Importance of Equivalent Annual Annuity

What equivalent annual annuity means ? The method of assessing projects with a diverse duration of life is known as Equivalent Annual Annuity or EAA. The overall viability of financial projects can also be determined by specific traditional metrics to assess the profitability of the projects like IRR, Payback period or NPV etc. but to find out financial efficiency of projects equivalent annual annuity is the right metric.

How to calculate equivalent annual annuity?

To explain the present net value of a sequence of investments for a certain period for the equal flow of cash formula is used in capital budgeting to calculate EAA. The formula is

C = (r x NPV) / (1 – (1 + r)^-n )

Where:

R is the discount rate of the project

NPV is the Net present value of the cash flows of the project

n is the life of the project in years

The current worth of an investment with irregular flows of cash is used as NPV in the formula. The period of the investment or n’ is not considered while using NPV to compare two investments in different projects. The NPV of the financing for 15 years will be higher than the investment for a period of 4 years. The formula of an equivalent annual annuity can help in factoring the period of the investment by showing its NPV as a sequence of flow of cash.

How to calculate equivalent annual annuity in Excel?

Usefulness of the formula of EAA

What does the equivalent annual annuity tell us ?
The formula of the EAA can be useful to compare two projects with the same NPV, but with different life, term say 15 years and 4 years. The project with 4 years life term will show a higher flow of cash in the formula of EAA as the return will be received sooner by it than the project with 15 years life term. This formula should be applied while distinguishing two investments in real life, as it may not be possible otherwise.

The formula of EAA can also be useful while reinvesting in a project. While using this formula to evaluate the possibilities of reinvestment in a project with a short life term, the income on the investment will not be considered. The reinvestment with similar earnings will not be regarded as the present investment while using this formula for comparing the EAA of two projects based on their life term.

Derivation of the formula of the Equivalent Annual Annuity

The formula of the EAA has been derived from the equation of the annuity payment for a given value. The relevance of using the method of EAA is based on the replacement of present value with NPV or net present worth.

Example for using the formula of Equivalent Annual Annuity

Suppose there are two machines – machine A, a machine to mix dough and machine B, an icing machine. Let the life span of machine A is 6 years and that of machine B is 4 years. Now the owner of a doughnut shop wants to buy one of these machines. So he will compare their equivalent annual annuity by using NPV and life span of each machine. Suppose the NPV of machine A is $4 million and Machine B is $3 million and the cost of capital of doughnut shop is 10% the EAA of each device will be calculated as under

On the basis of the EAA of both the machines it is advisable for the doughnut shop to invest in machine B due to its higher EAA.

What does perpetuity mean in business ?
Perpetuity – Does It Really Mean Forever?

Browsing through financial-related literature, you will sometimes meet the word “perpetuity.” In the corporate and investing world, the term perpetuity generally means indefinitely. It’s basically saying “eternal,” but with a financial connotation.

Understanding what perpetuity is can help corporate decision-makers or investors when it comes to a better understanding of how money flows.

Perpetuity – What Is it And Importance

In the financial world, perpetuity is commonly used by companies to place value on certain investments like real estate, stocks, and bonds. However, it’s very widely used on annuities. In theory, receiving payments from such investment doesn’t end. Thus, you can consider it as perpetual.

However, what is usually considered as perpetuity investment is when a firm or individual buys a perpetuity-based investment and expect to receive payment indefinitely. Generally, such kind of investment will require an upfront payment either in a lump sum or paid over some time.

For example, an investor purchases a stock that gives the shareholders a handsome dividend. If the company is already mature and announces that they will be paying dividends regularly onwards, then you can consider it theoretically perpetual.

The same idea can be applied to real estate investors. For example, an investor buys a property and rents it out, he or she can receive payments indefinitely. Of course, this is assuming that the investor will maintain the property, so there will be willing renters.

Annuities – The Most Common Perpetuity Investment

When you talk about perpetuity investment, most people would assume you are talking about annuities. The reason for this is because annuities are modeled to pay the investor a specific amount of money indefinitely once the investor has paid his or her part of the bargain.

It’s the reason why annuities are a common financial term in the realm of retirement planning. What happens is an investor pays the insurance company upfront. In return, the insurance company will pay the investor with regular payments that will go on indefinitely. And yet, despite being popularly considered as a perpetuity investment, not all annuities can be considered as such. This is because some are annuities are not indefinite.

The Formula – Perpetuity calculation

While the term perpetuity denotes an investment that lasts indefinitely, there’s a formula that can be used for some investment to determine it’s present value. The formula is very simple:

Present Value = Dividend Or Payments / Discount Rate
When to use perpetuity formula ? For example, if a bond pays $10 per year indefinitely and it has a discount rate of 5%. Your calculation would like like this – $10 / 0.05 = $200.

With this calculation, the bond’s present value is $200.

Is It Really Forever?
What does perpetuity period mean ?

When hearing about receiving payments forever, it sounds too good to be true. Hence, you may ask if it is truly indefinite.

The short answer is yes. However, it’s not all that great. Keep in mind that, in most cases, the amount you receive is fixed. As time moves forward, inflation will start chewing through the amount of money you receive. In other words, you will still receive the same amount, but it’s buying power is slowly diminishing because of inflation.

Having said that, there’s a form of perpetuity that counterbalances the effect of inflation, and its called growing perpetuity. With such kind of perpetuity, you will not receive a fixed amount indefinitely. Instead, it will be growing to counteract the effects of inflation. Keep in mind that growing perpetuity is primarily designed to offset inflation. And, that does not mean that the buying power of the money you receive will also increase.

Like most things in the investment world, there’s no such thing as a free lunch. With growing perpetuity, it is typical that the money you receive will be lesser when compared to traditional perpetuity. However, you will enjoy the benefit of inflation protection. With traditional perpetuity investment, the early years will have a high payment. However, the value of payments will gradually deteriorate due to inflation.

Wrapping It All Up

Perpetuity in the financial world is a term that denotes an investment that will give payments until the end of time. However, this is only theoretical as real-world perpetuity investments will typically come with a clause that triggers the end of the payments. Even if it is a true perpetuity investment that will pay forever, inflation would still slowly deteriorate the value of the received payments.

Things To Know About Preferred Stocks

A preferred stock is a type of hybrid stock that provides dividends prior to any dividend paid to common stocks (have a higher claim to dividends or asset distribution than common stockholders) including properties of both an equity and a debt instrument.

So, is preferred stock a hybrid security ? Yes.
Why preferred stock is hybrid security ? It is because preferred stocks including properties of both an equity and a debt instrument and have a higher claim to dividends.

Importance of preferred stocks

Preferred shareholders have priority over common stockholders when it comes to dividends

The rank of preferred stock is higher than usual stocks but in the conditions of claim, it ranks lower than bonds. In terms of liquidation and dividend payments preferred stock is better than common stocks. The terms of preferred stock are explained in the articles of incorporation or association of the issuing companies. Moreover, preferred stocks are evaluated like bonds by major companies of credit rating. But these stocks are rated lower than bonds because the dividends of stocks are not guaranteed as the payment of interest on the bonds.

Features of preferred stocks

The shares which have a naumber of features not found in normal stocks are known as preferred stocks. Some of the features of the preferred stocks may include:

Preference in dividends: The preference of preferred stocks is to pay dividends but does not assure to pay it which should be paid while paying dividends on common stocks. There are two types of preferred stocks- non-cumulative and cumulative. The number of payable dividends is accumulated to pay later on, in case of cumulative preferred stocks, if the company does pay the passed’ dividends at the scheduled time. All the amounts of unpaid passed’ dividends on cumulative stocks become arrears on dividends. But in case of non-cumulative preferred stocks, you may lose passed dividends if they are not declared by the issuing company.

Preference in assets: In the case of liquidation, preferred stock is considered as an asset as it does not have a predetermined value to be liquidated. The money invested at the time of the initial issuing of stocks is represented in terms of preferred stocks. They can be liquidated at their value in the stock market, at par or at the negotiated price. This feature makes preferred stocks better than common stocks.

Call-ability to allow the holder to redeem it before maturity: Preferred stocks in the U.S. usually have a provision to call which allows the issuing company to buy back the stocks as per its discretion.

Higher yields in dividends: Most of the preferred stocks have a fixed amount of dividend but in certain cases it can be negotiable. Normally dividend is mentioned in terms of certain percent of the face value or a set amount but if it is negotiable then it can vary according to the benchmark index of the interest rate.

Non-voting: Some of the preferred stocks have special rights to vote for the approval of exceptional events like electing the directors but they must have arrears of preferred dividends many times to avail this right. Usually, preferred stocks have no voting rights.

Types of preferred stocks

Along with cumulative and noncumulative preferred stocks, other types of these stocks may comprise of:

Prior preferred stock: These stocks are designated as the stocks of the highest priority. The company makes payment on the prior preferred stocks if enough money is available with the company to meet the schedule of the dividend on the preferred stocks. So the risk of credit is less in prior preferred stocks than preferred stocks of other types.

Preference preferred stock: These stocks are preferred than other preferred stocks because they are issued by the companies when they issue more than one issue of preferred stocks and rank them on their seniority.

Convertible preferred stock: A predetermined number of these preferred stocks can be exchanged with the common stocks of the company. But once to stocks are converted into common stocks cannot be converted to preferred stocks again.

Exchangeable preferred stock: These preferred stocks can be exchanged with other types of securities.

Participating preferred stock: The holders of these stocks can get their predetermined dividend regularly even if the company performs well or not. But they can get an additional dividend from the company if the company has achieved its financial targets.

Perpetual preferred stock: The date of the refund of invested capital to the investors in these stocks is not fixed. So, for this reason, these stocks are issues without any date of redemption.

Putable preferred stock: These stocks are privileged with the Put’ option which allows their holders to force the issuing company to redeem their stocks when required.

Monthly income preferred stock: These stocks have a combination of subordinated debts and preferred stocks. The holder of these stocks earns a monthly income on their investments.

Usage of preferred stocks

A company uses preferred stocks as a source of financing just like funds from the pension earning people. Sometimes, companies go into arrears of dividends by delaying their payment against some penalty. It can affect the credit rating as well as a negative effect on the financial contracts of the company as it is not meeting the required conditions. Still, it is better than traditional debt as the company can be in default if the payment of the debt is missed.

Preferred stocks are occasionally used by the companies for creating stocks with conversion features or features of forced exchange or to prevent the aggressive takeovers to avoid any change in control. Some of the companies, while issuing preferred stocks, authorize their board of directors to determine the terms and conditions of the stocks by mentioning provisions in their charters. In this way, these stocks are used as blank checks’ to defend the company from takeover by assigning them the superpower of voting or a very high value of liquidation.

The company must have enough money to repay the capital of the holders of preferred senior’ stocks when it is going bankrupt. In this situation, they can ignore the payment of junior’ stocks. For this reason, while issuing preferred stocks for the first time, their documents may include provisions to prevent the issuing of new stocks to be claimed as senior stocks. There can be a senior, equal or junior relationship between a series of preferred stocks and preferred stocks of other series of the same company.

Total stock return for stock investors

Most investors usually have multiple options for investing their money. While the investors would like to maximize the return on their investment, they would also like to ensure that their investment is safe, they can get the principal amount invested back whenever they wish. For many investments like stocks or mutual funds the return on the investment consists of both the dividend which is declared by the company and the increase in the value of the stock. Hence the Total Stock Return, abbreviated as TSR is the relevant parameter for evaluating stock market investments.

Definition

The Total stock return or combined stock return includes the total return on the stock investment for the investor. Typically the company will declare a dividend for the stock annually, and the value of the stock could increase, though it may also decrease. For calculating the TSR the dividend which is declared will be reinvested in the stock. In some cases the company may also declare some bonus shares for the share holders of the company. The TSR is usually expressed as a percentage of initial investment, though in some cases the cash TSR is calculated.

Formula – How to calculate total return ?

The formula for total return ratio is:

TSR = ( (P1-P0)+ D )/ P0

where P1 is the value of the stock at the end of the period for which the TSR is being calculated,
P0 is the stock value at the time of purchase,
and D is the dividend declared if any.

The first part is only looking at the increase in the stock price, while the second part is the dividend which is declared. While most investors prefer to calculate the TSR percentages for the various stocks before finalizing their investment, some investors may wish to use the cash TSR which is defined as cash TSR = (P1-P0)+ D

There is also an alternative way of calculating the TSR combining the increasing in stock value and dividend yield

TSR = Capital gains yield + Dividend yield for the stock

Importance

One of the reasons why the TSR is important for an investor is because the performance of various stocks varies depending on the industry sector. For many of the high dividend yield stocks, the share prices will not increase significantly over a period of time, due to low growth potential. In other cases for high growth stock, no dividends may be declared, though the stock prices may increase faster. Hence the investor should look at the overall picture, consider both the dividends received and the increase in the stock prices for calculating the TSR.

Typically the investor should check the TSR of the company over a period of several years, to find out trends and also compare the TSR with other companies in the same sector. He can also compare the TSR with the benchmark indices for the related sector. This information will help the investor plan his finances and know what kind of returns he can expect from the stock if he chooses to invest in it. There may some brokerage and other charges for purchasing the stocks, and these are usually not considered for calculations.

Capital gains yield for investors

Investors are always interested in getting the best returns for their investment. For their stock investments in the various companies the dividend declared is not the most accurate way to determine the total returns on their investment. Many companies do not payout all their net income to the shareholders as dividend since they reinvest some of the income to help the company grow faster. The growth of the company usually results in an increase in the stock price. Hence another parameter the Capital gains yield, abbreviated as CGY is also used by investors to measure their returns.

Definition

The Capital gains yield measures the increase in the value of a particular security like shares over a period of time.

The increase in the security value is compared to the original value of the security. The CGY will be positive only if the value of the share or other security will increase over a period of time. The CGY is an important parameter for an investor who is interested in investing in growth stocks, which do not declare large dividends or have not declared any dividend for many years. Investors should be aware that capital gains are usually taxable in most countries, though the taxes can be offset by other losses.

Formula

The formula for expected capital gains yield is :

CGY = (P1-P0)/P0,
where P0 is the initial price of the security or stock, while P1 is the price of the stock/security at the end of the period which is being considered. The CGY formula is a formula which calculates the rate of return. The formula for can CGY does not consider any dividends which may be paid on the stock investment, which are calculated separately with the dividend yield formula. The CGY is combined with the dividend yield to determine the total return for the stock. If a company does not pay any dividend the total stock return is equal to CGY

Expected capital gains yield calculator

Explanation

Investors should consider both the CGY and the total returns from their investment. In some cases the dividends may form a large part of the returns for investment, and CGY does not include the dividend. The share prices for a company may either increase or decrease over a period of time or remain the same. So it is possible that the CGY is negative for a company, resulting in a capital loss for the investor. However, despite having a negative CGY, the investor may make a profit, if the dividend yield for the business is substantial.

Analysis

The CGY of a company is unpredictable and varies depending on the companies performance and other macroeconomic factors.It is usually calculated at different periods, like annually, monthly or quarterly. It is different from the dividends of the company which are usually paid to the shareholders on specified dates. Companies which are paying high dividends usually have lower capital gains since the amount paid out, cannot be reinvested in the company. Some companies declare low dividends yet have a higher CGY, since the profit is mainly reinvested in the company to help it grow faster. There are also companies which do not pay dividends and have no capital gain or negative capital gain.

Investors can use the CGY to get information about the price fluctuation of the share and decide if they wish to invest in the share.