As the cryptocurrency market continues to grow, stablecoins have emerged as an essential component of the digital currency ecosystem. These coins are designed to maintain a stable value relative to a particular asset or basket of assets, such as the US dollar, gold, or other cryptocurrencies. Binance USD (BUSD) is one of the most popular stablecoins in the market, backed by one of the leading cryptocurrency exchanges, Binance. In this article, we provide a detailed analysis of BUSD and explore its potential benefits and risks.

Binance USD was launched in September 2019 by Binance, one of the world's largest cryptocurrency exchanges. The coin is issued by Paxos Trust Company, a regulated financial institution that operates as a trust company under the New York State Department of Financial Services. BUSD is pegged 1:1 to the US dollar and is fully backed by USD deposits and US Treasury bonds held by Paxos.

Binance USD works by maintaining a 1:1 peg to the US dollar. This means that for every BUSD in circulation, there is an equivalent amount of US dollars held in reserve by Paxos. BUSD is built on the Ethereum blockchain and is an ERC-20 token, which means that it is compatible with all Ethereum-based wallets and decentralized applications (dApps). Users can purchase BUSD on Binance or other cryptocurrency exchanges, and it can also be used for payments and remittances, trading, and as collateral for loans.

Binance USD offers several potential benefits for users, including:

1. Stability: As a stablecoin, BUSD is designed to maintain a stable value relative to the US dollar, which reduces the volatility associated with other cryptocurrencies.

2. Accessibility: BUSD is widely available on major cryptocurrency exchanges, making it easy to purchase and use.

3. Speed and Low Transaction Costs: Transactions with BUSD are fast and low-cost compared to traditional banking systems, making it an attractive option for international payments and remittances.

4. Decentralization: BUSD is built on the Ethereum blockchain, which is a decentralized and trustless network, providing users with greater control and transparency over their funds.

Like any investment, there are risks associated with using Binance USD. One of the main risks is the potential for the coin's value to decline due to factors such as market volatility or a lack of demand. Additionally, since Binance USD is centralized, there is always the risk of the platform being hacked or experiencing a security breach.

Another risk associated with using Binance USD is the potential for regulatory scrutiny. As stablecoins continue to grow in popularity, regulators around the world are taking notice and beginning to scrutinize them more closely. This could potentially result in increased regulations and oversight, which could impact the value and utility of Binance USD.

Additionally, there is always the risk of counterparty risk when using Binance USD. This refers to the risk that the counterparty you are transacting with may not fulfill their obligations, leaving you with losses. While Binance USD is backed by fiat reserves, there is always the potential for these reserves to be mismanaged or not properly allocated, leading to losses for users.

Finally, Binance USD may also be subject to liquidity risk. This refers to the risk that there may not be enough demand for the coin, making it difficult to sell at the desired price. While Binance USD has generally maintained a stable value and high liquidity, there is always the potential for market conditions to change.

Overall, Binance USD is a promising stablecoin that has gained popularity due to its association with the Binance platform and its strong fiat reserves. With its ease of use, low fees, and strong liquidity, Binance USD has become a popular choice for those looking to invest in cryptocurrencies while minimizing their exposure to market volatility.

However, as with any investment, there are risks associated with using Binance USD. Investors should carefully consider these risks before making a decision to invest and should keep a close eye on market conditions and regulatory developments that could impact the value and utility of the coin.

In conclusion, Binance USD is a valuable addition to the growing stablecoin market and is likely to continue gaining popularity as more investors look to minimize their exposure to market volatility. However, as with any investment, it is important to carefully consider the risks involved and to monitor market conditions and regulatory developments closely.

A Bollinger Band® is a technical analysis tool defined by a set of trendlines plotted two standard deviations (positively and negatively) away from a simple moving average (SMA) of a security's price, but which can be adjusted to user preferences.

Bollinger Bands® were developed and copyrighted by famous technical trader John Bollinger, designed to discover opportunities that give investors a higher probability of properly identifying when an asset is oversold or overbought.How to Calculate Bollinger Bands®

The first step in calculating Bollinger Bands® is to compute the simple moving average (SMA) of the security in question, typically using a 20-day SMA. A 20-day moving average would average out the closing prices for the first 20 days as the first data point. The next data point would drop the earliest price, add the price on day 21 and take the average, and so on. Next, the standard deviation of the security's price will be obtained. Standard deviation is a mathematical measurement of average variance and features prominently in statistics, economics, accounting, and finance.

For a given data set, the standard deviation measures how spread out numbers are from an average value. Standard deviation can be calculated by taking the square root of the variance, which itself is the average of the squared differences of the mean. Next, multiply that standard deviation value by two and both add and subtract that amount from each point along the SMA. Those produce the upper and lower bands.

What Do Bollinger Bands® Tell You?

Bollinger Bands® are a highly popular technique. Many traders believe the closer the prices move to the upper band, the more overbought the market, and the closer the prices move to the lower band, the more oversold the market. John Bollinger has a set of 22 rules to follow when using the bands as a trading system.1

In the chart depicted below, Bollinger Bands® bracket the 20-day SMA of the stock with an upper and lower band along with the daily movements of the stock's price. Because standard deviation is a measure of volatility, when the markets become more volatile the bands widen; during less volatile periods, the bands contract.

The Canadian government sets the year's maximum pensionable earnings (YMPE) figure. The YMPE determines the maximum amount on which to base contributions to the Canada or Quebec Pension Plan (C/QPP). The YMPE specifies the earnings amount that can be used in calculating pension contributions for each year.1 2

KEY TAKEAWAYS

• The CPP determines the maximum earnings amount for contributions to the CPP.

• The maximum pensionable earnings under the Canada Pension Plan (CPP) for 2020 are $58,700.3

• The size of those payments depends on an individual's earnings during their working years, the age an individual starts receiving their pension, and how much and for how long an individual contributes to the CPP.

Understanding Year's Maximum Pensionable Earnings (YMPE)

The Canada Pension Plan (CPP) determines the maximum earnings amount for which contributions to the Canada Pension Plan can be made. According to the Government of Canada, the maximum pensionable earnings under the Canada Pension Plan (CPP) for 2020 are $58,700—up from $57,400 in 2019. Contributors who earn more than $58,700 in 2020 cannot make additional contributions to the CPP.3

Beginning in 2024, a separate contribution rate will be implemented for earnings above the YMPE (expected to be 4% each for employers and employees).4

Year's Maximum Pensionable Earnings and CPP Contributions

The Canada Pension Plan is similar to the Social Security program in the United States. It provides workers with a series of monthly payments in retirement. The size of those payments depends on an individual's earnings during their working years.5

On June 20, 2016, Canada's ministers of finance agreed to augment the CPP. The deal increased how much working Canadians would receive from the CPP—from one-quarter of the employees' eligible earnings to one-third, with a boost to the earnings limit. Changes will be phased in gradually over seven years—from 2019 to 2025—so that the impact is measured and piecemeal.4

The enhancement has the following features:

• The income replacement level will be raised to one-third of employees' income.

• The upper earnings limit is set at $82,700 for 2025.

• There will be a gradual seven-year phase-in, starting on January 1, 2019; this will consist of a five-year contribution rate phase-in below the yearly maximum pensionable earnings followed by a two-year phase-in of the upper earnings limit.

• The Working Income Tax Benefit will increase to help low-income earners.

• The enhanced part of employee CPP contributions will be tax-deductible.4

$58,700

The maximum pensionable earnings under the Canada Pension Plan (CPP) for 2020.3

The higher contribution rate on earnings below the YMPE ($58,700 in 2020) will be phased-in over the first five years. In 2023, the CPP contribution rate, as estimated by the Department of Finance Canada, will be one percentage point higher for both employers and employees on earnings up to the YMPE.4 3

In 2024, a separate contribution rate (expected to be 4% each for employers and employees) will be implemented for earnings above the YMPE at that time.4

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The yearly rate of return method, commonly referred to as the annual percentage rate, is the amount earned on a fund throughout an entire year. The yearly rate of return is calculated by taking the amount of money gained or lost at the end of the year and dividing it by the initial investment at the beginning of the year. This method is also referred to as the annual rate of return or the nominal annual rate.

KEY TAKEAWAYS

• Yearly rate of return is computed by looking at the value of an investment at the end of one year and comparing it to the value to the beginning of the year.

• The rate of return for a stock includes capital appreciation and any dividends paid.

• A disadvantage of the yearly rate of return is that it only includes one year and does not consider the potential for compounding over many years.

The Formula for Yearly Rate of Return

\begin{aligned} &\text{Yearly Rate of Return} = \Big ( \frac {\text{EYP} - \text{BYP} }{\text{BYP} } \Big ) \times 100 \\ &\textbf{where:} \\ &\text{EYP} = \text{End of year price} \\ &\text{BYP} = \text{Beginning of year price} \\ \end{aligned}​Yearly Rate of Return=(BYPEYP−BYP​)×100where:EYP=End of year priceBYP=Beginning of year price​

Example of Yearly Rate of Return Method Calculation

If a stock begins the year at $25.00 per share and ends the year with a market price of $45.00 a share, this stock would have an annual, or yearly, rate of return of 80.00%. First, we subtract the end of year price from the beginning price, which equals 45 - 25, or 20. Next, we divide by the beginning price, or 20/25 equals .80. Lastly, to arrive at a percentage, .80 is multiplied by 100 in order to arrive at a percentage and the rate of return 80.00%.

It should be noted that this would technically be called capital appreciation, which is only one source of an equity security’s return. The other component would be any dividend yield. For instance, if the stock in the earlier example paid $2 in dividends, the rate of return would be $2 greater or, using the same calculation, roughly 88.00% over the one-year period.

As a measure of return, the yearly rate of return is rather limiting because it delivers only a percentage increase over a single, one-year period. By not taking into consideration the potential effects of compounding over many years, it’s limited by not including a growth component. But as a single period rate, it does serve its purpose.

Other Return Measures

Other common return measures, which may be an extension of the basic return method, include adjusting for discrete or continuous time periods, which is helpful for more accurate compounding calculations over longer time periods and in certain financial market applications.

Asset managers commonly use money-weighted and time-weighted rates of return to measure performance or the rate of return on an investment portfolio. While money-weighted rates of return focus on cash flows, the time-weighted rate of return looks at the compound rate of growth of the portfolio.

In an effort to be more transparent with investors, particularly retail, measuring and disseminating investment performance has become its niche within capital markets. The CFA Institute, a worldwide leader in the advancement of financial analysis, now offers a professional Certificate in Investment Performance Measurement (CIPM) designation.

According to the CIPM Association, the CIPM program was developed by the CFA Institute as a specialty credentialing program that develops and recognizes the performance evaluation and presentation expertise of investment professionals who "pursue excellence with a passion."

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Zero-bound is an expansionary monetary policy tool where a central bank lowers short-term interest rates to zero, if needed, to stimulate the economy. A central bank that is forced to enact this policy must also pursue other, often unconventional, methods of stimulus to resuscitate the economy.

KEY TAKEAWAYS

• Zero-bound is an expansionary monetary policy tool where a central bank lowers short-term interest rates to zero, if needed, to stimulate the economy.

• Central banks will manipulate interest rates to either stimulate a stagnating economy or dampen an overheating one.

• The Great Recession forced some international central banks to push the limits of zero-bound below the numerical level and implement negative rates to spur growth and spending.1

Understanding Zero-Bound

Zero-bound refers to the lowest level that interest rates can fall to, and logic dictates that zero would be that level. The main arrow in a central bank's monetary policy quiver is interest rates. The bank will manipulate interest rates to either stimulate a stagnating economy or dampen an overheating one. Clearly, there are limits, especially at the lower end of the range.

The zero-bound is the lower limit that rates can be cut to, but no further. When this level is reached, and the economy is still underperforming, then the central bank can no longer provide stimulus via interest rates. Economists use the term liquidity trap to describe this scenario.

When faced with a liquidity trap, alternative procedures for monetary stimulus often become necessary. Conventional wisdom was that interest rates could not move into negative territory, meaning once interest rates reach zero or are close to zero, for example, 0.01%, monetary policy has to be altered to continue to stabilize or stimulate the economy.

The most familiar alternative monetary policy tool is perhaps quantitative easing (QE). This is where a central bank engages in a large-scale asset-buying program, often involving treasuries and other government bonds. Not only will this keep short-term rates low, but it will push down longer-term rates, which further incentivizes borrowing.2

Negative Rates

Since the Great Recession of 2008 and 2009, some central banks pushed the limits of zero-bound below the numerical level and implemented negative rates.3 As the global economy plummeted, central banks slashed rates to spur growth and spending. However, as the recovery remained slow, central banks began entering the uncharted territory of negative rates. 

Sweden was the first country to enter this territory, when in 2009 the Riksbank cut the repo rate to 0.25%, which pushed the deposit rate to -0.25%.4 Since then, the European Central Bank (ECB), the Bank of Japan (BOJ), and a handful of others followed suit at one time or another. 

There are instances where negative rates have been implemented during normal times. Switzerland is one such example; through much of the 2010s, its target interest rate was-0.75%, which was raised to -0.50% in 2021.5 Japan similarly had adopted a negative interest rate policy (NIRP), with a target rate of -0.1%.

Example of Zero-Bound and Negative Interest Rates in Switzerland

The Swiss National Bank (SNB) maintains a negative interest-rate policy. While there are other examples of negative interest rates, the Swiss example is rather unique in that the country is opting to keep rates very low (and negative) to prevent its currency from rising too significantly.

In the Swiss example, negative interest rates are only applied to Swiss franc bank balances over a certain threshold.

Switzerland is viewed as a safe-haven, with low political and inflation risk. Other examples of negative and zero-bound interest rate policies have often come about because of economic turmoil, which requires cutting interest rates to stimulate the economy. The Swiss situation doesn't fit this scenario.

The SNB has maintained that it must keep rates low to prevent its already relatively high currency value from going even higher. A rising currency hurts the Swiss export industry. Therefore, the SNB has taken a two-pronged approach to control the currency. The Bank has actively engaged in currency market interventions to help cap the strong Swiss franc, and also keeps interest rates low or negative to dissuade strong speculative buying of the franc.

In this situation, the SNB will eventually adopt a zero-bound strategy for moving back to 0% and above. However, that won't happen until the central bank feels it can raise rates without causing too significant of a rise in the currency.

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Return on investment (ROI) is a performance measure used to evaluate the efficiency or profitability of an investment or compare the efficiency of a number of different investments. ROI tries to directly measure the amount of return on a particular investment, relative to the investment’s cost.

To calculate ROI, the benefit (or return) of an investment is divided by the cost of the investment. The result is expressed as a percentage or a ratio.

KEY TAKEAWAYS

• Return on Investment (ROI) is a popular profitability metric used to evaluate how well an investment has performed.

• ROI is expressed as a percentage and is calculated by dividing an investment's net profit (or loss) by its initial cost or outlay.

• ROI can be used to make apples-to-apples comparisons and rank investments in different projects or assets.

• ROI does not take into account the holding period or passage of time, and so it can miss opportunity costs of investing elsewhere.

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1:28

How To Calculate Return On Investment (ROI)

How to Calculate Return on Investment (ROI)

The return on investment (ROI) formula is as follows:

\begin{aligned} &\text{ROI} = \dfrac{\text{Current Value of Investment}-\text{Cost of Investment}}{\text{Cost of Investment}}\\ \end{aligned}​ROI=Cost of InvestmentCurrent Value of Investment−Cost of Investment​​

"Current Value of Investment” refers to the proceeds obtained from the sale of the investment of interest. Because ROI is measured as a percentage, it can be easily compared with returns from other investments, allowing one to measure a variety of types of investments against one another.

Understanding ROI

ROI is a popular metric because of its versatility and simplicity. Essentially, ROI can be used as a rudimentary gauge of an investment’s profitability. This could be the ROI on a stock investment, the ROI a company expects on expanding a factory, or the ROI generated in a real estate transaction.

The calculation itself is not too complicated, and it is relatively easy to interpret for its wide range of applications. If an investment’s ROI is net positive, it is probably worthwhile. But if other opportunities with higher ROIs are available, these signals can help investors eliminate or select the best options. Likewise, investors should avoid negative ROIs, which imply a net loss.

For example, suppose Jo invested $1,000 in Slice Pizza Corp. in 2017 and sold the shares for a total of $1,200 one year later. To calculate the return on this investment, divide the net profits ($1,200 - $1,000 = $200) by the investment cost ($1,000), for a ROI of $200/$1,000, or 20%.

With this information, one could compare the investment in Slice Pizza with any other projects. Suppose Jo also invested $2,000 in Big-Sale Stores Inc. in 2014 and sold the shares for a total of $2,800 in 2017. The ROI on Jo’s holdings in Big-Sale would be $800/$2,000, or 40%.

Limitations of ROI

Examples like Jo's (above) reveal some limitations of using ROI, particularly when comparing investments. While the ROI of Jo's second investment was twice that of the first investment, the time between Jo’s purchase and the sale was one year for the first investment but three years for the second.

Jo could adjust the ROI of the multi-year investment accordingly. Since the total ROI was 40%, to obtain the average annual ROI, Jo could divide 40% by 3 to yield 13.33% annualized. With this adjustment, it appears that although Jo’s second investment earned more profit, the first investment was actually the more efficient choice.

ROI can be used in conjunction with the rate of return (RoR), which takes into account a project’s time frame. One may also use net present value (NPV), which accounts for differences in the value of money over time, due to inflation. The application of NPV when calculating the RoR is often called the real rate of return.

Developments in ROI

Recently, certain investors and businesses have taken an interest in the development of a new form of the ROI metric, called "social return on investment," or SROI. SROI was initially developed in the late 1990s and takes into account broader impacts of projects using extra-financial value (i.e., social and environmental metrics not currently reflected in conventional financial accounts).1

SROI helps understand the value proposition of certain environmental social and governance (ESG) criteria used in socially responsible investing (SRI) practices.1 For instance, a company may decide to recycle water in its factories and replace its lighting with all LED bulbs. These undertakings have an immediate cost that may negatively impact traditional ROI—however, the net benefit to society and the environment could lead to a positive SROI.

There are several other new variations of ROI that have been developed for particular purposes. Social media statistics ROI pinpoints the effectiveness of social media campaigns—for example how many clicks or likes are generated for a unit of effort. Similarly, marketing statistics ROI tries to identify the return attributable to advertising or marketing campaigns.

So-called learning ROI relates to the amount of information learned and retained as a return on education or skills training. As the world progresses and the economy changes, several other niche forms of ROI are sure to be developed in the future.

How Do You Calculate Return on Investment (ROI)?

Return on investment (ROI) is calculated by dividing the profit earned on an investment by the cost of that investment. For instance, an investment with a profit of $100 and a cost of $100 would have a ROI of 1, or 100% when expressed as a percentage. Although ROI is a quick and easy way to estimate the success of an investment, it has some serious limitations. For instance, ROI fails to reflect the time value of money, and it can be difficult to meaningfully compare ROIs because some investments will take longer to generate a profit than others. For this reason, professional investors tend to use other metrics, such as net present value (NPV) or the internal rate of return (IRR).

What Is a Good ROI?

What qualifies as a “good” ROI will depend on factors such as the risk tolerance of the investor and the time required for the investment to generate a return. All else being equal, investors who are more risk-averse will likely accept lower ROIs in exchange for taking less risk. Likewise, investments that take longer to pay off will generally require a higher ROI in order to be attractive to investors.

What Industries Have the Highest ROI?

Historically, the average ROI for the S&P 500 has been about 10% per year.2 Within that, though, there can be considerable variation depending on the industry. For instance, during 2020, many technology companies generated annual returns well above this 10% threshold. Meanwhile, companies in other industries, such as energy companies and utilities, generated much lower ROIs and in some cases faced losses year-over-year.3 Over time, it is normal for the average ROI of an industry to shift due to factors such as increased competition, technological changes, and shifts in consumer preferences.

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The price-to-earnings ratio is the ratio for valuing a company that measures its current share price relative to its earnings per share (EPS). The price-to-earnings ratio is also sometimes known as the price multiple or the earnings multiple.

P/E ratios are used by investors and analysts to determine the relative value of a company's shares in an apples-to-apples comparison. It can also be used to compare a company against its own historical record or to compare aggregate markets against one another or over time.

P/E may be estimated on a trailing (backward-looking) or forward (projected) basis.

KEY TAKEAWAYS

• The price-to-earnings (P/E) ratio relates a company's share price to its earnings per share.

• A high P/E ratio could mean that a company's stock is overvalued, or that investors are expecting high growth rates in the future.

• Companies that have no earnings or that are losing money do not have a P/E ratio because there is nothing to put in the denominator.

• Two kinds of P/E ratios—forward and trailing P/E—are used in practice.

• A P/E ratio holds most value when compared against similar companies in the same industry or compared for a single company across a period of time.

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The Price To Earnings Ratio Explained

P/E Ratio Formula and Calculation

The formula and calculation used for this process are as follows.

\text{P/E Ratio} = \frac{\text{Market value per share}}{\text{Earnings per share}}P/E Ratio=Earnings per shareMarket value per share​

To determine the P/E value, one must simply divide the current stock price by the earnings per share (EPS).

The current stock price (P) can be found simply by plugging a stock’s ticker symbol into any finance website, and although this concrete value reflects what investors must currently pay for a stock, the EPS is a slightly more nebulous figure.

EPS comes in two main varieties. TTM is a Wall Street acronym for "trailing 12 months". This number signals the company's performance over the past 12 months. The second type of EPS is found in a company's earnings release, which often provides EPS guidance. This is the company's best-educated guess of what it expects to earn in the future. These different versions of EPS form the basis of trailing and forward P/E, respectively.

Understanding the P/E Ratio

The price-to-earnings ratio (P/E) is one of the most widely used tools by which investors and analysts determine a stock's relative valuation. The P/E ratio helps one determine whether a stock is overvalued or undervalued. A company's P/E can also be benchmarked against other stocks in the same industry or against the broader market, such as the S&P 500 Index.

Sometimes, analysts are interested in long-term valuation trends and consider the P/E 10 or P/E 30 measures, which average the past 10 or past 30 years of earnings, respectively. These measures are often used when trying to gauge the overall value of a stock index, such as the S&P 500, because these longer-term measures can compensate for changes in the business cycle.

The P/E ratio of the S&P 500 has fluctuated from a low of around 5x (in 1917) to over 120x (in 2009 right before the financial crisis). The long-term average P/E for the S&P 500 is around 16x, meaning that the stocks that make up the index collectively command a premium 16 times greater than their weighted average earnings.1

Analysts and investors review a company's P/E ratio when they determine if the share price accurately represents the projected earnings per share.

Forward Price-to-Earnings

These two types of EPS metrics factor into the most common types of P/E ratios: the forward P/E and the trailing P/E. A third and less common variation uses the sum of the last two actual quarters and the estimates of the next two quarters.

The forward (or leading) P/E uses future earnings guidance rather than trailing figures. Sometimes called "estimated price to earnings," this forward-looking indicator is useful for comparing current earnings to future earnings and helps provide a clearer picture of what earnings will look like—without changes and other accounting adjustments.

However, there are inherent problems with the forward P/E metric—namely, companies could underestimate earnings in order to beat the estimated P/E when the next quarter's earnings are announced. Other companies may overstate the estimate and later adjust it going into their next earnings announcement. Furthermore, external analysts may also provide estimates, which may diverge from the company estimates, creating confusion.

Trailing Price-to-Earnings

The trailing P/E relies on past performance by dividing the current share price by the total EPS earnings over the past 12 months. It's the most popular P/E metric because it's the most objective—assuming the company reported earnings accurately. Some investors prefer to look at the trailing P/E because they don't trust another individual’s earnings estimates. But the trailing P/E also has its share of shortcomings—namely, that a company’s past performance doesn’t signal future behavior.

Investors should thus commit money based on future earnings power, not the past. The fact that the EPS number remains constant, while the stock prices fluctuate, is also a problem. If a major company event drives the stock price significantly higher or lower, the trailing P/E will be less reflective of those changes.

The trailing P/E ratio will change as the price of a company’s stock moves because earnings are only released each quarter, while stocks trade day in and day out. As a result, some investors prefer the forward P/E. If the forward P/E ratio is lower than the trailing P/E ratio, it means analysts are expecting earnings to increase; if the forward P/E is higher than the current P/E ratio, analysts expect them to decrease.

Valuation From P/E

The price-to-earnings ratio or P/E is one of the most widely used stock analysis tools by which investors and analysts determine stock valuation. In addition to showing whether a company's stock price is overvalued or undervalued, the P/E can reveal how a stock's valuation compares to its industry group or a benchmark like the S&P 500 Index.

In essence, the price-to-earnings ratio indicates the dollar amount an investor can expect to invest in a company in order to receive $1 of that company’s earnings. This is why the P/E is sometimes referred to as the price multiple because it shows how much investors are willing to pay per dollar of earnings. If a company was currently trading at a P/E multiple of 20x, the interpretation is that an investor is willing to pay $20 for $1 of current earnings.

The P/E ratio helps investors determine the market value of a stock as compared to the company's earnings. In short, the P/E ratio shows what the market is willing to pay today for a stock based on its past or future earnings. A high P/E could mean that a stock's price is high relative to earnings and possibly overvalued. Conversely, a low P/E might indicate that the current stock price is low relative to earnings. 

Example of the P/E Ratio

As a historical example, let's calculate the P/E ratio for Walmart Inc. (WMT) as of Feb. 3, 2021, when the company's stock price closed at $139.55.2 The company's earnings per share for the fiscal year ending Jan. 31, 2021, was $4.75, according to The Wall Street Journal.3

Therefore, Walmart's P/E ratio is $139.55 / $4.75 = 29.38.

Comparing Companies Using P/E

As an additional example, we can look at two financial companies to compare their P/E ratios and see which is relatively over- or undervalued.

Bank of America Corporation (BAC) closed out the year 2021 with the following stats:

• Stock Price = $30.31

• Diluted EPS = $1.87

• P/E = 16.21x ($30.31 / $1.87)4

In other words, Bank of America traded at roughly 16x trailing earnings. However, the 16.21 P/E multiple by itself isn't helpful unless you have something to compare it with, such as the stock's industry group, a benchmark index, or Bank of America's historical P/E range.

Bank of America's P/E at 16x was slightly higher than the S&P 500, which over time trades at about 15x trailing earnings.

To compare Bank of America's P/E to a peer's, we calculate the P/E for JPMorgan Chase & Co. (JPM) as of the end of 2020:

• Stock Price = $127.07

• Diluted EPS = $8.88

• P/E = 14.31x5

When you compare Bank of America's P/E of 16x to JPMorgan's P/E of roughly 14x, Bank of America's stock does not appear as overvalued as it did when compared with the average P/E of 15 for the S&P 500. Bank of America's higher P/E ratio might mean investors expected higher earnings growth in the future compared to JPMorgan and the overall market.

However, no single ratio can tell you all you need to know about a stock. Before investing, it is wise to use a variety of financial ratios to determine whether a stock is fairly valued and whether a company's financial health justifies its stock valuation.

Investor Expectations

In general, a high P/E suggests that investors are expecting higher earnings growth in the future compared to companies with a lower P/E. A low P/E can indicate either that a company may currently be undervalued or that the company is doing exceptionally well relative to its past trends. When a company has no earnings or is posting losses, in both cases, the P/E will be expressed as N/A. Though it is possible to calculate a negative P/E, this is not the common convention.

A P/E ratio of N/A means the ratio is not available or not applicable for that company's stock. A company can have a P/E ratio of N/A if it's newly listed on the stock exchange and has not yet reported earnings, such as in the case of an initial public offering (IPO), but it also means a company has zero or negative earnings, Investors can thus interpret seeing N/A as a company reporting a net loss.

The price-to-earnings ratio can also be seen as a means of standardizing the value of $1 of earnings throughout the stock market. In theory, by taking the median of P/E ratios over a period of several years, one could formulate something of a standardized P/E ratio, which could then be seen as a benchmark and used to indicate whether or not a stock is worth buying.

P/E vs. Earnings Yield

The inverse of the P/E ratio is the earnings yield (which can be thought of as the E/P ratio). The earnings yield is thus defined as EPS divided by the stock price, expressed as a percentage.

If Stock A is trading at $10, and its EPS for the past year was 50 cents (TTM), it has a P/E of 20 (i.e., $10 / 50 cents) and an earnings yield of 5% (50 cents / $10). If Stock B is trading at $20 and its EPS (TTM) was $2, it has a P/E of 10 (i.e., $20 / $2) and an earnings yield of 10% = ($2 / $20).

The earnings yield as an investment valuation metric is not as widely used as its P/E ratio reciprocal in stock valuation. Earnings yields can be useful when concerned about the rate of return on investment. For equity investors, however, earning periodic investment income may be secondary to growing their investments' values over time. This is why investors may refer to value-based investment metrics such as the P/E ratio more often than earnings yield when making stock investments.

The earnings yield is also useful in producing a metric when a company has zero or negative earnings. Because such a case is common among hi-tech, high-growth, or startup companies, EPS will be negative producing an undefined P/E ratio (denoted as N/A). If a company has negative earnings, however, it will produce a negative earnings yield, which can be interpreted and used for comparison.

P/E vs. PEG Ratio

A P/E ratio, even one calculated using a forward earnings estimate, doesn't always tell you whether the P/E is appropriate for the company's forecasted growth rate. So, to address this limitation, investors turn to another ratio called the PEG ratio.

A variation on the forward P/E ratio is the price/earnings-to-growth ratio, or PEG. The PEG ratio measures the relationship between the price/earnings ratio and earnings growth to provide investors with a more complete story than the P/E can on its own. In other words, the PEG ratio allows investors to calculate whether a stock's price is overvalued or undervalued by analyzing both today's earnings and the expected growth rate for the company in the future. The PEG ratio is calculated as a company’s trailing price-to-earnings (P/E) ratio divided by the growth rate of its earnings for a specified time period.

The PEG ratio is used to determine a stock's value based on trailing earnings while also taking the company's future earnings growth into account and is considered to provide a more complete picture than the P/E ratio can. For example, a low P/E ratio may suggest that a stock is undervalued and therefore should be bought—but factoring in the company's growth rate to get its PEG ratio can tell a different story. PEG ratios can be termed “trailing” if using historic growth rates or “forward” if using projected growth rates.

Although earnings growth rates can vary among different sectors, a stock with a PEG of less than 1 is typically considered undervalued because its price is considered low compared to the company's expected earnings growth. A PEG greater than 1 might be considered overvalued because it might indicate the stock price is too high compared to the company's expected earnings growth.

Absolute vs. Relative P/E

Analysts may also make a distinction between absolute P/E and relative P/E ratios in their analysis.

Absolute P/E

The numerator of this ratio is usually the current stock price, and the denominator may be the trailing EPS (TTM), the estimated EPS for the next 12 months (forward P/E), or a mix of the trailing EPS of the last two quarters and the forward P/E for the next two quarters.

When distinguishing absolute P/E from relative P/E, it is important to remember that absolute P/E represents the P/E of the current time period. For example, if the price of the stock today is $100, and the TTM earnings are $2 per share, the P/E is 50 = ($100 / $2).

Relative P/E

The relative P/E compares the current absolute P/E to a benchmark or a range of past P/Es over a relevant time period, such as the past 10 years. The relative P/E shows what portion or percentage of the past P/Es the current P/E has reached. The relative P/E usually compares the current P/E value to the highest value of the range, but investors might also compare the current P/E to the bottom side of the range, measuring how close the current P/E is to the historic low.

The relative P/E will have a value below 100% if the current P/E is lower than the past value (whether the past high or low). If the relative P/E measure is 100% or more, this tells investors that the current P/E has reached or surpassed the past value.

Limitations of Using the P/E Ratio

Like any other fundamental designed to inform investors as to whether or not a stock is worth buying, the price-to-earnings ratio comes with a few important limitations that are important to take into account because investors may often be led to believe that there is one single metric that will provide complete insight into an investment decision, which is virtually never the case.

Companies that aren't profitable and, consequently, have no earnings—or negative earnings per share—pose a challenge when it comes to calculating their P/E. Opinions vary as to how to deal with this. Some say there is a negative P/E, others assign a P/E of 0, while most just say the P/E doesn't exist (N/A or not available) or is not interpretable until a company becomes profitable for purposes of comparison.

One primary limitation of using P/E ratios emerges when comparing the P/E ratios of different companies. Valuations and growth rates of companies may often vary wildly between sectors due to both the different ways companies earn money and the differing timelines during which companies earn that money.

As such, one should only use P/E as a comparative tool when considering companies in the same sector because this kind of comparison is the only kind that will yield productive insight. Comparing the P/E ratios of a telecommunications company and an energy company, for example, may lead one to believe that one is clearly the superior investment, but this is not a reliable assumption.

Other P/E Considerations

An individual company’s P/E ratio is much more meaningful when taken alongside the P/E ratios of other companies within the same sector. For example, an energy company may have a high P/E ratio, but this may reflect a trend within the sector rather than one merely within the individual company. An individual company’s high P/E ratio, for example, would be less cause for concern when the entire sector has high P/E ratios.

Moreover, because a company’s debt can affect both the prices of shares and the company’s earnings, leverage can skew P/E ratios as well. For example, suppose there are two similar companies that differ primarily in the amount of debt they assume. The one with more debt will likely have a lower P/E value than the one with less debt. However, if business is good, the one with more debt stands to see higher earnings because of the risks it has taken.

Another important limitation of price-to-earnings ratios is one that lies within the formula for calculating P/E itself. Accurate and unbiased presentations of P/E ratios rely on accurate inputs of the market value of shares and of accurate earnings per share estimates. The market determines the prices of shares through its continuous auction. The printed prices are available from a wide variety of reliable sources. However, the source for earnings information is ultimately the company itself. This single source of data is more easily manipulated, so analysts and investors place trust in the company's officers to provide accurate information. If that trust is perceived to be broken, the stock will be considered riskier and therefore less valuable.

To reduce the risk of inaccurate information, the P/E ratio is but one measurement that analysts scrutinize. If the company were to intentionally manipulate the numbers to look better, and thus deceive investors, they would have to work strenuously to be certain that all metrics were manipulated in a coherent manner, which is difficult to do. That's why the P/E ratio continues to be one of the most centrally referenced points of data when analyzing a company, but by no means is it the only one.

What Is a Good Price-to-Earnings Ratio?

The question of what is a good or bad price-to-earnings ratio will necessarily depend on the industry in which the company is operating. Some industries will have higher average price-to-earnings ratios, while others will have lower ratios. For example, in January 2021, publicly traded broadcasting companies had an average trailing P/E ratio of only about 12, compared to more than 60 for software companies.6 If you want to get a general idea of whether a particular P/E ratio is high or low, you can compare it to the average P/E of the competitors within its industry.

Is It Better to Have a Higher or Lower P/E Ratio?

Many investors will say that it is better to buy shares in companies with a lower P/E because this means you are paying less for every dollar of earnings that you receive. In that sense, a lower P/E is like a lower price tag, making it attractive to investors looking for a bargain. In practice, however, it is important to understand the reasons behind a company’s P/E. For instance, if a company has a low P/E because its business model is fundamentally in decline, then the apparent bargain might be an illusion.

What Does a P/E Ratio of 15 Mean?

Simply put, a P/E ratio of 15 would mean that the current market value of the company is equal to 15 times its annual earnings. Put literally, if you were to hypothetically buy 100% of the company’s shares, it would take 15 years for you to earn back your initial investment through the company’s ongoing profits assuming the company never grew in the future.

Why Is P/E Ratio Important?

The P/E ratio helps investors determine whether the stock of a company is overvalued or undervalued compared to its earnings. The ratio is a measurement of what the market is willing to pay for the current operations as well as prospective growth of the company. If a company is trading at a high P/E ratio, the market thinks highly of its growth potential and is willing to potentially overspend today based on future earnings.

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Monopolistic competition characterizes an industry in which many firms offer products or services that are similar (but not perfect) substitutes. Barriers to entry and exit in a monopolistic competitive industry are low, and the decisions of any one firm do not directly affect those of its competitors. Monopolistic competition is closely related to the business strategy of brand differentiation.

KEY TAKEAWAYS

• Monopolistic competition occurs when an industry has many firms offering products that are similar but not identical.

• Unlike a monopoly, these firms have little power to curtail supply or raise prices to increase profits.

• Firms in monopolistic competition typically try to differentiate their products in order to achieve above-market returns.

• Heavy advertising and marketing are common among firms in monopolistic competition and some economists criticize this as wasteful.

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Monopolistic Competition

Understanding Monopolistic Competition

Monopolistic competition is a middle ground between monopoly and perfect competition (a purely theoretical state) and combines elements of each. The term was first used in the 1930s by economists Edward Chamberlain and Joan Robinson, to describe the competition between firms with similar, but not identical, product offerings.1 All firms in monopolistic competition have the same relatively low degree of market power; they are all price makers.

In the long run, demand is highly elastic, meaning that it is sensitive to price changes. In the short run, economic profit is positive, but it approaches zero in the long run. Firms in monopolistic competition tend to advertise heavily.

Monopolistic competition is characterized by heavy spending on advertising and marketing, which some economists characterize as a waste of resources.

Example of Monopolistic Competition

Monopolistic competition is a form of competition that characterizes a number of industries that are familiar to consumers in their day-to-day lives. Examples include restaurants, hair salons, clothing, and consumer electronics. To illustrate the characteristics of monopolistic competition, we'll use the example of household cleaning products.

Competing Companies

Say you've just moved into a new house and want to stock up on cleaning supplies. Go to the appropriate aisle in a grocery store, and you'll see that any given item—dish soap, hand soap, laundry detergent, surface disinfectant, toilet bowl cleaner, etc.—is available in a number of varieties. For each purchase you need to make, perhaps five or six firms will be competing for your business.

Product Differentiation

Because the products all serve the same purpose, there are relatively few options for sellers to differentiate their offerings from other competing firms. There might be "discount" varieties that are of lower quality, but it is difficult to tell whether the higher-priced options are in fact any better. This uncertainty results from imperfect information: the average consumer does not know the precise differences between the various products, or what the fair price for any of them is.

Monopolistic competition tends to lead to heavy marketing because different firms need to distinguish broadly similar products. One company might opt to lower the price of their cleaning product, sacrificing a higher profit margin in exchange—ideally—for higher sales. Another might take the opposite route, raising the price and using packaging that suggests quality and sophistication.

A third might sell itself as more eco-friendly, using "green" imagery and displaying a stamp of approval from an environmental certifier. In reality, every one of the brands might be equally effective.

Hair salons, restaurants, clothing, and consumer electronics are all examples of industries with monopolistic competition. Each company offers products that are similar to others in the same industry. However, they can distinguish themselves through marketing and branding.

Special Considerations

Firms in monopolistic competition face a significantly different business environment than those in either a monopoly or perfect competition. In addition to competing to reduce costs or scaling up production, companies in monopolistic competition can also distinguish themselves through other means.

Decision-Making

Monopolistic competition implies that there are enough firms in the industry so that one firm's decision does not require other companies to change their behavior. In an oligopoly, a price cut by one firm can set off a price war, but this is not the case for monopolistic competition.

Pricing Power

As in a monopoly, firms in monopolistic competition are price setters or makers, rather than price takers. However, their nominal ability to set prices is effectively offset by the fact that demand for their products is highly price-elastic. In order to actually raise their prices, the firms must be able to differentiate their products from those of their competitors by increasing their quality, real or perceived. 

Demand Elasticity

Due to the range of similar offerings, demand is highly elastic in monopolistic competition. In other words, demand is very responsive to price changes. If your favorite multipurpose surface cleaner suddenly costs 20% more, you probably won't hesitate to switch to an alternative, and your countertops probably won't know the difference.

Economic Profit

In the short run, firms can make excess economic profits. However, because barriers to entry are low, other firms have an incentive to enter the market, increasing the competition, until overall economic profit is zero. Note that economic profits are not the same as accounting profits; a firm that posts a positive net income can have zero economic profit because the latter incorporates opportunity costs.

Advertising in Monopolistic Competition

Economists who study monopolistic competition often highlight the social cost of this type of market structure. Firms in monopolistic competition expend large amounts of real resources on advertising and other forms of marketing.

When there is a real difference between the products of different firms but that the consumer might not be aware of, these expenditures can be useful. However, if it is instead the case that the products are near-perfect substitutes, which is likely in monopolistic competition, then real resources spent on advertising and marketing represent a kind of wasteful rent-seeking behavior, which produces a deadweight loss to society.

What Are the Characteristics of Monopolistic Competition?

Monopolistic competitive industries generally consist of many different companies that produce products that are similar but not identical. These companies spend many of their resources on advertising to make their products stand out. Competition is rife and barriers to entry are low, meaning companies must work hard and be creative to squeeze out a profit and be aware that hiking prices too much might lead customers to opt for an alternative.

What Are Some Examples of Monopolistic Competition?

Monopolistic competition is present in many familiar industries, including restaurants, hair salons, clothing, and consumer electronics. A good example would be Burger King and McDonald's. Both are fast food chains that target a similar market and offer similar products and services. These two companies are actively competing with one another, as well as countless other restaurants, and seek to differentiate themselves through brand recognition, price, and by offering slightly different food and drink packages.

What Is the Difference Between Monopolistic Competition and a Monopoly?

A monopoly is when a single company dominates an industry. This lack of competition means the company can set prices as it pleases, provided, of course, that there is demand for what it offers.

Monopolistic competitive companies don’t enjoy this luxury. Such entities must compete with others, restricting their ability to substantially hike prices and circumvent the natural laws of supply and demand. Monopolistic competition is viewed as healthier for the economy and is much more common than monopolies, which are generally frowned upon in free-market nations because they can lead to price-gouging and deteriorating quality due to a lack of alternative choices.

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A kickback is an illegal payment intended as compensation for preferential treatment or any other type of improper services received. The kickback may be money, a gift, credit, or anything of value. Paying or receiving kickbacks is a corrupt practice that interferes with an employee's or a public official’s ability to make unbiased decisions. Kickbacks are often referred to as a type of bribery.

KEY TAKEAWAYS

• A kickback is an illegal payment intended as compensation for preferential treatment or any other type of improper services received.

• Kickbacks are often referred to as a type of bribery.

• While kickbacks can take many different forms, they all feature some sort of collusion between two parties.

• Paying or receiving kickbacks is a corrupt practice that interferes with an employee's or a public official’s ability to make unbiased decisions.

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Click Play to Learn What Kickbacks Are

How a Kickback Works

While kickbacks can take many different forms, they all feature some sort of collusion between two parties. For example, the bookkeeper for a business or government office might approve an invoice for goods, knowing that the bill is inflated. The seller of the goods might then pay the bookkeeper part of the difference (or some other kind of reward). Kickback schemes are among the most difficult white-collar crimes to detect and investigate.

Kickbacks can also be used to buy a positive recommendation for the kickback provider. For example, a government employee responsible for managing contractors on an infrastructure project–such as the building of a bridge–might receive a kickback for choosing one contractor over another. This may result in a better-qualified contractor not winning the bid.

Procurement contracts can be fertile ground for kickback schemes. For example, in the granting of a government contract for office equipment, contractors interested in winning the business are typically required to bid against each other. Rather than playing fair, a contractor might reach out to a procurement officer and indicate that, if the contractor were to win, the officer would be rewarded. The reward might be cash, concert tickets, etc.

These are some common kickback warning signs. They don't necessarily mean that anything nefarious is going on, but the more of them there are, the greater the likelihood of a kickback scheme.

• No competitive bidding process (or lower bids are ignored)

• Lack of appropriate supervision during the purchasing process

• Higher-than-average prices for goods or services

• Recommendation to use a vendor that others shun

• A vendor with frequent legal or regulatory problems

• Employees are too friendly with vendors

• Management pressures staff to use a particular vendor

• Vendors are in an industry where kickbacks are common

• Employees continue to use vendors that provide poor products or services

• Delivery dates are repeatedly missed

Kickbacks increase the cost of doing business in countries around the world; they also form the basis for much of the world's government corruption. Companies looking to supply products or services to countries known for corruption may find that they have to pay numerous officials in order to be considered for a contract. The perception that a kickback scheme will go unpunished—or that punishment will be light—is a primary driver for officials willing to take bribes. In some cases, they may be poorly paid and see kickbacks as a way to supplement a meager salary.

Even if it is the local custom, the U.S. Foreign Corrupt Practices Act makes bribing foreign officials illegal for all companies listed with the Securities and Exchange Commission (SEC), any company organized in the United States, or any citizen or resident.1

Example of a Kickback

On Wall Street, brokers sometimes route all orders to a particular exchange (even though they are required by law to execute trades with the one that offers the best terms, or best-execution, for their clients). Rather than choosing the exchange that offers the most competitive price and has the highest likelihood of completing the trade in a timely manner, the broker may take a kickback in exchange for routing all of their trades to that particular exchange. This can ultimately lead to slower execution and higher transaction costs for clients. The industry refers to the practice as "rebates." While rebates may amount to only a fraction of a cent of each share traded, over time, considerable sums can be accrued.

In the advertising business, kickbacks can take the form of rebates or fraudulent billing for nonexistent services. Clients pay the price with higher costs or a lower level of service than they normally would expect for their money. Shrinking agency fees and a hard-to-understand digital marketplace are providing the motivation and cover for such actions.

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Nash equilibrium is a concept within game theory where the optimal outcome of a game is where there is no incentive to deviate from the initial strategy. More specifically, the Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from their chosen strategy after considering an opponent's choice.1

Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all.

KEY TAKEAWAYS

• The Nash equilibrium is a decision-making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy.

• In the Nash equilibrium, each player's strategy is optimal when considering the decisions of other players. Every player wins because everyone gets the outcome they desire.

• The prisoners' dilemma is a common game theory example and one that adequately showcases the effect of the Nash equilibrium.

• The Nash equilibrium is often discussed in conjunction with dominant strategy, which states that the chosen strategy of an actor will lead to better results out of all the possible strategies that can be used, regardless of the strategy that the opponent uses.

• The Nash equilibrium does not always mean that the most optimal strategy is chosen.1

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The Nash Equilibrium

Understanding Nash Equilibrium

Nash equilibrium is named after its inventor, John Nash, an American mathematician. It is considered one of the most important concepts of game theory, which attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves.

The reason why Nash equilibrium is considered such an important concept of game theory relates to its applicability. The Nash equilibrium can be incorporated into a wide range of disciplines, from economics to the social sciences.

To quickly find the Nash equilibrium or see if it even exists, reveal each player's strategy to the other players. If no one changes their strategy, then the Nash equilibrium is proven.

Nash Equilibrium vs. Dominant Strategy

Nash equilibrium is often compared alongside dominant strategy, both being strategies of game theory. The Nash equilibrium states that the optimal strategy for an actor is to stay the course of their initial strategy while knowing the opponent's strategy and that all players maintain the same strategy, as long as all other players do not change their strategy.

Dominant strategy asserts that the chosen strategy of an actor will lead to better results out of all the possible strategies that can be used, regardless of the strategy that the opponent uses.

All models of game theory only work if the players involved are "rational agents," meaning that they desire specific outcomes, operate in attempting to choose the most optimal outcome, incorporate uncertainty in their decisions, and are realistic in their options.

Both the terms are similar but slightly different. Nash equilibrium states that nothing is gained if any of the players change their strategy if all other players maintain their strategy. Dominant strategy asserts that a player will choose a strategy that will lead to the best outcome regardless of the strategies that other plays have chosen. Dominant strategy can be included in Nash equilibrium whereas a Nash equilibrium may not be the best strategy in a game.

Example of Nash Equilibrium

Imagine a game between Tom and Sam. In this simple game, both players can choose strategy A, to receive $1, or strategy B, to lose $1. Logically, both players choose strategy A and receive a payoff of $1.

If you revealed Sam's strategy to Tom and vice versa, you see that no player deviates from the original choice. Knowing the other player's move means little and doesn't change either player's behavior. Outcome A represents a Nash equilibrium.

Investopedia/Julie Bang

Special Considerations

The prisoner's dilemma is a common situation analyzed in game theory that can employ the Nash equilibrium. In this game, two criminals are arrested and each is held in solitary confinement with no means of communicating with the other. The prosecutors do not have the evidence to convict the pair, so they offer each prisoner the opportunity to either betray the other by testifying that the other committed the crime or cooperate by remaining silent.

If both prisoners betray each other, each serves five years in prison. If A betrays B but B remains silent, prisoner A is set free and prisoner B serves 10 years in prison or vice versa. If each remains silent, then each serves just one year in prison.

The Nash equilibrium in this example is for both players to betray each other. Even though mutual cooperation leads to a better outcome if one prisoner chooses mutual cooperation and the other does not, one prisoner's outcome is worse.

Nash Equilibrium FAQs

What is a Nash Equilibrium in game theory?

Nash equilibrium in game theory is a situation in which a player will continue with their chosen strategy, having no incentive to deviate from it, after taking into consideration the opponent's strategy.

How do you find Nash Equilibrium?

To find the Nash equilibrium in a game, one would have to model out each of the possible scenarios to determine the results and then choose what the optimal strategy would be. In a two-person game, this would take into consideration the possible strategies that both players could choose. If neither player changes their strategy knowing all of the information, a Nash equilibrium has occurred.

Why is Nash Equilibrium important?

Nash equilibrium is important because it helps a player determine the best payoff in a situation based not only on their decisions but also on the decisions of other parties involved. Nash equilibrium can be utilized in many facets of life, from business strategies to selling a house to war, and social sciences.

How do you calculate Nash Equilibrium?

There is not a specific formula to calculate the Nash equilibrium, but rather it can be determined by modeling out different scenarios within a given game to determine the payoff of each strategy and which would be the optimal strategy to choose.

What are the limitations of Nash Equilibrium?

The primary limitation of the Nash equilibrium is that it requires an individual to know their opponent's strategy. A Nash equilibrium can only occur if a player chooses to remain with their current strategy if they know their opponent's strategy.

In most cases, such as in war, whether that be a military war or a bidding war, an individual rarely knows the opponent's strategy or what they want the outcome to be. Unlike dominant strategy, the Nash equilibrium doesn't always lead to the most optimal outcome, it just means that an individual chooses the best strategy based on the information they have.

Furthermore, in multiple games played with the same opponents, the Nash equilibrium does not take into consideration past behavior, which often predicts future behavior.

The Bottom Line

The Nash equilibrium is a component of game theory that asserts that a player will continue with their chosen strategy while knowing their opponent's strategy as they have no incentive to change course. The Nash equilibrium can be applied in a variety of real-life situations in determining what the best payoff in a scenario will be based on your decisions as well as your opponent's decisions.

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The free carrier is a trade term dictating that a seller of goods is responsible for the delivery of those goods to a destination specified by the buyer. When used in trade, the word "free" means the seller has an obligation to deliver goods to a named place for transfer to a carrier. The destination is typically an airport, shipping terminal, warehouse, or other location where the carrier operates. It might even be the seller's business location.

The seller includes transportation costs in its price and assumes the risk of loss until the carrier receives the goods. At this point, the buyer assumes all responsibility.

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Free Carrier

KEY TAKEAWAYS

• Free carrier is a trade term requiring the seller of goods to deliver those goods to a named airport, shipping terminal, warehouse, or other carrier location specified by the buyer.

• The seller includes transportation costs in its price and assumes the risk of loss until the carrier receives the goods.

• Once the seller delivers the goods to the carrier, the buyer assumes all responsibility for the goods.

• The International Chamber of Commerce updated Incoterms in 2010 to include the free carrier provision.

• As part of the liability transfer, the seller is only responsible for delivery to the specified destination but isn't obligated to unload the goods.

How Free Carrier (FCA) Works

Buyers and sellers engaged in economic trade requiring the shipment of goods can use a free carrier agreement (FCA) to describe any transportation point, regardless of the number of transportation modes involved in the shipping process. The point must be a location within the seller’s home country, however. It's the seller's duty to safely transport the goods to that facility. The carrier can be any kind of transportation service, such as a truck, train, boat, or airplane.

Liability for the merchandise transfers from the seller to the carrier or buyer at the time the seller delivers the goods to the agreed port or area. The seller is only responsible for delivery to the specified destination as part of the liability transfer. It isn't obligated to unload the goods, but the seller might be responsible for ensuring that the goods have been cleared for export out of the United States if the destination is the seller's premises.

The buyer doesn't have to deal with export details and licenses because this is the responsibility of the seller. The buyer must arrange for transport, however. Once goods arrive at the carrier and title transfers to the buyer, the goods become an asset on the buyer's balance sheet.

The Importance of Incoterms

Contracts involving international transportation often contain abbreviated trade terms, or terms of sale, that describe shipment specifics. These might include the time and place of delivery, payment, the point at which the risk of loss shifts from the seller to the buyer, and the party responsible for freight and insurance costs. The details are highly specific in nature because identifying the exact moment when liabilities and cost responsibilities transfer are key points within the agreement.

The most commonly known trade terms are international commercial terms or Incoterms, which are internationally recognized standards published by the International Chamber of Commerce (ICC). These are often identical in form to domestic terms, such as the Uniform Commercial Code (UCC), but there can be slight differences in their official interpretations. Parties to a contract must expressly indicate the governing law of their terms and which edition of the published Incoterms they're using.

The ICC updates Incoterms every 10 years. The following is an example of the kinds of terms included in Incoterms:

• Ex works (EXW).

• Delivered at place (DAP).

• Delivered duty paid (DDP).

• Free alongside (FAS).

• Free on board (FOB).

• Cost and freight (CFR).

• Cost, insurance, and freight (CIF).

All Incoterms are legal terms, but their exact definitions can differ by country. Using clarity and specificity when citing them is critical.

Experts recommend that any party involved in international trade consult with an appropriate legal professional—such as a trade attorney—before using any trade term within a contract.

Example of Free Carrier (FCA)

The seller delivers the goods to the destination named by the buyer. The shipper assumes responsibility for the goods when they arrive there. The buyer would be responsible for loading the goods for transport.

For example, Joe Seller ships goods to Bob Buyer. Bob opts to use his shipper with whom he's done business before. Joe agrees, and it's his responsibility to deliver the goods to the shipper. At this point, all liability passes to Bob.

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Delivered duty paid (DDP) is a delivery agreement whereby the seller assumes all of the responsibility, risk, and costs associated with transporting goods until the buyer receives or transfers them at the destination port. This agreement includes paying for shipping costs, export and import duties, insurance, and any other expenses incurred during shipping to an agreed-upon location in the buyer's country.1

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Delivery Duty Paid (DDP)

• Delivered duty paid (DDP) is a delivery agreement whereby the seller assumes all responsibility of transporting the goods until they reach an agreed-upon destination.

• The seller must arrange for all transportation and associated costs including export clearance and customs documentation required to reach the destination port.2

• The risks to the seller are broad and include VAT charges, bribery, and storage costs if unexpected delays occur.2

• A DDP benefits a buyer as the seller assumes most of the liability and costs for shipping.2

Understanding Delivered Duty Paid (DDP)

Delivered duty paid (DDP) is a shipping agreement that places the maximum responsibility on the seller. In addition to shipping costs, the seller is obligated to arrange for import clearance, tax payment, and import duty. The risk transfers to the buyer once the goods are made available to the buyer at the port of destination. The buyer and seller must agree on all payment details and state the name of the place of destination before finalizing the transaction.1

DDP was developed by the International Chamber of Commerce (ICC) which sought to standardize shipping globally; hence, DDP is most commonly used in international shipping transactions. The benefits of DDP lean in favor of the buyer as they assume less liability and fewer costs in the shipping process, this, therefore, places a great deal of burden on the seller.3

Seller's Responsibilities

The seller arranges for transportation through a carrier of any kind and is responsible for the cost of that carrier as well as acquiring customs clearance in the buyer's country, including obtaining the appropriate approvals from the authorities in that country. Also, the seller may need to acquire a license for importation. However, the seller is not responsible for unloading the goods.2

The seller’s responsibilities include providing the goods, drawing up a sales contract and related documents, export packaging, arranging for export clearance, satisfying all import, export, and customs requirements, and paying for all transportation costs including final delivery to an agreed-upon destination.2

The seller must arrange for proof of delivery and pay the cost of all inspections and must alert the buyer once the goods are delivered to the agreed-upon location. In a DDP transaction, if the goods are damaged or lost in transit, the seller is liable for the costs.2

Managing Customs

It is not always possible for the shipper to clear the goods through customs in foreign countries. Customs requirements for DDP shipments vary by country. In some countries, import clearance is complicated and lengthy, so it is preferable if the buyer, who has intimate knowledge of the process, manages this process.

If a DDP shipment does not clear customs, customs may ignore the fact that the shipment is DDP and delay the shipment. Depending on the customs' decision, this may result in the seller using different, more costly delivery methods.

Special Considerations

DDP is used when the cost of supply is relatively stable and easy to predict. The seller is subject to the most risk, so DDP is normally used by advanced suppliers; however, some experts believe that there are reasons U.S. exporters and importers should not use DDP.4

U.S exporters, for example, may be subject to value-added tax (VAT) at a rate of up to 20%.5 Moreover, the buyer is eligible to receive a VAT refund. Exporters are also subject to unexpected storage and demurrage costs that might occur due to delays by customs, agencies, or carriers. Bribery is a risk that could bring severe consequences both with the U.S government and a foreign country.

For U.S. importers, because the seller and its forwarder are controlling the transportation, the importer has limited supply chain information. Also, a seller may pad their prices to cover the cost of liability for the DDP shipment or markup freight bills.

If DDP is handled poorly, inbound shipments are likely to be examined by customs, which causes delays. Late shipments may also occur because a seller may use cheaper, less reliable transportation services to reduce their costs.

Since DDP is an important aspect of customer relationship management (CRM) for delivery companies, it's important for businesses to invest in the best CRM software currently available.

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An automated teller machine (ATM) is an electronic banking outlet that allows customers to complete basic transactions without the aid of a branch representative or teller. Anyone with a credit card or debit card can access cash at most ATMs.

ATMs are convenient, allowing consumers to perform quick self-service transactions such as deposits, cash withdrawals, bill payments, and transfers between accounts. Fees are commonly charged for cash withdrawals by the bank where the account is located, by the operator of the ATM, or by both. Some or all of these fees can be avoided by using an ATM operated directly by the bank that holds the account.

ATMs are known in different parts of the world as automated bank machines (ABM) or cash machines.

KEY TAKEAWAYS

• Automated teller machines (ATMs) are electronic banking outlets that allow people to complete transactions without going into a branch of their bank.

• Some ATMs are simple cash dispensers while others allow a variety of transactions such as check deposits, balance transfers, and bill payments.

• The first ATMs appeared in the mid- to late-1960s and have grown in number to over 2 million worldwide.

• Today's ATMs are technological marvels, many capable of accepting deposits as well as several other banking services.

• To keep ATM fees down, use an ATM branded by your own bank as often as possible.

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Click Play to Learn How ATMs Work

Understanding Automated Teller Machines (ATMs)

The first ATM appeared at a branch of Barclay's Bank in London in 1967,1 though there are reports of a cash dispenser in use in Japan in the mid-1960s.2 The interbank communications networks that allowed a consumer to use one bank's card at another bank's ATM came later, in the 1970s.

Within a few years, ATMs had spread around the globe, securing a presence in every major country. They now can be found even in tiny island nations such as Kiribati and the Federated States of Micronesia.3

2.2 million

There are now more than 2.2 million ATMs in use across the world.4

Types of ATMs

There are two primary types of ATMs. Basic units only allow customers to withdraw cash and receive updated account balances. The more complex machines accept deposits, facilitate line-of-credit payments and transfers, and access account information.

To access the advanced features of the complex units, a user often must be an account holder at the bank that operates the machine.

Analysts anticipate ATMs will become even more popular and forecast an increase in the number of ATM withdrawals. ATMs of the future are likely to be full-service terminals instead of or in addition to traditional bank tellers.

Cryptocurrency enthusiasts can now buy and sell Bitcoin and other crypto tokens via Bitcoin ATMs, internet-connected terminals that will dispense cash in return for crypto or accept cash or credit card to purchase. There are now nearly 10,000 Bitcoin ATMs located throughout the world.5

ATM Design Elements

Although the design of each ATM is different, they all contain the same basic parts:

• Card reader: This part reads the chip on the front of the card or the magnetic stripe on the back of the card.

• Keypad: The keypad is used by the customer to input information, including personal identification number (PIN), the type of transaction required, and the amount of the transaction.

• Cash dispenser: Bills are dispensed through a slot in the machine, which is connected to a safe at the bottom of the machine.

• Printer: If required, consumers can request receipts that are printed here. The receipt records the type of transaction, the amount, and the account balance.

• Screen: The ATM issues prompts that guide the consumer through the process of executing the transaction. Information is also transmitted on the screen, such as account information and balances.

Full-service machines now often have slots for depositing paper checks or cash.

Special Considerations: Using ATMs

Banks place ATMs inside and outside of their branches. Other ATMs are located in high-traffic areas such as shopping centers, grocery stores, convenience stores, airports, bus and railway stations, gas stations, casinos, restaurants, and other locations. Most ATMs that are found in banks are multi-functional, while others that are offsite tend to be primarily or entirely designed for cash withdrawals.

ATMs require consumers to use a plastic card—either a bank debit card or a credit card—to complete a transaction. Consumers are authenticated by a PIN before any transaction can be made.

Many cards come with a chip, which transmits data from the card to the machine. These work in the same fashion as a bar code that is scanned by a code reader.

$60

The average amount of cash withdrawn from an ATM per transaction.6

ATM Fees

Account-holders can use their bank's ATMs at no charge, but accessing funds through a unit owned by a competing bank usually incurs a fee. According to MoneyRates.com, the average total fees to withdraw cash from an out-of-network ATM was $4.55 as of 2021.7

Some banks will reimburse their customers for the fee, especially if there is no corresponding ATM available in the area.

So, if you're one of those people who draws weekly spending money from an ATM, using the wrong machine could cost you nearly $240 a year.

ATM Ownership

In many cases, banks and credit unions own ATMs. However, individuals and businesses may also buy or lease ATMs on their own or through an ATM franchise. When individuals or small businesses, such as restaurants or gas stations own ATMs, the profit model is based on charging fees to the machine's users.

Banks also own ATMs with this intent. They use the convenience of an ATM to attract clients. ATMs also take some of the customer service burdens from bank tellers, saving banks money in payroll costs.

Using ATMs Abroad

ATMs make it simple for travelers to access their checking or savings accounts from almost anywhere in the world.

Travel experts advise consumers to use foreign ATMs as a source of cash abroad, as they generally receive a more favorable exchange rate than they would at most currency exchange offices.

However, the account holder's bank may charge a transaction fee or a percentage of the amount exchanged. Most ATMs do not list the exchange rate on the receipt, making it difficult to track spending.

How Much Can You Withdraw From an ATM?

The amount that you can withdraw from an ATM per day, per week, or per month will vary based on your bank and account status at that bank. For most account holders, for instance, Capital One imposes a $1,000 daily ATM withdrawal limit and Well Fargo just $300.8 You may be able to get around these limits by calling your bank to request permission or upgrading your banking status by depositing more funds.

How Do You Make a Deposit at an ATM?

If you are a bank's customer you may be able to deposit cash or checks via one of their ATMs. To do this, you may simply need to insert the checks or cash directly into the machine. Other machines may require you to fill out a deposit slip and put the money into an envelope before inserting it into the machine. For a check, be sure to endorse the back of your check and also note "for deposit only" to be safe.

Which Bank Installed the First ATM Machine in the United States?

The first ATM in the U.S. was installed by Chemical Bank in Rockville Center (Long Island), NY in 1969 (2 years after Barclays installed the first ATM in the U.K.). By the end of 1971, more than 1,000 ATMs were installed worldwide.9

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