# Posts

## Depository Institutions

Depository Institution are financial intermediaries that accept deposit. They include commercial banks (or simply bank) saving and loan association and credit union. It is common to refer to the depository institutions other than banks as  depository institutions  are highly related and supervised because of the important role that they play in the financial system.

Checking accounts are still the principal means that people and business entities use for making payments.

Government monetary policy is implemented through various activities with banks. Because of their important role, depositor institution are afforded special privileges such as access to federal deposits insurance and access to a government entity in order to acquire funds for liquidity or emergency needs.

Deposits represent the liabilities(debt) of the deposit accepting institution with the funds raised through deposits and other funding sources, depository institution make direct loans to various entities and invest in securities.

Their income is demand the interest income from their portfolio of loans, income from their portfolio of securities and fee income.

The asset liability problem of depository institutions

The asset liability problem that depositor institution face is quite simple to explain although not necessarily easy to solve. A depository institution seeks to earn a positive spread between the assets it invest in (loans securities) and the costs of its funds ( deposits and other sources). This difference between income and cost is referred to as spread income, or margin income. The spread income should allow the institution to meet operating expenses and earn a fair profit on its capital.

In generating spread income a depository institution faces several risks. These include credit risk.regulatory risks and interest rate (or funding risk)

## Interest rate risk

Interest rate risk is the risk that a depository institution’s spread income will suffer because of changes in interest rate. This kind of risk can be explained by illustration. Suppose that a depository institution raises $100 million by issuing a deposit account that has maturity of 1 year and by agreeing to pay an interest rate 7%. Ignoring for the time being the fact that the depository institution can not invest the entire 100 million because of reserve requirements suppose that$100 million is invested in a U.S.treasury security that matures in 15 years paying an interest rate of 9% Because the funds are invested in U.S. Treasury security there is no credit of risk.

All depository institution face this interest rate risk, or funding problem. Manager of a depository institution who have particular expectation about the future directions of interest rates  will seek to benefit from these expectation. Those who expect interest rates to rise may pursue a policy to borrow funds for the bay term and lend funds for the share term. If interest rates are expected to drop, managers may elect to borrow short and lend funds for the short term. If interest rate are expected to drop, managers may elect to borrow short and lend long.

The problem of pursuing a strategy of positioning a depository institution based on interest rate expectation is that considerable adverse financial consequences will result if those expectation are not realized. The evidence on interest rate forecasting suggest that it is a risky business.

Some interest rate risk, however, is interest in any balance sheet of a depository institution. Managers must be willing to accept some risk but they can take various measures to address the interest rate sensitivity of the institution’s liabilities and its assets.

A depository institution should have an asset liability committee that is responsible for monitoring the exposure to interest rate risk.

## Investment decisions rule under inflation

A common problem, which complicates the practical investment decision-making , is inflation, to be consistent in treating inflation in the cash flows and the discount rate.

Inflation is fact of life all over the world.A double -digit rate of inflation is a common feature in developing countries. Because the cash flows of an investment project occur over a long period of time, a firm should usually be concerned about the impact of inflation on the project’s profitability. The capital budgeting results will be biased if the impact of inflation is not correctly factored in the analysis.

Business executives do recognise that inflation exists but they do not consider it necessary to incorporate inflation in the analysis of capital investment. They generally estimate cash flows assuming unit costs and selling price prevailing in year zero to remain unchanged. They argue that if there is inflation prices can be increased to cover increasing costs.

The impact on the project’s profitability would be the same if they assume rate of inflation prices, can be increased to cover increasing costs; therefore , the impact on the projects’s profit ability would be the same if they assume rate inflation to zero. This line of argument although seems to be convincing , is fallacious for two reason.

1) The discount rate used for discounting cash flow is generally expressed in nominal terms. It would be inappropriate and inconsistent to use a nominal rate to discount constant cash flows. Pm

2) Selling prices and costs show different degrees of responsiveness to inflation. In the case of certain products, prices may be controlled by the government , or by restrictive competition , or there may exist a long-term contract to supply goods or services at fixed price.

However, some costs ride faster than others. For example wages may increase at a rate higher than, say fuel and power , or even raw material. The depreciation tax shield remains unaffected  by inflation since depreciation us allowed on the book value of an asset, irrespective of its replacement or market price, for tax purposes.

The working capital tied up in an investment project may also increase during inflationary conditions. Because of the increasing input prices and manufacturing costs, more funds may have to be tied up in inventories and receivable . The salvage value of the project may also be affected by inflation.

Nominal Vs.Real Rates of Return

Suppose a person -we call him jose, deposits rs.100 in the state bank of india for one year at 10 percent rate of interest . This means that the bank agrees to return rs.110 to jose after a year , irrespective of how much goods or services this money can buy for him. The sum of. Rs.110 is stated in nominal terms .

The rs.110 is expressed in nominal terms since they have not been adjusted for the effect of inflation. On the other hand , the rs. 110 rs.102.80 are in real terms since they have not been adjusted for the effect of inflation.

The opportunity cost of capital of a firm or project is generally market determined and is based on expected future returns.It is, therefore, usually expressed in nominal terms and reflects the expected rate of inflation . The opportunity cost of capital of the discount rate is a combination of the real rate( say, k ) and the expected inflation rate. This relationship, long ago recognised in the economic theory, is called the Fisher’s effect . It may be stated as follows.

Nominal discount rate= (1+Real discount rate)×(1+inflation rate)-1

K=$K=(1+k)(1+\alpha)-1$

If a firms expect a 10 percent real rate of return an investment project under consideration and the expected inflation rate is 7 percent, the nominal required rate of return on the project would be.

K=(1.10)(1.07)-1=1.177-1=0.177 0r 17.7%

In practice, it is customary to add the real rate and the expected inflation rate to obtain the nominal required rate of return:k=k+$\alpha$

## Bond duration and interest rate sensitivity

by We have discussed that bond prices are sensitive to changes the interest rate, and they are inversely related to the interest rates. The intensity of the price sensitivity depends on a bond’s maturity and the coupon rate of interest. The longer the interest rate changes. Similarly, the price of a bond with low coupon rate will be more sensitive to the interest rate changes.

A bond’s maturity and coupon rate provide a general idea of its price sensitivity to interest rate changes. However , the bond’s price Sensitivity can be more accurately estimated by duration. A bond’ s duration is measured as the weighted average of time to each cash flow( interest payment or repayment of principal).

Duration calculation gives importance to the timing of cash flows; the weight is determined as the present value of cash flow to the bond value. Hence two bonds with similarly maturity but different coupon rates and cash flow patterns will have different duration.

Let us consider two bonds with five year maturity. The percent rate bond of rs.1000 face value has a current market value of rs.954.74 and YTM of 10 percent, and the 11.5 rate bond of rs.1000 face value has a current market value of rs.1044.57 and a yield to maturity of 10.6 percent . The duration of the bond is calculated as the weighted average of times to the proportion of the present value of cash flows.

The volatility or the interest rate sensitivity of a bond is given by its duration and YTM . A bond’s volatility, referred to as its modified duration, is given as follows:

Volatility of bond=$\frac{Duratiin}{(1+YTM)}$

THE TERM STRUCTURE OF INTEREST RATES

So far in our discussion, we did not explicitly mention whether there were one single interest rate or several rates. In fact, there are several interest rates in practice. Both companies and the Government of India offer bonds with different maturities and risk features. Debt in a particular risk class will have its own interest rate.

Yield curve shows the relationship between the yields to maturity of bonds and their maturities. It is also called the term structure of interest rates. The upward sloping yield curve implies that the long-term yields are higher than the short-term yields. This is the normal shape of the yield curve l, which is generally verified by historical evidence. However, many economics in high – inflation periods have witnessed the short term yields being higher than the long-term yields being higher than the long-term yields. The inverted yields curves result when the short-term rates are higher than the long-term rates.

Following theory for yield curve structure.

1) Expectation theory- The expectation theory supports the upward slopping yield curve since investor always expect the short-term rates to increase in the future. This implies that the long-term rates will be higher than the short-term rates will be higher than the short-term rates.

But in the present value terms, the return from investing in a long-term security will equal to the return from investing in a series of a short-term security.

A significant implication of the expectation theory is that given their investment horizon, investor will earn the same average expected returns on all maturity combination .Hence a firm will not be able to lower its interest cost in the long run by the maturity structure of its debt.

2) The liquidity premium theory-  The liquidity or risk premium theory provides an explanation for the expectation of the investors. We have explained earlier that the prices of the long-term bonds are more sensitive than the prices of the short-term bonds to the changes in the market rates of interest. Hence investor prefer short-term bonds to the long-term bonds.

The investor will be compensated for risk by offering higher returns on long-term bonds.This extra return, which is called liquidity premium, gives the yield curve its upward bias.

3) The segmented market theory- The segmented markets theory assumes that the debt market is divided into several segment based on the maturity of debt. In each segment , the yield of debt depends on the demand and supply.Investors’ preferences of each segment arise because they want to match the maturities of assets and liabilities to reduce the susceptibility to interest rate changes.

The segmented markets theory approach assumes investors do not shift from one maturity to another in their borrowing lending activities and therefore, the shift in yields are caused changes in the demand and supply for bonds of different maturities.

## Corporate restructuring

Activities related to expansion of a firm’s operations or changes in its assets or financial or ownership structure are referred to as corporate restructuring. The most common forms of corporate restructuring are mergers/amalgamation and acquisitions.

## Conceptual framework

Profitable growth constitutes one of the prime objective of most of the business firms. It can be achieved internally either through the process of introducing / developing new products or by expanding enlarging capacity of existing products.Alternative, the growth process can be facilitated externally by acquisition of existing business firms. This acquisition may be in the form of mergers, acquisitions, amalgamation, takeovers, absorption, consolidation, and so on.

Although the legal procedure involved in these are different,in view of the perspective of economic considerations these terms are used interchangeably here.

There are strengths and weakness of both the process of promoting growth. For instance internal expansion apart from enabling the firm to retain control with itself also provides flexibility in terms of choosing equipment, mode of technology , location and the like which are compatible with its existing operations. However,internal expansion usually involves a longer implementation period and also entails greater uncertainties particular associated with developing new product. Above all, there may be sometimes an added problem of of raising adequate funds to execute the required capital budgeting projects involving expansion. Acquisition obviate  in most of the situations, financing problem as substantial payment are normally made in the form of share of the purchasing company.

Further, it also expedites the pace of growth as the acquired firm already firm already has the facilities or products and therefore obviously, saves the time otherwise required in building up the new facilities from scratch in the case of internal expansion programme.

Merger evaluation are relatively more difficult budgeting decision, the two chief reason being.i) all benefit from merger are not easily quantifiable and so also all costs, for instance benefits of less competition and economics of scale are not easily measurable attributes

ii) Buying a company is more complicated than buying a new machine in that the firm is to address itself to many tax, legal and accounting issues.

### Types of Mergers

Merger can be usefully distinguished into the following three types

i) Horizontal Merger- Horizontal merger take place when two or more corporate firms dealing in similar lines of activity combine together. Elimination or reduction in competition, putting an end to price cutting, economies of scale in production, research and development, marketing and management are often motives underlying such mergers.

2) Vertical Merger- Vertical merger occurs when a firm acquires firms “upstream” from it and or firms supplying raw materials and to those firms that sell eventually to the consumer in the event of a ‘downstream’ merger. Thus, the combination involves two or more stages of production or distribution that are usually separate.

iii) Conglomerate merger- Conglomerate merger is a  combination in which a firm established in one industry combines with a firm from an unrelated industry. In other words, firms engaged in two different economic business activities combine together .Diversification of risk constitutes the rationale for such mergers.

## Real options

We have been almost entirely concerned with the valuation of derivative dependent on financial assets. Real assets include land, building, plant, and so on.Often there are embedded options.Valuation is difficult because market prices are not readily available.

We start by explaining the traditional approach to evaluating investments in real assets and their shortcomings.

CAPITAL INVESTMENT APPRAISAL

The traditional approach to valuing a potential  capital investment project is known as the “net” present value” or NPV  approach. The NPV of a project is the present value of its expected future incremental cash inflows and outflows. The discount rate used to calculate the present value is a “risk-asjusted” discount rate, chosen to reflect the risk of the project. As the riskness of the project increases, the discount rate also increases.

As an example consider an investment that costs $100 million. If the risk-adjusted discount rate is 12%,the net present value of the investment is(in million of dollars) $-100+\frac{25}{1.12}+\frac{25}{1.12^{2}}+\frac{25}{1.12^{3}}+\frac{25}{1.12^{4}}+\frac{25}{1.12^{5}}=&space;-9.88$ A negative NPV, such as the one we have just calculated,indicates that the project will reduce the value of the company to its shareholder and should not be undertake. A positive NPV indicates that the project should be the undertaken because it will increase shareholder wealth. The risk adjusted discount rate should be the return required by the company, or the company’s shareholder, on the investment. This can be calculated in a number of ways. One approach often recommended involves the capital asset pricing model. The steps are as follows. 1) Take a sample of companies whose main lines of business is the same as that of the project being contemplated. 2) Calculate the betas of the companies and average them to obtain a proxy beta for the project. 3) Set the requested rate of return equal to the risk-free rate plus the proxy beta times the excess return of the market portfolio over the risk-free rate. One problem with the traditional NPV approach is that many projects contain embedded options. Consider, for example, a company that is considering building a plant to manufacture a new product. Often the company has the option to abandon the project if things do not work out well. It may also have the option to expand the plant if demand for the output exceeds expectations. These options usually have quite different risk characteristics from the base project and require different discount rate. This involved a stock whose current is$20. In three months ‘ time the price will be either $22 or$18. Risk neutral valuation shows that the value of a three-month call option on the stock with a strike price of 21 is 0.633.

The expected return required on the call option is 42.6%.In practice it would be very difficult to estimate these expected returns directly in order to value the option on real assets.

There is no easy way of estimating the risk-adjusted discount rates appropriate for cash flows when they arise from abandonment, expansion , and other options. This is the motivation for exploring whether the risk-neutral valuation principal can be applied to options on real assets as well as options on financial assets.

Another problem with the traditional NPV approach lies in the estimation of the appropriate risk-adjusted discount rate for the base project. The companies that are used to estimate a proxy beta for the project in the three-step procedure above have expansion options and abandonment options of their own. Their betas reflect these options and may not therefore be appropriate for estimating a beta for the base project.

EXTENSION OF THE RISK-NEUTRAL VALUATION

Consider an asset whose price, f , depends on variable 0 and time t. Assume that the process followed by 0 is.

$\frac{d\theta&space;}{\theta&space;}=m&space;dt+s&space;dz$

Where dz is a Wiener process. The parameters m and s are the expected growth rate in $\Theta$ and t. The variable $\Theta$ need not be a financial variable. It could be something as far removed from financial markets as the temperature in the Centre of New Orleans.

The asset price f follows a process of the form

df= $\mu&space;f&space;dt+\sigma&space;fdz$

Any solution to equation for s is a solution to equation for $\theta$, and vice versa , when the substitution

$q=&space;r-m+&space;\lambda&space;s$

Using risk- neutral valuation. This involves setting the expected growth rate of a equal to r-q and discounting expected payoffs at the risk-free interest rate. It follows that we can solve by setting the expected growth of $\theta$ equal to

$r=&space;(r-m+&space;\lambda&space;s)=&space;m-\lambda&space;s$

and discounting expected payoffs at the risk-free interest rate.

APPLICATION TO THE VALUATION OF A NEW BUSINESS

Traditional methods of business valuation, such as applying a price earnings multiplier to current earnings, do not work well for new business. Typically a company ‘s earnings are negative during  it’s really years as it attempt to gain market share and establish relationship with customers. The company must be valued by estimating future earnings and cash flows under different scenarios.

The company ‘ future cash flows typically depend on a number of variables such as sales, variable costs as a percent of sales, fixed costs, and so on. Single estimates should be sufficient for outlined in the previous two sections. A Monte Carlo simulation can then be carried out to generate alternative scenario for the net cash flows per year in a risk-neutral world.  It is likely that under some of these scenarios the company does very well and under others it becomes bankrupt and ceases operations.

The simulation must have a built-in  rule for determining when bankruptcy happens. The value of the company is the present value of the expected cash flow in each year using the risk -free rate for discounting.

## Cash management

Cash is the important current asset for the operations of the business. Cash is the basic input needed to keep the business running on a continuous basis.It is also the ultimate output expected to be realised by selling the service or product manufactured by the firm. The firm should keep sufficient cash neither more or less.

Cash shortage will disrupt the firm’s manufactured operation while excessive cash will simply remain idle, without contributing anything towards the firm’s manufacturing operation as while excessive cash will simply remain idle, without contributing anything towards the firm’s profitability.

Cash is the money which a firm can disburse immediately without any restriction. The term cash included coins, currency and cheques held by the firm, and balances in its bank accounts. Sometimes near-cash itmes,such as marketable securities or bank times deposits, are also included in cash.

The basic characteristic of near-cash asset is that they can readily be converted into cash. Generally, when a firm has excess cash, it invest it in marketable securities . This kind of investment contribute some profit to the firm.

## FACETS OF CASH MANAGEMENT

Cash management is concerned with the manager of

i) Cash flows into and out of the firm.

ii) Cash flows within the firm.

iii) Cash balances held by the firm at a point of time by financing deficit or investing surplus cash.

It can be represented by a cash management cycle.Sales generate cash which has to be disbursed out. The surplus cash has to be invested while deficit has to be borrowed. Cash management seeks to accomplish this cycle at a minimum cost. At the same time, it also seeks to achieve liquidity and control.

Cash management assume more importance than other current assets because cash is the most significant and the least productive assets that a firm holds.

It is significant because it is used to pay the firm’s holds. It is significant because it is used to pay the firm’s obligations.However, cash is unproductive. Unlike fixed assets or inventories, it does not produce goods for sale. Therefore,  the aim of cash management is to maintain adequate control over cash position to keep the firm sufficiently liquid and to use excess cash in some profitable way.

Cash management is also important because it is difficult to  predict cash flows accurately, particular the inflows, and there is no perfect coincidence between the inflows and outflows of cash.The firm should evolve strategies regarding the following four facets of cash management.

1)Cash planning- Cash inflows and outflows should be planned to project cash surplus or deficit for each period of the planning period. Cash budget should be prepared for this purpose.

2)Managing the cash flows-The flow of cash should be properly managed. The cash inflows should be accelerated while,as far as possible, the cash outflows should be decelerated.

3) Optimum cash level- The firm should decide about the appropriate level of cash balances. The cost of excess cash and danger of cash deficiency should be matched to determine the optimum level of cash balances.

4) Investing surplus cash- The surplus cash balances should be properly invested to earn profits. The firm should decide about the division of such cash balance between alternative short-term investment opportunities such as bank deposits, marketable securities, or inter-corporate lending.

### MOTIVES FOR HOLDING CASH

The firm’s need to hold cash may be attributed to the following three motives.

1) The transaction motive-The transactions motive requires a firm to hold cash to conduct its business in the ordinary course. The firm needs cash primarily to make payments for purchase, wages and salaries, other operating expenses, taxes, dividends etc. The need to hold cash would not arise if there were perfect synchronization between cash receipts and cash payments.

2) Precautionary Motive- The precautionary motive is the need to hold cash to meet contingencies in the future. It provides a cushion or buffer to withstand some unexpected emergency. The precautionary amount of cash depends upon the predictability of cash flows. If cash flows can be predicted with accuracy, less cash will be maintained for an emergency. The amount of precautionary cash is also influenced by the firm’s ability of the firm to borrow at short notice,less the need for precautionary balance.

Speculative Motive- The speculative motive relates to the holding of cash for investing in profit-making opportunities as and when they arise. The opportunity to make profit may arise when the security prices will hold cash, when it is expected that interest rates will rise and security prices will fall.

Securities can be purchased when the interest rate is expected to fall. The firm will benefit by the subsequent fall in interest rate is expected to fall; the firm will benefit by the subsequent fall in interest rates and increase in security prices.

Cash planning-Cash flows are inseparable parts of the business operations of firms. A firm needs cash to invest in inventory,receivable and fixed assets and to make payment for operating expenses in order to maintain growth in sales and earning.

Cash planning is a technique to plan and control the use of cash. It helps to anticipate the future cash flows and needs of the firm and reduces the possibility of idle cash balances.

In under to transact business in the securities market, an investor has to route her order is through a brokerage firms as only member broker are allocated to enter the trading floor trading among the member of a recognized  stock exchange is carried on within  the framework of rules, bye laws and regulation of the exchange.

## Function of brokerage firm

1) The business of broker consists of searching out buyer when their customer wish to sell and locating sellers when their customers wish to buy so as to executes transaction as per customer instruction.

2) The broker do not function as principals in the transaction, they are agents only.

3)The exercise of care and skill require that the broker follows instructions and places the order in the market. When the security is traded in the fastest possible time.¹

4) The brokerage firm may be hold liable for any losses resulting its mistake.

5)The brokerage firm can not act as  both broker and dealer in the same transaction because these could be  conflict of interest or double commission might result.

6) The broker makes his fee from the difference between the price at which he buys the shares for his own account and the price at which he sells their to customer.

### Functional specialization  of members

Functional specialization of member at the stock exchange helps a lot in making it is free active and continuous market. In  India the stock exchange rules, by-laws and regulation do not prescribe any functional distinction between member.

1)Commission broker-Almost all members act as commission brokers. The commission broker executes buying and selling orders on the floor of the exchange. For that, he charges a commission not exceeding the official scale of brokerage.

2) Floor broker- The floor brokers are not officially attached to other members. The floor broker executes orders for any members and receives as his compensation a share of the brokerage charged by commission broker to his constituent.

3) Taravniwalla or jobber- The taraniwalla may be a jobber or specialist who specializes in stocks located at the same trading post.  He trades in and out of the market for small difference in price and as such is an important factor in.

4) Dealers in non-cleared securities- The dealer in non-cleared securities specializes in buying and selling on his own account shares which are not in the active list.

5) Odd-lot-dealer- The odd-lot dealer specializes in buying and selling in amount less than the prescribed trading units or lots. He buys odd lots and makes them up into marketable trading units.

6) Budliwala- The Budliwala or financier lends money to the market by taking up delivery on the due date at the end of the clearing for those who wish to carry over their purchase or loans securities to the market when it is short by giving delivery on the due date at the end of the clearing for those who wish to carry over their sales.

7) Arbitrageur-The arbitrageur specializes in making purchase and sales in different markets at the same time and profits by the differences in prices between the two centres.

8) Security dealer-The security dealer specialises in buying and selling gilt-edged securities that is securities issued by the central and state Governments and by statutory public bodies such as Municipal Corporation.

Types of transactions in a stock exchange

The member of recognized stock Exchanges are permitted to enter into transactions in securities as under.

a) For “spot delivery” i.e for delivery and payment on the same day as the date of the contract or on the next day.

b) For “hand delivery”, i.e, for delivery a d payment within the time or on the date stipulated when entering into bargain, which time or date shall not be more than 14 days following the date of the contract.

C) For “special delivery”,i.e. for delivery and payment within any time exceeding 14 days following the date of contract as may be stipulated when entering into the bargain and permitted by the Govering Board or the President

Basic types of  transaction

Long purchase– The long purchase is a transaction in which investor buy securities in the hope that they will increase in value and can be sold at a later date or profit. The object, then, is to buy low and sell high. A long purchase is the most common type of transaction.

Each of the basic types of orders described above can be used with long transaction. Because investor generally expect the price of the security to rise over the period of time they plant to hold it, their returns comes from any dividend or interest received during the ownership period, plus the difference between the price of the security to rise over the period of time they plant to hold it.

Their returns comes from any dividend or interest received during the ownership period l,plus the difference between the price at which they sell the security and the price paid to purchase it. This return, of course, is reduced by the brokerage fees paid to purchase and sell the securities.

Margin trading– Most security purchase do not have to be made on a cash basis borrowed funds can be used instead. This activity is referred to as margin trading and it is used for one basic reason to magnify returns. This is possible because the use of borrowed funds reduce the amount of capital that must be put by the investor. As peculiar as it may sound, the term margin itself refers to the amount of equity in an investment, or the amount that is not borrowed.

Essential of margin trading-Margin trading can be used with most kinds of securities. It normally leads to increased returns, but there are also some substantial risks. One of the biggest is that the issue may not perform as expected. If this in fact occurs, no amount of margin trading can corrects matters. Margin trading can only magnify, not produce them. Because the security being margins is always the ultimate source of returns, the security selection process is critical to this trading strategy.

## Volatility smiles

A plot of the implied volatility of an option as a function  of its strike price is known as a volatility smile.

Describe volatility smiles in different way.

## Put call parity

Put-call parity provides a good starting point for understanding volatility smiles. It is an important relationship between the price,c, of a European call and the price,p,of a European put .

$P+Soe^{-qt}$ = $C+k^{-rt}$

The call and the put have the same strike price ,k, time to maturity,T,

So= The variable is the price of the underlying assets today

r= Risk free interest rate

q= the yield on the assets

A key feature of the put-call parity relationship is that it is based on a relatively simple no-arbitrage argument. It does not require any assumptions about the future probability distribution of the assets price. It is true the when the assets price distribution is log normal and when it is not log normal.

Suppose that for a particular value of the volatility, PBs and CBs are the value of European put and call option calculate using the Black-Schloes model suppose further that Pmkt and Cmkt are the market values of these option.Because put-call parity holds for the market value of these option.Because put-call parity holds for the Black-Schloes model, we must have.

$P^{_{Bs}^{}$+$Soe^{-qt}=C^{_{Bs}$+$Ke^{-rt}$

Because it also holds  for the market prices we have

$P^{_{mkt}}$+$Soe^{-qt}$ =$C^{_{mkt}}+Ke^{-rt}$

Substracting these two equation gives

$P^{_{Bs}}$$P^{_{mkt}}$ = $C^{_{Bs}}$$C^{_{mkt}}$

### Foreign currency option

The volatility smile used by traders to price foreign currency options. The volatility is relatively low for at-the-money options.It becomes progressively higher as an option moves either in the money or out of the money.

We show how to determine the risk-neutral probability distribution for an assets price at future time from the volatility smile given by options maturing at that time. We refer to this as the implied distribution.

A log normal distribution with the same mean and standard deviation as the implied distribution has heavier tails than the log normal distribution.

Consistent with each other consider first a drop-out of the money call option with a higher strike price of K2. This option pays off only if the exchange rate proves to be above K2.

The probability of this is higher for the implied probability distribution than for the implied probability distribution. We therefore expect the implied distributed to give a relatively high price for the option. A relatively high price leads to a relatively high implied volatility.

#### Equity options

The volatility smile used by traders to price equity options (both those an individual stocks indices) This is some times referred to as a volatility skew. The volatility decrease as the price increase. The volatility used to price increase.

The volatility use in  price a low strike price option.(deep-out-of the money put on a drop-in-the money call) is significantly higher strike price option (deep-in-the-money put on a deep-out- of -the money call.

The volatility smile for the equity option corresponds to the implied probability distribution given by the solid  line. A log normal distribution with same mean and standard rather than as the relationship between the implied volatility and K. The smile is then usually much less dependent on the time to maturity.

## Non-banking financial company

Finance may be defined as the art and service of managing money. The two major areas of finance are.

1) Financial management managerial finance corporate finance.

II) Finance services.

Financial management is concerned with duties of the financial manager in the business firm who perform such varied tasks as budgeting financial forecasting,cash management credit administration investment analysis funds management and so on financial services is concerned with the design and delivery of advice and financial products to individuals and business within the areas of banking and related institution.

Personal financial planning investment real assets and so on. A wide variety of funds assets based and non- fund based advisory services are provided mainly by the non-banking finance compsnies(NBFCs).

Non-banking financial company(NBFC)

It means i) A financial institution that is a company.

ii) A non-banking institution that business is the receiving of deposits under any scheme arrangements in any other manner or lending in any manner.

iii) Such other non-banking institution class of institution as the RBI may specify with the prior approval of the government and by notification in the official Gazette

## Scope of NBFC

The direction supply to a NBFC which is defined to include only non-banking institution that is any purchase  finance investment loan of mutual benefit financial company and an equipment leasing company but excludes an insurance company stock exchange .

Stockbroking company merchant banking company.The directions are ads not applicable to NBFCs that do not accept/hold public deposit.NBFCs have to pass a resolution in a meeting of the have neither accepted nor would accept any public deposit doing the year to the effect that they have neither accepted nor would accept any public deposit during the year.

### Repayment of deposit by a non problem NBFC

A non-problem NBFC may

1)Permit premature repayment of a public deposit at its sole direction.

2)Grant a laon upto 75 percent of the deposit after 3 month from the date of deposit at a rate of interest percent points above the rate of interest payable on the deposits.

Repayment by a problem NBFC

A problem NBFC means a NBFC which

i) Has refused to meet within 5 days lawful demand for repayment of a matured deposit.

ii) Intermate the company law Board under section 58-AA of the companies act about its default to a depositor in repayment of any part of it’s any interest on it.

iii) approaches the RBI for withdrawal of liquid asset securities to meet deposit obligation, or for any relief relaxation from the provisions of the RBI public.

iv) It has been identified by the RBI to be ment of public deposits/dues. Such a company may, to enable a depositor to meet expenses of an emergent nature l, prematurely(a) repay a tiny deposit that is aggregate amount not exceeding Rs.10000 in the name of the sole/first named depositor in all the branches of the NBFC) in entirely upto rs.percentage points above the rate of interest payable on the deposit.

For the purpose of premature repayment, all deposit accounts standing to the credit of sole first a named depositor should be clubbed and treated as one account. Where an NBFC prematurely repays a public deposit for any of the reason. a) after 3 months but more than 6 months not interest b) after 6 months but before maturity 2 percent lower than the interest applicable to a deposit for the period for which the concerned deposit has run. If no rate has been specified for that period l, 3 percent lower than the minimum rate at which public deposit is are accepted by the NBFC.

Deposits Receipts- All NBFC have to furnish deposit joint deposits or their agents with a receipt of the deposit stating the date of deposit name of the depositors, the amount of deposit (in words and figure), rate of interest and date of maturity. It must be signed by an officer who can act on behalf of the company in this regard.

Register of deposits- All NBFCs have to keep register of deposit, containing cache depositor particular as detailed below .

b) Date and amount of each deposit

C) Duration and due date of each deposit.

d) Date and amount of accrued interest premium on each deposit.

e) Date of claim made by depositor,

f) Date and amount of each repayment of principal/ interest.

g) Reason for delay in repayment beyond five working days and

h) Any other particulars relating to the deposits.

## Cost of debt

A company may raise debt in a variety of ways. It may borrow funds from financial institutions or public either in the form of public deposit or debentures (bonds) for a specified period of time at a certain rate of interest.

A debenture or bond may be issued at par or at a discount or premium as compared to its face value. The contractual rate of interest or the coupon rate from that basis for calculating the cost of debt.

Debt issued at par

The before-tax cost of debt is the rate of return required by lenders. It is easy to compute before-tax cost of debt issued and to be redeemed at par;  It is simply equal to the contractual or coupan rate of interest.

For example, a company decides to sell a new issue of 7  years 15 percent bonds of Rs. 100 bonds and will pay Rs. two each at par. If the company realises to bond holders at maturity, the before-tax cost of debt will simply be equal to the rate of interest of 15 percent.

Kd =i= $\frac{INT}{Bo}$

Where

Kd= before-tax cost of debt

i= the coupan rate of interest

Bo= the issue price of the bond(debt)

INT= Amount of interest

The before tax cost of bond in the example

Kd = $\frac{15}{100}$= 0.15 or 15%

Debt issued at discount and premium

When debt is issued at par and redeemed at par. This equation can be rewritten as follows to compute the before-tax cost of debt.

Bo = $\frac{\sum_{}^{n}}{t=1}$ $\frac{INTt}{(1+kd)t}+\frac{Bn}{(1+kd)}n$

Bn= The repayment of debt on maturity

If the discount or premium is adjusted for computing taxes, following short-cut method can also be used to calculate the before-tax cost debt.

Cost of the existing debt

Sometime a firm may like to compute the current cost of the existing debt. In such a case the cost of debt should be approximate by the current market yield of the debt.

Firm has 11 percent debenture of Rs. 100000(rs.100 face value l) out standing at 31 December.19×1 matured on December 31. 19×6 ). If a new issue of debentures could be sold at net reliable price Rs.80 in the beginning of 19×2.

The interest paid on debt is tax deductible. The higher the interest charges the lower will be the amount of tax payable by the firm. This implies that the government indirectly pays a part of the lender’s required rate of return. As a result of the interest tax shield, the after tax cost of debt to the firm will be substantially less than the investor required rate of return.

The before-tax cost of debt kd should therefore, be adjusted for the tax effect as follows.

After tax cost of debt

Kd(I-T), where T= the corporate tax

Kd(1-T)=0.1650(1-0.35)=0.1073 or 10.73%

It should be noted that the tax benefit of interest deductibility would be available only  when the firm is profitable and is paying taxes.

An unprofitable firm is not required to pay any taxes. It would not gain any tax benefit associated with the payment of interest and it’s true  cost of debt is the before-tax cost.

It is important to remember that in the calculation of the average cost of capital. The after-tax cost of debt must be used, not the before-tax cost of debt.