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Becoming An Investor: Building Wealth By Investing In Stocks, Bonds, And Mutual Funds

Chapter 3: An Introduction To Compounding or How To Get Rich Over Long Time Periods


Many investors have made significant wealth over long time periods. It is not that they are brilliant investors. Usually, they have kept at it, squirreling money away on a regular basis or as they can. Company growth often occurs exponentially. Hence, so does the growth of the stock market. I discussed this in my book, Thinking Like An Entrepreneur. In business, steps could be taken to decrease the compounding interval or increase the compounding rate. Either of these increases the power of compounding and helps you get richer faster.

Investment differs significantly from entrepreneurship in that an in depth understanding of the nature of compounding will not benefit the investor. It is sufficient to know that compounding exists. Because of this you want to keep money invested for as long as is reasonably possible. That is the sole goal of this chapter. To convince you that money saved and invested over long time periods can add up significantly. To convince you that you should not assume a meager sum is insignificant and therefore can be withdrawn and spent without losing a significant future amount.

Calculating how much a given sum compounds to in a given number of years at a given rate is easy. All you need to do is to add the compounding rate, expressed as a decimal, to one. Then raise the result to the number of years you will let the money compound. This gives a multiplier factor that you multiply by your starting amount to get the future amount.

So, for example, compounding for ten years at 12% gives (1.12)10= 3.1 as the multiplying factor. This means that $5,000 grows into (3.1)($5,000) = $15,500 in ten years. This assumes only a one time investment is made. No more money is added over the ten years.

To see why this formula works, consider how your $5,000 investment grows at a 12% rate of return.

At the end of year one, you have your $5,000 back, plus your 12% rate of return:

End Year 1 Amount = $5,000 + (0.12)($5,000)
= (1.12) $5,000 = $5,600

Now your second year of compounding, the starting amount is the ending amount for last year, or $5,600. This amount grows at 12% over the second year:

End of Year 2 Amount = $5,600 + (0.12)($5,600)
= (1.12)($5,600) = $6,272

But notice that the amount $5,600 was just equal to (1.12)($5,000). Hence,

End of Year 2 Amount = (1.12)(1.12)($5,000)
= (1.12)2 ($5,000)

Notice that (1.12)2 is just a short hand notation saying "multiply 1.12 by itself twice."

For each year of compounding, you pick up another factor of (1.12).

So,
End of Year 3 Amount = (1.12)(End of Year 2 Amount) = (1.12)(1.12)(1.12)($5,000) = (1.12)3 ($5,000)

Again (1.12)3 is just a short hand notation saying "multiply 1.12 by itself three times."

Continuing in this way, we see at the end of 10 years of compounding at 12% gives ten factors of 1.12 multiplying our starting amount of $5,000:

End of Year 10 Amount
= (1.12) (1.12) (1.12) (1.12) (1.12) (1.12) (1.12) (1.12) (1.12) (1.12)($5,000) = (1.12)10 ($5,000) = (3.10)($5,000)= $15,500.

In particular, notice the effect of the last year of these ten years of compounding:

End of Year 10 Amount = (End of Year 9 Amount) + (0.12) (End of Year 9 Amount) = ($13,865) + (0.12) ($13,865) = ($13,865) + $1664.

The last year of compounding adds $1664 to our overall amount. This is nearly three times as great as the $600 which was added during the first year. This is why time is so crucial to compounding. The later years are growing your money much more rapidly.

If you have a calculator, you can do compounding calculations easily to see how much your present savings might grow into if invested for a given number of years, achieving a given rate of return.

If you don't have a calculator, the table below will give you an idea of how your money will grow. There are also "financial calculators" online, where all you need to do is enter the initial amount, your estimated rate of return, and the number of years you will let the money compound, and the online calculator will tell you immediately how much your money will grow into. http://www.kiplinger.com has great financial calculators.

Here are the results of some other compounding calculations:

Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 5 5% 1.28$12,800
$10,000 5 8 1.47 $14,700
$10,000 5 10 1.61 $16,105
$10,000 5 12 1.76 $17,600
$10,000 5 15 2.01 $20,100
$10,000 5 18 2.29 $22,880
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 10 5% 1.63 $16,300
$10,000 10 8 2.16 $21,600
$10,000 10 10 2.59 $25,900
$10,000 10 12 3.10 $31,000
$10,000 10 15 4.05 $40,500
$10,000 10 18 5.23 $52,340
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 15 5% 2.08 $20,800
$10,000 15 8 3.17 $31,700
$10,000 15 10 4.18 $41,800
$10,000 15 12 5.47 $54,700
$10,000 15 15 8.14 $81,400
$10,000 15 18 11.97 $119,740
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 20 5% 2.65 $26,500
$10,000 20 8 4.66 $46,600
$10,000 20 10 6.73 $67,300
$10,000 20 12 9.64 $96,400
$10,000 20 15 16.37 $163,665
$10,000 20 18 27.39 $273,930
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 25 5% 3 $33,860
$10,000 25 8 6.85 $68,500
$10,000 25 10 10.8 $108,350
$10,000 25 12 17.00 $170,000
$10,000 25 15 32.92 $329,200
$10,000 25 18 62.67 $626,700
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 30 5% 4.32 $43,200
$10,000 30 8 10.06 $100,626
$10,000 30 10 17.45 $174,500
$10,000 30 12 29.96 $299,600
$10,000 30 15 66.21 $662,100
$10,000 30 18 143.37 $1,433,700
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 35 5% 5.52 $55,200
$10,000 35 8 14.79 $147,900
$10,000 35 10 28.10 $281,000
$10,000 35 12 52.80 $528,000
$10,000 35 15 133.17 $1,331,700
$10,000 35 18 328.00 $3,280,000
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 40 5% 7.04 $70,400
$10,000 40 8 21.72 $217,200
$10,000 40 10 45.26 $452,600
$10,000 40 12 93.05 $930,500
$10,000 40 15 267.86 $2,678,600
$10,000 40 18 750.38 $7,503,800
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 45 5% 8.99 $89,900
$10,000 45 8 31.92 $319,200
$10,000 45 10 72.89 $728,900
$10,000 45 12 163.99 $1,639,900
$10,000 45 15 538.77 $5,387,700
$10,000 45 18 1716.69 $17,166,900
 
Initial
Amount
Years
Compounding
Return
Rate
Multiplier
Factor
Final
Amount
$10,000 50 5% 11.47 $114,700
$10,000 50 8 46.90 $469,000
$10,000 50 10 117.39 $1,173,900
$10,000 50 12 289.00 $2,890,000
$10,000 50 15 1083.66 $10,836,600
$10,000 50 18 3927.36 $39,273,600

We could extend the chart for rates of return in excess of 18%, however, achieving rates of return of over 18% is not easy. There is no evidence that such rates can be achieved with any certainty. Some will tell you that they can achieve such rates. Be very wary of letting these people have your money. Usually, they are using a momentum-based investment strategy with a high portfolio turnover. That might have worked well for the bull-stock market we have had over the 1980's and 1990's.

But it is extremely risky that such a strategy would be at all desirable in a more subdued market. You could wind up losing a significant portion of your principal investment in a bear market. Intelligent investors do not assume optimal investment conditions will last forever!

We also are not looking at investment periods in excess of 50 years. If you want to think more than 50 years ahead, you need to get out and enjoy life more! You think too far ahead! However, keep squirreling the money away. If your time frame is greater than 50 years, you'll be worth bazillions, providing you don't start spending the money!

It could be argued that the real power of compounding kicks in after about 100 years.

For example, if you achieved a 12% return for 100 years, your compounding factor is a whopping (1.12)100= 83,522. That's eighty-three thousand five hundred and twenty two! Each $1 invested grows into $83,522! So if you started with only $5,000 you would have about $417 million. Unfortunately, the chances that you will be around 100 years from now to enjoy your wealth are slim. The greatest investors tend to be patient and think ahead to the future, but as with many things, one can go too far.

One way the investor can take advantage of ultra-long-term compounding periods is by investing money for their children, made available to the children when the children become much older. This won't, of course, help you personally, but suppose you are 30-years old and about to have a child. To help assure their financial future, if you could afford it, you could set aside $1,000 or $5,000, invested for them to be given to them when they reach age 65. That would give 65 years of compounding! Just $1,000 set aside returning 12% would give them $1.6 million at their retirement.

Here, however, you face two complications. First, you need to be sure the money is not withdrawn prematurely, spoiling your good intentions. Second, if you were to die, you must assure that the amount is invested intelligently and not abused by the trustee. Demanding that the money be indexed would be one approach.

So, typically as stock-market investors, we will be investing over time periods of 10 to 40 years. As discussed in Chapter 1, rates of return of 10% to 15% should be achievable over long investment periods. A more conservative portfolio consisting not only of stocks but also bonds might yield 8% as a reasonable return.

In general, the longer your holding period, the more volatility you can tolerate, the more aggressively you can invest, and the higher the rate of return you can reasonably expect to achieve.

Although you will never be able to exactly predict what rate of return your portfolio will give you, over long periods, by knowing how your capital is invested among aggressive stocks, conservative stocks, and bonds, you will be able to make a reasonable estimate as to the rate of return you can reasonably expect. Professional investors for pension funds do this all the time, for example. It is largely your asset allocation discussed in Chapter 1 which determines what your long-term wealth will compound into by determining the long-term rate of return your portfolio will achieve.

Looking at the above tables gives you a good idea of how much money you would need to set aside so that you had a given amount in the future. Let's suppose you wanted to retire in 30 years with $1 million dollars. If you assumed a rate of return of 10%, you would need about $60,000. $60,000 times 17.45, which is the multiplier factor for 10% over 30 years, yields $1,047,000. So, if you already had $60,000 saved and you are relatively young, it is likely that you will be a millionaire when you retire.

Notice longer investment periods work strongly in your favor. If you are only 20 years old and you have $10,000 and you feel you can achieve a 12% rate of return, by the time you are age 60 and ready for retirement, you would nearly be a millionaire just by putting the $10,000 into investments rather than spending it.

However, if you go out and buy an expensive car using the $10,000 as a down payment, there is no money to compound over the 40 years. Many young people miss that fact. Money saved is not just money saved. It is money saved to be compounded and which can grow exponentially. You start with $10,000 but you end up with a million dollars. That's the power of compounding. Time is the force that works in your favor.

Conversely, if you want to save for retirement, and you delay saving until only five years before you plan to retire, you will only have small compounding factors to help you grow your money. Further, as you have a shorter investment horizon for keeping your money invested, you cannot tolerate the higher volatility of a more aggressive portfolio.

So, you might only be able to expect a 9% return. And, the uncertainty in what return will actually materialize is quite high. At 9% for five years, you would only have a multiplying factor of 1.54 to work with. This means if you hope to retire with $1 million dollars, you would need to have about $650,000 saved right now.

Rule of Investing Get started investing as early as possible and let the power of compounding grow your portfolio.




But, what if you are already 55 or 60 years old and haven't exploited long-term compounding during your earlier years? You don't have a windfall saved for retirement. You might feel it is too late to benefit from the power of compounding.

It may be true you won't be worth bazillions by only investing a few dollars, but it is never too late to begin intelligent saving, investing, and prudent financial and money management.

Any way you look at it, your future financial position will either get better or worse. Whether it will get better or worse is largely dependent upon the financial decisions you make today (and whether or not you stick with those decisions, of course). Never take the attitude that it's too late to get started doing something which is important to your life.

Such an attitude will kill your future chances of success by preventing you from taking the appropriate actions today. This applies to financial matters as well as anything else in life. Remember Colonel Sanders was 65-years old when he started Kentucky Fried Chicken (KFC).

Plus, if you are 60-years old, you're expected to live another 18 to 22 years. Saving and investing what you can over this time period will add up and help assure that you feel more financially secure as the years go on, rather than less financially secure.

A big part of feeling financially secure is not being rich, but rather knowing you are moving in the correct direction.

As Mr. Micawber advises his young friend David Copperfield in Charles Dickens' David Copperfield, "Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery."

Now, I know many out there are saying, "Gosh. I don't even have $5,000 to invest right now. How can the power of compounding work for me?" It can! The answer is to start squirreling away money as you can. Try to set aside a certain amount of money to add to your portfolio every month, or every paycheck. Just as it is easy to misjudge the power of compounding and just how much $10,000 can grow to over 20 years, it is easy to overlook the amount you will have if you just save regularly. Even if the amounts are far less than $10,000. You might only see the amount saved but miss the growth in compounding.

For example, suppose you have 30 years till retirement. Yet, you only feel you can save $200 a month or so. Now that's $2,400 per year. That will add up significantly over the years when you realize that the contributions will be compounding.

So, we could take this amount and compound it forward for 30 years. Let's assume a compounding rate of 12%. We get $2,400 (1.12)29 = $64,200. Notice that we used 29 years as we won't have all the money until the end of the first year. Technically, we are overlooking the compounding that occurs over the first year.

In particular, if you put $200 per month into your investments at the start of each month, then the first $200 you invested would have the full 30 years to compound. The next $200 would have 29 years and 11 months. And, so on. For your first year, only your last $200 monthly investment contribution would compound for exactly 29 years and one month. All the other $200 contributions would compound slightly longer.

However, this is a level of calculation detail that we want to avoid. Remember, we are doing these calculations for the sake of making reasonable estimates. We might not achieve 12%. We might only get 11%. Or, maybe, we will get 13%. Similarly, maybe we will wait one extra year before retiring. Or, maybe, we will retire one year early. Given the uncertainties, there is little justification to work out more complex mathematical results that would be fully accurate, accounting for the exact length each $200 is compounding.

Rather than using 29 years, which assumes all the money is invested at the end of the first year, we might just have made the assumption that all the money was invested at the start of the first year. Then we would have used 30 years as our compounding period. We would have then gotten $2,400 (1.12)30 = $71,900 as the amount that our first years investment grows to by retirement time.

The advantage to using 29 years is that this is the more conservative estimate. By making our estimates conservative, rather than optimistic, there is less likelihood of being disappointed. If we assumed we needed $1 million to retire, and we made optimistic calculations, we might be quite unhappy when we find, upon retirement, that we only have $600,000. That could put retirement in jeopardy!

But, if on the other hand, you find in 30 years that you have $1.2 million, more than you expected, there is little cause for concern. You will be quite happy. This is a principal we should follow in general. Make conservative estimates, approximations, and assumptions when planning for investment. This is a variation of margin of safety, which will be a reoccurring theme throughout this book.

So, you are at the end of year one. Only 29 more years to go until you can retire! While you are scouting out the local Gander Mountain for a new fishing rod to use in retirement, and during this second year, you also invest $2,400 more dollars into the stock market. This money only compounds for 28 years under our conservative assumption. So it grows into $2,400 (1.12)28 = $57,300 under our conservative assumption. I pose a simple question "What is the estimate amount you now will have upon retirement?"

The answer is that you will have $121,500 which is the sum of the $64,200 and the $57,300. $64,200 represents what your first years investment will compound to and $57,300 represents what your second years investment will compound to by retirement. You can simply add the amounts to get the total you will have upon retirement.

So after just two years of savings you now have an estimated retirement nest egg of $121,500. And, all you actually invested was a total of $4,800. This is the power of time in compounding.

You can begin to see that regularly squirreling away money over long time periods can lead to substantial sums. Notice that the first year's amount of $64,200 is $6,900 more than the second year's amount. This illustrates that dollar investments made earlier are more significant than dollar investments made later. The reason is that the earlier investments have more time to compound!

We could work out what our third year of savings would contribute to our retirement fund just as we did before. It would be $2,400 (1.12)27 = $51,200. But, I will show you a simple formula that will add up all the yearly amounts quite naturally and easily.

That formula is Sn = (xn+1- 1)/(x-1)

where n is the number of years you will be adding the money to your portfolio minus one. And, x is one plus the assumed rate of return expressed as a decimal. Finally, the result of the formula Sn is the number you multiply by your annual contribution to your portfolio to get the total amount of money you will have after n years. Appendix A shows how we derive the above formula.

Now, all the above assumes that we are using the overall net after tax return you expect over the years. If you receive a pretax return of 12% but must pay taxes on that year's return, then your actual return will be reduced. For example, if your return comes in the form of income and is taxed at the 31% federal tax rate, rather than 12% you have only 12%(1- .31) = 8.28%. This is a significant difference! Remember, 12% is an outstanding long-term return corresponding to aggressive investment, such as in small company stocks, but 8% is relatively easy to get with very safe investments, such as a mix of conservatively chosen larger company stocks and bonds.

Knowing how much you must save regularly so that you have a given amount upon retirement is very important. This allows you to plan backward from the amount you need at retirement, and be sure you are contributing enough money today toward your retirement savings.

Let's discuss how we can minimize our tax bite and maximize our overall net after-tax return. The most obvious way is to invest the money in a tax-deferred retirement vehicle like an IRA or a 401(k) plan. Then we are not taxed on the amount we invest, nor are we taxed on the compounded earnings, which is even more important to our building wealth.

If your money is invested in an IRA and you contribute $2,000 every year, and you have 30 years to invest, and we assume you will get somewhere between a 10% and 12% rate of return, we can use values calculated previously to say your overall multiplier factor is between 164.5 and 241.33. So you can expect to have somewhere between $329,000 and $482,660. If you have more or fewer years till retirement, you can use the expressions above to do the calculations appropriate to your time frame.

As a quick example to be sure you are comfortable with the calculations, let's do one more. Let's assume you have 35 years till retirement. Assuming a net rate of return between 10% and 13%, and that we are investing $6,000 each year, say in a 401(k), the appropriate sums are:

S34 = ((1.10)35 - 1)/(1.10 - 1) = 271 representing 10% over 35 years

and

S29 = ((1.13)35 - 1)/ (1.13 - 1) = 547 representing 13% over 35 years

We then multiply these sums by our yearly contribution of $6,000 to predict we will have somewhere between $6,000 (271) = $1.63 million dollars and $6,000 (547) = $3.28 million dollars.

In addition to tax-deferred retirement vehicles, another strategy is to hold your investments for over one year so that they will be taxed at the favorable capital gains tax rate. This is a most effective way to minimize your tax bite for a non-tax-deferred portfolio such as a standard brokerage account. The capital gains tax rate limits you to paying 20% federal tax regardless of your personal income. Further, you only pay taxes on your capital gains when you realize the gain.

So, for example, if you bought Dell computer stock back in 1993 and you sold it in 1998, you would maybe have gotten about a one-hundred-fold increase in your stock's value. That's certainly more than you had a right to expect! If you invested $10,000 you had a million dollars in 1998. Yet, no taxes are owed until you realize the gain by selling the stock. If you don't sell, but hold on for another ten years, you won't need to pay any taxes until then!

But, let's assume that you felt that Dell was now grossly overpriced and you didn't feel like holding it anymore in 1998. You decide to sell all your shares. You must pay taxes on your $1 million dollar capital gain minus your initial investment, which was $10,000. So you pay only (.20)(990,000) = $198,000. This is not only a favorable tax rate when compared to personal income tax rates, but for all of the years 1993 to 1998 you received the power of tax-deferred compounding. No money was taken away from your Dell shares to pay any taxes at all. Your money just sat there compounding.

Had you been in the 31% personal income tax bracket, and if this return were considered income, taxable to you upon the sale, you would have paid $306,900 in taxes. This gives you an idea of how much more favorable the capital gains tax rate is. Of course, tax laws change all the time. (in fact, in 1997, the TaxPayer Relief Act lowered the capital gains tax rate from 28% to 20% for stocks held 18 months or more.) But, there is every reason to believe that capital gains tax rates will remain favorable when compared to personal income tax rates.

Now suppose that this huge return had occurred uniformly over 6 years, and assume that personal taxes were owed on any unrealized gain, i.e., because the stock went up, let's assume you had been forced to pay taxes each year on the gain. You would have ended with a grand total after tax of about $330,000. Compare this to the approximately $800,000 you actually received after tax.

The above is very important. Intelligent investors try to hold on to their stock investments as long as it is reasonable, if the stock is held outside of a tax-deferred portfolio. Some very rich people have held onto stocks like Philip Morris, 3M, Merck, and similar high-quality stocks for 30 years or more. Huge wealth can be built by holding good stocks over long periods.

However, should our above investor continued to hold a grossly overvalued stock? The answer is a definitive "no." Do not hold grossly overvalued stocks hoping that they will become even more grossly overvalued. That is an unreasonable thing to expect.

 

© 2000 by Peter Hupalo, all rights reserved.


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