funds in the 403b until I retire and can roll over would be best. The glaring exception to this rule was the basic Vanguard S&P index fund (I believe) whose ER was so low that it nearly instantly beat the 403b. Does that make more sense?

Not really.  For the same marginal tax bracket, and same investment return rate, there is no difference in the final amount between a Roth IRA vs. a Traditional IRA.  Same applies to Roth 403b vs. Traditional 403b.  Same applies to ____ IRA vs. ____ 403b (use either Roth or Traditional in the blanks).  The IRS gets its cut either in the beginning (Roth) or upon withdrawal (Traditional) and you get the same amount in the end either way.

Did you mean taxable instead of either IRA or 403b?

ApplePI

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Re: Case Study - New job, New life
« Reply #12 on: May 19, 2015, 10:17:40 PM »
Not really.  For the same marginal tax bracket, and same investment return rate, there is no difference in the final amount between a Roth IRA vs. a Traditional IRA.  Same applies to Roth 403b vs. Traditional 403b.  Same applies to ____ IRA vs. ____ 403b (use either Roth or Traditional in the blanks).  The IRS gets its cut either in the beginning (Roth) or upon withdrawal (Traditional) and you get the same amount in the end either way.

Did you mean taxable instead of either IRA or 403b?

Seems like I either used the formulas wrong, or have a misconception about the whole thing. This IRS gets their cut, sure, but since there is pretax money compounding in the 403b, do we not expect the value pre-withdrawal to be higher in the 403b than the Roth IRA given equal investments which grew at the same rate? The issue is how long it takes the higher ER in the 403b funds to drag the 403b's value down below that of the IRA, which is how I interpreted the graphs provided above. If I am way off, don't be gentle. I want to get this right.

MDM

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Re: Case Study - New job, New life
« Reply #13 on: May 19, 2015, 10:31:40 PM »
This IRS gets their cut, sure, but since there is pretax money compounding in the 403b, do we not expect the value pre-withdrawal to be higher in the 403b than the Roth IRA given equal investments which grew at the same rate? The issue is how long it takes the higher ER in the 403b funds to drag the 403b's value down below that of the IRA, which is how I interpreted the graphs provided above. If I am way off, don't be gentle. I want to get this right.
Yes, "pre-withdrawal" is as you say.

But that's not terribly interesting, as one can't spend pre-withdrawal dollars.  When the 403b money is withdrawn, it provides exactly the same spendable amount as the Roth IRA - specifically because we made the assumption of equal marginal rates at contribution and withdrawal.

The result is the same for Roth or traditional: (1-a) * P * (1+i)^n  =  P * (1+i)^n * (1-a) 

The convoluted algebra and graphed curve above are for the comparison of tax-advantaged (either Trad or Roth) vs. taxable.

Now if the withdrawal marginal rate differs from the contribution marginal rate, things change.  The obvious change is the Roth vs. Traditional comparison: pick the one that pays the lower marginal rate.  The algebra for the taxable comparison will need a little work.  I've been thinking about doing that...maybe this will provide incentive to do so.

MDM

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Re: Case Study - New job, New life
« Reply #14 on: May 20, 2015, 02:19:52 AM »
The algebra for the taxable comparison will need a little work.  I've been thinking about doing that...maybe this will provide incentive to do so.

Not as bad as I feared.  The Roth vs. Taxable comparison doesn't change because the "ordinary marginal tax bracket at withdrawal" is irrelevant for both Roth and Taxable.

Ok, here goes.  To complicate things, assume unequal tax brackets at contribution and withdrawal.

a = ordinary tax rate at contribution time, fraction.  E.g., 0.25
b = expense ratio difference, fraction.  E.g., 0.007
e = ordinary tax rate at withdrawal time, fraction.  E.g., 0.15
i = taxable investment return, fraction.  E.g., 0.05
n = number of years
P = Principal available for investment
w = tax rate on long term capital gains, fraction.  E.g., 0.15
y = fraction of investment return subject to annual tax.  E.g., 0.5 (1/2 from dividends, 1/2 from appreciation)
z = tax rate on annual investment returns, fraction.  E.g., 0.15

In the discussion below, references to "Roth" or "Traditional" (unless followed immediately by "IRA") refer to a 401k-like account with expense ratios higher than available on the open market.

The equation for tax-advantaged accounts is straightforward because there are only ordinary taxes and those happen only once, either at contribution or withdrawal.
  Roth:          (1-a) * P * (1+i-b)^n
  Traditional: P * (1+i-b)^n * (1-e)

Roth vs. Traditional
The P * (1+i-b)^n terms can be eliminated from both equations above so we get Roth - Traditional = (1-a) - (1-e) = e-a. In other words, when the withdrawal tax rate is higher, choose Roth; when the contribution tax rate is higher, choose Traditional.  When they are equal, choose either (but see http://www.bogleheads.org/forum/viewtopic.php?f=10&t=140758 for another layer of complexity).


Taxable is messier because taxes occur at contribution, during investment growth, and at withdrawal.

Taken in pieces:
  Amount contributed = (1-a) * P
  After 1 year, before tax = (1-a) * P * (1 + i)
  Tax on the first year = (1-a)*P* i*y*z
  After 1 year, after tax = (1-a)*P * (1 + i*(1-y*z))
  After n years, before withdrawal = (1-a)*P * (1 + i*(1-y*z))^n
  Taxable amount to withdraw = (1-a)*P * (1 + i*(1-y*z))^n - (1-a)*P
  Tax on above amount =   w * ((1-a)*P * (1 + i*(1-y*z))^n - (1-a)*P)

Taxable amount after withdrawal after tax = (1-a) * P * (1 + i*(1-y*z))^n - w * ((1-a) * P * (1 + i*(1-y*z))^n - (1-a)*P)


Roth vs. Taxable
The (1-a)*P term cancels from both the Roth and taxable equations, leaving
Roth - Taxable = (1+i-b)^n - (1-w) * (1+i*(1-y*z))^n - w

If the equation above is positive, Roth is better.
If the equation above is negative, Taxable is better.

Assume i = 0.05, w = 0.15, y = 0.5, z = 0.15 and look at the resulting equation as a function of b and n:
(1.05 - b)^n - 0.85 * 1.04625^n - .15

The curvature of this equation as a function of n depends on the value of b.
If b<=0.375% (=i*y*z), it starts positive and stays positive.  In other words, if the Roth expense ratio is 0.375% or less above the taxable, Roth is always better.
If n=1, we get 0.0106875 - b.  In other words, if the Roth expense ratio is more than 1.06875% above the taxable, taxable is always better (for >1 year).
If b = 0.7%, the Roth is better for 45 years (see plot in previous post), after which taxable would be better.  But if you retire in <45 years, you could roll the Roth over to a Roth IRA and get a low expense ratio.


Traditional vs. taxable
The P term cancels from both the Traditional and taxable equations, leaving
Traditional - Taxable = (1-e)/(1-a)*(1+i-b)^n - (1-w) * (1+i*(1-y*z))^n - w

If the equation above is positive, Traditional is better.
If the equation above is negative, Taxable is better.

Assume i = 0.05, a = 0.25, e = 0.15, w = 0.15, y = 0.5, z = 0.15 and look at the resulting equation as a function of b and n:
0.85/0.75*(1.05 - b)^n - 0.85 * 1.04625^n - .15

The curvature of this equation as a function of n depends on the value of b.
If b<=0.375% (=i*y*z), it starts positive and stays positive.  In other words, if the Traditional expense ratio is 0.375% or less above the taxable, Traditional is always better.
If n=1, we get 0.1506875 - 85/75*b.  In other words, the Traditional expense ratio has to be more than 13.3% above the taxable for taxable to be better always (for >1 year).
If b = 1.22%, the Traditional is better for 30 years (see plot below), after which taxable would be better.  But if you retire in <30 years, you could roll the Traditional over to a tIRA and get a low expense ratio.




And all this is based on all the assumptions listed.  As the saying goes, YMMV.  But you could take these formulas, put them in Excel, and enter the values specific to your situation.

ApplePI

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Re: Case Study - New job, New life
« Reply #15 on: May 20, 2015, 05:35:41 AM »
When I was messing around with formulas the first time and was looking at Roth vs Trad, I noted that I couldn't use "b" the way you are:

  Roth:          (1-a) * P * (1+i-b)^n
  Traditional: P * (1+i-b)^n * (1-e)

Since the expense ratios for similar funds are different between these investment vehicles, using "b" in this manner is incorrect: (1+i-b) does not represent the growth rate for a similar index fund in both vehicles. Rather, for similar funds where i remains constant, ER1 and ER2 are the respective expense rations:

Roth - Taxable: (1-a)*P*(1+i-ER1)^n - P*(1+i-ER2)*(1-e),

which does not simplify to just e-a, but should also rely on ER1 and ER2. The shapes I found when playing with assumptions were similar to the one for 403b vs taxable.

MDM

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Re: Case Study - New job, New life
« Reply #16 on: May 20, 2015, 01:21:48 PM »
When I was messing around with formulas the first time and was looking at Roth vs Trad, I noted that I couldn't use "b" the way you are:

  Roth:          (1-a) * P * (1+i-b)^n
  Traditional: P * (1+i-b)^n * (1-e)

Since the expense ratios for similar funds are different between these investment vehicles, using "b" in this manner is incorrect: (1+i-b) does not represent the growth rate for a similar index fund in both vehicles. Rather, for similar funds where i remains constant, ER1 and ER2 are the respective expense rations:

Roth - TaxableTraditional: (1-a)*P*(1+i-ER1)^n - P*(1+i-ER2)*(1-e),

which does not simplify to just e-a, but should also rely on ER1 and ER2. The shapes I found when playing with assumptions were similar to the one for 403b vs taxable.
Oh, yes, if we start talking about different expense ratios (or for that matter, different returns) when choosing between Roth vs. Traditional then things can change.  Once the assumptions are changed, any previous conclusion has to be reexamined.

Usually one can choose either Roth or Traditional for a given fund and have the same returns and fees.

ApplePI

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Re: Case Study - New job, New life
« Reply #17 on: May 20, 2015, 07:36:34 PM »
Makes sense. I wanted to say thanks again - your posts have been very enlightening, and that I love the mathematical approach to answering my questions. I will be using this information frequently to try and pinpoint the best set of options before pulling the trigger this August.

MDM

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Re: Case Study - New job, New life
« Reply #18 on: May 20, 2015, 08:03:26 PM »
Makes sense. I wanted to say thanks again - your posts have been very enlightening, and that I love the mathematical approach to answering my questions. I will be using this information frequently to try and pinpoint the best set of options before pulling the trigger this August.
Great!

Good to see you (and anyone) treating the math with healthy suspicion.  As stated by a master statistician, "all models are wrong, but some are useful."


MDM

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Re: Case Study - New job, New life
« Reply #19 on: June 09, 2015, 10:43:59 PM »
Taxable is messier because taxes occur at contribution, during investment growth, and at withdrawal.

Taken in pieces:
  Amount contributed = (1-a) * P
  After 1 year, before tax = (1-a) * P * (1 + i)
  Tax on the first year = (1-a)*P* i*y*z
  After 1 year, after tax = (1-a)*P * (1 + i*(1-y*z))
  After n years, before withdrawal = (1-a)*P * (1 + i*(1-y*z))^n
  Taxable amount to withdraw = (1-a)*P * (1 + i*(1-y*z))^n - (1-a)*P
  Tax on above amount =   w * ((1-a)*P * (1 + i*(1-y*z))^n - (1-a)*P)

Taxable amount after withdrawal after tax = (1-a) * P * (1 + i*(1-y*z))^n - w * ((1-a) * P * (1 + i*(1-y*z))^n - (1-a)*P)

The bolded line is wrong because it ignores the basis added by the dividends reinvested.  To make a long story short:
Taxable amount after withdrawal after tax = (1-a) * P * (1 + i*(1-y*z))^n - w * ((1-a) * P * (1 + i*(1-y*z))^n - (1-a)*P*(1 + i*y*(1-z)*((1+i*(1-y*z))^n - 1)/(i*(1-y*z)))

Perhaps a separate thread might be in order....