What Is Absorption Rate?

Absorption rate most commonly refers to a metric used in the real estate market to evaluate the rate at which available homes are sold in a specific market during a given time period. It is calculated by dividing the number of homes sold in the allotted time period by the total number of available homes. This equation can also be reversed to identify the amount of time it would take for the supply to be sold.

Absorption rate is also a key part of the accounting industry. In this context, absorption rate refers to the way in which businesses calculate their overhead costs.

Understanding Absorption Rate

Absorption rate provides insight into how quickly or slowly houses are selling in the real estate market. Absorption rate does not take into account additional homes that enter the market at various times. While an absorption rate calculation can be projected, it’s most commonly used based on current available data and actual inventory.

A high absorption rate may indicate that the supply of available homes will shrink rapidly. A homeowner is typically able to sell their property faster during periods of high absorption. However, the time period associated with an absorption rate calculation is important to consider.

Traditionally, an absorption rate above 20% signaled a seller’s market in which homes are sold quickly. An absorption rate below 15% is an indicator of a buyer’s market in which homes are not being sold as fast.

Influence in the Real Estate Market

In market conditions with low absorption rates, a real estate agent may be forced to reduce a listing price to entice a sale. Alternatively, the agent can increase the price without sacrificing demand for the home if the market has a high absorption rate. The absorption rate is also important for buyers and sellers to follow as they make decisions on the timing of purchases and sales.

The absorption rate is also a signal for developers to start building new homes, though developers often use long lead times to forecast periods of higher absorption. During market conditions with a high absorption rate, demand may be high enough to warrant the further development of properties. Meanwhile, periods with lower absorption rates indicate a cooling period for construction.

Appraisers use the absorption rate to determine the value of a property. Some procedures require an addendum showing that absorption rates were considered in appraisal calculations. In general, appraisers are responsible for analyzing market conditions and maintaining an awareness of the absorption rates for all types of appraisal values.

Most appraisers include this data metric in the neighborhood section of the appraisal forms. The current valuation of a home would be reduced during periods of decreased absorption rates and increased when absorption rates are high.

Lenders and banking institutions will also consider market conditions when evaluating loan and credit terms. During periods of low absorption, banks may feel tempted to entice clients to borrow money with more favorable loan terms. Alternatively, lenders can be more selective during high absorption periods as they are more likely to have a broader portfolio of prospective borrowers.

Example of the Absorption Rate

Suppose a city has 1,000 homes currently on the market to be sold. If buyers purchase 100 homes per month, the absorption rate is 10% (100 homes sold per month divided by 1,000 homes available for sale). This also indicates that the supply of homes will be exhausted in 10 months (1,000 homes divided by 100 homes sold/month).

Absorption Rate in Accounting

Absorption rate is also used in an entirely different manner in accounting.

In accounting, absorption rate (or the rate of absorption) is the rate at which companies calculate and allocate their overhead expenses. These are the costs associated with providing goods and services to their customers, though these expenses aren’t directly traceable to end products. As such, it’s also often called an overhead absorption rate.

Companies often have to use estimates to determine their overhead costs. That’s because they don’t know what the actual costs are until they come in. In order to determine their overhead, companies divide the total budgeted overhead costs divided by the total budgeted production base. This requires an adjustment at the end of the accounting period to make up for any difference between the predicted and actual costs.

Alternatively, a company may know its actual overhead costs but not know how to trace those costs to final products or services. To overcome this hurdle, companies use estimated cost drivers to guess what non-financial measures cause changes in financial measures.

This can be problematic, especially when companies use very conservative estimates to predict their costs. Doing so may throw off their balance sheets because the actual costs may be higher at the end of the reporting period or if costs fluctuate. However, this practice has the benefit of making sure all costs including estimated amounts and estimated allocations are included when evaluating their products.

The Bottom Line

The absorption rate is a very important metric used in the real estate and accounting.

Realtors use it to determine how many homes are sold in a particular area at any given time. These professionals can also use the rate to determine the kind of market they are facing, whether that’s a buyer’s, seller’s, or a balanced market. This rate is also important for the construction industry, as it indicates when developers should start buying.

Equally important, absorption rate is used in the accounting field—notably for companies to estimate their overhead. Absorption costing entails estimating overhead costs, determining overhead cost drivers, and having products absorb these untraceable costs.

What Is Annualized Total Return?

An annualized total return is the geometric average amount of money earned by an investment each year over a given time period. The annualized return formula is calculated as a geometric average to show what an investor would earn over a period of time if the annual return was compounded.

An annualized total return provides only a snapshot of an investment’s performance and does not give investors any indication of its volatility or price fluctuations.

Understanding Annualized Total Return

To understand annualized total return, we’ll compare the hypothetical performances of two mutual funds. Below is the annualized rate of return over a five-year period for the two funds:

• Mutual Fund A Returns: 3%, 7%, 5%, 12%, and 1%
• Mutual Fund B Returns: 4%, 6%, 5%, 6%, and 6.7%

Both mutual funds have an annualized rate of return of 5.5%, but Mutual Fund A is much more volatile. Its standard deviation is 4.2%, while Mutual Fund B’s standard deviation is only 1%. Even when analyzing an investment’s annualized return, it is important to review risk statistics.

Annualized Return Formula and Calculation

The formula to calculate annualized rate of return needs only two variables: the returns for a given period of time and the time the investment was held. The formula is:


$\begin{aligned} \text{Annualized Return} = &\big ( (1 + r_1 ) \times (1 + r_2) \times (1 + r_3) \times \\ &\dots \times (1 + r_n) \big ) ^ \frac{1}{n} – 1 \\ \end{aligned}$Annualized Return=​((1+r1​)×(1+r2​)×(1+r3​)×⋯×(1+rn​))n1​−1​

For example, take the annual rates of returns of Mutual Fund A above. An analyst substitutes each of the “r” variables with the appropriate return, and “n” with the number of years the investment was held. In this case, five years. The annualized return of Mutual Fund A is calculated as:


$\begin{aligned} \text{Annualized Return} &= \big ( (1 + .03) \times (1 + .07) \times (1 + .05) \times \\ &\quad \quad (1 + .12) \times (1 + .01) \big ) ^ \frac{1}{5} -1 \\ &= 1.309 ^ {0.20} – 1 \\ &= 1.0553 – 1 \\ &= .0553, \text{or } 5.53\% \\ \end{aligned}$Annualized Return​=((1+.03)×(1+.07)×(1+.05)×(1+.12)×(1+.01))51​−1=1.3090.20−1=1.0553−1=.0553,or 5.53%​

An annualized return does not have to be limited to yearly returns. If an investor has a cumulative return for a given period, even if it is a specific number of days, an annualized performance figure can be calculated; however, the annual return formula must be slightly adjusted to:


$\begin{aligned} &\text{Annualized Return} = ( 1 + \text{Cumulative Return} ) ^ \frac {365}{ \text{Days Held} } – 1 \\ \end{aligned}$​Annualized Return=(1+Cumulative Return)Days Held365​−1​

For example, assume a mutual fund was held by an investor for 575 days and earned a cumulative return of 23.74%. The annualized rate of return would be:


$\begin{aligned} \text{Annualized Return} &= ( 1 + .2374) ^ \frac{365}{575} – 1 \\ &= 1.145 – 1 \\ &= .145, \text{or } 14.5\% \\ \end{aligned}$Annualized Return​=(1+.2374)575365​−1=1.145−1=.145,or 14.5%​

Difference Between Annualized Return and Average Return

Calculations of simple averages only work when numbers are independent of each other. The annualized return is used because the amount of investment lost or gained in a given year is interdependent with the amount from the other years under consideration because of compounding.

For example, if a mutual fund manager loses half of her client’s money, she has to make a 100% return to break even. Using the more accurate annualized return also gives a clearer picture when comparing various mutual funds or the return of stocks that have traded over different time periods. 

Reporting Annualized Return

According to the Global Investment Performance Standards (GIPS)—a set of standardized, industry-wide principles that guide the ethics of performance reporting—any investment that does not have a track record of at least 365 days cannot “ratchet up” its performance to be annualized.

Thus, if a fund has been operating for only six months and earned 5%, it is not allowed to say its annualized performance is approximately 10% since that is predicting future performance instead of stating facts from the past. In other words, calculating an annualized rate of return must be based on historical numbers.

The Bottom Line

Annualized total return represents the geometric average amount that an investment has earned each year over a specific period. By calculating a geometric average, the annualized total return formula accounts for compounding when depicting the yearly earnings that the investment would generate over the holding period. While the metric provides a useful snapshot of an investment’s performance, it does not reveal volatility and price fluctuations.

What Is Average Inventory?

Average inventory is a calculation that estimates the value or number of a particular good or set of goods during two or more specified time periods. Average inventory is the mean value of inventory within a certain time period, which may vary from the median value of the same data set, and is computed by averaging the starting and ending inventory values over a specified period.

Understanding Average Inventory

Inventory is the value of all the goods ready for sale or all of the raw materials to create those goods that are stored by a company. Successful inventory management is a key focal point for companies as it allows them to better manage their overall business in terms of sales, costs, and relationships with their suppliers.

Since two points do not always accurately represent changes in inventory over different time periods, average inventory is frequently calculated by using the number of points needed to more accurately reflect activities across a certain amount of time.

For instance, if a business was attempting to calculate the average inventory over the course of a fiscal year, it may be more accurate to use the inventory count from the end of each month, including the base month. The values associated with each point are added together and divided by the number of points, in this case, 13, to determine the average inventory.

The average inventory figures can be used as a point of comparison when looking at overall sales volume, allowing a business to track inventory losses that may have occurred due to theft or shrinkage, or due to damaged goods caused by mishandling. It also accounts for any perishable inventory that has expired.

The formula for average inventory can be expressed as follows:

Average Inventory = (Current Inventory + Previous Inventory) / Number of Periods

Average inventory is used often in ratio analysis; for instance, in calculating inventory turnover.

Moving Average Inventory

A company may choose to use a moving average inventory when it’s possible to maintain a perpetual inventory tracking system. This allows the business to adjust the values of the inventory items based on information from the last purchase.

Effectively, this helps compare inventory averages across multiple time periods by converting all pricing to the current market standard. This makes it similar to adjusting historical data based on the rate of inflation for more stable market items. It allows simpler comparisons on items that experience high levels of volatility.

Example of Average Inventory

A shoe company is interested in better managing its inventory. The current inventory in its warehouse is equal to $10,000. This is in line with the inventory for the three previous months, which were valued at $9,000, $8,500, and $12,000.

When calculating a three-month inventory average, the shoe company achieves the average by adding the current inventory of $10,000 to the previous three months of inventory, recorded as $9,000, $8,500 and $12,000, and dividing it by the number of data points, as follows:

Average Inventory = ($10,000 + $9,000 + $8,500 + $12,000) / 4

This results in an average inventory of $9,875 over the time period being examined.

What Is Arc Elasticity?

Arc elasticity is the elasticity of one variable with respect to another between two given points. It is used when there is no general way to define the relationship between the two variables. Arc elasticity is also defined as the elasticity between two points on a curve.

The concept is used in both economics and mathematics. In economics, is it commonly used to measure the changes between the quantity of goods demanded and their prices.

Understanding Arc Elasticity

In economics, arc elasticity is commonly used in relation to the law of demand to measure percentage changes between the quantity of goods demanded and prices.

There are two possible ways of calculating elasticity—price (or point) elasticity of demand and arc elasticity of demand. Price elasticity of demand measures the responsiveness of quantity demanded to a price. It takes the elasticity of demand at a particular point on the demand curve, or between two points on the curve. Arc elasticity of demand uses a midpoint between the two points.

Formula for Price (Point) Elasticity of Demand


$PE_d = \dfrac{\text{\% Change in Qty}}{\text{\% Change in Price}}$PEd​=% Change in Price% Change in Qty​

How to Calculate the Price Elasticity of Demand

If the price of a product decreases from $10 to $8, leading to an increase in quantity demanded from 40 to 60 units, then the price elasticity of demand can be calculated as:

• % change in quantity demanded = (Qd₂ – Qd₁) / Qd₁ = (60 – 40) / 40 = 0.5
• % change in price = (P₂ – P₁) / P₁ = (8 – 10) / 10 = -0.2
• Thus, PE_d= 0.5 / -0.2 = 2.5

Since we’re concerned with the absolute values in price elasticity, the negative sign is ignored. You can conclude that the price elasticity of this good, when the price decreases from $10 to $8, is 2.5.

Arc Elasticity of Demand

One of the problems with the price elasticity of demand formula is that it gives different values depending on whether price rises or falls. If you were to use different start and end points in our example above—that is, if you assume the price increased from $8 to $10—and the quantity demanded decreased from 60 to 40, the Pe_d will be:

• % change in quantity demanded = (40 – 60) / 60 = -0.33
• % change in price = (10 – 8) / 8 = 0.25
• PE_d = -0.33 / 0.25 = 1.32, which is much different from 2.5

How to Calculate the Arc Elasticity of Demand

To eliminate this problem, the arc elasticity of demand can be used. Arc elasticity of demand measures elasticity at the midpoint between two selected points on the demand curve by using a midpoint between the two points. The arc elasticity of demand can be calculated as:

• Arc E_d = [(Qd₂ – Qd₁) / midpoint Qd] ÷ [(P₂ – P₁) / midpoint P]

Let’s calculate the arc elasticity following the example presented above:

• Midpoint Qd = (Qd₁ + Qd₂) / 2 = (40 + 60) / 2 = 50
• Midpoint Price = (P₁ + P₂) / 2 = (10 + 8) / 2 = 9
• % change in qty demanded = (60 – 40) / 50 = 0.4
• % change in price = (8 – 10) / 9 = -0.22
• Arc E_d = 0.4 / -0.22 = 1.82

When you use arc elasticity of demand you do not need to worry about which point is the starting point and which point is the ending point since the arc elasticity gives the same value for elasticity whether prices rise or fall.

The Bottom Line

Arc elasticity is commonly used in economics to determine the percentage of change between the demand for goods and their price. Elasticity can be calculated in two ways—price elasticity of demand and arc elasticity of demand. The latter is more useful when there is a significant change in price.