What Is the Applicable Federal Rate (AFR)?

The applicable federal rate (AFR) is the minimum interest rate that the Internal Revenue Service (IRS) allows for private loans. Each month the IRS publishes a set of interest rates that the agency considers the minimum market rate for loans. Any interest rate that is less than the AFR would have tax implications. The IRS publishes these rates in accordance with Section 1274(d) of the Internal Revenue Code.

Understanding the Applicable Federal Rate (AFR)

The AFR is used by the IRS as a point of comparison versus the interest on loans between related parties, such as family members. If you were giving a loan to a family member, you would need to be sure that the interest rate charged is equal to or higher than the minimum applicable federal rate.

The IRS publishes three AFRs: short-term, mid-term, and long-term. Short-term AFR rates are determined from the one-month average of the market yields from marketable obligations, such as U.S. government T-bills with maturities of three years or less. Mid-term AFR rates are from obligations of maturities of more than three and up to nine years. Long-term AFR rates are from bonds with maturities of more than nine years.

Example of How to Use the AFR

As of Apr. 2022, the IRS stated that the annual short-term AFR was 1.26%, the mid-term AFR was 1.87%, and the long-term AFR was 2.25%. Please bear in mind that these AFR rates are subject to change by the IRS.

Which AFR rate to use for a family loan would depend on the length of time designated for payback. Let’s say you were giving a loan to a family member for $10,000 to be paid back in one year. You would need to charge the borrower a minimum interest rate of 1.26% for the loan. In other words, you should receive $126 in interest from the loan.

In our example above, any rate below 1.26% could trigger a taxable event. For example, let’s say you gave the same loan, but you didn’t charge any interest. By not charging any interest, you would have “foregone” $126 in interest income, and according to the IRS, it would be considered a taxable gift. Any interest rate charged below the stated AFR for the particular term of the loan would be considered foregone interest and, as a result, be taxable.

Special Considerations

When preparing to make a loan between related parties, taxpayers should consider two factors to select the correct AFR. The length of the loan should correspond to the AFRs: short-term (three years or less), mid-term (up to nine years), and long-term (more than nine years).

If the lender charges interest at a lower rate than the proper AFR, the IRS may reassess the lender and add imputed interest to the income to reflect the AFR rather than the actual amount paid by the borrower. Also, if the loan is more than the annual gift tax exclusion, it may trigger a taxable event, and income taxes may be owed. Depending on the circumstances, the IRS may also assess penalties.

What Is Appreciation?

Appreciation, in general terms, is an increase in the value of an asset over time. The increase can occur for a number of reasons, including increased demand or weakening supply, or as a result of changes in inflation or interest rates. This is the opposite of depreciation, which is a decrease in value over time.

How Appreciation Works

Appreciation can be used to refer to an increase in any type of asset, such as a stock, bond, currency, or real estate. For example, the term capital appreciation refers to an increase in the value of financial assets such as stocks, which can occur for reasons such as improved financial performance of the company.

Just because the value of an asset appreciates does not necessarily mean its owner realizes the increase. If the owner revalues the asset at its higher price on their financial statements, this represents a realization of the increase.

Another type of appreciation is currency appreciation. The value of a country’s currency can appreciate or depreciate over time in relation to other currencies.

How to Calculate the Appreciation Rate

The appreciation rate is virtually the same as the compound annual growth rate (CAGR). Thus, you take the ending value, divide by the beginning value, then take that result to 1 dividend by the number of holding periods (e.g. years). Finally, you subtract one from the result. 

 However, in order to calculate the appreciation rate that means you need to know the initial value of the investment and the future value. You also need to know how long the asset will appreciate.

For example, Rachel buys a home for $100,000 in 2016. In 2021, the value has increased to $125,000. The home has appreciated by 25% [($125,000 – $100,000) / $100,000] during these five years. The appreciate rate (or CAGR) is 4.6% [($125,000 / $100,000)^(1/5) – 1].

Appreciation vs. Depreciation

Appreciation is also used in accounting when referring to an upward adjustment of the value of an asset held on a company’s accounting books. The most common adjustment on the value of an asset in accounting is usually a downward one, known as depreciation.

Certain assets are given to appreciation, while other assets tend to depreciate over time. As a general rule, assets that have a finite useful life depreciate rather than appreciate.

Depreciation is typically done as the asset loses economic value through use, such as a piece of machinery being used over its useful life. While appreciation of assets in accounting is less frequent, assets such as trademarks may see an upward value revision due to increased brand recognition.

Real estate, stocks, and precious metals represent assets purchased with the expectation that they will be worth more in the future than at the time of purchase. By contrast, automobiles, computers, and physical equipment gradually decline in value as they progress through their useful lives.

Example of Capital Appreciation

An investor purchases a stock for $10 and the stock pays an annual dividend of $1, equating to a dividend yield of 10%. A year later, the stock is trading at $15 per share and the investor has received the dividend of $1.

The investor has a return of $5 from capital appreciation as the price of the stock went from the purchase price or cost basis of $10 to a current market value of $15. In percentage terms, the stock price increase led to a return from capital appreciation of 50%. The dividend income return is $1, equating to a return of 10% in line with the original dividend yield. The return from capital appreciation combined with the return from the dividend leads to a total return on the stock of $6 or 60%.

Example of Currency Appreciation

China’s ascension onto the world stage as a major economic power has corresponded with price swings in the exchange rate for its currency, the yuan. Beginning in 1981, the currency rose steadily against the dollar until 1996, when it plateaued at a value of $1 equaling 8.28 yuan until 2005. The dollar remained relatively strong during this period. It meant cheaper manufacturing costs and labor for American companies, who migrated to the country in droves.

It also meant that American goods were competitive on the world stage as well as the U.S. due to their cheap labor and manufacturing costs. In 2005, however, China’s yuan reversed course and appreciated 33% in value against the dollar. As of May 2021, it’s still near that retraced level, trading at 6.4 yuan.

Appreciation FAQs

What Is an Appreciating Asset?

An appreciating asset is any asset which value is increasing. For example, appreciating assets can be real estate, stocks, bonds, and currency.

What Is Appreciation Rate?

Appreciation rate is another word for growth rate. The appreciation rate is the rate at which an asset’s value grows.

What Is a Good Home Appreciation Rate?

A good appreciation rate is relative to the asset and risk involved. What might be a good appreciation rate for real estate is different than what is a good appreciation rate for a certain currency given the risk involved.

What Is Meant by Capital Appreciation?

Capital appreciation is the increase in the value or price of an asset. This can include stocks, real estate, or the like.  

The Bottom Line

Appreciation is the rise in the value of an asset, such as currency or real estate. It’s the opposite of depreciation, which reduces the value of an asset over its useful life. Increases in value can be attributed to interest rate changes, supply and demand changes, or various other reasons. 

What Is an American Depositary Receipt (ADR)?

The term American depositary receipt (ADR) refers to a negotiable certificate issued by a U.S. depositary bank representing a specified number of shares—usually one share—of a foreign company’s stock. The ADR trades on U.S. stock markets as any domestic shares would.

ADRs offer U.S. investors a way to purchase stock in overseas companies that would not otherwise be available. Foreign firms also benefit, as ADRs enable them to attract American investors and capital without the hassle and expense of listing on U.S. stock exchanges.

How American Depositary Receipts (ADRs) Work

American depositary receipts are denominated in U.S. dollars. The underlying security is held by a U.S. financial institution, often by an overseas branch. These securities are priced and traded in dollars and cleared through U.S. settlement systems.

In order to begin offering ADRs, a U.S. bank must purchase shares on a foreign exchange. The bank holds the stock as inventory and issues an ADR for domestic trading. ADRs list on either the New York Stock Exchange (NYSE) or the Nasdaq, but they are also sold over-the-counter (OTC).

U.S. banks require that foreign companies provide them with detailed financial information. This requirement makes it easier for American investors to assess a company’s financial health.

Types of American Depositary Receipts

American depositary receipts come in two basic categories:

Sponsored ADRs

A bank issues a sponsored ADR on behalf of the foreign company. The bank and the business enter into a legal arrangement. The foreign company usually pays the costs of issuing an ADR and retains control over it, while the bank handles the transactions with investors. Sponsored ADRs are categorized by what degree the foreign company complies with Securities and Exchange Commission (SEC) regulations and American accounting procedures.

Unsponsored ADRs

A bank also issues an unsponsored ADR. However, this certificate has no direct involvement, participation, or even permission from the foreign company. Theoretically, there could be several unsponsored ADRs for the same foreign company, issued by different U.S. banks. These different offerings may also offer varying dividends. With sponsored programs, there is only one ADR, issued by the bank working with the foreign company.

One primary difference between the two types of ADRs is where they trade. All except the lowest level of sponsored ADRs register with the SEC and trade on major U.S. stock exchanges. Unsponsored ADRs will trade only over the counter. Unsponsored ADRs never include voting rights.

ADR Levels

ADRs are additionally categorized into three levels, depending on the extent to which the foreign company has accessed the U.S. markets.

Level I

This is the most basic type of ADR where foreign companies either don’t qualify or don’t want to have their ADR listed on an exchange. This type of ADR can be used to establish a trading presence but not to raise capital.

Level I ADRs found only on the over-the-counter market have the loosest requirements from the Securities and Exchange Commission (SEC) and they are typically highly speculative. While they are riskier for investors than other types of ADRs, they are an easy and inexpensive way for a foreign company to gauge the level of U.S. investor interest in its securities.

Level II

As with Level I ADRs, Level II ADRs can be used to establish a trading presence on a stock exchange, and they can’t be used to raise capital. Level II ADRs have slightly more requirements from the SEC than do Level I ADRs, but they get higher visibility and trading volume. 

Level III

Level III ADRs are the most prestigious. With these, an issuer floats a public offering of ADRs on a U.S. exchange. They can be used to establish a substantial trading presence in the U.S. financial markets and raise capital for the foreign issuer. Issuers are subject to full reporting with the SEC.

American Depositary Receipt Pricing and Costs

An ADR may represent the underlying shares on a one-for-one basis, a fraction of a share, or multiple shares of the underlying company. The depositary bank will set the ratio of U.S. ADRs per home-country share at a value that they feel will appeal to investors. If an ADR’s value is too high, it may deter some investors. Conversely, if it is too low, investors may think the underlying securities resemble riskier penny stocks.

Because of arbitrage, an ADR’s price closely tracks that of the company’s stock on its home exchange. Remember that arbitrage is buying and selling the same asset at the same time in different markets. This allows traders to profit from any differences in the asset’s listed price. 

ADR Fees

Investing in an ADR may incur additional fees that are not charged for domestic stocks. The depositary bank that holds the underlying stock may charge a fee, known as a custody fee, to cover the cost of creating and issuing an ADR.

This fee will be outlined in the ADR prospectus, and typically ranges from one to three cents per share. The fee will be either deducted from dividends, or passed on to the investor’s brokerage firm.

ADRs and Taxes

Holders of ADRs realize any dividends and capital gains in U.S. dollars. However, dividend payments are net of currency conversion expenses and foreign taxes. Usually, the bank automatically withholds the necessary amount to cover expenses and foreign taxes.

Since this is the practice, American investors would need to seek a credit from the IRS or a refund from the foreign government’s taxing authority to avoid double taxation on any capital gains realized.

Those interested in learning more about ADRs and other financial topics may want to consider enrolling in one of the best investing courses currently available.

Advantages and Disadvantages of American Depositary Receipts

As with any investment, there are distinct advantages and disadvantages of investing in ADRs. We’ve listed some of the main ones below.

Advantages

As noted above, ADRs are just like stocks. This means they trade on a stock exchange or over the counter, making them fairly easy to access and trade. Investors can also easily track their performance by reviewing market data.

Purchasing ADRs is easy because they’re available directly through American brokers. This eliminates the need to go through foreign channels to buy stock in a company in which you may be interested. Since they’re available domestically, shares are denominated in U.S. dollars. But that doesn’t mean you avoid any direct risks associated with fluctuations in currency rates.

One of the most obvious benefits of investing in ADRs is that they provide investors with a way to diversify their portfolios. Investing in international securities allows you to open your investment portfolio up to greater rewards (along with the risks).

Disadvantages

The main problems associated with ADRs are that they may involve double taxation—locally and abroad—and how many companies are listed. Unlike domestic companies, there are a limited number of foreign entities whose ADRs are listed for the public to trade.

As noted above, some ADRs may not comply with SEC regulations. These are called unsponsored ADRs, which have no direct involvement by the company. In fact, some companies may not even provide permission to list their shares this way.

Although investors can avoid any of the direct risks that come with currency exchange, they may incur currency conversion fees when they invest in ADRs. These fees are established in order to directly link the foreign security and the one traded on the domestic market.

History of American Depositary Receipts

Before American depositary receipts were introduced in the 1920s, American investors who wanted shares of a non-U.S. listed company could only do so on international exchanges—an unrealistic option for the average person back then.

While easier in the contemporary digital age, there are still drawbacks to purchasing shares on international exchanges. One particularly daunting roadblock is currency exchange issues. Another important drawback is the regulatory differences between U.S. and foreign exchanges.

Before investing in an internationally traded company, U.S. investors have to familiarize themselves with the different financial authority’s regulations, or they could risk misunderstanding important information, such as the company’s financials. They might also need to set up a foreign account, as not all domestic brokers can trade internationally.

ADRs were developed because of the complexities involved in buying shares in foreign countries and the difficulties associated with trading at different prices and currency values. J.P. Morgan’s (JPM) predecessor firm Guaranty Trust pioneered the ADR concept. In 1927, it created and launched the first ADR, enabling U.S. investors to buy shares of famous British retailer Selfridges and helping the luxury depart store tap into global markets. The ADR was listed on the New York Curb Exchange.

A few years later, in 1931, the bank introduced the first sponsored ADR for British music company Electrical & Musical Industries (also known as EMI), the eventual home of the Beatles. Today, J.P. Morgan and BNY Mellon, another U.S. bank, continue to be actively involved in the ADR markets.

Real-World Example of ADRs

Between 1988 and 2018, German car manufacturer Volkswagen AG traded OTC in the U.S. as a sponsored ADR under the ticker VLKAY. In August 2018, Volkswagen terminated its ADR program. The next day, J.P. Morgan established an unsponsored ADR for Volkswagen, now trading under the ticker VWAGY.

Investors who held the old VLKAY ADRs had the option of cashing out, exchanging the ADRs for actual shares of Volkswagen stock—trading on German exchanges—or exchanging them for the new VWAGY ADRs.

The Bottom Line

American Depositary Receipts, or ADRs, allow Americans to invest in foreign companies. Although these companies do not ordinarily trade on the U.S. stock market, an ADR allows an investor to buy these stocks as easily as they would invest in any domestic stock. The arrangement also benefits foreign firms, allowing them to raise capital from the U.S. market.

Correction—Jan. 24, 2023: A previous version of this article wrongly stated that foreign currency exchange rate fluctuations do not affect the price of ADR and therefore ADR holders avoid any direct risks associated with fluctuations in currency rates. Actually, ADR have exchange rate risk and the price of an ADR is affected by the movements of both the company’s local share price and the national currency rate of exchange against the U.S. dollar.

What Is the Annual Equivalent Rate (AER)?

The annual equivalent rate (AER) is the interest rate for a savings account or investment product that has more than one compounding period. AER is calculated under the assumption that any interest paid is included in the principal payment’s balance and the next interest payment will be based on the slightly higher account balance.

The AER method means that interest can be compounded several times in a year, depending on the number of times that interest payments are made.

AER is also known as the effective annual interest rate or the annual percentage yield (APY).

The AER is the actual interest rate that an investor will earn for an investment, a loan, or another product, based on compounding. The AER reveals to investors what they can expect to return from an investment (the ROI)—the actual return of the investment based on compounding, which is more than the stated, or nominal, interest rate.

Assuming that interest is calculated—or compounded—more than once a year, the AER will be higher than the stated interest rate. The more compounding periods, the greater the difference between the two will be.

Formula for the AER


$\begin{aligned} &\text{Annual equivalent rate}=\left(1 + \frac{r}{n}\right)^n-1\\ &\textbf{where:}\\ &n=\text{The number of compounding periods (times per year interest is paid)}\\ &r = \text{The stated interest rate}\\ \end{aligned}$​Annual equivalent rate=(1+nr​)n−1where:n=The number of compounding periods (times per year interest is paid)r=The stated interest rate​

How to Calculate the AER

To calculate AER:

1. Divide the stated interest rate by the number of times a year that interest is paid (compounded) and add one.
2. Raise the result to the number of times a year that interest is paid (compounded)
3. Subtract one from the subsequent result.

The AER is displayed as a percentage (%).

Example of AER

Let’s look at AER in both savings accounts and bonds.

For a Savings Account

Assume an investor wishes to sell all the securities in their investment portfolio and place all the proceeds in a savings account. The investor is deciding between placing the proceeds in Bank A, Bank B, or Bank C, depending on the highest rate offered. Bank A has a quoted interest rate of 3.7% that pays interest on an annual basis. Bank B has a quoted interest rate of 3.65% that pays interest quarterly, and Bank C has a quoted interest rate of 3.7% that pays interest semi-annually.

Therefore, Bank A would have an annual equivalent rate of 3.7%, or (1 + (0.037 / 1))¹ – 1. Bank B has an AER of 3.7% = (1 + (0.0365 / 4))⁴ – 1, which is equivalent to that of Bank A even though Bank B is compounded quarterly. It would thus make no difference to the investor if they placed their cash in Bank A or Bank B.

On the other hand, Bank C has the same interest rate as Bank A, but Bank C pays interest semi-annually. Consequently, Bank C has an AER of 3.73%, which is more attractive than the other two banks’ AER. The calculation is (1 + (0.037 / 2))² – 1 = 3.73%.

With a Bond

Let’s now consider a bond issued by General Electric. As of March 2019, General Electric offers a noncallable semiannual coupon with a 4% coupon rate expiring Dec. 15, 2023. The nominal, or stated rate, of the bond, is 8%—or the 4% coupon rate times two annual coupons. However, the annual equivalent rate is higher, given the fact that interest is paid twice a year. The AER of the bond is calculated as (1+ (0.04 / 2 ))² – 1 = 8.16%.

Annual Equivalent Rate vs. Stated Interest

While the stated interest rate doesn’t account for compounding, the AER does. The stated rate will generally be lower than AER if there’s more than one compounding period. AER is used to determine which banks offer better rates and which investments might be attractive.

Advantages and Disadvantages of the AER

The primary advantage of AER is that it is the real rate of interest because it accounts for the effects of compounding. In addition, it is an important tool for investors because it helps them evaluate bonds, loans, or accounts to understand their real return on investment (ROI).

Unfortunately, when investors are evaluating different investment options, the AER is usually not stated. Investors must do the work of calculating the figure themselves. It’s also important to keep in mind that AER doesn’t include any fees that might be tied to purchasing or selling the investment. Also, compounding itself has limitations, with the maximum possible rate being continuous compounding.

Special Considerations

AER is one of the various ways to calculate interest on interest, which is called compounding. Compounding refers to earning or paying interest on previous interest, which is added to the principal sum of a deposit or loan. Compounding allows investors to boost their returns because they can accrue additional profit based on the interest they’ve already earned.

One of Warren Buffett’s famous quotes is, “My wealth has come from a combination of living in America, some lucky genes, and compound interest.” Albert Einstein reportedly referred to compound interest as mankind’s greatest invention. 

When you are borrowing money (in the form of loans), you want to minimize the effects of compounding. On the other hand, all investors want to maximize compounding on their investments. Many financial institutions will quote interest rates that use compounding principles to their advantage. As a consumer, it is important to understand AER so you can determine the interest rate you are really getting.