Acids are substances that donate protons or hydrogen ions when they are in a solution and have a sour taste, while bases donate OH^{–} ions, also known as hydroxide ions, and tend to have a bitter taste and a slippery or soapy feel to touch.

More specifically pH quantifies the concentration of hydrogen ions present in a solution per litre of the solution, in other words, the molarity of hydronium ions. Generally, you would use some pH indicator solution or colored paper to determine the pH of a solution, the color change of the pH indicator is an easy way to compare different solutions and determine which ones are more acidic or basic. The pH scale goes from 0 to 14, and in this scale 7 is a neutral pH. Below 7, substances are considered acids and above 7 substances are considered basic. In this article we will see how pH is calculated and where this measurement comes from.

**The mathematical definition of pH is simply the negative logarithm of the molarity of hydronium ions in a solution. In general you will need to know the concentration of you acid or base in a solution to be able to calculate the pH.**

pH= -log [H^{+}] or more precisely pH= -log [H_{3}O^{+ }]

**But these two equations are considered equivalent.**

Knowing the pH is very important for many industries, such as food production, cleaning and self-hygiene products, clothing, printing, and even art preservation. For example, to ensure the shelf life of canned goods in the supermarket, that soaps or shampoos do not irritate the skin of those using them, or that cleaning products do not corrode the surfaces that you might be trying to clean.

Although in this last case in the cleaning product industry is where you will find the strongest acids and bases because that corrosive quality is what we use to remove things like grease and grime. The reason for this is because both strong acids and bases are very reactive, precisely for that tendency they have to donate or accept protons or hydrogen ions, this makes acids positively charged while bases by accepting hydrogen ions are negatively charged. In other words, the stronger the acid or base the more corrosive it is, that is why maintaining or regulating the pH of many products is fundamental. It is also worth to note that strong acids and bases dissociate completely in solution, releasing all its hydronium or hydroxide ions.

But how do we know at what point substances stop being corrosive? What would be that limit when substances are neutral? Well, the answer is in water. Water is very interesting because it is composed exactly and solely by the two ions that we have been talking about! And which cause many substances to behave like acids or bases, therefore water is technically both an acid and base at the same time, which actually makes it neutral.

Water has a very familiar molecular structure, is H_{2}O, however, water molecules are constantly dissociating themselves into hydronium ions and hydroxide ions, these ions when in contact with each other form a water molecule again, following this chemical reaction:

2H_{2}O_{(l)} <=> H_{3}O^{+} + OH^{–}

In the equation above you can see that we need two molecules of water and that one of them loses a hydrogen to form the positively charged hydronium ion H_{3}O^{+}, while the other one loses it and becomes the negatively charged OH^{–} or hydroxide ion. This reaction is constantly happening in water albeit in very small amounts or concentration. This dissociation happens very fast as well, two water molecules will exchange a proton forming the two ions and revert to water in fractions of a second. This allows for the properties of water to remain constant and its pH neutral despite behaving both as an acid and a base.

Based on the balanced equation, you can see that the number of hydronium ions will be exactly the same as the hydroxide^{ }ions. This means that the concentration of hydronium ions will be exactly the same as the concentration of hydroxy ions in pure water at all times (at 25 °C, because pH changes with temperature).

The equilibrium constant equation for the concentration of both ions is known as the water dissociation constant:

Kw= [H3O+][OH-]= 1X10^{-14 }mol/L

Since the concentration of each ion would be the same, we can calculate each one as:

Kw= [H3O+][OH-]= [x][x]= 1X10^{-14 }

Naming the unknown concentrations as x. Then we can simplify like this:

Kw= [H3O+][OH-]= [x]^{2}= 1X10^{-14 }M

And resolve x noting that the ions will be in the same concentration:

Ka=[H3O+]=[OH-]=1 X10-14=1×10^{-7 }M

We can conclude then that concentration of hydronium ions in pure water is always 1×10^{-7 }M, if we calculate the negative logarithm of that concentration, we will have calculated the pH:

pH=-log[H3O+]=-log 1×10^{-7 }=7

The pH of water is 7, and since this equilibrium is maintained, water is then electrically neutral and non-corrosive, and this is why acids and bases fall on either side of this number as the concentration of hydronium ions increases or decreases. At this point you will be probably wondering why acids fall below the 7 treshhold if they have higher hydronium concentrations than bases. It would be expected that the pH would be higher. The answer is in the negative logarithm. The reason for using the negative logarithm is because the concentration of the ions varies greatly, several orders of magnitude, but always in very small amounts, in the order of 1×10^{-14}mol/L. and it is always in values less than 1. This is why using the logarithm transforms those values into more manageable and especially more comparable numbers, the negative is used solely to turn a positive value as the logarithm of numbers below 1 will always be a negative number.

pH is generally estimated by using either some color indicator such as phenolphthalein or malachite green, or to measure it more precisely, a pH meter is generally used. The pH meter works by measuring the voltage (or electrical potential) of our sample and compares it to a reference solution, to later deduce the difference between them too.

Imagine that you are a chemical+ engineer in a factory and that you are preparing a solution of hydrochloric acid to perform some other reactions. Hydrochloric acid is always found in aqueous solution and it’s the perfect example of a substance that donates protons as it dissociates completely when dissolved in water, it has the molecular formula HCl. So, let’s say that you have 0.3L of 0.08 M hydrochloric acid, and that you want to dilute it in 0.5L of water and find the pH of that. Fortunately, every seller of chemical products must inform you of the concentration of these solutions.

So, let’s calculate the molarity of your resulting solution using our known concentration (M), and the volumes we want to dilute (V_{1} and V_{2}):

M_{1}V_{1}=M_{2}V_{2 }

Reorganising the equation, we can calculate the molarity of the resulting solution:

M_{1}V_{1 }/ V_{2}= M_{2}

Let’s put in our values:

0.08M*0.3L/0.5L=0.048M

Now let’s calculate the pH of that solution, since we know the concentration of acid, we know the concentration of hydronium ions.

pH=-log[0.048M]

pH=1.31

As you can see this solution is very acidic so you can expect for it to be very corrosive.

]]>Another example is hydroelectric energy production: in a dam, water is collected at a certain height and then left to fall freely to a lower height while passing through a turbine, which converts water’s *potential energy* into *electrical energy*. This energy is then used in your house to power different home appliances, such as a washing machine, a microwave, or an electric stove. Here, electrical energy is converted into *rotational*, *electromagnetic*, and *thermal energies*, respectively.

All these types of energies can be categorized into two main groups: potential and kinetic energies. The latter are related to *movement* and are usually applied in the context of rigid moving objects. For example, a moving car has a certain kinetic energy, which is the result of many energy transformations starting from burning the fuel. A heavy rock falling down a cliff also has a certain kinetic energy, which is the result of its gravitational potential energy being continuously transformed into movement.

Let’s learn what exactly is kinetic energy, how it relates to moving objects and how to calculate it.

**To calculate the kinetic energy of a moving object, follow these simple steps: **

**Measure the body’s mass,***m***, in kilograms.****Determine the body’s speed,***v***, in m/s. This value equals the magnitude of its velocity vector at the desired moment at which the kinetic energy will be determined.****Use the following equation to calculate the body’s kinetic energy in joules:**

(1) |

When we talk about moving objects, we tend to relate their motion to a certain force. For example, if you kick a ball resting on the ground, you will probably say it moves *because* a force was applied to it by your foot. Here, Newton’s second law of motion comes in handy, since it directly relates the acceleration (*a*) experienced by any body of mass *m*, when a force (*F*) acts on it:

(2) |

When you see a falling object, for instance, an apple falling from a tree, you might relate its movement to the force of gravity, which acts on all bodies in virtue of their mass. The difference between these two examples is that, while your foot needs to come in contact with the ball to effectively make it move, gravity can act on any mass without having to *touch* it.

In our first example, a force acts on the ball *while* your foot touches it. According to equation 2, the ball will accelerate depending both on its mass and on how hard you kick it. Nevertheless, once the ball moves away from your foot and is no longer in contact with it, the force you apply on it disappears. In this case, equation 2 indicates the ball will not accelerate further. However, if you do this experiment, you will observe the ball will keep moving for a while. Let’s try and understand this further:

Newton’s second law of motion describes how and why objects *accelerate*, meaning, how their velocity changes with time due to forces. These changes can refer to both a magnitude and a direction change of the velocity vector. The first alter the object’s speed, while the latter only change their trajectory. If you are not sure about these concepts, go ahead and read our article on how to calculate acceleration.

We have established that, in our previous example, the ball will not accelerate further after it has been kicked. This means, it will tend to move in a straight line at constant speed. According to the definition of acceleration, if the ball does not change its direction of movement and keeps a constant speed, its acceleration will be zero. Nevertheless, something has changed: the ball, which was originally at rest, is now moving.

If you do this experiment on a soccer field, you will probably notice the ball will eventually stop moving after rolling for some distance. This is due to another force acting in the direction opposite to the ball’s movement: friction. This corresponds to the horizontal component of the reaction force being applied by the ground to the ball, as the following free body diagram shows:

Here, the normal force is opposite to the ball’s weight, and the force of the kick, Fk, is opposite to friction, Ff. In this scenario, the ball keeps rolling after departing from your foot because it has gained energy from the kick. This initial energy would be “stored” in the ball forever if no friction was present —as in space—, but, since friction against the ground exists, it is slowly converted into another form of energy: heat. You may observe a similar phenomenon when rubbing your hands together: after doing it for a while your palms get hot due to the friction between both surfaces. Since the ball continuously loses energy to friction, it moves slower and slower, until it eventually stops.

Thinking about motion in terms of energy and energy transfers, instead of considering the forces that make objects move or stop moving, can be very helpful sometimes. When you kick a ball, for example, energy is transferred from your foot to the ball. Since energy cannot be destroyed, it stays “within” the ball, until it is either transferred to another body or converted into another type of energy. This is why the ball keeps moving in a straight line even if you don’t continue exerting a force on it.

Now, you might wonder, what type of energy does the ball, and for that matter, any type of body store, when moving? This is called *kinetic energy*. Its name comes from the Greek *kinein*, which means “to move”. This is a type of energy bodies possess due to their movement. Put in simple words: if a body is moving, it contains a certain amount of kinetic energy.

When fuel inside a rocket is burnt, the explosion releases the chemical energy stored in it and transfers a part of it to the body of the rocket in form of kinetic energy. The rest is released as heat, a type of *thermal energy*. When riding a bicycle, your muscles convey kinetic energy to the pedals by contracting and relaxing, which is possible because your body’s cells release energy from sugars and other substances.

We know now that kinetic energy exists in a body if it is moving. Macroscopic objects move in two different ways: *translating* and *rotating*. The first refers to the body’s center of mass changing its position over time. A clear example of this is kicking a soccer ball: its center of mass, which is probably located somewhere near its center, will displace in three-dimensional space once you kick it. The other type of movement, rotation, occurs when an object *revolves* around its center of mass. In our previous example, the soccer ball will also probably rotate while displacing across the field. In this case, the ball exhibits both translation and rotation.

Kinetic energy refers to the energy contained by an object in virtue of its movement. Since macroscopic objects exhibit two types of movement, namely translation and rotation, kinetic energy is also differentiated into *translational kinetic energy* and *rotational kinetic energy*.

As we have seen so far, kinetic energy relates to a body’s movement. The faster it moves, the higher the kinetic energy it should contain. If the object is then subjected to friction, its speed will decrease, as will its kinetic energy.

There seems to be a relationship between the speed of a moving body and its kinetic energy. Since any change in an object’s speed is related to the appearance of an acceleration, we can use Newton’s second law of motion to describe kinetic energy. Let’s consider a simple case where a body of mass *m* is moving along a straight line with an initial speed vi and no friction. If we want to make the object move faster or slower, we need to apply a force to it, thus creating an acceleration, as shown by equation 2.

Imagine the body is moving to the right. If you want to increase its speed, you will have to push it to the right. When you do so, the force you apply increases the kinetic energy of the body until you stop exerting it, thus increasing its speed to a final value vf. Let’s suppose you applied said force for a period in which the body displaced a total distance *s*, as the following image shows.

According to basic mechanics, the final speed of the object depends on its initial speed, the acceleration created by the force you applied and the total length along which it accelerated:

(3) |

Where *a* is the body’s acceleration (which is assumed constant) and *s* the magnitude of its displacement. If we solve for the acceleration:

(4) |

Since this acceleration is caused by a force acting on the body, we may use equation 2 to relate both quantities:

(5) |

This equation may also be written as:

(6) |

To explain this result, we need to make use of a very important concept in mechanics: *work*. It is defined as the energy transferred by a force to a body in virtue of the displacement that is generated by it. In our example, when the object is pushed to be accelerated, it displaces a certain distance, which means work is being performed on it. By definition, work is equal to the applied force times the object’s displacement: *W = F × s*. Therefore, equation 6 can be written as:

(7) |

This equation indicates that the total work performed upon a moving object is directly proportional to the difference between its final and initial speeds. This makes sense if we consider that the greater the difference between both speeds, the greater had to be the work that generated said acceleration.

The terms including the initial and final velocities are defined as the initial and final kinetic energies of the body, respectively. Since energy is not created nor destroyed, any change from the initial to the final kinetic energy of the body, which in turn implies there was a change of speed —given mass is assumed constant—, indicates work had to be performed.

Conversely, the final kinetic energy of a body equals the work needed to make it move at its final speed starting from rest, when the initial speed is zero. The same applies when slowing down a moving body: work will have to be performed on it to decrease its speed, using a force pointing in the direction opposite to the body’s movement. In this case, since work would be negative, the correct expression is that the body performs work on the object that is slowing it down, for example, your hand. In general, the kinetic energy is defined as:

(8) |

The units for the kinetic energy are joules (N × m). Since the term for the speed is squared, it is implied that *K* will always be positive. In turn, if *K = 0*, the body’s speed is zero, meaning it does not move at all.

If the difference between the final and the initial kinetic energy is positive, work will be positive, which means it was performed *on* the moving object in order to increase its total movement. In the opposite case, if the difference between the final and initial kinetic energy is negative, it means work was performed *by* the object onto another object or mean (such as the ground or the air surrounding it), thus decreasing its total movement.

Finally, equation 7 can be written as following, which is known as the *work-energy theorem*:

(9) |

As we mentioned before, kinetic energy is divided into two main types: translational and rotational kinetic energy. In the second case, this quantity results from the addition of the kinetic energies of all the particles that make up a rigid body which is rotating around its center of mass. In this case:

(10) |

Where *I* is the body’s moment of inertia and *ω* its angular velocity. For bodies exhibiting both rotation and translation, the total kinetic energy is given by the sum of the rotational and translational kinetic energies:

(11) |

Use the Energy Skate Park simulator by PhET to observe how the potential, kinetic, and thermal energies of a skater are transformed from one into the other when rolling on a ramp. Set the skater on either side of the ramp using your mouse and let him roll down. Make sure to tick the “Bar graph” option to see how the different energies vary in time.

]]>Carpentry might be a thrilling and creative activity, but it also requires you to carefully plan, calculate, and get hold of the necessary materials in the correct amounts, especially if you want to stick to a budget.

In this field you will find several specialized units of measurement. A very important one —at least in Canada and the United States— is the *board foot*, which refers to a certain volume of lumber, or wood that has been processed and cut into boards. Knowing how to express the correct amount of lumber you need for your project is critical. Let’s learn more about this convenient measurement unit.

**Follow these steps:**

**Measure the thickness (***t***) of the wood board you need in inches (in).****Measure the width (***w***) of the wood board in inches (in).****Measure the length (***l***) of the board in feet (ft).****Use the following equation to calculate the equivalent board feet of lumber:**

(1) |

*Lumber* refers to differently shaped pieces of wood which have been cut from a tree log and, in some cases, surfaced on one or more faces. These pieces are then sold as raw materials for a great variety of applications, like construction, furniture making, decoration, etc.

Logs are usually sawn into boards of specific dimensions. Those that comply with standardized sizes are therefore called *dimensional lumber* and are commonly found at most wood stores.

Wood boards are basically 3-dimensional rectangles, or *rectangular cuboids*, which have a specific width (*w*), thickness (*t*), and length (*l*). Although these labels are completely interchangeable, given they all represent a length, there is a widely accepted way of using them on a piece of lumber.

In the case of a long board, width and thickness often refer to the two dimensions of a cross-section of the lumber, whereas the length corresponds to the longer remaining dimension. In the case of rectangular boards, width and length refer to the sides of the lumber when viewed from the top, while the thickness refers to the dimension perpendicular to them. Look at the following image to clarify this:

The specific characteristics of a piece of lumber, whether mechanical —like the forces it can withstand, how hard its surface is, or how much it will bend before breaking— or aesthetic —like its tone or its grain—, depend on the specific hardwood used to obtain it. Given that many different types of wood are currently used for carpentry, suppliers could have a hard work selling lumber if all these previous variables had to be considered to quote a simple board.

This is precisely where the unit of *board feet* comes in handy. Since it represents a certain volume of wood, which already takes into account the lumber’s width, thickness and length, it reduces the number of variables to consider. Keep in mind, board feet refer to *volume* and not *length*, even if you are used to using feet in the context of measuring a certain distance.

The volume of a wood board is defined as: *V = w *×* l *×* t*. One board foot of lumber is therefore defined as the volume of a wood board with a width of 1 foot, a length of 1 foot, and a thickness of 1 inch. The mix of different units (feet and inches) comes from the fact that, in boards as the one shown on the left in the previous image, both width and length are most likely measured in feet, while thickness —the smallest dimension— is measured in inches.

If the units are kept for each dimension of the lumber, any wood board’s board feet can be mathematically calculated as:

(2) |

Where the brackets indicate the units in which each variable must be measured in order to comply with the definition of board feet. Given that 1 foot = 12 inches, equation 2 is most often written as:

(3) |

Keep in mind that, in this equation, the width is measured in inches, not in feet. This is most likely to happen when dealing with boards such as the one shown on the right in the previous image.

Now, to calculate the amount of board feet you need for a project, first measure each board’s width, thickness and length using the appropriate units, and then use equations 2 or 3 to calculate BF. Keep in mind that, if you need several boards with the same dimensions, you just need to measure one of them and then multiply the resulting board feet by the number of boards you need.

Use this simple calculator to obtain the total board feet required for any of your projects, just by inputting the basic dimensions of each wood board and the total number of boards you require.

If you want to learn more details about hardwood, its standards and uses, visit the website of the National Hardwood Lumber Association.

]]>Since ancient times, humans have been attracted to this simple but puzzling geometry for many different reasons: it has no straight sides, it possesses an infinite number of symmetry planes, and it is closely related to the mathematical constant *π* (keep reading to learn more about this!).

An important characteristic of circles is their *circumference*, or the distance covered around it. Let’s learn how to calculate it without the need of flexible measuring tape, and let’s discover why so many great mathematicians are so attracted to it.

**To calculate a circle’s circumference first find its radius, ***r***, which equals half of its diameter. Then, apply the following equation to find its circumference, ***C***:**

**Where π = 3,14159.**

Circumference is defined as the *perimeter* of a circle. But what exactly is the perimeter? Its name comes from Greek, as many concepts in geometry do, and is formed by *περί *(peri), which means “around”, and *μέτρον* (metron), which means “to measure”. Together, they form an expression that means “to measure around” something, in this case, around the space enclosed by geometrical figures.

Ancient Greeks loved to experiment with different shapes they called *polygons*. These are shapes built with straight segments called *sides*, which form a closed figure. You have probably seen many polygons. For example, triangles are 3-sided polygons, while rectangles —and squares among them— are 4-sided polygons. Every polygon has a specific perimeter, which depends on how long its sides are.

Another figure Greeks were very fond of is the circle. In this case, the perimeter is referred to as *circumference*, which in turn comes from the Latin *circum*, which means “around”, and *ferre*, which means “to carry”. This is because, as with any type of perimeter, it refers to the length of the path that outlines a shape. Since, in this case, the shape is circular, the perimeter will revolve around it, and thus the Latin expression to “carry around” something makes perfect sense.

A circle’s circumference can be measured as any other length using a measuring tape. Nevertheless, this is not practical at times. For example, imagine you need to determine the perimeter of a circular piece of land to install a fence of a proper length. If the land is too big, going around it to measure its perimeter in sections would simply take a lot of time and effort.

Another way to measure a circle’s circumference could be by extending its perimeter in a straight line, and then measuring it with any suitable device. This is, of course, not possible in many scenarios, but it could look something like the following image. Here, *C* represents the circle’s circumference.

Finally, a more practical way to determine a circle’s circumference is by use of its enigmatic properties. Let’s see how:

A very interesting property of circles is the relationship between their perimeter and their diameter. The latter simply refers to how wide a circle is. It is alternately defined as the length of any line that connects two points on its perimeter, and which at the same time passes through its center. The following image shows both quantities:

What is interesting about circles is that no matter its size, the ratio of its circumference and its diameter will always result in the same number: 3,14159265359… We call this number pi and represent it with the Greek letter π. This simple but puzzling phenomenon has been known for thousands of years, and can be written as:

It is important to remember that this equation holds for any circle in the universe. Since it relates two basic characteristics of a circle, it can be used to calculate them if the other one is known. If we solve the equation for the circumference we get:

This way, a new method to find a circle’s circumference can be extracted from the definition of π. A third important characteristic of a circle is its *radius*, which simply equals half of its diameter:

By replacing equation 4 in equation 3, we get equation 1, which is the most common mathematical definition of the circumference. Now, to calculate this value for any circle, you only need to find its radius, multiply it by 2 and then by the mathematical constant π. Since π is unitless, the circumference inherits the units of length from the radius.

Equation 3 implies that, for any circle with diameter *d*, its circumference will have a value of pi times *d*. If we choose a circle of diameter equal to 1 m, its circumference will be pi meters, as the following animation shows:

Taken from: Wikimedia Commons, John Reid, 2006.

Example 1:

Find the circumference of a circle with a diameter equal to 1,5 m.

Answer: 4,71 m

Example 2:

What is the diameter of a circle with a circumference of 10,3 m?

Answer: 3,28 m

]]>Expressed as a percentage, ROI can be used to compare various investment opportunities to select the most effective or profitable for an investor. ROI can also be used to calculate the return of previous investments to measure their historical efficiency.

This article will explain the ROI definition and what is a good ROI. This article will also illustrate the ROI equation and demonstrate how to calculate ROI step by step.

Return on investment (ROI) is a popular performance metric utilized to measure the effectiveness and profitability of an investment’s performance. As expressed in this ROI definition, this metric considers an investment’s net profit or loss and its initial cost or outlay. Articulated in percentage terms, ROI directly measures the return of a particular investment relative to its cost.

**Return on investment (ROI) is calculated by dividing the return of an investment by the initial cost or outlay of the investment. The return of an investment is found by subtracting the amount spent on an investment from the final amount gained on the investment. The sum of these values then divided by the amount spent and multiplied by 100 to express ROI in percentage terms.**

**Return on Investment (ROI) = **[Amount Gained – Amount SpentAmount Spent]** x 100**

** ***Where:*

* ***Amount Gained = total final value of the investment**

** ****Amount Spent = total initial cost of the investment**

- Determine the total initial cost and the total final value of the investment.
- Subtract the total initial cost from the total final value of the investment.
- Divide the product of Step 2 by the total initial cost.
- Multiply the product of Step 3 by 100 to express ROI in percentage terms.

An investor is determining the ROI from a prior investment into a publicly-traded company’s stock. The investor recently sold their shares in the company and liquidated their total investment.

Based on information obtained from the sale of the shares, the investor has gathered the following information:

Initial Investment: $20,000

Fees from Purchase: $55

Final Value of Investment: $26,000

Fees from Sale: $85

Given this information, the investor can determine the amount spent:

Amount Spent = Total Initial Cost of the Investment

Amount Spent = Initial Investment + Any Additional Fees or Costs

Amount Spent = $20,000 + $55

**Amount Spent = $20,055**

The investor can also determine the amount gained based on this information:

Amount Gained = Total Final Value of the Investment

Amount Gained = Value of Investment – Any Fees or Costs of Liquidating Investment

Amount Gained = $26,000 – $85

**Amount Gained = $25,915**

With this information, the investor can populate the ROI equation and begin solving:

ROI = [Amount Gained – Amount SpentAmount Spent] x 100

ROI = [25,915 -20,05520,055] x 100

ROI = [25,915 -20,05520,055] x 100

ROI = [5,86020,055] x 100

ROI = (0.292) x 100

**ROI = 29.2%**

Here we can see that this investor’s purchase of company stock produced a ROI of 29.2%. This value represents the efficiency and profitability of the investment, as the initial outlay grew by $5,860 to a final value of $25,915.

Understanding how to calculate ROI like this is important for investors making forward-facing investment decisions as well. When historical data is present, average ROI can be estimated to compare the profitability of future investments between different opportunities. Using this information allows investors to make the most beneficial investment decision.

The ROI of an investment will not always be a positive value. When the amount spent exceeds the amount gained from an investment, a net loss has occurred. This net loss will produce a negative ROI, which investors should actively avoid. Most opportunities with positive ROIs are considered worthwhile, but opportunities with the highest ROIs should be prioritized first.

The ROI equation does not take the need for liquidity of an investment into consideration. Since the passage of time or the length of an investment holding period are not accounted for in the ROI equation, the equation fails to measure the opportunity costs of investments which are missed when the investment cannot be liquidated. If an investment is selected when evaluating ROI, but does not allow the investor to sell their position over a period of time, any investment opportunities which arise during that time period are lost.

ROI should not be confused with rate of return (ROR), which accounts for an investment’s time frame. Unlike ROR, ROI does not consider the amount of time during which an investment grows, as there are no values in the ROI equation representing the time period of an investment. Instead, ROI can be used in conjunction with ROR or net present value (NPV) to determine the real rate of return of an investment.

Microsoft Excel can be used to effectively calculate ROI. For investors making quick decisions between several investments, having a ROI calculator available will decrease the amount of time it takes to determine an investments ROI. When setting up an ROI calculator using Excel, follow these simple steps.

For this example, we will calculate the ROI for a $5,000 investment, which was later liquidated at a final value of $6,000, as shown below:

Based on this information, the following formulas will be inserted into cells D7 and D8 to determine the amount spent and amount gained from the investment, as follows:

**Amount Spent: =SUM(D2:D3)**

**Amount Gained: =SUM(D4,-D5)**

After calculating the amount spent and amount gained, the total profit from the investment (the amount gained minus the amount spent) will be determined by inserting the following formula into the corresponding cell D9:

**=SUM(D8,-D7)**

Once the investment profit has been calculated, the profit will be divided by the amount spent on the investment to determine the overall ROI. The following formula will be inserted into cell D11, as shown below:

**=IMDIV(D9,D7)*1**

For investors wondering “What is a good ROI?”, know that any positive ROI is a good ROI. Any profitable investment is worthwhile, although investments should be measured such that those which will yield higher ROIs are prioritized.

Average profitable ROI varies depending on the industry the investment was made into. For the S&P 500 index, an average ROI is considered to be at least 7%. A rate equal to or higher than this amount is considered a good ROI for investments in the stock market.

Other investments grow at lower rates, such as government bonds or United States treasury bills. Government bonds have an average ROI of over 5-6%, while treasury bills have an average ROI of over 3%. While these rates are lower than that of the S&P 500 index, a ROI around these averages is still considered good for these types of investments.

Return on investment (ROI) is a profitability gauge used to determine the efficiency of an investment, measuring an investment’s return based on the initial cost or outlay of the investment. As explained in the ROI definition, ROI is written as a percentage and can be used to compare different investment opportunities to select the most profitable option for an investor.When calculating ROI, be sure to consider any additional costs present in the initial outlay or deducted from the final value of an investment, such as brokerage or holding fees. Knowing how to calculate ROI is important when comparing various investment opportunities.

]]>Taking into consideration price levels, purchasing power, and time, the inflation rate represents the rate of decline of purchasing power for a particular currency. Expressed in percentage terms, inflation indicates a unit of currency purchases less than it could in previous periods of time.

This article will illustrate the inflation rate formula, how to calculate inflation rate step by step, and provide examples on how to apply inflation rate to various scenarios.

As an indicator of the decrease in purchasing power of a currency, the inflation rate is defined as the rate of which the value of a currency diminishes and the level at which prices for goods or services rise. Inflation is commonly recorded by the Consumer Price Index (CPI) and the Wholesale Price Index (WPI). Other indexes are used for specific countries as well, such as the Producer Price Index (PPI).

Inflation measures the overall impact of price and purchasing power changes over various goods and services during a certain period of time.

The Consumer Price Index (CPI) tracks the prices of goods and services purchased by consumers like businesses and individuals. This index is compiled by the U.S. Bureau of Labor Statistics and can be found here.

The Wholesale Price Index (WPI) tracks the prices of wholesale goods sold or traded in bulk quantities between businesses. This index is compiled by The World Bank and can be found here for the United States economy specifically.

Other indexes used to track inflation exist as well and can be used interchangeably depending on the type or area of inflation being measured. All indexes account for seasonal or cyclical price changes in their calculations of price levels as to accurate identify how much price changes are resultant of inflation.

**The inflation rate over the period of one year is calculated by dividing the result of the final CPI value minus the initial CPI value by the initial CPI value of a given period of time and multiplying the product by 100. This formula yields the inflation rate in percentage terms. **

** Where:**

* ** ***CPI**_{x+n}** ****= CPI value of final period**

** **** ****CPI**_{x}** ****= CPI value of initial period**

** **** ****x ****= initial period**** **** **

**n ****= number of periods after initial period**** **** **

**Note: ***CPI values can be substituted by WPI, PPI, or other index values when desired.*

- Determine the initial period and final period prices will be measured between.
- Locate the corresponding CPI values for the initial and final periods.
- Subtract the initial CPI value from the final CPI value, and divide by the initial CPI value.
- Multiply the product of Step 3 by 100 to solve for the inflation rate.

An economist is determining the amount of inflation in food prices in U.S. cities from August 2011 to August 2021. The economist wants to determine how much the purchasing power of $1 decreased by calculating how much food prices in U.S. cities increased over this time period.

After obtaining consumption data for urban consumers from the U.S. Bureau of Labor Statistics, the economist determined the following values:

CPI for August 2021: 279.135

CPI for August 2011: 229.554

Since the economist is measuring price levels from the same month in two different years, the periods can be assumed to be annual. Since there are exactly 10 years between August 2021 and August 2011, there are ten periods present here.

In this example, the economist can predict the following values based on this assumption and their data:

Initial period (x): **2011**

Periods after Initial Period (n): **10 periods**

Final CPI Value (CPIx+n): **279.135**

Initial CPI Value (CPIx):** ****229.554**

Given these values, the economist can now populate the inflation rate formula as follows to determine the initial and final CPI periods:

Rate of Inflation = (CPIx+n) – CPIxCPIx

Rate of Inflation = (CPI2011+10) – CPI2011CPI2011

**Rate of Inflation = **[(CPI2021) – CPI2011CPI2011]** x 100**

Now that the inflation rate formula has been simplified, the economist can now insert the values obtained for price levels from August 2021 to August 2011 and begin solving as follows:

Rate of Inflation = [(CPI2021) – CPI2011CPI2011] x 100

Rate of Inflation = [279.135- 229.554229.554] x 100

Rate of Inflation = (49.581229.554) x 100

Rate of Inflation = (0.216) x 100

**Rate of Inflation = 21.6%**

Here we can see that the rate of inflation in food prices in U.S. cities from August 2011 to August 2021 was 21.6%. This value represents both the increase in food prices in U.S. cities and the decreased purchasing power of U.S. dollars for foodstuffs in U.S. cities over the past 10 years.

For individuals determining how the value of their assets may have changed or how much the purchasing power of money has decreased, knowing how to calculate inflation rate like this is critical.

Inflation represents the decrease in purchasing power of currency and the increase in price levels for certain goods or services. Inflation should not be confused with deflation, which has the opposite impact on purchasing power and price levels. When solving for the inflation rate, if a negative value is returned, this value indicates that deflation occurred as price levels dropped while the purchasing power of currency rose.

The inflation formula can be used to identify inflation over any number of periods. Major indexes track prices at least a decade into the past, while CPI specifically has calculated prices as far in the past as 1913. Using this information, inflation can be determined for any number of periods between as small as a month to as large as over multiple decades. CPI measures the weighted average of prices available for a variety of goods or services over a spectrum of geographic locations within the United States, so the formula is highly customizable in this regard.

Inflation does not always increase at a steady rate and can spike depending on several factors. When calculating for inflation, price level changes over certain periods will reflect this. Outstandingly high rates of inflation therefore do not imply the answer is necessarily incorrect, as inflation at these levels is known as ‘hyperinflation.’ For example, Germany experienced a rate of inflation from August 1922 to November 1923 of over 332%. Similarly, Venezuela experienced a rate of inflation in 2020 alone of approximately 2,355%.

The inflation rate is the measure of how much the purchasing power of currency decreased and prices of goods or services increased over a certain time period. Inflation rate can be calculated by using data from major price indexes like the CPI, WPI, or PPI and is expressed in percentage terms.

When calculating the inflation rate, negative values imply deflation occurred where purchasing power of currency increased and prices of goods or services decreased. If the rate of inflation is outstandingly high, hyperinflation occurred over the time period measured.

]]>This concept considers the value placed on goods or services, the future time value of money, and illustrates how even simple financial decisions can create lasting impacts.

This article will explain the opportunity cost definition and illustrate the opportunity cost formula, how to calculate opportunity cost step by step, and provide examples on how to recognize this sort of cost in various scenarios. For the purposes of this article, only cost for financial decisions between two alternatives will be reviewed (although it is present in all decisions we make).

Opportunity cost is the benefit forgone from an option not chosen during a decision. This cost definition applies prominently to financial decisions, as the cost concept represents the potential benefits passed up when choosing one option over another. Evaluating this type of cost accounts for both the costs and benefits of multiple options being selected from.

**For decisions between two options, the cost is calculated by subtracting the return on the option chosen from the return on the best forgone option. The values for the chosen option and the forgone option can be measured depending on the decision being evaluated. **

**OC = FO – CO**

** ***Where:*

**OC = opportunity cost**

* ** ***FO = return on the forgone option**

** **** ****CO = return on the option chosen**

- Determine the return on the forgone option.
- Determine the return on the option chosen.
- Subtract the return on the option chosen from the return on the forgone option.

In the following opportunity cost example, an investor is determining which index to invest money into as to generate the highest return on investment (ROI). The investor is considering investing in the Dow Jones Industrial Average or the S&P 500 index.

To decide where his money will best grow, the investor needs to evaluate the cost present in this decision.

Based on review of historical data, the investor has gathered the following information:

Average annual ROI for the Dow Jones Industrial Average: 5.42%

Average annual ROI for the S&P 500 index: 7.96%

With this information, the investor can now evaluate the cost of choosing to invest in the Dow Jones Industrial Average. Since the investor has chosen to invest in the Dow Jones Industrial Average and will forgo the S&P 500, the values of the opportunity cost formula are as follows:

**Return on the forgone option (FO):**** ****7.96%**

**Return on the chosen option (CO):**** ****5.42%**

Now, the investor will populate the opportunity cost formula with these values, as follows:

OC = FO – CO

**OC = 7.96 – 5.42**

Next, the investor will subtract the cost of the option chosen from the cost of the forgone option to yield the cost, as shown:

OC = 7.96 – 5.42

**OC = 2.54%**

Here we can see that since the investor chose to forgo investing in the S&P 500 index, they also passed up on annual returns of 2.54%, as their investment would have grown more within a year in the S&P 500. The annual returns of 2.54% forgone by the investor represent the cost of not choosing the alternative opportunity in this scenario.

As this example shows, calculating for the cost of a financial decision helps individuals and businesses make sound and informed choices to maximize the benefits of a decision.

Calculating opportunity cost accurately for forward-facing decisions requires historical data if the potential returns are not clear. When evaluating an investment decision, the potential ROI from an investment option is not always clear. For instances such as this, try to gather as much historical data as possible to make an informed estimate of the potential ROI from an operation. Having accurate values for the returns of the options chosen and forgone will produce a true and accurate cost.

Opportunity cost can be represented in various units, such as in currency, percentage terms, or even in numbers of goods. For example, the cost choosing between two different jobs to work could be represented in currency, as the amount of revenue forgone will be the opportunity cost of this scenario. Alternatively, for farmers deciding what type of crop to grow, the cost could be represented in terms of units of the type of crop forgone by the farmer.

The evaluation of cost for investment decisions does not consider the need for liquidity. For example, when deciding between two investment opportunities, one option provides a higher return but requires the investment to remain untouched for a period of time. This option could cost the investor more if they miss out on a lucrative future investment opportunity because their money was unreachable over the period of time. Opportunity cost should therefore be considered in accordance with other factors when making an investment decision.

Microsoft Excel can be used to effectively calculate opportunity cost. When deciding between financial decisions quickly, having an opportunity cost calculator available hastens the evaluation process.

For this example, an individual decides how to spend their time. The individual works as a consultant and charges clients $200 per hour. The consultant chooses to perform some maintenance on their vehicle, which takes 3 hours of their time and therefore represents $600 of lost revenue from time the consultant could have spent working instead. A mechanic would have charged $300 for the repairs.

In this example, the value of the forgone option is $600 since the consultant chose to forgo revenue of $600 from working three hours as they instead chose to repair their vehicle. The value of the chosen option is $300, as this is what the consultant could have made if they chose to pay a mechanic to complete the job and work the three hours instead (since $600 – cost to repair of $300 = $300 return).

To create the calculator, format the forgone option, chosen option, and opportunity cost cells as shown and insert the following formula into cell C4. This formula will subtract the chosen option from the forgone option, as follows:

**=SUM(C2,-C3)**

Since the forgone option was $600 of revenue and the option chosen was to repair the vehicle, which could have been completed by mechanics and allowed the consultant to still make $300, the formula will appear as follows:

Opportunity cost represents the benefit which is passed up when selecting one alternative over another. This cost concept applies to all financial decisions made between two or more options and should be evaluated as to make the decision which provides the most benefit.Cost predictions for future investment decisions requires historical data to ensure accuracy. This concept does not take the liquidity of an investment into consideration, so this calculation should always be used in conjunction with other evaluating factors.

]]>Real GDP considers both nominal GDP and GDP deflators in establishing the value of goods and services generated within an economy. This metric is used beyond measuring for economic growth, as it can also be applied to the analysis of a currency’s purchasing power within an economy.

This article will explain what is real GDP and how to find real GDP. This article will also illustrate how to calculate real GDP, how to format a real GDP calculator, and address the question, “Why is real GDP a more accurate measure of an economy’s production than nominal GDP?”

Real gross domestic product is a macroeconomic metric which measures the inflation-adjusted value of the goods and services produced by an economy over a period. The value is considered the total economic output of a country and is often used by economists and governments to estimate the growth and overall strength of a country’s economy.

In the United States, a quarterly report on GDP including both real and nominal GDP data is published by the Bureau of Economic Analysis (BEA).

**Real gross domestic product is calculated by dividing the nominal GDP for a given period by the GDP deflator. Nominal gross domestic product (Nominal GDP) is measured in the value of ‘current dollars,’ whereas the GDP deflator is a measurement of inflation since a given base year, set by the BEA, which adjusts the nominal GDP for inflation to yield the answer.**

**RGDP = Nominal GDP / GDP Deflator**

*Where:*

**RGDP = Real gross domestic product**

- Determine the period GDP will be measured during.
- Identify the nominal GDP for the period being measured and the corresponding GDP deflator.
- Divide the nominal GDP by the GDP deflator to yield adjusted GDP for the period.

An economist is measuring the GDP in the United States for the fourth quarter of 2020. Based on information published by the BEA, the economist has identified the following values:

GDP Deflator (2020): **114.44**

Nominal GDP (2020): **$21.48 trillion**

With this information, the economist can use the real GDP formula to calculate total economic output within the United States in the fourth quarter of 2020. The economist will populate the formula as follows:

RGDP = Nominal GDP / GDP Deflator

**RGDP = 21,480,000,000,000 / 114.44**

The economist will now divide the nominal GDP by the GDP deflator to solve:

RGDP = 21,480,000,000,000 / 114.44

RGDP = 187,696,609,557

**RGDP = $18.77 trillion **

After solving for GDP and rounding, we can determine that economic output within the United States for the fourth quarter of 2020 was $18.77 trillion. This value represents the total economic output of the United States during this period, adjusted for inflation.

Having information on real GDP is important for governments analyzing the strength of their economy. For example, during the onset of the COVID-19 pandemic, the United States economy was largely shuttered due to protection protocols.

As a result, GDP in the United States dropped drastically during the first and second quarters of 2020. By the third quarter of 2020, the economy began to reopen as protection protocols were lifted, leading to a surge in GDP as the economy resumed producing goods and services.

During this time, the United States was closely monitoring the output of its economy to assess economic health throughout the initial stages COVID-19 pandemic. As shown in the table below, sourced from the BEA, percent changes over this period provides a clear view into how the pandemic impacted the United States economy:

The base year used to select the GDP deflator will significantly influence the adjusted GDP. The BEA identifies several base years for determining the GDP deflator. Since the GDP deflator adjusts the nominal GDP for inflation, the base year selected will change the value of the GDP deflator – thus impacting the real GDP value. When calculating for this adjusted GDP, make sure to choose the proper base year, typically identified by the BEA, to produce an accurate result.

Real GDP measures a country’s economic output over the course of a year by adjusting nominal GDP for inflation. Nominal GDP within the United States is calculated by considering the consumption, government spending, and other actions within an economy in a given year. The formula for GDP = Consumption (C) + Government Spending (G) + Investment (I) + Net Exports (NX). The result of this formula is then divided by a GDP deflator to yield real GDP.

Real GDP will always be lower than nominal GDP during inflationary periods. Since prices of goods and services rise during inflationary periods, nominal GDP can be a misleading figure, which explains why real GDP is always a smaller value when adjusted for inflation. Alternatively, this type of GDP will always be higher than nominal GDP during deflationary periods. Since the prices of goods and services decrease during as a result of deflation, nominal GDP may appear lower and underestimate the actual health of an economy.

This type of GDP can be calculated by using Microsoft Excel. To build a real GDP calculator, follow the steps shown below.

Insert the following formula into the cell C5 for adjusted GDP as demonstrated:

**=(C2/C3)**

This formula will yield the GDP as a several-trillion-dollar figure. To round the GDP value down to be measured in the trillions, insert the following formula into the cell below:

**=C5*0.0000000001**

A common question asked regarding GDP is, “How is Real GDP a More Accurate Measure of an Economy’s Production than Nominal GDP?”

Real GDP is more accurate and favored by economists than nominal GDP, as nominal GDP does not consider inflation. Inflation decreases the purchasing power of currency. As a result of inflation, the price of goods and services rise during a period.

Although these prices rise, the nominal GDP formula (GDP = C + G + I + NX) does not take price fluctuations into account, as the product of the formula is simply the sum of the economic output of a country measured in “current collars.”

To adjust nominal GDP for inflation, a GDP deflator based on a predetermined base year is used. Dividing nominal GDP by this GDP deflator produces a GDP value adjusted for the amount of inflation which occurred over a given period.

In periods of high inflation (or deflation), the adjusted GDP more accurately describes the overall health and strength of an economy. Major differences between the values of real and nominal GDP will show if significant inflation is occurring. Governments can then enact the proper economic policy of most benefit to an economy, rather than potentially damaging the economy based on misleading information.

For those asking “What is Real GDP?”, this kind of adjusted GDP is a popular measurement of the economic output of a country and is used to gauge an economy’s overall health. This value is calculated by dividing nominal GDP for a given period by a GDP deflator associated with a base year.

Knowing how to find adjusted GDP is essential, as this is a more accurate measurement of a country’s economic health as it accounts for inflation or deflation.

]]>For those wondering “What is Net Worth?” or “Why is Net Worth Important to Me?”, know that this number is an important calculation for individuals just as much as for businesses. For determining retirement or financial aid eligibility, a statement disclosing an individual’s worth is often required. This information helps individuals know whether they can afford to take on additional loans, retire from their occupation, and can assists with other important financial decisions.

For investors in businesses, this calculation is important to determine the value of a business. Investors want to make sure the judgments they make with their money are sound and true. Knowing the worth of a business helps investors make sound investment choices, as they can avoid investing in a business heavily overburdened with liabilities.

This article will illustrate the net worth formula, how to calculate net worth step by step, and provide further examples on how net worth can be utilized in various scenarios.

The definition of net worth is the total liabilities subtracted from the total assets of an entity. Total liabilities include loans, debts, mortgages, credit card payments, accounts payable, salaries payable, taxes, and other liabilities commonly found on an entity’s financial statements. Total assets include tangible assets like capital including land or machinery and intangible assets like intellectual property.

This amount can also be expressed as ‘net value.’

**Net worth is calculated by subtracting an entity’s total liabilities from their total assets. Total liabilities include all liabilities of an entity. Total assets include all assets of an entity. When solving for worth, no assets or liabilities are excluded from this calculation. **

*Where:*

**NW = Net Worth**

**The formula can also be expressed in terms of the tangible and intangible assets. Total assets include both tangible and intangible assets. ****Tangible assets**** are capital like land, machinery, or equipment. Intangible assets are assets which are not physical or are intellectual property, including goodwill, trademarks, patents, or copyrights. ***

******If a company is trying to determine its worth in terms of only tangible assets, the intangible assets of a company can be removed from the formula. This is known as ‘Tangible Net Worth.’*

- Determine total assets by adding all tangible and intangible assets.
- Determine total liabilities by adding all liabilities.
- Subtract the total liabilities from the total assets.

Following these steps will yield the net worth expressed in terms of currency like dollars, euros, or British pounds. This value represents the overall value of an entity in terms of its assets compared to its liabilities.

If the amount of an entity’s total liabilities is greater than its total assets, then the net worth of an entity will be a negative value. Having a negative worth can be common for individuals who have several liabilities like loans, debts, or a mortgage.

A manufacturing company needs to determine its total value as of the second quarter of 2021.

Based on their entire business, the manufacturing company calculated the following values for their tangible and intangible assets:

Cash: $300,000

Investments: $1,000,000

Property: $2,000,000

Equipment: $500,000

Intellectual property: $1,000,000

The manufacturing company also calculated the following values for their total liabilities:

Property loans: $1,000,000

Other loans: $500,000

Accounts payable: $500,000

Salaries payable: $400,000

First, the manufacturing company will calculate all of their total assets:

Total Assets = Tangible Assets + Intangible Assets

Total Assets = (Cash + Investments + Property + Equipment) + Intellectual Property

Total Assets = ($300,000 + $1,000,000 + $2,000,000 + $500,000) + $1,000,000

**Total Assets = $4,800,000**

Next, the manufacturing company will calculate all of their total liabilities:

Total Liabilities = Property loans + Other loans + Accounts payable + Salaries payable

Total Liabilities = $1,000,000 + $500,000 + $500,000 + $400,000

**Total Liabilities = $2,400,000**

Finally, the manufacturing company will subtract their total liabilities from their total assets to determine the net worth of their business as of the second quarter of 2021:

NW = Total Assets – Total Liabilities

NW = $4,800,000 – $2,400,000

**Net Worth = $2,400,000**

Here we can see that the net worth of the manufacturing company is a positive value of $2,400,000. This indicates the total assets of the business outweigh their total liabilities, meaning the company is not overburdened with debt or other liabilities.

This information can help the company determine whether or not to take on additional loans, spending, or other purchases.

The net worth formula can be used to determine worth based on only tangible or only intangible assets. If an entity wants to know its value based only on the tangible assets in its possession, intangible assets can be removed from the equation. Alternatively, if an entity specializes in intellectual property, or has valuable patents or trademarks, tangible assets can be dropped from the equation to determine worth based solely on intangible assets.

Net worth can be either a positive or negative value based on the value of assets or liabilities a company has. If an entity has more liabilities than assets, their worth will be negative. A common example of entities with negative worth are students, who often have little assets (like property, investments, or cash), but often have substantial liabilities in the form of student loans or credit card payments.

Pricing both assets and liabilities accurately is critical to calculating the real net worth of an entity. While amounts like loans or cash on-hand are simpler to determine, deriving some values like estimates on equipment or the value of land can be more difficult. Intangible assets specifically are hard to assign accurate values to. For entities with intangible assets, ensure the value of these assets are calculated accurately, as they can easily skew an entity’s real worth – creating misleading information.

]]>For some investors, certain companies are targeted investments based on the consistency and yield of the dividends paid by the targeted company. This calculation helps investors determine which companies to invest in and how much taxes to expect to pay on those dividends.

This article will illustrate the dividend yield formula, how to calculate dividend yield step by step, and how to create a dividend yield calculator.

**Dividend yield is calculated through dividing the annual ****dividends**** per share by the price per share for a particular company’s stock then multiplying the product by 100. Data for this calculation can be gathered from the previous year’s financial report or from the last four quarters of dividends paid by the company.**

**DY = (Annual Dividends per Share / Price per Share) x 100**

*Where:*

**DY = Dividend Yield**

- Determine the price per share of a company’s stock.
- Determine the annual dividends per share of a company’s stock.
- Divide annual dividends per share by the price per share to solve.

Following these steps will produce the result expressed in terms of a percentage reflecting the amount of money a company distributed to shareholders for owning a share of its stock divided by the current price of that stock.

An investor is trying to determine the dividend yield for a publicly-traded financial services company in order to make a sound investment decision.

Based on information the investor has gathered, the **price per share of the company is** **$32.00 per share**.

After reviewing the previous year’s financial report, the investor has determined the company’s **annual dividend per share to be** **$1.08 per share. **Since the dividend paid by this company is on a quarterly basis at a consistent rate, the investor is comfortable using this figure in their dividend yield formula as they feel it is an accurate value.

Using this information, the investor will identify the yield by dividing the annual dividends per share by the price per share of this company’s stock and multiplying the product by 100:

DY = (Annual Dividends per Share / Price per Share) x 100

DY = (1.08 / 32.00) x 100

DY = (0.03375) x 100

**Dividend Yield = 3.38%**

Here we can see that the yield for the publicly-traded financial services company is 3.38%, which reflects the amount of money a company will pay its shareholders for owning a share of its stock divided by the price of the share.

If the investor is comparing this yield to that of another company, the investor will be more likely to purchase shares of the company with the higher yield percentage (assuming all other factors are equal).

For investors comparing the yields of multiple companies, building a dividend yield calculator can significantly simplify the process – especially since the way companies pay dividends differs and may require different approaches.

How to calculate dividend yield using two different methods can be integrated into a calculator using Microsoft Excel.

When the annual dividends per share can be accurately calculated from a company’s financial report, the Excel formula to calculate the yield is relatively simple.

The annual dividends per share, share price, and yield cells will be arranged as follows:

After formatting the dividend calculator as shown, the following formula will be inserted into cell C7, which contains the product of the calculator:

**=IMDIV(C3,C5)*1**

Once the dividend yield formula has been entered into cell C7, the annual dividends per share and share price of a particular company can be entered into cells C3 and C5. Based on the earlier example of the publicly-traded financial services company, if the annual dividends per share were $1.08 per share and the price per share was $32.00, then the calculator would appear as the following:

At some points, it may make more sense for an investor to add the dividends paid from the previous four quarters to calculate the annual dividends per share, rather than using the last financial report of a company. When the rate of dividends paid changes or if the financial report has become old and outdated, this method is more sufficient to provide an accurate value for annual dividends per share.

The quarterly dividends per share paid, the share price, and the yield will be arranged as follows:

Once the dividend yield calculator has been arranged as shown, the following formula will be inserted into the annual dividends per share cell of F7. This formula will add the quarterly dividends paid to determine the annual dividends paid per share:

**=SUM(F3:F6)**

Next, the following formula will be inserted into the yield cell of F11 in order to derive the dividend yield from the annual dividends per share and the price per share:

**=IMDIV(F7,F9)*1**

Once this formula has been inserted into the yield cell, the other cells can now be populated with the relevant information. For example, if a company has a share price of $52.00 and quarterly dividends per share of $0.40, $0.42, $0.44, and $0.46, the dividend yield calculator will show the following:

The dividend yield formula is only as accurate as the information used in the calculation. If the dividend rate has changed since a company’s last financial report, use the method of drawing dividend data from the past four quarters to calculate the annual dividends per share value. Using more recent and more similar data such as this will help you produce a yield with higher confidence and accuracy.

Dividend yield represents the rate of return of cash dividends paid to shareholders over the course of a year. This is not the same as the dividend payout ratio, which illustrates how much of a particular company’s net earnings are eventually paid out as dividends to shareholders. The two are very different indicators and should be recognized accordingly. The dividend yield only takes into consideration the annual dividends per share and the price per share.

After calculating the dividend yield of a company, compare the company’s yield to the yield average of the industry that company is a part of. The yield average varies by industry. For example, real estate companies and real estate investment trusts (REITs) have higher average yields, whereas companies specializing in various technologies return lower average yields.

For those wondering “What is dividend yield?”, this type of yield is calculated by dividing the annual dividends per share by the price per share of a particular company. This popular metric represents the amount of cash paid to a shareholder for owning one share of a company’s stock, divided by the price of that share.

For investors comparing different companies to invest in, comparing various yields is helpful to making a sound investment decision, as some companies pay higher dividends more often than others. When calculating this value, make sure the annual dividends per share is accurately calculated to produce a reliable result.

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