# Posts Tagged value

### ANNUITY AND ITS TYPES

Posted by Awais Ahmad in ACADEMIC on November 4, 2012

*Author: Awais Ahmad (comsian027@gmail.com)*

**Annuity:**

An Annuity is a series of equal payments made at fixed intervals for a specified number of periods. These equal payments are denoted by the PMT and can occur at either the beginning or the end of each period. Future and Present Values of Annuity: Future Value of an Annuity can be calculated, where a series of equal payments are made at a fixed intervals for a specific number of periods. The principle applied here is just like Compounding. However, method of calculating Future Value of Annuity differs in Ordinary Annuity and Annuity Due. Similarly, Present Value of an Annuity can also be calculated by using the principle of Discounting, but the method of calculating Present Value of Annuity differs in Ordinary Annuity and Annuity Due. Types of Annuity: Annuity has following types depending on the period of payment.

**1. Ordinary/Deferred Annuity:**

If the payments of Annuity occur at the end of each period, it is called Ordinary or Deferred Annuity.

**Future Value of Ordinary Annuity:**

If equal payments PMT is made at the end of n periods, providing a saving of i, then Future Value of Annuity (FVa or FVAn) can be calculated as:

**Present Value of Ordinary Annuity:**

If equal payment PMT is made at the end of n periods, providing a saving of *i*, then Present Value of Annuity PVA_{n} can be calculated as:

**2. ****Annuity Due**

If the payments of Annuity occur at the beginning of each period, such Annuity is called Annuity Due.

**Future Value of Annuity Due:**

If equal payment PMT is made at the beginning of n periods, providing a saving of *i*, then Future Value of such Annuity *FVA _{n}* can be calculated as:

The only difference between Future Value of Deferred Annuity and Annuity Due is that every term of Future Value of Annuity Due is compounded for one extra period, reflecting the fact that each payment for an Annuity Due occurs one period earlier than Ordinary Annuity.

**Present Value of Annuity Due:**

If equal PMT is made at the beginning of n periods, providing a saving of *i*, then Present Value of such Annuity PVA_{n} can be calculated as:

The only difference between Present Value of Deferred Annuity and Annuity Due is that every term of Present Value of Annuity Due is discounted for one extra period, reflecting the fact that each payment for an Annuity Due occurs one period earlier than for Ordinary Annuity.

**3. ****Perpetuity**

Some Annuities go on indefinitely, or perpetually, and are called Perpetuities. The Present Value of such Annuities is simple to calculate.

**REFERENCES:**

Financial Management – Theory & Practice by *Eugene F. Brigham *&* Michael C. Ehrhardt*

Notes on Investment Analysis and Portfolio Management

Lectures of Respectable Teahers

### Compounding, Discounting and Effective Annual Rate

Posted by Awais Ahmad in ACADEMIC on October 20, 2012

*Author: Awais Ahmad (comsian027@gmail.com)*

**Compounding:**

The process of going from today’s value (Present Value; denoted by PV) to Future Value (denoted by FV) is called Compounding. If *i *is the Interest Rate, then Interest Amount (INT) can be calculated as:

INT ($) = PV x *i*

The Future Value will be the Present Value plus the amount of Interest, so:

FV = PV + INT

FV = PV + PV x *i*

FV = PV (1 + *i*)

If the amount is deposited or invested for *n* periods, the same formula can be written as:

FV_{n} = PV_{n} (1 + *i*) ^{n}

The term (1 + *i*)^{n} is known as *Future Value Interest Factor* and is denoted by FVIF_{i,n}, so:

FV_{n} = PV_{n} (1 + *i*)^{n} = PV (FVIF_{i,n})

In some cases, Interest is paid semiannually, which means Interest is paid twice a year. Similarly Interest payment 4 times a year means Interest is paid quarterly. For such cases, the above formula can be more generalized:

Where *m *is the number of times Interest Payment is made in a year. However, in such case, *i* is taken as *Nominal Rate of Interest*.

**Discounting:**

The process of calculating Present Value (PV) from Future Value (FV) is called Discounting. As we know:

FV_{n} = PV_{n} (1 + *i*) ^{n}

Solving for PV, we have:

Or we can write it as under:

PV_{n} = FV_{n} (1 + *i*)^{-n}

The term (1 + *i*)-^{n} is called *Present Value Interest Factor*, and is denoted by PVIF_{i,n}; therefore:

PV_{n} = FV_{n} (1 + *i*)^{-n} = FV (PVIF_{i,n})

Same as previous case, if the Interest is paid semiannually or quarterly, a more general formula is applicable:

Where *i* is taken as *Nominal Rate of Interest*.

**Effective Annual Rate (EAR):**

Effective Annual Rate is defined as the rate which would produce the same Future Value, if annual Compounding had been used. It is also called *Equivalent Annual Rate*, and can be calculated as:

As we have taken Annual Compounding, therefore n is not shown in the formula, and *i* will be taken as *Nominal Rate of Interest*.

**References:**

Financial Management – Theory & Practice by *Eugene F. Brigham & Michael C. Ehrhardt*

Investment Analysis & Portfolio Management – Lectures

### Market or Investment Portfolio, Investors, Securities, Time Value of Money Concepts

Posted by Awais Ahmad in ACADEMIC on October 19, 2012

*Author: Awais Ahmad (comsian027@gmail.com)*

**Investment/Market Portfolio:**

When an investor invests in multiple

stocks/securities, it is called Investment Portfolio. Maintaining a Portfolio

is a very important step taken by investors. By maintaining a Portfolio, Risk

can be mitigated / minimized by maintaining a portfolio and higher margins of

profits can be earned. In this case, if one stock/security defaults, it does

not necessarily mean Investor is also in loss. Instead, investor can compensate

the loss of one stock from other stocks/securities. Fig. 5 shows how

maintaining a Portfolio minimizes the Portfolio Risk. Fig shows that Portfolio

size is taken on x-axis and portfolio risk on y-axis, which results a curved

graph.

**Classification of Investors:**

Investors can be classified on the basis of their risk-taking/bearing capacity. How much risk an investor bears, depends on investor’s personal capacity, attitude, interest and behavior. For example:

**1.****Risk Seekers**

Risk seekers seek for riskier investment. They are capable of assuming a higher risk and have strong and healthy financial position.

**2.****Risk Avoiders**

They avoid riskier investments, because they have not strong and healthy financial position. They choose those instruments, which have less variation in returns.

**3.****Risk Bearers**

Risk bearers fall in between the above categories. They choose moderate levels of risk they can bear according to their capacity.

**Hedging:**

Risk reduction is known as Hedging. They do it by using *Derivative Instruments*.

**Security:**

A Security refers to a publicly traded financial instrument, as opposed to a privately placed instrument. Securities have greater liquidity than otherwise similar instruments, which are not traded in Open Market. Security is considered to be an insurance against an emergency, according to banking definitions.

**Classification of Securities:**

The securities have been classified according to the functional operation aspects as under:

**1.****Intangible Securities**

These are personal exclusive undertakings by a party to pay the amount of advances outstanding against a borrower. Examples of such securities are Demand Promissory Note, bill of exchange or a Bond, Guarantee and Indemnity etc.

**2.****Tangible Securities**

These are the securities which can be realized from sale or transfer. Examples of such securities are Shares, Stock, Land, Building and Goods.

**3.****Prime Securities**

These are also called Primary Securities. Such securities are main covers for an advance and are deposited by the borrower himself. When a depositor of term deposits offers his *Term Deposit Receipt* to cover and advance, it is the Primary Security according to banking term.

**4.****Collateral Securities**

These are the securities provided as an additional cover for an advance, where either he security is not very stable in value, or where the realization of the security to cover the outstanding amount of balance is difficult. In case of the default by borrower, bank has the authority to sell these shares of security and adjust the advance.

**5.****Movable Securities**

These are the securities, which are legally and physically both in possession of the lending bank. Examples are Term Deposit Receipts, Goods, Vehicles and Merchandise etc.

**6.****Immovable Securities**

These are the securities, where the legal possession or right to takeover is entrusted to the lending bank, but the physical possession remains with borrowers.

**7.****Government Securities**

These are the long-term securities issued by the government for financing social programs. They are perceived as Risk-free, are highly liquid and carry attractive coupon rates. Like T-bills (Treasury Bills), government securities are sold through auctions and are actively traded in secondary markets.

**Time Value of Money:**

The theory of Time Value of Money states that the value of money decreases with the passage of time. This concept can be described as “A Dollar in hand today is more worth of a Dollar tomorrow”. This happens because of *Inflation*. Inflation is a situation, where the prices as a whole are increasing. The rate at which the prices are increase is known as *Inflation Rate*. Two terms are necessary to explain while discussing Inflation and theory of Time Value of Money:

**1.****Nominal Interest Rate/Quoted Interest Rate:**

Nominal Interest Rate is a rate at which money invested grows. Banks generally offer Nominal Rate of Interest to the depositors.

**2.****Real Interest Rate**

Real Interest is a rate, at which the purchasing power of an investment increases. Market Interest Rates are Nominal Interest Rates.

**Relationship of Inflation, Nominal and Real Interest Rates:**

Real Interest Rates, Nominal Interested Rates and Inflation Rates have strong relationship with each other, which can be expressed in the form of an equation:

The above equation shows that if Inflation Rate increases, then Real Interest Rate decreases and vice versa.

Another approximate relationship also exists between the three rates:

It means, by subtracting Inflation Rate from Nominal Interest Rate, the approximate Real Interest Rate can be calculated.

**References:**

Financial Management – Theory & Practice by *Eugene F. Brigham, Michael C. Ehrhardt*

Management of Banking and Financial Services by *Padmalatha Suresh & Justin Paul*

Handouts Investment Analysis and Portfolio Management

Lectures on Financial Investment and Portfolio