If you use flexible spending account, you should be familiar with the use-it-or-lose-it rule. If you put too much in the FSA, you will lose what you can’t use. In the past I always estimated conservatively. I’ve never lost any money to the FSA. However there is also a cost to that approach. After the money in the FSA is used up, any additional expenses must be paid with after-tax dollars. There has to be a point where losing a little pre-tax money in the FSA is less expensive than paying a lot with after-tax money.

This becomes an interesting math problem.

Suppose your best estimate for next year’s FSA-eligible expenses is $1,000, plus or minus $500 because you can never be sure what your actual expenses will be. Your marginal tax rate for FSA contributions is 32% (you have to include the Social Security and Medicare taxes if your income is below the Social Security Wage Base, $106,800 in 2009). How much should be put in your FSA?

So your expenses will range from $500 to $1,500 next year. We can divide it up into ten smaller intervals: $500-600, $600-700, …, $1,400-1,500. For each interval, we use the mid-point as the proxy and calculate the total after-tax cost. The total after-tax cost is:

FSA Contributions * (1 – Marginal Tax Rate) + Expenses Above & Beyond FSA

For example, if you contribute $1,000 to FSA, and your actual eligible expenses are:

Over the full range of likely expenses, your average total after-tax cost is $805 if you contribute $1,000 to your FSA. After calculating the same for other contribution amounts, we get this nice graph.

The graph shows that putting in the most conservative amount ($500) isn’t the best strategy. Putting in your best estimate ($1,000) isn’t the best either. The lowest average total after-tax cost over the full range of the estimated expenses is achieved when you put in somewhere in between those two numbers, around $800 in our example.

If you’d like to play with your own numbers, here’s the spreadsheet I created.

Spreadsheet: How Much Should You Put Into Flexible Spending Account (FSA)

Math-minded readers probably noticed that by taking a straight average of the total after-tax costs for all ten intervals, I’m giving each interval equal weight. In math terms, it’s called a uniform distribution. In real life, the intervals at either end of the range ($500-600 and $1,400-1,500) will be less likely than the intervals in the middle. So here’s the challenge question for interested readers:

If you assume your next year’s FSA-eligible expenses follow a normal distribution with a mean of $1,000 and a standard deviation of $250 (same $500 to $1,500 range with 95% confidence), how much should you put into the flexible spending account in order to minimize your expected total after-tax cost?

Who knew a flexible spending account involves this much math?

Finally, if you are married and one of you earns an income above the Social Security Wage Base and another earns below, you should have the spouse with the lower income contribute to the FSA. This was explained by indexfundfan.

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While the stock market was in turmoil, the real yields on Treasury Inflation Protected Securities (TIPS) rose to an attractive level. The real yield on 10-year TIPS broke the magic 3% number, a level that hasn’t been reached for many years. Many TIPS buyers including myself thought the high real yields in the first few years after TIPS first came out in late 1990s were a fluke. The real yields were high because TIPS were new and illiquid. I thought we’d never see 3% again. It’s amazing how fast things change. Back in the spring, the 10-year TIPS real yield was under 1% while the 5-year TIPS real yield was negative (please note all yield numbers for TIPS are expressed as real yield, which is on top of inflation).

It’s always hard to explain why the market moved the way it did because previously when the stock market ran into trouble, the bond prices went up (real yields down ). The concern for deflation was raised as one possible explanation for the rising TIPS real yields. A poster on the Bogleheads forum asked whether the real Yield to Maturity (YTM) number quoted when an investor buys a TIPS on the secondary market will still hold if there is deflation instead of inflation.

It’s a good question. So I created an online spreadsheet for the calculation.

Spreadsheet: TIPS During Deflation

I drew the following conclusions from the spreadsheet exercise:

1. As long as there is cumulative inflation between the date you purchase the bond and the date the bond matures, and you hold the bond to maturity, the actual real Yield to Maturity (YTM) will match the real YTM quoted at the time of the purchase. It doesn’t matter whether the bond was purchased at the initial offering or purchased a few years later on the secondary market.

If you buy bonds with a long maturity, say 10 years or more, it’s hard to imagine there will be cumulative deflation for that long. Even Japan didn’t have deflation for more than a few years. It doesn’t matter if there is deflation in some years and inflation in some years, as long as there is net cumulative inflation between the purchase date and the maturity date, the above conclusion holds true. If you don’t believe we will have net deflation lasting a decade or longer, you can skip the rest of the conclusions because they become only academic exercises. Plus if we have deflation for that long, there are probably bigger problems to worry about than TIPS yields.

If you buy TIPS with short maturities, like a 5-year TIPS, it’s possible to have deflation for 5 years. Read on.

2. If there is net cumulative deflation, there’s a chance your real YTM can increase but it will never go lower than what you were quoted when you bought the bond. The possible boost to real YTM comes from the par floor feature in all TIPS. United States Treasury will pay the deflation adjusted principal at maturity or the face value, whichever is higher. If there is net cumulative deflation between the date the bond was originally issued and the date the bond matures, you will be paid more than the deflation adjusted principal value and therefore your real yield will be higher. Please note the relevant date is the original issuing date, not the date you purchased the bond if you bought on the secondary market. It’s possible that even if there is only deflation after you bought the bond, the bond itself could still experience net inflation during its full lifespan due to inflation between the original issue date and your purchase date.

3. All else being equal, a TIPS bond with a lower index ratio at the time of the purchase can receive a higher boost to real YTM during deflation. The index ratio reflects net inflation from the original issuing date to the date you buy the bond on the secondary market. A lower index ratio gives you a better chance for a bonus from deflation.

4. All else being equal, a TIPS bond with a lower coupon rate can receive a higher boost to real YTM during deflation , although the boost to real YTM is not as sensitive to the coupon rate as to the index ratio.

In short, when you buy a TIPS bond on the secondary market, be confident that your real YTM will never go lower than the quote even if there’s deflation after you buy the bond. If the real YTM and maturity are comparable between two bonds, first choose the bond with a lower index ratio, then choose the bond with a lower coupon rate, for a better chance for a bonus from deflation. Finally, remember all these finer points are moot unless there is net cumulative deflation from the purchase date to the maturity date. If there is no net cumulative deflation, all bonds receive the quoted real YTM. One should never say “never” but it is very unlikely to have net cumulative deflation for many years.

If you’d like to play with the spreadsheet, go ahead. Like all my other spreadsheets, the numbers in blue are inputs. The other numbers are calculated from the inputs.

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“Also, never ever borrow against your 401k plan because you will pay double taxation on the money you borrow. Because you don’t pay taxes on the money you put into a 401k, when you pay back the loan (which you must do within five years, or 15 years if used to buy a home), you pay it back with money you have paid taxes on. Then, when you retire and take the money out again, you end up paying taxes on it a second time.”

This allegation is all over the place — MSN, USA Today, The Motley Fool, Moolanomy blog. It is a myth because there is NO double taxation. It’s a mind trick similar to that well-known “where’s the missing dollar” puzzle.

“Three men went into a hotel. The manager said the room was $30 so each man paid $10. A while later the manager realized the room was only $25 so he sent the bellboy to the 3 guys’ room with $5. The bellboy only gave each man $1 back and kept the other $2 for himself. Now 3 men paid $9 each for the room, which is $27. Add the $2 that the bellboy kept, and that’s $29. But the 3 men paid $30 originally. Where is the other dollar?”

I was able to find a good explanation for this puzzle. The $30 number is irrelevant. The correct math is $27 – $2 = $25. It makes no sense to add $2 to the $27 because it’s already a part of the $27. The $2 should be subtracted from the $27.

Now, back to our 401k double taxation myth. The fact that the loan has to be repaid with after-tax dollars is irrelevant, just like the $30 number in the hotel puzzle. If you didn’t borrow from the 401k plan but you borrowed from a bank, you’d have to pay the bank back with after-tax dollars as well. If you didn’t borrow from your 401k plan but you dipped into your own savings, you have to replace those savings with after-tax dollars too. What it really means is that a 401k loan is not tax deductible, just like any other consumer loan except a mortgage or a HELOC. Instead of saying you will be double taxed, they should just say that a 401k loan is not tax deductible, plain and simple.

I have this post in draft for a long time but Jonathan at My Money Blog beat me to it recently with two posts trying to debunk this myth (post 1, post 2). After so much discussion some folks are still not convinced. I think this issue is best illustrated by this chart below:

The left hand side represents a typical consumer loan, like a car loan. The arrows represent “borrows from” and “pays back to.” You borrow from a bank. The bank borrows from the financial market. Your 401k invests in the financial market. I think we all agree there is no double taxation in this case. You pay after-tax dollars to the bank for both principal and interest. Your 401k earns from the financial market but the earnings have to be taxed when you withdraw from your 401k.

The right hand side represents a 401k loan. Now, if you put an imaginary box in the middle on the right hand side, it becomes exactly the same as the left hand side. You borrow from an imaginary middleman and pay after-tax dollars for both principal and interest. This imaginary middleman then borrows from your 401k and passes the same dollars it receives from you to your 401k. All of a sudden you are not double taxed any more because it looks exactly the same as a car loan on the left hand side. Because this middleman is only imaginary, it follows that you are not double taxed with a 401k loan, whether for the principal repayments or for the interest.

Whether or not you are mathematically better off with a 401k loan depends on how these three rates play out:

• your alternative after-tax interest rate from a bank loan
• what bond funds in your 401k are expected to earn from the market
• the interest rate on your 401k loan

Suppose your alternative after-tax interest rate from a bank loan is 7% and the interest rate on your 401k loan is 5%. If you borrow from your 401k, you save 2% in interest cost in after tax dollars. But also suppose the bond funds in your 401k are expected to earn 8%. If you borrow from it, your 401k plan can only earn 5% from you. So your 401k plan account is 3% worse off in before-tax dollars. Between 2% better off after tax and 3% worse off before tax, it can become a wash. The reason you have to compare it with what bond funds can earn is because the 401k loan payments are not subject to market fluctuation. If you do borrow from your 401k, increase your allocation to stocks for what’s left in the plan.

While there is no double taxation on a 401k loan, there are other negatives on borrowing from your 401k plan. The biggest negative is that if you change jobs (voluntarily or involuntarily), you often have to repay the outstanding balance of the loan within a short period of time, like 60 days. Some plans actually allow you to continue the loan repayment even after you terminate employment, but not all plans do that. If you really need cash and you don’t have any other source except your 401k, taking out a 401k loan is at least better than taking a hardship withdrawal from the plan. Just be absolutely sure you will be able to repay the loan and you won’t change jobs before paying off the loan. And don’t reduce your regular 401k contributions while you are paying off the loan.

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ESPP Rate of Return – Calculates the annualized return from Employee Stock Purchase Plan (ESPP) purchase and sale. See previous post Employee Stock Purchase Plan (ESPP) Is A Fantastic Deal.

TIPS Pricing – Estimates how much cash you will need for buying TIPS at auction. See previous post TIPS: Inflation Linked Bonds.

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The plunge is quite impressive, isn’t it? Now look at this second chart.

What do you see? A long rise followed by a small drop. The two charts are actually based on the same underlying data for the same time period. This is another case of when charts lie. The first chart from S&P plots the year-over-year growth *rate*, not the price index itself. I created the second chart from the 10-city composite data from S&P. It plots the 10-city composite price index. Before home prices reached a top in June 2006, the year-over-year growth rate slowed, but the prices were still growing. They were just growing more slowly than before. Lately the prices also dropped. That’s for sure. However the growth rate nose-dived much more than the price index itself. If you look at the first chart, you would think the housing market is so bleak. If you look at the second chart, things are not so bad after all. Even with the price drop, the price index is still higher than it was before late 2004. In 20 months since June 2006, it merely gave up the gains of the previous 19 months. The index remains substantially higher than the trendline (red) established before the growth took off in 2000.

You can make charts tell whatever story you want. It depends on your perspective. Extending the decline in the second chart back to the trendline will be interesting.

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Let’s use this hypothetical example.

100 RSUs vested on 4/20/2007. The closing price on the vesting date is $50 per share. The company sold 40 shares for taxes. You received 60 shares. Without the RSUs, your W-2 income for the year would’ve been $60,000, with $8,000 withheld for various taxes (federal, state, social security, medicare).

This transaction can be deconstructed into 5 steps as follows.

1. The company gives you a cash bonus. In our example, the bonus is $5,000, which is the closing price on the vesting date ($50) times the number of RSUs vested (100). The company adds this cash bonus to your W-2. If your W-2 income without the RSUs is $60,000, your W-2 income with RSUs now becomes $65,000. After the end of the year, they will issue you a W-2 showing $65,000 in box 1.

2. You use the cash bonus to buy shares. $5,000 bonus buys 100 shares at $50 a share. Buying shares by itself does not trigger any taxes. Your cost basis in these 100 shares is $50 a share, for a total of $5,000.

3. The company sells some shares on your behalf. In our example, they sell 40 shares on your behalf. You must report sales of stocks on Form 1040 Schedule D. There can be a few variations here.

3a. The company does not use a broker. The shares are sold on the vesting date at the same closing price. You report on your Schedule D:

3b. The company uses a broker. The shares are sold on the next day after vesting at a different price. Suppose the sale price is $50.60 and the broker’s commission is $20. The net proceeds of the sale is $50.60 * 40 – $20 = $2,004. You report on your Schedule D:

If the shares are sold at a lower price, you show a loss instead of a gain. The loss can offset capital gains elsewhere. After that, it can offset up to $3,000 of your ordinary income. If you still have more losses, the remainder is carried over to the next year, offsetting any gains you have next year and up to $3,000 of your ordinary income again next year.

4. You hand over the money from the stock sale to your employer. Your employer remits the money to the federal and state tax authorities. They add the taxes paid to the withholding numbers on your W-2. If your tax withholdings without RSUs would’ve been $8,000, your tax withholdings with RSUs now become $10,000. After the year end, the W-2 you receive from your employer shows $65,000 of income (step 1) and $10,000 in withholdings.

5. Finally, your employer gives you the remaining shares. You bought 100 shares in step 2. They sold 40 shares on your behalf in step 3. You have 60 shares left.

Now, when you file your tax return,

• Enter the income and taxes paid from your W-2 as-is. The RSU related income and tax withholdings are already included on your W-2. You don’t have to do anything else with them. Do not add more income. Do not add more taxes paid.
• Report the stock sale on Schedule D as shown in step 3. If the company does not use a broker and sells the shares at the same price as the closing price on the vesting date, you should have a zero gain/loss for that sale. Others might have a small gain or loss depending on the sale price and brokerage commission if any.

Your cost basis in the remaining shares stays at $50 a share. In our example it’s $50 * 60 = $3,000 in total. Whenever you sell these shares, you have to remember this cost basis. If you sell them for more than $50 a share, you have a capital gain. If you sell them for less than $50 a share, you have a capital loss. You will report the gain or loss in the year you sell these remaining shares. The gain/loss will be a short-term gain/loss or a long-term gain/loss depending on your holding period after the vesting date.

I hope this post addresses all the questions. If you break up the RSU vesting and sale this way, it’s not that complicated.

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The rationale behind these proposals is that the mortgage interest deduction and the property tax deduction benefit only the well-off. They say people who don’t itemize their deductions don’t get those deductions. From Obama’s Tax Fairness Plan:

"Owning a home is the culmination of the American dream that so many Americans work so hard for. The tax code is supposed to encourage home ownership with a mortgage interest deduction, but it goes only to people who itemize their tax deductions. Like so much in our tax code, this tilts the scales toward the well-off. The current mortgage interest deduction excludes nearly two-thirds of Americans who do not itemize their taxes."

Is that so? On the surface, yes. If you don’t itemize your deductions, you use the standard deduction, which in 2008 is $5,450 for single and $10,900 for married filing jointly. If you pay mortgage interest and/or property tax, but if they are not large enough, you still use the standard deduction. That’s why by definition Americans who don’t itemize their deductions don’t show a mortgage interest deduction on their tax return.

However, to say that those Americans don’t benefit from the mortgage interest deduction or the property tax deduction is a misunderstanding of how taxes and math work. The tax law says everybody is allowed to itemize their deductions. Everybody starts out listing their mortgage interest, property tax, state income tax, plus any other deductions they are allowed. Say for a married couple filing jointly, those deductions add up to $6,000, then the IRS tells them

"Guess what, you are lucky. We are going to let you deduct even more than what you’ve already got here. Would you like us to top off your deductions to $10,900?"

Now they can take the IRS up on the offer or say "no thanks" and stick to their original list of deductions, which include their mortgage interest, property tax, state income tax, and everything else. In reality, when one has less in deductions than the standard deduction, nobody declines the sweet offer from the IRS because they get to deduct all the deductions they are allowed, plus a bonus deduction offered by the IRS.

Now tell me who’s better off? The taxpayers who don’t itemize their deductions but end up deducting even more than their deductions, or the taxpayers who itemize their deductions? The non-itemizers get to deduct everything they are allowed plus a bonus deduction they receive from the IRS. Itemizers don’t receive such bonus. The non-itemizers are already better off than the itemizers. If we allow a new property tax deduction under the proposed housing legislation or a new "universal mortgage credit" under Obama’s tax plan, the non-itemizers will deduct their mortgage interest and property tax twice, plus taking a bonus deduction from the IRS. Does that sound fair to you?

I’m afraid our legislators and presidential candidates don’t understand how taxes and math work because they don’t do their own taxes.

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1. Same Day Sale. This is the simplest. On the vesting date, I sell everything. After subtracting for tax withholding, I end up with net cash.

2. Sell to Cover. If I choose this option, they will sell just enough shares to cover the tax withholding. I keep the remaining shares and I can sell them myself whenever I want to.

3. Cash Transfer. For this option I will have to come up with cash myself to cover the tax. After that I have all the shares and I can sell them whenever I want to.

Which should I choose? Let’s use an example and see the math. Suppose I will have 100 shares vested; the price on the vesting date is $50; and the tax withholding is 40%.

1. Same Day Sale. I will have $50 * 100 * (1 – 40%) = $3,000.

2. Sell to Cover. I will have 100 * (1 – 40%) = 60 shares and no cash.

3. Cash Transfer. I will be out $50 * 100 * 40% = $2,000 cash but I will keep 100 shares.

Option (2) Sell to Cover is equivalent to doing Option (1) Same Day Sale and immediately buying 60 shares with cash on the open market.

Option (3) Cash Transfer is equivalent to doing Option (1) Same Day Sale and immediately adding $2,000 from my own pocket and then buying 100 shares.

If I find my employer’s stock attractive, I can buy it at any time for however many shares I want. I don’t have to buy it on the RSU vesting date or buy those exact number of shares. So there is no advantage whatsoever for them to do it for me. This is a no-brainer. I chose Same Day Sale.

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Because of an exemption phase-out rule, people whose incomes are in the middle of the AMT range pay a higher AMT marginal tax rate than people on either the low or the high end. This is relatively unknown. Many people think there are just two brackets in AMT, 26% and 28%. There are actually four brackets. In addition to 26% and 28%, there are also 32.5% and 35% brackets for people who are in the exemption phase-out range. Unfortunately many people who are hit by the AMT also fall in the phase-out range.

For each filing status, three numbers are pertinent for calculating the AMT brackets.

The AMT exemption amount (E) is the number congress has been increasing temporarily every year in the last few years. The other two numbers have not been changed lately. If your income is below E, you are not subject to the AMT. If your AMT Income is between E and P, your AMT marginal tax rate is 26%. The other two milestones, which I call X and Y, are given by the following formula:

X = (B + E + 0.25 * P) / 1.25

Y = 4 * E + P

For AMT Income between P and X, the marginal AMT rate is 32.5%; between X and Y, it’s 35%. Once you go over Y, the AMT rate drops to 28%. If you are curious in how the formula for X and Y are derived, please read this blog post by IndexFundFan.

For 2007, using values for E, B and P in the table above, X comes out to $223,000 for married filing jointly, $197,980 for single or head of household; Y is $415,000 for married filing jointly, $289,900 for single or head of household. Here’s the complete AMT rate table for the 2007 tax year:

* QD = Qualified Dividends; LTCG = Long Term Capital Gains

First notice the marriage penalty. If each spouse earns $80,000, a married couple is in the 32.5% bracket. If they were single, they are both in the 26% bracket. That’s a big difference. Throw in the state income tax and Social Security and Medicare tax, the couple’s combined marginal tax bracket can reach nearly 50%. Also notice the significant penalty on qualified dividends and long term capital gains for people in the phase-out zones . Together with state income tax, the marginal tax rate on qualified dividends and long term capital gains can exceed 30%. That’s a lot higher than the 15% number everybody talks about.

What do you do if you are affected by the AMT, or worse yet, if you are in the AMT exemption phase-out zone? Not much unless you are willing to move to a low/no tax state or not have kids. Know what your marginal tax bracket really is. Use an AMT-free tax-exempt money market fund instead of a regular money market fund or savings account. If you are in the phase-out zone, minimize even qualified dividends and long term capital gains.

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“While you’re correct that this overstates the problem in that people won’t miss just the 10 best days of the market, you’re forgetting that the biggest days often come in the earliest stages of a recovery.

“For example, looking over the past 25 years, three of the 10 biggest days came in the week and a half following Black Monday, and two more of them occur in close succession at the very tail end of the dot bomb debacle. Thus, these days are concentrated into periods when people are especially likely to have bailed on the market and not gotten back in.

“Consider the scenario in which sometimes gets smacked on Black Monday, jumps out of the market to lick their wounds, and then immediately misses gains of 9.3%, 5.3% and 4.9%. They’ve now locked in a huge loss that they had little chance of avoiding in the first place, and they also missed out on a huge recovery.

“Calculating the probability that people will randomly miss the ten best days is a *huge* oversimplification, and it casts doubt on your entire argument.”

I want to thank Nickel for the comments and address the issue of best days coming right after the stock market bottom. Since he brought up Black Monday in 1987 and the dot com bubble, let’s take a closer look.

Black Monday was October 19, 1987. The S&P 500 dropped a whopping 20.5% on a single day, from 282.70 to 224.84. Let’s say a nervous investor sold the very next day on the open. The price was 225.06, close to the bottom made on the previous day. In the next 10 days, he would’ve missed 3 of the 10 best days in the next 20 years, which had returns of +5.33%, +9.10%, and +4.93% respectively. Does it mean this investor missed a total of (1 + 5.33%) * (1 + 9.10%) * (1 + 4.93%) – 1 = 20.6% of returns? No, after 3 best days passed, S&P 500 closed at 244.77 on 10/29/1987, up 8.8%, not 20.6%, from the 225.06 level he sold at. A little over a month later, on 12/3/1987, the market returned to 225.21, which was about the same level as the previous bottom. Now, having missed 3 of the 10 best days in the next 20 years, this investor didn’t suffer any damage if he got back in a month and half later.

Now, let’s look at the same for the 2 best days in 2002. On 7/24/2002 and 7/29/2002, the S&P 500 had two best days, up 5.73% and 5.41% respectively. By then the bear market had gone on for over two years. If an investor was nervous, he would’ve sold way before then, perhaps in early 2001 when the S&P 500 dropped to 1,300 from 1,500 in the previous year, or in early 2002 when the S&P 500 dropped more than 20% in two years. For argument’s sake, let’s say our unlucky investor sold right before the best days, on 7/23/2002, at the close of 797.70. After two of the 10 best days in 25 years, the market closed on 7/29/2002 at 898.96, up by 12.7%. Was that a permanent loss of opportunity if the investor missed those two best days? Once again, no. 2 months and 10 days later, on 10/7/2002, the S&P 500 went back to 785.28, lower than the 797.70 price before the best days.

Will the market always return to the previous low before the best days? I don’t think anybody has an answer to that. The market is volatile and unpredictable. I continue to believe that (a) it’s impossible to miss only the 10 best days; and (b) even if some best days were missed, the damage isn’t nearly as bad as those meaningless stats imply.

Suppose calculating random odds is a *huge* oversimplification like Nickel said, and because the best days often come in the early recovery days, I’m off by a factor of a billion. That is huge, right? Say instead of one in 2.8 billion billion billion, the odds of missing the 10 best days in 10 years is actually only one in 2.8 billion billion. That is still 100 times less likely than winning 2 consecutive Powerball jackpots with the same set of numbers. If I write about what I would do if I won 2 consecutive Powerball jackpots with the same numbers, nobody will take me seriously because it’s meaningless to talk about impossible events. Well the stats on missing the 10 best days in 10 years fall into the same camp. They are not worth the attention given to them.

Trust me, I don’t advocate timing the market. I just think this missing the 10 best days in 10 years thing is over-hyped by at least a factor of a billion. My question to Nickel and all other readers, if it’s not one in 2.8 billion billion billion, or one in 2.8 billion billion, what do you think the odds are for missing the 10 best days in 10 years and how do you prove it?

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