How to Use the Rule of 72

How to Use the Rule of 72.

The Rule of 72 is a handy tool used in finance to estimate the number of years it would take to double a sum of money through interest payments, given a particular interest rate. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years. The rule states that the interest rate multiplied by the time period required to double an amount of money is approximately equal to 72.
The Rule of 72 is applicable in cases of exponential growth, (as in compound interest) or in exponential "decay," as in the loss of purchasing power caused by monetary inflation.

Method 1 Estimating "Doubling" Time.
1. Let R x T = 72. R is the rate of growth (the annual interest rate), and T is the time (in years) it takes for the amount of money to double.
2. Insert a value for R. For example, how long does it take to turn $100 into $200 at a yearly interest rate of 5%? Letting R = 5, we get 5 x T = 72.
3. Solve for the unknown variable. In this example, divide both sides of the above equation by R (that is, 5) to get T = 72 ÷ 5 = 14.4. So it takes 14.4 years for $100 to double at an interest rate of 5% per annum. (The initial amount of money doesn't matter. It will take the same amount of time to double no matter what the beginning amount is.)
4. Study these additional examples:
How long does it take to double an amount of money at a rate of 10% per annum? 10 x T = 72. Divide both sides of the equation by 10, so that T = 7.2 years.
How long does it take to turn $100 into $1600 at a rate of 7.2% per annum? Recognize that 100 must double four times to reach 1600 ($100 → $200, $200 → $400, $400 → $800, $800 → $1600). For each doubling, 7.2 x T = 72, so T = 10. So, as each doubling takes ten years, the total time required (to change $100 into $1,600) is 40 years.

Method 2 Estimating the Growth Rate.
1. Let R x T = 72. R is the rate of growth (the interest rate), and T is the time (in years) it takes to double any amount of money.
2. Enter the value of T. For example, let's say you want to double your money in ten years. What interest rate would you need in order to do that? Enter 10 for T in the equation. R x 10 = 72.
3. Solve for R. Divide both sides by 10 to get R = 72 ÷ 10 = 7.2. So you will need an annual interest rate of 7.2% in order to double your money in ten years.

Method 3 Estimating Exponential "Decay" (Loss).
1. Estimate the time it would take to lose half of your money (or its purchasing power in the wake of inflation). Let T = 72 ÷ R. This is the same equation as above, just slightly rearranged. Now enter a value for R. An example.
How long will it take for $100 to assume the purchasing power of $50, given an inflation rate of 5% per year?
Let 5 x T = 72, so that T = 72 ÷ 5 = 14.4. That's how many years it would take for money to lose half its buying power in a period of 5% inflation. (If the inflation rate were to change from year to year, you would have to use the average inflation rate that existed over the full time period.)
2. Estimate the rate of decay (R) over a given time span: R = 72 ÷ T. Enter a value for T, and solve for R. For example.
If the buying power of $100 becomes $50 in ten years, what is the inflation rate during that time?
R x 10 = 72, where T = 10. Then R = 72 ÷ 10 = 7.2%.
3. Ignore any unusual data. If you can detect a general trend, don't worry about temporary numbers that are wildly out of range. Drop them from consideration.

Method 4 Derivation.
1. Understand how the derivation works for periodic compounding.
For periodic compounding, FV = PV (1 + r)^T, where FV = future value, PV = present value, r = growth rate, T = time.
If money has doubled, FV = 2*PV, so 2PV = PV (1 + r)^T, or 2 = (1 + r)^T, assuming the present value is not zero.
Solve for T by taking the natural logs on both sides, and rearranging, to get T = ln(2) / ln(1 + r).
The Taylor series for ln(1 + r) around 0 is r - r2/2 + r3/3 - ... For low values of r, the contributions from the higher power terms are small, and the expression approximates r, so that t = ln(2) / r.
Note that ln(2) ~ 0.693, so that T ~ 0.693 / r (or T = 69.3 / R, expressing the interest rate as a percentage R from 0-100%), which is the rule of 69.3. Other numbers such as 69, 70, and 72 are used for easier calculations.
2. Understand how the derivation works for continuous compounding. For periodic compounding with multiple compounding per year, the future value is given by FV = PV (1 + r/n)^nT, where FV = future value, PV = present value, r = growth rate, T = time, and n = number of compounding periods per year. For continuous compounding, n approaches infinity. Using the definition of e = lim (1 + 1/n)^n as n approaches infinity, the expression becomes FV = PV e^(rT).
If money has doubled, FV = 2*PV, so 2PV = PV e^(rT), or 2 = e^(rT), assuming the present value is not zero.
Solve for T by taking natural logs on both sides, and rearranging, to get T = ln(2)/r = 69.3/R (where R = 100r to express the growth rate as a percentage). This is the rule of 69.3.
For continuous compounding, 69.3 (or approximately 69) gives more accurate results, since ln(2) is approximately 69.3%, and R * T = ln(2), where R = growth (or decay) rate, T = the doubling (or halving) time, and ln(2) is the natural log of 2. 70 may also be used as an approximation for continuous or daily (which is close to continuous) compounding, for ease of calculation. These variations are known as rule of 69.3, rule of 69, or rule of 70.
A similar accuracy adjustment for the rule of 69.3 is used for high rates with daily compounding: T = (69.3 + R/3) / R.
The Eckart-McHale second order rule, or E-M rule, gives a multiplicative correction to the Rule of 69.3 or 70 (but not 72), for better accuracy for higher interest rate ranges. To compute the E-M approximation, multiply the Rule of 69.3 (or 70) result by 200/(200-R), i.e., T = (69.3/R) * (200/(200-R)). For example, if the interest rate is 18%, the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, which better approximates the actual doubling time 4.19 years at this rate.
The third-order Padé approximant gives even better approximation, using the correction factor (600 + 4R) / (600 + R), i.e., T = (69.3/R) * ((600 + 4R) / (600 + R)). If the interest rate is 18%, the third-order Padé approximant gives T = 4.19 years.
To estimate doubling time for higher rates, adjust 72 by adding 1 for every 3 percentages greater than 8%. That is, T = [72 + (R - 8%)/3] / R. For example, if the interest rate is 32%, the time it takes to double a given amount of money is T = [72 + (32 - 8)/3] / 32 = 2.5 years. Note that 80 is used here instead of 72, which would have given 2.25 years for the doubling time.


FAQ.
Question : When would I need to use the rule of 72?
Answer : It's a handy shortcut when considering compounded, monetary gains or losses. For example, you might want to know how long it would take for invested money to double in value, given a specific rate of interest.
Question : How do I calculate compound interest?
Answer : The formula for annual compound interest (A) is: P [1 + (r / n)]^(nt), where P=principal amount, r = the annual interest rate as a decimal, n = the number of times the interest is compounded per year, and t = the number of years of the loan or investment.
Question : What is APY for an APR of 3.5% compounded?
Answer : It depends on how often the interest compounds: annually, semi-annually, quarterly, monthly or daily.

Tips.

Let the Rule of 72 work for you by starting to save now. At a growth rate of 8% a year (the approximate rate of return in the stock market), you would double your money in nine years (72 ÷ 8 = 9), quadruple your money in 18 years, and have 16 times your money in 36 years.
The value of 72 was chosen as a convenient numerator in the above equation. 72 is easily divisible by several small numbers: 1,2,3,4,6,8,9, and 12. It provides a good approximation for annual compounding at typical rates (from 6% to 10%). The approximations are less exact at higher interest rates.
You can use Felix's Corollary to the Rule of 72 to calculate the "future value" of an annuity (that is, what the annuity's face value will be at a specified future time). You can read about the corollary on various financial and investing websites.

Warnings.
Let the rule of 72 convince you not to take on high-interest debt (as is typical with credit cards). At an average interest rate of 18%, semiretired credit card debt doubles in just four years (72 ÷ 18 = 4), quadruples in eight years, and becomes completely unmanageable after that.

April 10, 2020

How to Find Great Companies to Invest In

How to Find Great Companies to Invest In.

Smart investors put their money in reputable companies and investigate new companies thoroughly before committing their money. By carefully considering the qualities of the companies you invest in and incorporating your own knowledge of the market, you can make informed decisions in the hopes of choosing stocks of good quality and value. Be aware, however, this is no small task. Mutual fund companies and the like dedicate entire teams of experts whose full-time jobs are to research and understand how to invest in companies. Be sure you have the time and inclination to do this yourself, as well as the willingness to take the risks of doing so.

Method 1 Buying What You Know.
1. Stay within your circle of competence. If you have a field of expertise, you may be best able to identify quality within that area. Experience can provide you with the insights you need to make more informed choices. For example, if you work in retail, you may be better positioned to determine if you should invest in companies like Walmart, Target, or Best Buy, than you are in evaluating the latest bio-tech company.
Having competence in a certain area doesn't have to come from workplace experience. If you're a techie who spends his time buying and reading about the latest gadgets, you can draw on the information you obtain to help you make decisions on how to invest in the technology sector.
2. Focus on a few industries or markets. These can be either your direct area of competence or other areas that you are interested in investing in. The important thing is to realize that you can't keep track of everything going on in the global economy. Large financial institutions have whole departments for doing this so don't think you can do it on your own. Instead, narrow your focus to include only a few key industries or markets.
This doesn't mean you should avoid focusing on individual companies. You should always investigate every company you plan to invest in individually.
3. Stay up to date on news within that industry. Examples of quality sources for this are online finance websites like Bloomberg and the Wall Street Journal. They'll give you up-to-date information on many of the goings-on in various sectors of the economy and the World. Again, focus your energy on a few key areas and become knowledgeable on the happenings in them. Look for things like trends, mergers, acquisitions, relevant legislation changes, and any global events that may affect your chosen market.
4. Plan ahead. Identify a company that you think stands to benefit from some change or trend in the market. Look ahead for when this change will take place and move around your money to prepare to invest in the company. For example, if you think that a new product being released by your favorite tech company is going to be a huge success, you may choose to invest in the company before the rest of the world realizes this and drives up the stock price.

Method 2 Investing in Companies with Competitive Advantages.
1. Understand competitive advantages. There are some companies that manage to be consistently profitable and successful in their industry over many years. These companies have succeeded in building a "moat" around them to keep their competitors away. This distance from their competitors is also known as a competitive advantage. Competitive advantages allow these companies to make money and retain customers more easily than others. In turn, these companies are able to provide greater value and return to their shareholders.
An investment in one of these companies allows you to participate in their competitive advantage. While they may not grow as quickly as smaller companies, they often can be less likely to fail in economic downturns and can provide consistent growth throughout the years to come.
Blue-chip stocks are examples of large, successful companies with competitive advantages. These companies have provided consistent growth or dividends over many years and are listed on large stock indexes.
2. Invest in trusted brands. Think Harley Davidson, Coke, BMW. These are brand names etched in the public mind as the best in their class. These companies can raise their prices on the strength of their brands, resulting in deeper profits.These companies are so well-known and essential that they are unlikely to lose a significant amount of customers to competitors.
3. Find companies with high switching costs. When was the last time you switched banks? Or cell phone providers? These services retain customers because switching between them is more time-consuming than it's worth. Companies that have high switching costs can be expected to hold on to their customers longer than companies that don't.
4. Search for economies of scale. Companies that are able to make products and sell them at much lower prices than their competition automatically attract customers -- lots of them -- as long as quality is not compromised. In a crowded market, this is generally the result of economies of scale, a phenomenon where a large company is able to experience lower production costs solely due to its size. Walmart and and Dell have perfected this concept to a science.
5. Invest in legal monopolies. Some companies are granted legal (if temporary) monopolies by the government. Large pharmaceutical companies and manufacturing companies with patents are able to bring a truly unique product to market. Companies that own copyrights, drilling rights, mining rights, and other forms of protected property are often the sole producer or service provider in their area. Thus, these companies can raise prices without fear of losing customers, resulting in higher profits.
Be sure to check how long the company's patent or usage rights are in effect. Some of these are temporary and when they go, there's a chance the company's profit will go with them.
6. Look for opportunities for easy growth. Some companies are easily scalable. That is, their products or services with the potential to network or add more users over time. Adobe has become the de facto standard in publishing; Microsoft's Excel has done the same in spreadsheets. eBay is a great example of a user network. Each additional user to the network costs the company virtually nothing. The additional revenues that come in as the network expands go straight to the bottom line.
For a more current example, consider Netflix. As a streaming service, they make more money for each subscriber, even as their costs remain virtually the same. That way, as they gain more users they will continue to grow in profitability, assuming they don't choose to increase costs significantly.

Method 3 Evaluating Company Performance and Valuation.
1. Check the quality of management. How competent is the management running the company? More importantly, how focused are they toward the company, customers, investors, and employees? In this age of rampant corporate greed, it's always a great idea to research the management of any company you're thinking of investing in. Newspaper and magazine articles are good places to get this information.
This doesn't just mean that management has provided good financial results recently. Rather, look for indications of other important qualities like responsiveness, adaptability, capacity for innovation, and organizational ability.
2. Watch for management changes. A good leader can successfully turn around a company that many consider to be a lost cause. Watch the news and financial reports for changes in management positions, especially CEOs. If you believe in the new CEO of a company, based on your research, you may choose to invest in that company. Here, you're essentially putting your faith in the person, not the company.
3. Avoid overvalued stocks. Even a great company can be overvalued. Learn to interpret financial statements and pick stocks with fundamental analysis to find companies the market has overvalued. Know that these companies may be some of the most buzzed-about and invested in companies around, but they are still overvalued and may experience drastic declines in price once their day in the spotlight is over.
One way to determine if a stock is overpriced is to examine its price-earnings-ratio. The price to earnings ratio can usually be found in the company's stock summary on financial websites. Generally, PE ratios are between 20-25, but this varies by industry.
To evaluate a company's PE ratio, search online for the average PE ratio in the company's industry. If the P/E ratio is over the industry average, the company could be overpriced in view of its earnings.
4. Buy undervalued stocks. Undervalued stocks are those that are trading at a lower value than their financial information would indicate. These may be companies that have only started to do well recently. In these cases, the market has not yet caught up with their newfound success. To identify stocks with room to grow in value, you can also use the price-earnings ratio mentioned above and look for companies with low PE ratios compared to the industry average.
You can also look for companies with a price-to-book-value of less than 2. The price-to-book ratio is the price of the company divided by the total value of its assets minus its liabilities and intangible assets. A low ratio may indicate that the company is relatively cheap.

FAQ.

Question : How can I know a company's management?
Answer : A company's stock prospectus will list its management personnel. For suggestions on researching company management, go here: Investopedia.com/articles/02/062602.asp.

Tips.
Start thinking about everyday companies in terms of this new framework.
Learn the basics of reading financial statements. Check the profitability of companies you're interested in. Check their debt position. See if they have been growing steadily.
Visit the company’s website and other financial websites that will give you insight into the stock.
While it may be advantageous to invest in companies you know, do not limit yourself to just one or two sectors of the economy. Try to research companies in a variety of sectors. Doing so further diversifies your portfolio to better insulate it from a downturn in a single sector or company.

Warnings.
Be aware of stock tips: Whether they come from someone you see on TV or someone you meet in person, these are more often not well-researched or are even based on someone's grandiose theory about getting rich quick. They may also be provided by salesmen paid to inflate a stock's price to allow a company to raise as much capital as possible.
Jumping into buying stocks in a company without doing thorough research can be a quick way to lose your money.
Investing always carries risk. Even if you do everything right, there's no guarantee that you'll make money.

April 07, 2020