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Posted: 2015-02-23

**Beta:**

Beta is a standardized estimation of systematic risk based upon a covariance of an asset with a market portfolio.

**Estimating Beta and Determining a Project Beta **

To use Capital Asset Pricing Model (CAPM) an analyst must have to calculate or estimate beta by calculating cost of equity. You have to face many challenges while estimating the beta. There are different types of method of beta estimation one amongst them is method of estimating a company’s beta for its stock by using market model regression of that company's stock returns (Rj) besides market returns (Rm) where Time periods (T) are 24

R_{jt} = ~~a~~ + ~~b~~ R_{m,jt} = 1, 2 . . . T(24)

Where the sign ~~a~~ is the estimation of intercept and ~~b~~ is the estimation slope of the regression equation which is used as an estimate of beta.

**The Security Market Line (SML) **

Security market line is the graphical presentation of the Capital Asset Pricing Model. It is quite common know that relevant risk measure for an individual risky asset is the covariance of that security or asset shown as covariance of market portfolio (COV_{i, M}). So, a risk-return relationship can be drawn shown as under:

We take the systematic covariance in other words Market beta variable (COV_{i,M}) as the risk measure. Return portfolio of market is given symbol as (R_{M}). It should be consistent with its own risk make the covariance of the market with. Covariance of the market with itself is the variance of the market all market rates of return COV_{M, M} = ø^{2 }_{M. }The equation for the risk-return becomes as under:

__RM - RFR__ (COV_{i, M})

E(Rj) = RFR + ø^{2 }_{M}

Defining (COV^{i, M})/ ø^{2 }_{M} as beta (β_{i}) this equation can be stated:

E(Rj) = RFR + β_{i }(RM - RFR)

Relation between Beta and SML

Beta is often considered as a standardized measure of systematic risk also called market risk. Particularly, the covariance of an asset or security i with the market portfolio (COV_{iM}) is a relevant risk measure. Betas are standardized risk measure as these relate the covariance to the variance of a market portfolio. Resultantly, the market portfolio has a beta is 1. Consequently, if the β for an asset is above 1.0, the asset has higher normal systematic risk in contrast to the market, which means that it is more volatile than the overall portfolio of market but if the beta is less than 1 then it has lower systematic risk than market index.

Beta and SML are interrelated as beta is also used while calculating SML.

**TIME VALUE OF MONEY**

Time value of money is the most important subject of Finance. A person often has to make decisions like saving money for the future use and borrowing money for current expenditures. Then one have to find out the profit amount he need to invest. If the matter is for saving, then he has to decide for the cost of borrowing. So, there is always a cost for the usage of money. An amount today should be much higher after five years. The percentage amount of cost incased after five years is the time value of money. In the similar way many times we have to evaluate transactions with present and future cash flows. If a person has lower amount should expect the higher amount in future and if the person relieve a lower amount today will have to pay higher in the future. The period by period calculations of the amount of money are called mechanics of time value of money. A person must discount the future cash flow as there is a time value of money in the shape of interest rates determinants given in the next part of the report.

**Solving for Interest Rates **

We can calculate or solve for the interest rate when all the other factors of interest rate formula are available. Example:

Suppose a person deposit of $100 in bank to generate a payoff of $111 after one year. With this information, we can derive the interest rate where present value is $100, future value of $111 and Number of period is 1

Equation: FV N= PV (l + r)^{ N}

Where N = 1, With PV, FV, and known, we can solve for r directly:

1 + r= FV/PV

1 + r= $111/$100 = 1.11 r= 0.11, or l1%

**Solving for Number of Periods:**

We can also calculate or determining that how long it will take an investment of $10000000 to double in value. Current Interest rate is 7% compounding annually.

Equation: FV N= PV (l + r)^{ N}

(l + r)^{ N}=FV/PV=2

=N ln (1+r) =in(2)

=N= in(2)/ln(1+r)

=N= in(2)/ln(1+1.07)

=10.24 years

**Annuity Due:**

Comparing to a simple annuity whose payments occurs at the end date of the period, in an annuity due a series of equal payments amounts occurring at the beginning of every period. So, we can calculate the future value of annuity due by adding 1 to the exponential power of the simple annuity formula for the future value or can multiply with (1+i) with the farmula.

Bond Valuation

A long term debt security with contractual obligations regarding interest payment and redemption is called bond. There are certain factors related for the bond valuations discussed as under:

**Estimating cash flows:**

There are two types of cash flows inflows called receipts and outflow named payments. We need to estimate both with the appropriate time period of flow of these cash flows. These are calculated by estimating the initial cash out flow and the expected payments.

**Determining the appropriate interest rates:**

The estimated interest rate is also a mandatory factor to determine for the valuation of bond. We can calculate it by estimated market rate of bond for the same business in which we are going to invest.

**Relation of Interest rate with Bond Value:**

Changing the interest rates does affect the value of the bond. It has an inverse relationship with the interest rate increases the value of bond deceases and if the interest rate decreases the value of bond increases.

**APPROPRIATE DISCOUNT RATES DETERMINANTS**

This part of the report describes the interest rate & feature which plays a vital role and should be kept in view while calculating or estimating interest rate. It is important that interest rate should be calculated while adding up all of these features. All of the interest rate determinants are discussed with the equation of calculating interest rate as under:

r (Interest Rate)= Real risk-free interest rate + Liquidity premium + Default risk premium + Maturity premium + Inflation premium

**Risk-free interest rate**

A Risk free interstate is that where there are not caches for loss in the investment. You can earn on a percentage of the value of money without investing in any business or going for any sort of risk of loss. The examples are the saving accounts in the banks and Bond issued by the government or corporation. Risk free rate is often kept as a benchmark for the minimum profit of any business to pay.

**Liquidity Premium:**

Liquidity Premium is another feature of interest rate determinants. It is frequently used for the determination of proper discount rate. It is assumed to be the compensation for the liquidity or in other words compensation for the time of amount block for the purpose of investment to get back. More the time the amount is blocked to get back higher it the compensation or percentage of interest would be.

**Inflation premium**

A common term is used called inflation which causes devaluation of the currency due to the increasing prices and deceasing buying power of any consumer. The inflation premium adds the percentage to the interest rate according to the percentage of inflation is increased.

**Default risk premium **

Default risk premium is compensation. This interest rate determinant is compensation for the chances of default of the firm invested in. The compensation increases as the financial position and credulity of the investee is decrease. Lower the credulity & higher the compensation you will get.

**Maturity premium**

This interest rate detriment resembles with the liquidity premium in which the compensation of amount is paid for the accessibility of the amount or chances of withdrawal from business. But in maturity premium the compensation is paid for the permanent blockage of amount for the time period invested in business. An example can be a fixed account in bank in which you can’t withdraw your amount for a specified time period. Longer the period higher the compensation would be paid.

Adding all of the interest rate determinants you will get the real rate of interest which is risk free rate added up to the different compensations for different reasons.

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