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Time Value of Money

I’m a firm believer that everyone should invest as soon as possible (and before they are born if possible). A great quote for a real life analogy is:

"The best time to plant a tree is twenty years ago. The second best time is now."
- Unknown Origin (Credited as Chinese Proverb)

What the quote is trying to get across is that a tree takes time to grow and if you want to enjoy the fruits produced by that tree today, then it should have been planted well into the past. The corollary is that if you plant that tree now, then you should be able to enjoy it well into the future.

The quote extends well past personal finance, but I feel it shines best in the context of the time value of money. One thing I want everyone to get out of this post is that

"A dollar today is worth 4 times as much as a dollar 20 years from now."
- Quick Maths

You can verify this by running the compound interest for 20 years at a 7 percent annual return. Another way to put it into perspective is to imagine you invested a dollar at 25 years old versus investing that same dollar at 45 years old. By the time you reach retirement at 65 years old you would have $14.97 vs $3.87. A 4 times difference for what? Making the small sacrifice today instead of 20 years from now? I think the conclusion we can all take from the math is that we really should plant our financial trees today instead of 20 years from now. And if possible we can compound this affect by leaving our children with trees that they can grow into orchards.

The remainder of this blog post will focus on what vehicles to use to invest your money. I will not be focusing on what to invest your money in. If you want to invest in bitcoin as opposed to the S&P 500 that is a personal decision that I will not comment on. So back to our tree analogy. We want the best field to grow our tree in. We know this tree is going to grow for years to come and we want to protect it from the elements and give it the best chance to flourish. So what are some things we want our field to have? It would be great if people planted trees for us in our field for free. It would be great if we could stop people from picking fruits from our tree without our permission. It would be great if the soil was conducive for growth. In terms of personal finance all of those requirements translate to the following respectively: We want other people to put money into the account for us, we do not want the government collecting taxes on the growth, we want the investment to grow faster than inflation. For the rest of the article I will talk about these characteristics in detail. Note that I am talking about these factors in order of importance for consideration.

Free Money

The first investment vehicle to consider is one that provides free money. When I say free money I mean that someone else is putting money into the account just for you on your behalf. These are far and few in between and should be taken advantage of right away. The concept might be confusing at first, because it almost contradicts the no free lunch principle. The reason why the no free lunch principle is not violated is, because the other party has some incentive, but that should not be factored in when making a decision.

401k Matching

401k matching is probably the most common form of free money there is. The idea is the government wants to encourage you to save for retirement, so they do not have to support you through welfare in your old age. The mechanics vary from company to company, but one example is a 2:1 match up to the contribution limit of $19,000. This means that if you contribute $19,000 to your 401k your employer will match half of that ($9,500) meaning that if you max out this benefit you will put $28,500 towards retirement every year, while only contributing $19,000 of your own money. It’s free money and an instant 50% percent return. You would be leaving money on the table for not taking advantage of this. Just for your reference $9500 matching compounded over 40 years at 7% will yield $2,029,290.91. So it will cost you over 2 million dollars to not take advantage of this matching if you can.

You might be wondering why your employer is offering such a program. A 401k attracts talent through retirement support, but also shifts the burden of saving from the employer to the employee. The alternative for your employer is a pension program that they contribute to for everyone, but with a 401k match they only have to contribute to those that take advantage of the program. For those of us with lower incomes or higher expenses $19,000 of contributions is a herculean task.

Employee Stock Purchase Plan

Another example of free money is an employee stock purchase plan. It is much less common than a 401k match, but I am including it to help you recognize when an opportunity is free money. An example of an employee stock purchase plan is that an employer might offer to sell you shares of the company at a 10% discount. This is advantageous for them, since it attracts talent and also allows them to buy back shares from the general stock market. Companies perform stock buybacks to artificially make shares more scarce and also boost common metrics like earnings PER share, which in turn drives up the price of the stock (for reasons I do not agree with). Regardless of the company’s reason for providing this plan you should be taking advantage of it. It provides an instant 10% return on investment. If you wanted to you could sell immediately and lock in the gains.

Tax Advantaged Accounts

The next thing to prioritize after free money is tax advantaged accounts. The reason this priority comes after free money is because you can pretty much always take the free money from the methods discussed above and then move that money into a tax advantaged account. Before getting into what a tax advantaged account is we need to take a step back and discuss the issue of saving in a non tax advantaged account. Without a tax advantaged account you would normally make some form of income -> that income would then be taxed and the remainder can go to an investment -> over time that investment makes gains -> you sell that investment and pay taxes on the gains. This process can be shortened to “Taxed on the way in and taxed on the way out.”. We can do some quick math to try and see how taxes affect your retirement goals. Suppose you have a tax rate of 30% and make $100 that you want to invest. That $100 is immediately turned into $70 post tax. You then invest the $70 dollars and it sees 100% growth over some period of time netting you an additional $70. When you sell the investment for $140 dollars $70 is non taxable contributions, but the other $70 are taxable gains which are again taxed at 30%, so you keep $49 dollars of your gains totaling you $119 after the double taxation. Imagine if you never paid any taxes and could keep the entire $200 dollars instead of $119. That difference is almost double, so we should try and account for it. You can skip this section completely if you think your government is the most effective charity in the world. Spoilers they probably are not. I would recommend saving the money on taxes and sending it to the charity of your choice instead if you value social progress. Here is the kicker; the government will match your contributions to this charity in the form of a tax writeoff, so it’s almost ethically wrong to pay taxes when you can avoid them.

Neither Taxed On The Way In, Nor On The Way Out

An investment not being taxed on the way in or the way out is really rare, since the government would not be able to run if they were in abundance. Your Health Savings Account is an example of an account that is exempt from all taxes. The HSA lets you contribute $3,500 of pre tax dollars every year meaning you do not pay any money to get it into the account. The primary purpose of this account is pay medical expenses as you need them. A lot of healthy people (politically correct way of saying young) stop reading into the account at this point, since they assume they will not incur $3500 worth of medical expenses every year. What they are missing out on is that the money can be invested along the way and when you are 65 years old you can withdraw this money tax free. We can do the math on two 25 year olds who make the same income that never end up having medical expenses. Only difference is one decides to invest in their HSA instead of a non tax advantaged account. The HSA contributed will invest $3500 a year, since they do not have to pay taxes on the way in, for 40 years and at a 7% rate of return they will have $747,633.49 and this where the story ends, since they do not have to pay taxes on the way out. The other person is able to invest $2450 a year post tax after a 30% tax rate. They also do this for 40 years at 7% and up with $523,343.45 in the account. The story unfortunately does not end here, since only $98,000 of that money was their contributions meaning they need to again pay 15% capital gains taxes on the gains netting $383,343 after all taxes. Ouch! The difference between the two people works out to $190,646.53 over a decision as simple as contributing to an HSA.

The table below summarizes this:

Not Taxed On The Way In vs Not Taxed On The Way Out

Rarely do you find investment opportunities that are neither taxed on the way in, nor on the way out, so you usually have to choose one or the other. Financially there is not much of a difference between these two assuming the tax rate on the way in (investing with post tax dollars) is the same as the rate on the way out (investing with pre tax dollars). Consider two people each with $100 and will see 100% returns over a certain amount of time and they each have a 30% tax rate for putting the money in and taking the money out. The only difference between these two is that one invests with pre tax dollars and the other invests with post tax dollars. The pre tax investor can put in $100 right away. After some time that money grows to $200. Finally they need to pay 30% tax leaving them with $140. The post tax investor pays 30% tax upfront leaving them with $70. After some time that money grows to $140. They have already paid taxes meaning they keep the entire $140. Both investors have $140. The reason for this, because the math is commutative:

Pre Tax = $100 * 2 * (1 - 0.3)  = $140 = $100 * (1 - 0.3) * 2 = Post Tax

Now the only time these tax advantaged accounts differ is when a person’s income tax now is different from their income tax when they retire and cash out their gains. This leads to the rule of thumb for pre tax vs post tax:

If your income tax now is greater than your income tax when you retire, 
then go with pre tax, 
else go with post tax.

However, since you do not have a crystal ball that tells you what your tax rate is going to be in retirement you should hedge your bets and go with both.

The 401k is an excellent example of a tax advantaged account and offers both pre tax and post tax components. The contribution limits are as follows assuming a 2:1 match:

• $19,000 - Matchable Pre or Post Tax
• $9,500 - Employee Match
• $27,500 - After Tax

Summing up to a total of $56,000. Now let’s run the numbers. For simplicity sake let’s say that someone contributes all $56,000 with After Tax dollars. After 40 years with 7% compound interest they will have $11,962,135.91 of non taxable dollars. Now suppose that the same person did not take advantage of the 401k. They would be able to contribute $46,500 every year, since they are missing out on the 401k match from their employer. Again with 40 years at 7% they would have $9,932,845.00. However only $1,860,000 is contributions meaning they would have to pay taxes on the remaining $8,072,845 at a 15% long term capital gains rate netting them $8,721,918.25. This works out to a difference of $3,240,217.66 just for taking advantage of the 401k.

However this is merely a theoretical number. In the real world is difficult to put away $56,000 post tax dollars every year. To motivate smaller goals I provide the table below, which shows how much you can save in taxes by taking advantage of the matched portion alone, the employee matching, and then the after tax:

Beating Inflation

The worst place to keep your money is under your mattress or buried in the ground. It’s going to be exposed to the elements and decay over time. So you might think of doing the obvious and just putting it into a checkings account where your bank will take care of it. Unfortunately those same banks lend out money at a rate faster than the underlying growth of the economy leading to inflation. The rate of inflation in the United States is sitting at about 2% every year. This means that if something costs $1.00 today it will probably cost about $1.02 next year. The reasons for why this happens deserves it’s own post with details on the macro economics, but for now you can consider it a tax on savings. Basically every year the federal reserve is going into your accounts and withdrawing 2% without your permission. So my homework assignment for you is to look up what your bank is giving you for keeping money in a checking account. If it is anything less than 2%, then I want you to let the irony sink. By putting money in a checking account you are giving money to a bank so that they can lend it out to other people at a rate that causes inflation which in turn devalues your money and to put salt on your wounds they give you back a fraction of the money they stole from you. Fun fact the average annual checking account yield is 0.06 percent APY, so on average leaving money in a checking account is costing you 1.94% every year. With this in mind, I strongly encourage you to leverage your money to beat inflation. If you are risk averse, then you can consider bonds or a money market fund.

Discussion

Contact Me

Email: bschong2@illinois.edu