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 the Arms Index (TRIN)?

The Arms Index, also called the Short-Term Trading Index (TRIN) is a technical analysis indicator that compares the number of advancing and declining stocks (AD Ratio) to advancing and declining volume (AD volume). It is used to gauge overall market sentiment. Richard W. Arms, Jr. invented it in 1967, and it measures the relationship between market supply and demand. It serves as a predictor of future price movements in the market, primarily on an intraday basis. It does this by generating overbought and oversold levels, which indicate when the index (and the majority of stocks in it) will change direction.

The Formula for Arms Index (TRIN) is:


$\begin{aligned} &\text{TRIN}\ =\ \frac{\text{Advancing Stocks/Declining Stocks}}{\text{Advancing Volume/Declining Volume}}\\ &\textbf{where:}\\ & \begin{aligned} \text{Advancing Stocks}\ =\ &\text{Number of stocks that are higher}\\ &\text{on the day}\end{aligned}\\ &\begin{aligned} \text{Declining Stocks}\ =\ &\text{Number of stocks that are lower}\\ &\text{on the day}\end{aligned}\\ &\begin{aligned} \text{Advancing Volume}\ =\ &\text{Total volume of all advancing}\\ &\text{stocks}\end{aligned}\\ &\begin{aligned}\text{Declining Volume}\ =\ &\text{Total volume of all declining}\\ &\text{stocks}\end{aligned} \end{aligned}$​TRIN = Advancing Volume/Declining VolumeAdvancing Stocks/Declining Stocks​where:Advancing Stocks = ​Number of stocks that are higher​Declining Stocks = ​Number of stocks that are lower​Advancing Volume = ​Total volume of all advancing​​

How to Calculate the Arms Index (TRIN)

TRIN is provided in many charting applications. To calculate by hand, use the following steps.

1. At set intervals, such as every five minutes or daily (or whatever interval is chosen), find the AD Ratio by dividing the number of advancing stocks by the number of declining stocks.
2. Divide total advancing volume by total declining volume to get AD Volume.
3. Divide the AD Ratio by AD Volume.
4. Record the result and plot on a graph.
5. Repeat the calculation at the next chosen time interval.
6. Connect multiple data points to form a graph and see how the TRIN moves over time.

What Does the Arms Index (TRIN) Tell You?

The Arms index seeks to provide a more dynamic explanation of overall movements in the composite value of stock exchanges, such as the NYSE or NASDAQ, by analyzing the strength and breadth of these movements.

An index value of 1.0 indicates that the ratio of AD Volume is equal to the AD Ratio. The market is said to be in a neutral state when the index equals 1.0, since the up volume is evenly distributed over the advancing issues and the down volume is evenly distributed over the declining issues.

Many analysts believe that the Arms Index provides a bullish signal when it’s less than 1.0, since there’s greater volume in the average up stock than the average down stock. In fact, some analysts have found that the long-term equilibrium for the index is below 1.0, potentially confirming that there is a bullish bias to the stock market.

On the other hand, a reading of greater than 1.0 is typically seen as a bearish signal, since there’s greater volume in the average down stock than the average up stock.

The farther away from 1.00 the Arms Index value is, the greater the contrast between buying and selling on that day. A value that exceeds 3.00 indicates an oversold market and that bearish sentiment is too dramatic. This could mean an upward reversal in prices/index is coming.

Conversely, a TRIN value that dips below 0.50 may indicate an overbought market and that bullish sentiment is overheating.

Traders look not only at the value of the indicator but also at how it changes throughout the day. They look for extremes in the index value for signs that the market may soon change directions.

The Difference Between the Arms Index (TRIN) and the Tick Index (TICK)

TRIN compares the number of advancing and declining stocks to the volume in both advancing and declining stocks. The Tick index compares the number of stocks making an uptick to the number of stocks making a downtick. The Tick Index is used to gauge intraday sentiment. The Tick Index does not factor volume, but extreme readings still signal potentially overbought or oversold conditions.

Limitations of Using the Arms Index (TRIN)

The Arms Index has a few mathematical peculiarities that traders and investors should be aware of when using it. Since the index emphasizes volume, inaccuracies arise when there isn’t as much advancing volume in advancing issues as expected. This may not be a typical situation, but it’s a situation that can arise and could potentially make the indicator unreliable.

Here are two examples of instances where problems may occur:

• Suppose that a very bullish day occurs where there are twice as many advancing issues as declining issues and twice as much advancing volume as declining volume. Despite the very bullish trading, the Arms Index would yield only a neutral value of (2/1)/(2/1) = 1.0, suggesting that the index’s reading may not be entirely accurate.
• Suppose that another bullish scenario occurs where there are three times as many advancing issues as declining issues and twice as much advancing volume than declining volume. In this case, the Arms Index would actually yield a bearish (3/1)/(2/1) = 1.5 reading, again suggesting an inaccuracy.

One way to solve this problem would be to separate the two components of the indicator into issues and volume instead of using them in the same equation. For instance, advancing issues divided by declining issues could show one trend, while advancing volume over declining volume could show a separate trend. These ratios are called the advance/decline ratio and upside/downside ratio, respectively. Both of these could be compared to tell the market’s true story.

What Is Adjusted Present Value (APV)?

The adjusted present value is the net present value (NPV) of a project or company if financed solely by equity plus the present value (PV) of any financing benefits, which are the additional effects of debt. By taking into account financing benefits, APV includes tax shields such as those provided by deductible interest.

The Formula for APV Is


$\begin{aligned} &\text{Adjusted Present Value = Unlevered Firm Value + NE}\\ &\textbf{where:}\\ &\text{NE = Net effect of debt}\\ \end{aligned}$​Adjusted Present Value = Unlevered Firm Value + NEwhere:NE = Net effect of debt​

The net effect of debt includes tax benefits that are created when the interest on a company’s debt is tax-deductible. This benefit is calculated as the interest expense times the tax rate, and it only applies to one year of interest and tax. The present value of the interest tax shield is therefore calculated as: (tax rate * debt load * interest rate) / interest rate.

How to Calculate Adjusted Present Value (APV)

To determine the adjusted present value:

1. Find the value of the un-levered firm.
2. Calculate the net value of debt financing.
3. Sum the value of the un-levered project or company and the net value of the debt financing.

How to Calculate APV in Excel

An investor can use Excel to build out a model to calculate the net present value of the firm and the present value of the debt.

What Does Adjusted Present Value Tell You?

The adjusted present value helps to show an investor the benefits of tax shields resulting from one or more tax deductions of interest payments or a subsidized loan at below-market rates. For leveraged transactions, APV is preferred. In particular, leveraged buyout situations are the most effective situations in which to use the adjusted present value methodology.

The value of a debt-financed project can be higher than just an equity-financed project, as the cost of capital falls when leverage is used. Using debt can actually turn a negative NPV project into one that’s positive. NPV uses the weighted average cost of capital as the discount rate, while APV uses the cost of equity as the discount rate.

Example of How to Use Adjusted Present Value (APV)

In a financial projection where a base-case NPV is calculated, the sum of the present value of the interest tax shield is added to obtain the adjusted present value.

For example, assume a multi-year projection calculation finds that the present value of Company ABC’s free cash flow (FCF) plus terminal value is $100,000. The tax rate for the company is 30% and the interest rate is 7%. Its $50,000 debt load has an interest tax shield of $15,000, or ($50,000 * 30% * 7%) / 7%. Thus, the adjusted present value is $115,000, or $100,000 + $15,000.

The Difference Between APV and Discounted Cash Flow (DCF)

While the adjusted present value method is similar to the discounted cash flow (DCF) methodology, adjusted present cash flow does not capture taxes or other financing effects in a weighted average cost of capital (WACC) or other adjusted discount rates. Unlike WACC used in discounted cash flow, the adjusted present value seeks to value the effects of the cost of equity and cost of debt separately. The adjusted present value isn’t as prevalent as the discounted cash flow method.

Limitations of Using Adjusted Present Value (APV)

In practice, the adjusted present value is not used as much as the discounted cash flow method. It is more of an academic calculation but is often considered to result in more accurate valuations.

Learn More About Adjusted Present Value (APV)

To dig deeper into calculating the adjusted present value, check out Investopedia’s guide to calculating net present value.

What Is the Altman Z-Score?

The Altman Z-score is the output of a credit-strength test that gauges a publicly traded manufacturing company’s likelihood of bankruptcy.

Understanding the Altman Z-Score

The Altman Z-score, a variation of the traditional z-score in statistics, is based on five financial ratios that can be calculated from data found on a company’s annual 10-K report. It uses profitability, leverage, liquidity, solvency, and activity to predict whether a company has a high probability of becoming insolvent.

NYU Stern Finance Professor Edward Altman developed the Altman Z-score formula in 1967, and it was published in 1968. Over the years, Altman has continued to reevaluate his Z-score. From 1969 until 1975, Altman looked at 86 companies in distress, then 110 from 1976 to 1995, and finally 120 from 1996 to 1999, finding that the Z-score had an accuracy of between 82% and 94%.

In 2012, he released an updated version called the Altman Z-score Plus that one can use to evaluate public and private companies, manufacturing and non-manufacturing companies, and U.S. and non-U.S. companies. One can use Altman Z-score Plus to evaluate corporate credit risk. The Altman Z-score has become a reliable measure of calculating credit risk.

How to Calculate the Altman Z-Score

One can calculate the Altman Z-score as follows:

Altman Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E

Where:

• A = working capital / total assets
• B = retained earnings / total assets
• C = earnings before interest and tax / total assets
• D = market value of equity / total liabilities
• E = sales / total assets

A score below 1.8 means it’s likely the company is headed for bankruptcy, while companies with scores above 3 are not likely to go bankrupt. Investors can use Altman Z-scores to determine whether they should buy or sell a stock if they’re concerned about the company’s underlying financial strength. Investors may consider purchasing a stock if its Altman Z-Score value is closer to 3 and selling or shorting a stock if the value is closer to 1.8.

In more recent years, however, a Z-Score closer to 0 indicates a company may be in financial trouble. In a lecture given in 2019 titled “50 Years of the Altman Score,” Professor Altman himself noted that recent data has shown that 0—not 1.8—is the figure at which investors should worry about a company’s financial strength. The two-hour lecture is available to view for free on YouTube.

2008 Financial Crisis

In 2007, the credit ratings of specific asset-related securities had been rated higher than they should have been. The Altman Z-score indicated that the companies’ risks were increasing significantly and may have been heading for bankruptcy.

Altman calculated that the median Altman Z-score of companies in 2007 was 1.81. These companies’ credit ratings were equivalent to a B. This indicated that 50% of the firms should have had lower ratings, were highly distressed and had a high probability of becoming bankrupt.

Altman’s calculations led him to believe a crisis would occur and there would be a meltdown in the credit market. He believed the crisis would stem from corporate defaults, but the meltdown, which brought about the 2008 financial crisis, began with mortgage-backed securities (MBS). However, corporations soon defaulted in 2009 at the second-highest rate in history.