## Fundamental analysis

The objective of fundamental security analysis is to appraise the intrinsic value of a security.The intrinsic value is the true economic worth of a financial asset.The fundamentalist maintain that at any point of time every share has an intrinsic value which should in principle be equal to the present value of the future stream of income from that share discounted at an appropriate risk related rate of interest.

The fundamentalist attempt to estimate the real worth of a security by considering.The real worth of a security by considering the earning potential of a firm which in turn will depend on investment environment factor such as state and growth of national economy,monetary policies of the reserve bank of India corporate laws environment and the factor relating to the specific Industry such as state of product and the growth potential of the industry.

It will depend to a large extent,on the firm’s competitiveness,its quality of management operational efficiency profitability,capital structure and dividend policy.

Fundamental analysis has consist with three factor.

1)Economy analysis

2)Industry analysis

3)Company analysis

First we consider economy analysis.

1)Economy analysis-An investment in the equity of any company is likely to be more profitable if the economy is strong and prosperous,so the expectation of the growth of the economy is favorable for the stock market.

Not all industries grow at the same rate,do all companies. The growth of a company or an industry depend basically on its ability to satisfy human wants through production of goods or performance of service.

Investment climate in an economy can be observed from the GNP and its components.GNP stand for gross national product,the broadest measure of economic activity used to determine where the national economy is where it has been and where it has been and where it is going.

Monetary and financial conditions are reflecting these demand supply gaps as well as the onset of a durable pick-up in aggregate spending.Banks non-food credit is beginning to dip after expanding abuse 30 percent for three years in succession.Driving up money supply and squeezing overall liquidity.The growth of bank.Credit has favored retail lending particular housing real estate trade,transport and professional service and non-banking financial companies sector which were not significant in the credit market.

The economic indicator are grouped into leading indexes to help in analysis and for casting.The coincidal indicator include GNP in constant or “real” terms,corporate profits,industrial production unemployment and the producer price index.There are many coincidental indexes,but these are the most common.The indicator tell us what is happening in the economy,but they do forecast the future.

The leading indicator tell us what to expect in the future.Some of the popular leading indexes are fiscal policy.Monetary policy,GNP deflator productivity,consumer spending, residential construction and stock prices as measured by the RBI etc.

The lagging indicators turn after the movement in the coincidental indicators.The best-know lagging indicator is the prime rate,which usually turns down a few months or quarters after a turn down in the economy.

Commercial paper rates, capital,expenditure the inventory sales,ratio retail sales and the consumer price index are other important lagging indicator.

Significance and Interpretation of the economic Indicators.

The investor makes an analysis of the economy primarily to determine an investment strategy,It is not necessary to make their own economic forecasts.The primary responsibility is to identity the trends in the economy and adjust the investment position accordingly many of the published forecasts are excellent and provide the necessary perspective.

The variance for analysis have their own significance.The GNP is nominal and real terms is a useful economic indicator.

2) Industry analysis

The industries that contribute to the output of the major segment of the economy vary in their growth rate and in their overall contribution to economic activity some have growth more rapidly than GNP and offer the expectation of continued growth other have maintained a growth comparable to that of the GNP.A flow have been unable to expand and have declined in economic.

Significance seeking industries that are expected to grow at faster than the “real rate of GNP for the future seems to be a logical starting position.

In a broad sense an industry might be considered a community of interests.This concept would reflect the idea of a group of people coming together because they do a certain type of work or produce a similar type of production.Such group would include agriculture as well as manufacturing,mining and merchandising.

The classification of an industry is important when we analyze its growth.Each industry takes the share of the GNP with every other industry .Thus,the manufacturing industry compete with agriculture, transaction and public utilities.

This inter industry competition is important and within each major industry classification.The product or service-oriented segments compete for share GNP.

A second reason for a domination in the industry growth rate is the nature of the technological change itself.The basic types of major technological changes help to produce an old product more cheaply or a completely new product on mass basis.

A high priced commodity or service is changed a low priced one making it available to a large market.

A third factor that tend to limit the growth of an industry is competitive pressure from other industries.The industry that first experienced a technological change may be restrained by the development of a new industry,competing directly for raw material and thus tending to raise costs for the original industry and limit its expansion potential.Sometime ,new industries are directly competitive with the old product or original product.

Fourth and final factor that might reduce the rate of growth of an industry is a decrease decreased population growth.In order for a product to expand its output at an increasing rate,per capita output would have to grow at an increasing rate.For this to occur,consumers would have to spend more of their income.

The consumer’s income does not increase as fast as the growth of the product,because the economy grows more slowly than an industry experiencing rapid growth, and so it is unlikely that the industry’s growth rate can be sustained.

### Investment classification of industries

• The discussion upto this point has been about the economic classification of industries.Investment services provide basic industry information more closely related to our needs and concentrate more on companies within the industry.If an industry appears yo offer attractive future benefit,we can easily translate this into the probability that a company’s equity will allow us to share in the industry’s prosperity.

Selecting an Expanding Industry

An understanding of the growth pattern of an industry and of the stages of growth pioneering,expansion and stagnation as well as the sign of obsolescence, should help us reach a solution to the problem of where to invest.the investor should select industries that are in the expansion stage of the growth cycle and should concentrate on these areas.Except for special circumstances brought about by individual portfolio needs,an investor should not invest in industries in the pioneering stage unless he or she is prepared to accept a great deal of speculative risk,comparable to that assumed by the innovator or speculator

3)Company Analysis

The specific market and economic environment may enhance the performance of a company for a period of time,it is ultimately the firm’s own capabilities that will judge its performance over a long period of time .

A)Marketing first variable that influences future earning in terms of both quality and quantity is the marketing results of the firm in comparison to industry.This in turn is determined by the share of the company in the industry,growth of its sales and stability of sales.A company in a strong competitive position will provide greater earning with more certainty.

1.Sales:The rupee amount of annual sales and its share market help to determine a company’s relative competitive position within the industry and how successful it has been RI meeting competition.Here to rank the company, the companies should be comparable in like product groups

2.Growth in sales:The annual growth in sales is equally if not more important than the amount of sale in determining the competitive position of the company.Expanding annual sales and adequate financing firm will be in a better position to earn money.

3.Stability of sales:Stability of sales will provide stable earning for a firm,other things of plant .Aggregate sales of various industries vary in their degree of stability and company’s sales should have same pattern as that of the industry.

B)Accounting policies:There is a risk of faulty Interpretation of corporate earnings and consequent bad judgement in purchasing,keeping or selling stock.

1)Inventory pricing:i)Cost or market value methods in which case inventory is priced at lower of average cost of inventory or the market price.

ii)First in first out,method in which the inventory is priced at the cost of last purchase and the cost of goods first acquired are adjusted in cost of sales.

iii)Last in first out method is just opposite of the FIFO method.Here cost of inventory is on basis of first purchase and last purchase and last purchase cost is adjusted in cost of sales.

2)Depreciation methods:The depreciation for wear and tear of the machinery and so reduction in value of assets is provided as fixed expenses.The change providing provision for depreciation will thus affect net income and also affect net income and also affect the valuation of the assets.

3)Non-operating Income:Non-operating income such as dividend income,interest,etc,generally occur to the firms.To avoid error of judgement these incomes should be studied.In certain accounting period the non-operating income for reason such as gains or losses due to sale of fixed asset of the comoany.

C)Profitability-We are interested in income amount stability a growth of these earning particularly the amount and when they will be recieved.This rest on the assumptions that the profitability the relationship between the sales and earning,will remain constant to study the relationship if expenses and sales,one needs to study the trends of the profitability ratios, namely, gross profit margin,net profit margin,earning power return on equity and earning per share.

D)Dividend policy:In most of the cases it is observed that the management tries to have a stable dividend policy and increase the dividend only when they expect they will be able to maintain the higher rate of dividend in future.

## Technical analysis

Technical analysis is probably the most controversial aspect of investment management.

The technical analysis is a delusion that it can never be any more useful in predicting stock performance than examining the inside of a dead sheep.In the ancient Greek traditions.

The term Technical analysis used to mean fairly wide range of techniques.All based on the concept that past information on prices and trading volume of stocks gives the enlightened investor a picture of what lies ahead.

The technical analysis believe that the price of a stock depends on supply and demand in the market place and has little relationship to value, if any such concept even exists price is governed by basic economic and psychological inputs so numerous and complex that no individual can hope to understand and measure then correctly.

A trend is believed to continue until there is definite information of a change.The past performance of a stock then be harnessed to predict the future.

## Technical analysis assumption

1) The market and or an individual stock act’s like a barometer rather than a usually discounted in advance with movement result of informed buyers and seller at work.

2)Before a stock experience a mark-up phase, whether it be minor or major a period of accumulation usually will take place conversely,before a stock enters into a major a minor downtrend,a period of distribution usually will be the preliminary accordance.

The ability to analyze accumulation or distribution within neutral price pattern will be,therefore,a most essential prerequisite.

3)The third assumption is actively tied into the first two It is an observation that deals with the scope and extend of market movement in relation to each other.As on example,in most cases,a small phase of stock price. consolidation, which is really phase of backing and filling will be followed by a relative short-term movement up or down in the stock’s price on the other hand a larger consolidation phase can lead to a greater potential stock price move.

### Technical v/s fundamental analysis

With a view to making a board comparison between technical analysis and fundamental analysis fundamental analysis

1)Fundamental study the course not the should,they make their decision on quality,value and depending on their specific investment goals,the yield or growth potential of the security .

2)Fundamental analyst are seldom expect meaningful profits in less than one year.

Compare with long-term investor ,technician seek to keep their money working as profitability as possible at all times.When trading,they want to score profits quickly and if the stock or market does not perform anticipated they are willing to trade as small fast,loss

#### What technical analyst think

1)Technicians believe that behind the fundamental are important factor:-At any given time,some investor have gains in the stock and usually some have losses.Those with gains want to safeguard them and if possible build them higher,they will hold the stocks.

Each of these decision points can be spotted on charts current configuration to show the action of the past week or so,intermediate and long-term pattern to find the previous important price level at which selling is likely and interim and long-term high point from which the stock is started to move down in the past.

2) Technicians act an the what no the why:-They recognize that formalities and pattern signify changes in real value as the result of investor expectation,Hope’s,fear industry development and so on.

3)Technician are not committed to buy and hold policy:-As long as the trend is up ,they will hold a stock.This may be for months or even years.

4)Technician do not separate income from capital gain:-They look for total return,that is,the realized price less the price paid plus dividend received.This is a sharp contrast to most long-term investor who buy a high-dividend paying stock and hold it for years.

5)Technicians insist that the market always repeats:-What has happened before will probably be repeated again,therefore,current movement can be used for future projections

6)Technicians use charts to confirm fundamental:-When both agree,the odds are favorable for profitable movement if the trend of the overall stock market is also favorable.

## Primary market

Primary market Primary capital market is a conduct of a new securities. New or listed companies may make the public issue of securities by new companies for the first time. In the IPO or public offerings by the established companies securities are sold to the public all individual and institutional investors.

The decade of eighties, however,with eased a sea change in the funds mobilization effects of companies through, public issues of equity an  debt encouraged by the deregulation of capital markets and other economic.

## Primary market   instruments

i)Equity

ii)Debt

Equity and debt are the two basic instrument of raising capital from the primary market.

Companies in practice offer a number  of variation of equity and debt securities.

>Ordinary shares-Ordinary shares represent the ownership position in a company. The holder of the equity shares are the owner of the company asset. They provide permanent capital. They have voting rights and receive dividend at the discretion of the directors.

>Preference share-The holder of the preference shares have a preference over the equity in the event of liquidation of the company. The preference dividend rate in fixed and known and is payable before paying dividend in the ordinary share capital.

A preference share may also provide for the accumulation of dividend.It called cumulative preference share.

>Debenture-Debenture represent long-term debt given by the holders of debenture to the company. Debenture may be secured or unsecured.Secured debenture also known as bonds. Debenture may be issued without an interest rate.They are called zero-interest debenture.

>Convertible debenture-A debenture may be issued with the feature of being convertible into equity shares after a specified period of time at a given price.

>Warrants-> A company may issue equity share or debentures attached with warrants entitle an investor to buy equity shares after a specified time period at a given price.

>Derivative securities-Securities with option to buy or sell are called derivative securities CDs,CPs, and warrants are example of derivative securities.

>Borrowing from financial institutions-In India,besides issuing debenture companies raise debt capital through borrowing from the financial institution and banks. Banks are the important source of working capital for companies.

### Type of primary market issuance

1)Euro issues-The increasing use of euro issues by the Indian companies also indicates that Indian capital market is integrating with the international capital markets companies in India have also started raising funds via euro  issues, in the foreign capital markets.

Euro issues included foreign currency convertible bonds.Global depository receipt (ADR),ADRs and GDRs are like share and they are trade in the overseas stock exchange.

2)Government securities-Both the central and state government borrow large sum of money from the primary market by issuing dated securities and Treasury Bills (T-bills),T-bill in India are issued for short duration.

The total issues government securities has increased over years.

3)Pricing of new Issues -A Company  required to issue prospectus when it issues share to the public .The prospectus should disclose fall information including the risk factor in the issue to the investor to be able to appraise the pricing and form a judgment.

4)Book Building and price discounting-In the case of normal public issue the price fixed  and known in advance at the close of subscription the company known the number of share applied for .

Book building is an alternative to the traditional fixed price method of security issue.

## Shareholders

• Buyer of share are called share holders or stock holders and they are the legal owner of the firm whose shares they hold share represent ownership right of their holders.Buyer are the legal owner of the firm whose shares they hold.

Share holders invest their money in the shares of a company in the expectation of a return on their invested capital.The return of shareholders consist of dividend and capital gain share holder make capital gain share hikder make capital gain or loss by selling their shares.

Type of shareholder

1)Preference shareholder 2)Ordinary shareholder

## Preference shareholder

Preference share is often  considerd to be a hybrid security.Since it has many features of both ordinary shares and debenture.

Preference share is senior security as compared to ordinary share it has a prior claim or the company’s income in the sense that the company must first pay preference dividend before paying ordinary dividend.

In preference share dividend rate is fixed and preference dividend are not tax deductible preference shareholder.

### Ordinary shareholder

Ordinary shares represent the ownership position in a company.The holders of ordinary shares called ordinary share holder are the legal owners of the company ordinary shares are the source of permanent capital since they do not have a maturity date.

The capital shares is by ordinary shares is called share capital or equity capital.It appears on the left-hand side of a firm account form balance sheet or on the top of sources of capital are generally contained in holders attached to the balance sheet.

Ordinary share holders have a residual ownership claim.They have a claim to the residual income which is earning available for ordinary shareholder after paying expenses interest charges taxes and preference dividend.

Ordinary shareholders also have a residual claim on the company’s assets in the case of liquidation.This share holder are required to vote on a number of important matters.

## Cash flow

• A statement of change financial position on a cash basis commonly known as the cash flow statement, Summarises the causes of change in cash position between dates of the two balance sheet, It indicates the source and uses of cash.
Thus, this is statement analysis changes in non-current accounts as well as current accounts.

## Sources and uses of cash

Sources of cash.

->The profitable operation of the firm.
->Decrease in assets(except cash)
->Increase in liabilities (including) debenture or bonds.
->Sale proceeds from an ordinary or preference share issue.

Uses of cash

->The loss from an operation
->increase in assets(except cash)
->decrease in liabilities
->redemption of redeemable preference share.
->Cash dividends

The easiest and the direct method of preparing a statement of changes in cash position is to only record inflow and outflow of cash and find out the net change during a given period.

The rupee received minus the rupees paid during a period is the cash position has to be found out from the income statement and comparative balance sheet. Adjustment for the no cash items is made.

### Change in current assets

An increase is current assets reduce the cash flow from operations while a decrease in current assets. that is, the beginning balance exceeding and of the year balance increase cash flow.

i)Increase in debtors implies that cash collection from customers or less them sales figure shown in the profit and loss statement while a decrease in debtors indicates that cash collections are greater than the sales figures.

ii)Increase or decrease in inventory adjusted to the cost of goods sold. An increase in inventory implies that cash outflow is greater than the cost of goods sold figure(shown in the profit and loss statement), while a decrease in inventory means that cash outflow is 100 than the cost of goods sold figure.

iii)Increase in prepaid expenses implies that cash outflow is more than the amount of actual expenses(shown in profit and loss statement, while a decrease in prepaid expenses means that cash outflow is less than the amount of actual expenses.

Change in current liabilities

increases in current liabilities increase cash flow from operation while a decrease in current liabilities reduces it.

i)Increase in creditors implies that cash payments to creditors are less than the purchase figure.
While a decrease in creditors indicates that cash payments to creditors are greater than purchase.

ii)Increase in ‘income in advance’ implies greater cash inflow than shown in the profit and loss statement as income, while a decrease in ‘income in advance’ means less cash inflow than shown as income.

#### Component of cash flow

i)Initial investment
ii)Annual net cash flows
iii)Terminal cash flow

Initial Investment

The initial investment is the net cash outlay in the period in which an asset is purchased. A major element of the initial investment is gross outlay or original value(ov) of the asset, which comprises of its cost (including accessories and spare parts) and freight and installation charges.

The original value included in the existing block of assets for computing annual depreciation. Original value minus depreciation is the assets’ book value(BV). It may require a lump sum investment in net working capital also.

Thus initial investment will be equal to gross investment plus an increase in networking capital also.

ii)Net Cash flows

An investment expected to generate annual cash flows from operations after the initial cash outlay has been made. Cash flows should always be estimated on an after-tax basis. Some people advocate the computing of cash flows before taxes and discounting them at the before-tax discount rate to find NPV.

Unfortunately, this will not work in practice since there does not exist an easy and meaningful way for adjusting the discount rate on a before-tax basis.

We shall refer to the after-tax cash flow as net cash flows(NCF) and use the term $C_{1},C_{2},C_{3}....C_{n}$ respectively for NCF in period 1,2,3,……n.

Net cash flow =Revenue-Expenses-Taxes
NCF=REV-EXP-TAX

3)Terminal cash flow

Salvage value (SV) is the most common example of terminal cash flows. Salvage value  defined as the market price of an investment at the time of its sale. The cash proceeds net of an investment at the time of its sale. The cash proceeds net of taxes from the sale of the assets treated as cash inflow in the terminal (last) year.

The effect of the salvage value of existing and new assets summarised as follows.

i)Salvage value of the asset-It will increase cash inflow in the terminal(last) period of the new investment.
ii)Salvage value the existing asset now-It will reduce the initial cash outlay of the new asset.
iii)Salvage value of the existing asset at the end of its normal life-It will reduce the cash flow of the new investment of in the period in which the existing asset sold.

## Over-the-counter market

The over-the-counter market is an important alternative to exchange and measured in terms of the total volume of trading has become much larger than the exchange-traded market.

The OTC market is a negotiated market. Transaction not handled on an organized exchange is handled in this market. The OTC  market is not a place it has no central location but it is rather a way of doing business. It consists of a network of dealers, linked together by communication devices including the latest technological equipment these dealers can deal directly with each other and with the customer.

The third term market describes over-the-counter trading of shares listed on an exchange, Although most transaction inlisted stock takes place on an exchange. An investment firm that is not a member of the exchange can make a market in the listed stock. The success or failure of the third market depends on whether the OTC market in these stocks is a good as the exchange market and whether the relative cost of the OTC transaction compares favorably with the cost on the exchange.

Future exchange arose to solve some of the problems associated with over-the-counter trading of forward that had existed previously, similarly the establishment of exchange-traded options led to an explosion of trading and resulted in markets that are much larger and more robust than the over-the-counter option market that came before.

## The function of the Over-the-counter market

->Dealers arrive at the prices of securities in the OTC market by both negotiating with customers specifically and making competitive bids.

->Dealers match the forces of supply and demand with each dealers making a market in certain securities.

->Dealers quote bid and ask prices for each security the bid price is the highest price offer by the dealers,and the ask price is the lowest price at which the dealers making a market in certain securities.

->Dealers quote bid and ask prices for each security,the bid price is the highest price is the lowest price at which the dealer is willing to sell

-> Actively traded stocks on the OTC market have a many us to 10 to 20 market makers(dealers functions must as the specialist does for an exchange-listed stock.

### Clearing of OTC

The marketing process for OTC trades is similar to that of the exchange-traded option. After the trade occurs, the firm’s back-office its paper processing center, Confirms the details of the trade.

1)Who bought and who sold
2)Put or call
3)Strike price
4)exercise date
5)Quantity of option
6)Underlying security
7) Identification of traders and firms
8)The timing of the premium payment
9)If upon exercise, the long is to receive a cash payment, determined by the difference between the security’s price and the strike price.

If the two firms have a master option agreement covering all such option trades, then need not be confirmed between back office for this information is specified in the master agreement.If all information fields match the back office of the respective firms agree that the trade is good, and each sends a paper confirmation to the other.

Since an OTC trade does not take place under the auspices of an exchange, there is no third party to guarantee the financial performance of the counter-parties to the trade. This requires that each party to the trade has some knowledge of the creditworthiness of the opposite party.

## Criteria of investment Evaluation

Investment  consist of these three steps
->Estmation of cash flow
->Estimation of the required rate of return
->Application of a decision rule for making the choice

Investment decision rule

i)Investment decision rule may be referred to as a capital budgeting technique or investment criteria. To measure the economic worth a sound appraisal technique is that it should maximize the shareholders shareholders‘ wealth for a sound investment.

ii)It should consider all cash flows to determine the true profitability of the period.

iii) It should provide an objective way of separating good projects from bad projects.

iv)It should help the ranking of projects according to their true profitability.

v) It should help to choose among mutually exclusive projects that project where maximize the shareholder wealth.

vi)It should be a criterion that is applicable to any conceivable investment project independent of others.

Evaluation criteria
Two type of investment criteria are in use in practice.
i) Discounted cash flow criteria
ii)Non-discounted cash flow criteria.

Discounted cash flow included
->Net present value(NPV)
->Internal rate of return
->Profitability Index

1)Net present value(NPV)-NPV is a DCF technique that explicitly recognizes the time value of money it correctly postulates that cash flows arising at different time periods differ in value.
The following steps are involved in the calculation of NPV
->Cash flows of the investment project should be forecasted based on realistic assumption.

->Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate.

->Net present value should be found out by subtracting present value of cash outflow from the present value of cash inflows.
Project should be accepted if NPV is positive NPV>0

Importance of NPV
NPV valuation supposes that the opportunity cost of capital is 10% percent and project X cost rs.2000 now and is expected to generate year-end cash inflow of Rs.900,800,700,600,500.

NPV=                         $[\frac{900}{(1+0.10)}+\frac{800}{(1+0.10)^{2}}+\frac{700}{(1+0.10)^{3}}+\frac{600}{(1+0.10)^{4}}+\frac{500}{(1+0.10)^{5}}]-2500$

$NPV=2725-2500=+225$

How to except NPV
i)Accept the project when NPV is positive NPV>0
ii)Reject the project when NPV is negative NPV<0
iii)May accept the project when NPV is zero NPV=0

2)Internal rate of return method-The internal rate of return method is another discounted cash flow technique which takes account of the magnitude and timing of cash flow. The concept of internal is quite simple to understand in the case of one project.
Suppose that 10000 Rs.deposit in a bank and would get back Rs.100800

$\frac{10800-10000}{&space;10000}$

1.08-1=0.08
0.08 or 8%

$r=\frac{C_{1}-C_{0}}{C_{0}}$

r=$\frac{C_{1}}{C_{0}}-L$

How to except IRR
i)Accept the project when r>k
ii)Reject the project when r<k
iii)May Accept the project when r=k

3)Profitability Index-Profitability index is the ratio of the present value of cash inflows , at the required rate of return ,to the initial cash outflow of the investment. The formula for calculating the benefit-cost ratio or profitability index as follows.

PI=

$\frac{PV(C_{1})}{C_{0}}&space;=&space;\sum_{t=1}^{n}\frac{C_{1}}{(1+k)^{t}}/C_{0}$

Suppose that initial cash outlay is Rs.100000 and it can generate cash inflow of rs.40000,30000,50000 and rs.20000 in a year.

$PV=&space;40000(PVF&space;_{1.0.10})+30000(PVF_{2.0.10})+50000(PVF_{3.0.10})+20000(PVF_{4.0.10})$

$=40000\times&space;0.909+30000\times0.826+50000\times&space;0.751+20000\times&space;0.68$

NPV =112350-100000=12350

PI  =$\frac{112350}{100000}=11235$

How to except profitability Index
i)Accept the project when PI is greater than one PI>1
ii)Reject the project when PI is less than one PI<1
iii)May accept the project when PI is equal to one PI=I

Non-discounted cash flow criteria

1)Payback -The payback (PB) is one of the most popular and widely recognized traditional methods of  evaluating investment proposals. Payback is the number of years required to recover the original cash outlay invested in a project.
If the project generator constant annual cash inflow the payback period can be computed by dividing cash outlay.

=

=         $\frac{C_{0}}{C}$

How to except payback
Many firms use the payback period as an investment evaluation criteria and a method of ranking project.

->The project would be accepted if its payback period is less than the maximum or standard payback period set by management.

->As ranking method it gives the highest ranking to the project.

->If the firm has to choose between two mutually exclusive projects, the project with a shorter payback period will be selected.

2)Discounted payback period-Payback method is that it does not discount the cash flows for calculating the payback period. The discounted payback period is the number of periods taken in recovering the investment outlay on the present value basis.
The discount payback period still fails to consider the cash flows occurring after the payback period.

Project P and Q involve the same outlay of Rs.4000 each opportunity cost of capital is 10%.

3)Accounting rate of return-The accounting rate of return (ARR), also known as the return on investment(ROI) .I uses accounting information on as revealed by financial statements to measure the profitability of an investment.
The accounting rate of return is the ratio of the average after-tax profit divided by the average  investment.

The average investment would be equal to half of the original investment if it were depreciated constantly.

$ARR=\frac{Average&space;income}{Average&space;investment}$

$ARR=\frac{\sum_{t=1}^{n}(I-t)}{(I_{0+I_{n}})/2}$
Where
EBIT=Earning before interest and tax
T=tax
I0=book value
In=Book value of investment at the end of the number of years

How to except ARR
This method will accept all those projects whose ARR is higher than the minimum rate established by the management.
Reject these project which has ARR less than the minimum rate.

## Perpetuities

A perpetuity is a stream of equal cash flows that occur at regular intervals for example. Perpetual bonds promise the owner a fixed cash flow every year forever.

Here is the timeline of perpetuity.
From the timeline that the first, cashflow does not occur immediately,it arrives at the end of the first period. This timing is sometimes referred to as payment in arrears and is a standard convention that we adopt.

## The present value of a perpetuity

Perpetuity is an annuity that occurs indefinitely perpetuities are not very common in financial decision making. But one can find a few examples for instance in the case of irredeemable preference share(i.e.preference shares without a maturity. The company expected to pay preference dividend perpetuity.
By definition, in perpetuity, time period n,  is so large C mathematically n approaches infinity that the expression$(1+i^)^{n}$, and the formula for perpetuity simply becomes.
Present value of a perpetuity

Perpetuity formula
$\frac{Perpetuity}{Interest&space;rate}$

P=$\frac{A}{i}$
Using the formula for the present value. The present value of a perpetuity with payment C and interest rate r is given by

PV= $\frac{C}{(1+r)}+\frac{C}{(1+r)2}+\frac{C}{(1+r)^{3}}+....=\sum&space;_{n=1}^{\infty&space;}\frac{C}{(1+r)^{n}}$

Notice that C=C in the present value formula because the cash flow for perpetuity is constant. Also because the first cash flow is in one period.

To find the value of perpetuity one cash flow at a time would take forever.
The term of an infinite number of positive terms could be finite. The answer is that the cash flows in the future. One discounted for an ever-increasing number of periods, so their contribution to the sum eventually becomes negligible.
To derive the shortcut. We calculate the value of perpetuity by creating our own perpetuity, We can then calculated the present value of the perpetuity because of the perpetuity, By the law of one price, the value of the perpetuity must be the same as the cost.

We incurred to create our own perpetuity. Suppose that you withdraw $5 and reinvest the$100 for a second year again you will have $105 after one year and you can withdraw$5 and reinvest $100 for another year. By doing this year after year, you can withdraw$5 every year in perpetuity.

By investing $100 in the bank today. You can in effect, create a perpetuity paying$5 per year

## Annuity

An annuity is a stream of N equal cash flows paid at regular intervals. The difference between an annuity and perpetuity is that an annuity ends after some fixed number of payments.

Not surprisingly, annuities are the most common kinds of financial instruments. The pensions that people receive when they retire are often in the form of. Most car loans, mortgages, leases, some bonds, and pension plans are also annuities.

We represent the cash flow of an annuity on a timeline as follows.
With perpetuity, we adopt the convention that the first payment take place at date, one period from today.

The present value of N-period annuity with payment C and interest rate is
$PV=\frac{C}{(1+r)}+\frac{C}{(1+r)^{2}}+\frac{C}{(1+r)^{3}}+----+\frac{C}{(1+r)^{N}}=\sum_{n=1}^{N}\frac{C}{(1+r)^{n}}$

## Types of annuity

1)The present value of an annuity
2)Future value of an annuity

1)The present value of a growing annuity:-In financial decision-making there are a number of situations where cash flows may grow at a constant rate. For example, Suppose that deposit 1000 rs.at 10 percent  for 5 years will the amount after 5 year

 Year-End Amount of       salary PVF@12% PV of salary(Rs) 1 1000 0.893 893 2 1100 0.797 877 3 1210 0.712 862 5 1331 0.636 847 5 1464 0.567 830 6105 4309

We can write the formula for calculating the present value of a growing annuity as follows:

Formula of annuity
$P=\frac{A}{(1+i)}+\frac{A(1+g)^{1}}{(1+i)^{2}}+\frac{A(1+g)^{2}}{(1+i)^{3}}+....+\frac{A(1+g)^{n-1}}{(1+i)^{n}}$

$P=A[\frac{1}{(1+i)}+\frac{(1+g)^{1}}{(1+i)^{2}}+\frac{(1+g)^{2}}{(1+i)^{3}}+...+\frac{(1=g)^{n-1}}{(1+i)^{n}}&space;]$

### 2)Future value of an annuity

How can we compute the compound value of an annuity due? The compound value of an annuity because it earns extra interest for one year. If you multiply the compound value of an annuity by(1+i), You would get the compound value of an annuity due.

The formula for the compound value of an annuity due is as follows.
Future value of an annuity$\times&space;(1+i)$
=A$\times&space;CVFA_{n,i}\times&space;(1+i)$
=A$[\frac{(1+i)^{n}-1}{i}](1+i)$

### Some tricks were also available to calculate annuity. Presents four tricks below.

Trick#1 A delayed annuity:-One of the trick in working with annuities or properties is getting the timing exactly right. This is particularly true. When an annuity or perpetuity begins at a date many periods in the future.

For example:-Mr.A will receive a four-year annuity of rs.500 per year Begining at date of 6. If the interest rate is 10 percent. What is the present value of her annuity?
This situation can be graphed.

This analysis involves two steps
1) Present value calculation.
The present value of annuity on date 5
$500$[\frac{1}{0.10}-\frac{1}{0.10(1.10)^{4}}]$=$500$\times&space;A_{0.10}^{4}$
=$500$\times&space;3.1699$ =$1584.95
Note that $1584.95 represents the present value on date 5$1584.95 is the present value at date 6, because the annuity begins on date 6, However, our formula values the annuity as of one period prior to the first payment. This can be seen in the most typical case where the first payment occurs at date 1.

2) Discount the present value of the annuity back to date 0. That is
Present value at date 0:
$\frac{1584.95}{(1.10)^{5}}=$$984.13 The annuity formula brings Mr. Annuity back to 5, the second calculation must discount over the remaining 5 periods. Two-step procedure graphed in the figure below . Date cash flow Trick#2 Annuity in advance:-If first payment of annuity received immediately. for example, Mr.B received first payment from the lottery immediately. The total number of payments remains 20. Under this new assumption. We have a 19-date annuity with the first payment occurring at date 1 plus an extra payment at date 0. The present value is$50000 payment at date 0+$50000$\times&space;A_{0.08}^{19}$ 19-year annuity =$50000+$50000$\times&space;96036$ =$530180

$530180, the present value in this example. This is to be expected because the annuity of the current example begins earlier. An annuity with an immediate initial payment is called an annuity in advance. Trick#3The infrequent annuity: An annuity with payments occurring less frequently than once a year. For example, Mr.C receives an annuity of$450.Payable once every two years. The annuity stretches out over 20 years. The first payment occurs at date 2 that is, two years from today. The annual interest rate is 6 percent.
The trick is to determine the interest rate over a two-year period. The interest rate  over two years is
$1.06\times&space;1.06-1=12.36%$
That is,$100 invested over two years will yield$112.36

Present value of a $450 annuity over 10 periods, with an interest rate of 12.36 percent per period. This is$450  $[\frac{1}{0.1236}-\frac{1}{0.1236\times(1.1236)^{10}&space;}]$=$450$\times&space;A_{0.1236}^{10}$=$2,505.57

Trick#4 Equating presents the value of two annuities: If a parent estimates college education for their new born daughter. They estimated that college expenses will run $30000 per year when their daughter reaches college in 18 years. The annual interest rate over the next few decades will 14 percent.How much money they deposit in the bank each year so that their daughter will completely supported through four years of college. We assume that the child born today. Her parents will make the first of her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of her first 17 birthdays. But no deposit at date 0. This calculation requires 3 steps. The first two determine the present value of the withdrawals. The final step determines yearly deposits that will have a present value equal to that of the withdrawals. 1. Calculation of the present value of the four years at college using the annuity formula.$30000$\times&space;[\frac{1}{0.14}]-\frac{1}{0.14\times&space;(1.14)^{4}}$ =$30000$\times&space;A_{0.14}^{4}$ =$30000$\times&space;2.9137$=$87,411 2.Calculation the present value of the college education at date 0 as $\frac{87411}{(1.14)^{17}}$=$9,422.91
3. Assuming that child’s parents make a deposit to the bank at the end of each of the 17 years, We calculate the annual deposit that will yield a present value of all deposit. This is calculated as
C$\times&space;A_{0.14}^{17}$=$9,422.91 Since$A_{0.14}^{17}$=6.3729 C=$\frac{9422.91}{6.3729}$=$1478.59

Thus, deposit of $1478.59 made at the end of each of the first 17 years and in other words invested at 14 percent will provide enough money to make tuition payments of$30000 over the following four years.

## Discounted cash flow

Discounted cash flow (DCF) approach is theoretically the most appropriate valuation approach. The value of a firm depends on the expected cash flows and the discount rate. The expected cash flow of the firm depends on the operating efficiencies and market conditions.
The discounted rate depends on the risk of the expected cash flows. Firm’s generating specify target capital structure in terms of fixed debt-to-value ratio. In conculsion, Wacc is the appropriate discount rate for valuing a firm.
To estimate a continuation value in year T using discounted cash flow. We assume a constant expected growth rate and constant debt-equity ratio.
$V=\sum_{t=1}^{n=\infty&space;}\frac{FCF_{t}}{(1+k_{0})^{t}}$

Where,
FCF=free cash flow
$K_{0}$ = weighted average  cost of capital(WACC)
If FCF remains constant forever, that is FCF is a perpetuity,  the value of the firm
$V=\frac{FCF}{K_{0}}$

Earnings are the basics for estimating fre cash flows of firm cash flows include an adjustment for depreciation, capital expenditure and working capital.

## Earning depends on capital

If we assume constant relation of earnings depends on sales.If we assume constant relation of earnings working capital and capital expenditure to sales.
NCF=FCF
=$SALES\times&space;P\times&space;(1-t)+DEP-(w+f)SALES$
Where,
P=EBIT
T=Corporate tax rate
DEP=depreciation
w=net working capital
f=capital expenditure