UNIT-1Nature of Financial

Management

MeaningWe find that corporate finance is based on two fields of study, Economics and Accounting. Economics provides us much of the theory that underlines our techniques, whereas Accounting provides the data which helps us in making decision. Financial Management is the maintenance and creation of economic value or wealth.Illustration :Consider two firms, Merck and General Motors (G.M.) at the end of 2007, the total market value of Merck, a large pharmaceutical Co. was $ 103 billons. Over the life of the business, Merck investor had invested about $ 30 billions in the business. In other words management created $ 73 billions in additional wealth for the Shareholders G M on the other hand, was valued at $ 30 billions at

the end of 2007; but over the year G M's investors had actually invested $ 85 billions-- a loss in value of $ 55 billions. Therefore Merck created wealth for its shareholder's, while G M lost shareholder's wealth.Financial Management is that branch of study which deals with finance and its functions which are- Raising of funds Allocations Controlling financial resources

The objective of all the above activities is to maximize shareholder's wealth."Financial Management is the operational activity of a business that is responsible for obtaining and effectively utilising the funds necessary for efficient operations."

Joseph & MassieThere are 3 A's of Financial Management. Anticipating Financial Needs Acquiring Financial Resources and Allocating Funds in Business

Since FM is concerned with the efficient use of capital funds which is an important economic resource.

Finance & EconomicsEconomics is concerned with the overall institutional environment in which the firm operates, which includes the internal and external environment. It is effect with the factors like. Growth rate of the economy Domestic saving rate The tax environment External economic relationship Demand and Supply relationship The rate of inflation The fiscal policy The terms on which the firm can raise

finance etc.No financial manager can afford to ignore the key development in the economic sphere and the impact of the same on the firm. Since the macro-economic environment defines the setting within which a firm operates and

micro-economic theory provides the conceptual underpinning(support) for the tools of financial decision making.Finance & AccountingThe finance and accounting functions are closely related and almost invariably fall within the domain of the chief financial officer. We can understand the relation of finance with account in the following three heads. Score Keeping Vs Value Maximising

Accounting is concerned with score keeping, whereas finance is aimed at value maximizing.“ The accountant role is to provide consistently developed and easily interpreted data about the firm’s past, present and future operations. The financial manager uses these data, either in raw form or after certain adjustment and analyses, as an important input to the decision- making process.”

Gitman Accrual Method Vs. Cash Method

The accountant prepares the accounting reports based on the accrual method which recognizes revenues when the sale occurs and matches expenses to sales. The focus of the manager, however, is on cash flows. He is concerned about the magnitude, timing and risk of cash flows as these are the fundamental determinants of value. Certainty Vs. Uncertainty

Accounting deals primarily with the past. It records what has happened. Hence, it is relatively more objective and certain. Finance is concerned mainly with the future. It involves decision making under imperfect information and uncertainty.

Scope Of Financial Management

The firm secures whatever capital needs and employs its activities which generates returns on invested capital. Finance is involved in all the activities of the firm such as buying a new machine or replacing an old machine for the purpose of increasing production capacity effects the flow of funds. Recruitment of employees in production is clearly a responsibility of the production department but it requires payment of wages and salaries and other benefits thus involves finance. Similarly sales promotion activities comes within the preview of marketing department but advertisement and other marketing activities involves the cash outflow hence finance is involved therefore, it is understood that the

scope of financial management is not restricted to finance department only but also effects production and marketing department as well. For better under standing the scope of financial management we can divide it into two approaches, Traditional and Modern Approach. Traditional Approach :- In early stage the role of FM was restricted upto raising and administrating of funds needed by the corporate enterprises to meet their financial needs such as; Arrangement of funds from financial

institutions. Arrangement of funds through financial

instruments like share, bonds etc. Looking after the legal and accounting

relationship between a corporation and its sources of funds.

Thus, the finance manager has a limited role to perform he was expected to keep accurate financial records, prepare reports on the corporation's status and performance and

manage cash in a way that the corporation was in a position to pay its bills on time.The term 'Corporate Finance' was used in place of the present term 'Financial Management'. The traditional approach now has been discarded as it suffers from certain limitation, the traditional approach implied a very narrow scope for financial management as it has not provided analytical framework for financial decision making.

Modern Approach :- Provides both conceptual and analytical framework for financial decision making. It means the financial function covers both, acquisition and allocating of funds the new approach is an analytical way of viewing the financial problems of a firm. the main contents of the modern approach are as, What is the total valume of funds, an

enterprise should have ?

What specific assets should an enterprise acquire ?

How are the funds required to be financed ?

Objective of Financial Management

Maintenance of Liquid Assets Maximization of profitability of the

firm Maximization of shareholder’s wealth Ensuring a fair return to shareholder’s Building up reserves for growth and

expansion Ensuring maximum operational

efficiency by efficient and effective utilization of finance

Ensuring financial discipline in the management

Function of Financial Management

It is very difficult to separate the function from production, marketing and other function of the organization but the function such as raising of funds, investing them in assets and distributing return earned from assets to shareholders can easily be identified.The function of financial management may be classified on the basis of Liquidity, Profitability and Management.

Liquidity : It is ascertained on the basis of three important considerations. Forecasting cash flows, i.e., matching the

inflows against the cash outflow. Raising funds, i.e., financial manager

will have to ascertain the sources from where the funds may be raised and the time when these funds are needed.

Managing the flow of internal funds.

Profitability : While ascertaining the profitability we have to look after Cost control Pricing Forecasting future profits

Management : Asset management has assumed an important role in financial management. It includes both long and short terms funds management.Beside the above mentioned main function there are some other functions also such as- Determining financial Need Determining sources of fund Profit allocation or dividend decision Financial analysis Optimal capital structure Cost volume profit analysis Profit planning and control Project planning and evaluation Working capital management

Acquisition and mergers Corporate taxation

Role of Finance Manager :

Who is a finance manager ? What is his or her role ? A financial manager is a person who is responsible in a significant way to carry out the financial function he occupies the key position in the enterprises now a days he is one of the member of the top management. In today’s scenario, the job of financial manager in India has become important, complex and demanding, due to certain changes such as. Industrial licensing framework has been

substantially relaxed, leading to considerable expansion in the scope of private sector investment.

The Monopolies and Restrictive Trade Practices (MRTP) has been virtually abolished and the Foreign Exchange

Management Act (FEMA) has been substantially liberalized.

Freedom has been given to companies in designing and pricing the securities issued by them.

The system of cash credit has been replaced by a system of working capital loan.

The pace of mergers, acquisitions and restructuring has intensified.

The scope for direct investment has expanded considerably and foreign portfolio investment has assumed great significance.

And also due to the wake of global competition, economic uncertainty, tax law changes, etc.The key challenges of financial manager may be as Investment planning Financial structure Mergers, acquisitions and restructuring Working capital management

Performance Management Risk Management Investor relations Utilized the fund in the most efficient

manner. Financial Negotiation.

In USA the function of the financial officer are divided into two i.e., Tresureship and Controller function. However these terms are not used in India. In many corporations of India financial managers are appointed to

perform the duties of the treasures and controller.

Decision Making in Financial Management :

Financial Management is indeed the key to successful business operations, without proper administration and effective utilizations of finance, no business enterprises can utilize its potentials for growth and expansions. FM is concerned with the acquisition, financing and management of assets with some overall goals in mind and for this purpose the decisions making process of FM can be broadly classified as Investment Decisions Financing Decisions Dividend Decisions

Investment Decisions : It is most important than the other two decisions. It

begins with the dertermination of total amount of assets needed to be held by the firm. How much of the fund it needed to be invested in fixed and current assets. Investment of funds in fixed assets has long term implications as funds are blocked for a long duration. But immediate returns can be expected from investment in current assets. Fixed assets are termed as long term assets and investment in it is popularly known as “Capital Budegeting.” It may be defined as the firm’s decision to invest its current funds most efficiently in fixed assets with an expected flow of benefits over a series of year. Current assets are termed as short term asset and investment in it is known as "Working Capital Management". The investment in current asset can be converted into cash within a financial year without diminution(reduction) in value.

Financial Decisions : Under this process the financial manager is concerned with make up of the left hand side of the balance sheet. It is related to the financing mix i.e., mix of debt and equity which is known as the firm's 'Capital Structure'. The financing manager must strike to obtain the best financing mix of the optimum capital structure for the firm. The capital structure is considered as optimum when the market value of shares is maximum. the proper balance must be maintained between return and risk. In the absence of debt, the shareholder’s return is equal to the firm’s return. The use of debt affects the return and risk of shareholders; it may increase the return on equity funds, but it always increases the risk as well. The change in the shareholder’s return caused by the change in the profits is called the financial leverage(relationship between

the amount of money a company owes and the value of its shares). A proper balance will have to be struck between return and risk. When the shareholder’s return is maximized with given risk, the market value per share will be maximized with given risk, the market value per share will be maximized and the firm’s capital structure would be considered optimum.Once the financial manager is able to determine the best combination of debt and equity, he or she must raise the appropriate amount through the best available sources.

Dividend Decisions : This is the third financial decision under this process the financial manager has to decide whether all profits be distributed or it should be retained. This distribution of dividends or retaining should be determined in terms of its impact on the shrehloder’s wealth. The financial manager should determined optimum dividend policy.

This policy is one which maximizes the market value of the firms shares. The financial manager should consider the questions of dividend stability, bonus shares and cash dividend in practice.

Inter-Relation Among Financial Decision :

Inter-relation between “Investment and Financing Decisions”: While taking the investment decision, the financial manger decides the type of asset or project that should be selected. The selection of a particular asset or project helps to determine the amount of funds required to finance the project or asset. For example, suppose the investment on fixed assets is Rs. 10 crore and investment in current assets or working capital is Rs. 4 crore. So the total fund required to finance the total assets is Rs. 14 crore.

Once the anticipation of funds required is completed then the next decision is financing decision. Financing decision means raising the required funds by various instruments.There is a inter-relation between investment decision and financing decision, without knowing the amount of funds required and types of fund (Short-term and long-term) it is not possible to raise fund. To put it in simple words, investment decision and financing decisions cannot be independent. They are dependent on each other.

Inter-relation between “Financing Decisions and Dividend Decision”: Financing decision influences and is influenced by dividend decision, since retention of profits for financing selected assets or projects, reduces the profit available to ordinary shareholder, thereby reducing dividend payout ratio. For example, to finance a certain project

amount required is Rs.14 crore. If the financial manager plan to raise only Rs.7 crore from outside and the remaining by way of retained earnings, and if the dividend decision is 100% payout ratio, then the financial manager has to depend completely on outside sources to raise the required funds. So dividend decision influences the financing decision. Hence, there is an inter-relation between financing decision and dividend decision.

Inter-relation between “Dividend Decisions and Investment Decisions”: Dividend decision and investment decision are inter-related because retention of profits for financing the selected assets depends on the rate of return on proposed investment and the opportunity cost of the retained profits. Profits are retained when return on investment is higher than the opportunity cost of retained profits and vice-versa.

Hence, there is inter-relation between investment decision and dividend decision.

The Fundamental Principle of Finance : The key question we asked before making a business decision is will the decision raise the market value of the firm ? To answer this question, we have to look at the fundamental principle of finance.“ A business proposal- required of whether it is a new investment or acquisition of another co. or a restructuring initiative- raises the value of the firm only if the present value of the future stream of net cash benefits expected from the proposal is greater than the initial cash outlay required to implement the proposal.”

The difference between the present value of future cash benefits and the initial outlay represent the net present value or NPV of the proposal.Net Present Value = Present Value of Future

Cash benefits – Initial Cash Outlay

Risk Return Trade Off : At some points we all saved some money. Why have we done this ?..........The answer is simple to expand our future consumption opportunities. Before investing, firstly, investor demand a min. return for delaying consumption that must be greater than the anticipated rate of inflation (“a general and progressive increase in prices; "in inflation everything gets more valuable

except money”). If they didn’t receive enough to compensate for anticipated inflation investors would purchase whatever goods they desired ahead of time or invest in assets that were subject to inflation and earn the rate of inflation on those assets. There isn’t much incentive to postpone consumption if your saving are going to decline in terms of purchasing power.Financial decisions often involve alternative cause of action. Should the firm set up a plant which has capacity of one million tons or two millions tons ? should the debt equity

ratio of the firm be 2:1 or 1:1 ? Should the firm pursue a generous credit policy or niggardly(miserly) credit policy ? should the firm carry a large inventory or a small inventory ?The alternative course of action typically have different risk-return implications. A large plant may have a higher expected return and higher risk exposure, whereas a small plant may have lower expected return and a lower exposure. A high debt equity ratio compared to a lower debt-equity ratio, may reduce the cost of capital but expose the firm to greater risk. A ‘hot’stock, compared to a defensive stock, may offer a higher expected return but also a greater possibility of loss. When investor choose to put his money in risky investment side by side he expected higher return. The more risk an investment has the higher will be its expected return. The relation between risk and expected return is shown in the following figure.

The Risk-Return Relationship

Your decision to invest your money in government bonds has less risk as interest rate is known and the risk of default is very less. On the other hand, you would incur more risk if you decide to invest your money in shares, as return is not certain. Financial decisions of the firm are guided by the risk return trade off. These decision are inter-related and jointly affect the market value of

its shares by influencing return and risk of the firm. The relationship between return and risk can be simply expressed by the following equation.

Return = Risk Free Rate + Risk Premium

Risk free rate is a rate obtainable from a default-risk free govt. security. An investor assuming risk from her investment require a risk premium above the risk free rate. Risk free rate is a compensation for time and risk premium for risk. A proper balance between return and risk should be maintained to maximize the market value of a firm’s share. Such balance is called risk return trade-off and every financial decision involves this trade off. We can also say that risk-return trade off is the desire for the lowest possible risk and highest possible return.

Profit Maximisation Versus Wealth Maximisation

For long range planning and management controls, a company establishes its overall objective, which helps us in measuring performance and control. Objective setting is most important phase in the business enterprises, since upon correct objective setting the entire structure of the strategies, polices and plans of a company rests. It is generally agreed in theory that the financial goal of the firm should be shareholder’s wealth maximization (SWM), as reflected in the market value of the firm share, the behavioral assumption of profit maximization has served economic theory as well. Let see the concept of profit maximization and wealth maximization.

Profit Maximisation : Profit as an Objective has emerged from over a century of economic theory. In this traditional

economic theory, the typical firm was small, over managed and competing with a large number of similar firms. In such a situation The profit of the firm become the income

of the owner The force of competition imposed profit

maximization upon the firm to survive in business.

Essential for growth and development of business.

Profit is the difference between revenue and costs, once revenue and costs are identified the assumption of profit maximization enables prediction to be readily made about the consequence of any environmental change.The following factors have served to cast doubt on the validity of the profit maximization. In twenty first century, there has been

substaibtial changes in the owernership and organization of business. The typical large co is owned by a diffusion

of shareholders and managed by salaried professionals with little or no ownership interest, paid salaries often unrelated to profit. Manager may then view profits as only of a wide range of performance indicators.

The same period has seen the concentration of markets dominated by large corporation (often mulitnational) so that competition may have been severely weakened, such corporations may well be able to survive at less than maximum possible profits, simply by virtue of their size.

It has traditionally been argued that the objective of a company is to earn profit hence the objective of financial management is also maximization of profit and this very objective has been criticized on the following ground. The concept of profit maximization is

vague & narrow (It is not clear that it

means total operating profit or profit occurring to shareholders ?)

It ignores the risk factor as well as timing of returns

It emphasizes the short run profitability and short-term projects

Ignores social and moral obligations of business.

A financial officer could easily increase current profit by eliminating research and development expenditures and cutting down routine maintenance in the short run, this might result in increased profits, but this is clearly not in the best of long-run interests of the firm.Wealth Maximization : Profit is the difference between revenue and costs and profit maximization leads to wealth maximization of the firm. The separation of ownership from management, the increase in the intensity of the competition has lead to the redefinition of profit maximization goal of a firm. As the

owners of the company are its shareholders the primary financial objective of corporate finance is usually stated to be maximization of shareholder wealth. Since shareholders receive their wealth through dividends and capital gains, shareholders wealth will be maximized by maximizing the value of dividends and capital gains that shareholders receive overtime. The shareholders wealth maximization goal states that management should seek to maximize the present value of the expected future returns to the owners of the firm. The wealth maximization goal is advocated on the following grounds: It takes into consideration long-run

survival and growth of the firm. It suggests the regular and consistent

dividend payment to the shareholder. The financial decisions are taken with a

view to improve the capital appreciation of the share price

It considers all future cash flows, dividends and earning per share (EPS)

Maximization of firm’s value is reflected in the market price of share, since it depends on shareholders expectations as regards profitability, long-run prospects, timing differences of returns, risk, distribution of return etc. of the firm.

Profit maximization partly enables the firm in wealth maximization.

The shareholders always prefer wealth maximization rather than maximization of inflow of profits.

Maximizes the net present value of a course of action to shareholders.

Accounts for the timing and risk of the expected benefits.

Benefits are measured in terms of cash flows.

Fundamental objective—maximize the market value of the firm’s shares.

Significance of Wealth- MaximizationThe company although it cares more for the economic welfare of the shareholders, it cannot forget others who directly or indirectly work for the overall development of the company. Thus Wealth- Maximization takes care of

Lenders or creditors Workers or Employees Public or Society Management or Employer Other objective – Ensuring fair

return to shareholder, Building up reserves for growth and expansion, ensuring financial discipline in the management

Time Value of Money

The value of money received today is different from the value of money received after some time in the future. The value of

money is time dependent which is based on four reasons.

1. Inflation : Under inflationary conditions the value of money, expressed in terms of its purchasing power over goods and services, declines.

2. Risk : ‘A bird in hand is worth two in the bush’. This statement implies that, people consider a rupee today, worth more than a rupee in the future, say after a year. This is because uncertainty connected with the future.

3. Personal Consumption Preference : Individuals generally prefer current consumption to future consumption. The promise of a bowl of rice next week counts for little to the starving man. He prefers to consume today because of the urgency of their present wants or because of the risk of not being in a position to enjoy future consumption

that may be caused by illness or death or because of inflation.

4. Investment Opportunity : Money like any other desirable commodity, has a price, given the choice of Rs.100 now or the same amount in one year’s time, it is always preferable to take the Rs.100 now because it could be invested over the next year at (say) 18% interest rate to produce Rs.118 at the end of one year. If 18% is the best risk free return available, then your could be indifferent to receiving Rs.100 now or Rs.118 in one year’s time or it can be said that the present value of Rs.118 receivable one year hence is Rs.100.

Time Value of money or time preference of money is one of the central ideas in finance. It becomes important and is of vital consideration in decision making.The following notation will be used in our discussion

PV = Present Value.FVn = Future Value n year hence.Ct = Cash Flow occurring at the end of year tA = A stream of constant periodic cash flow over a given time.r = Interest rate or discount rate. g = Expected growth rate in Cash Flows.n = Number of periods over which the cash flows occur. Future Value of a Single Amount :The process of investing money as well or reinvesting the interest earned therein is called compounding. The future value or compounded value of an investment after n year when the interest rate is r percent is

FVn = PV (1+r)n

In this equation (1+r)n is called the future value interest factor or compound value factor or simply future value factor.

Alternatively, we can consult a future value interest factor (FVIF) table.

Illustration : If you deposit Rs.1,000 today in a bank that pays 10% interest compounded annually, how much will the deposit grow to after 8 years and 12 years ? FV8 = Rs.1,000 (1.10)8

= Rs.1,000 (2.144) = Rs.2,144The Future Value, 12 year hence will be.FV12 = Rs.1,000 (1.10)12

= Rs.1,000 (3.318) = Rs.3,138Graphic View :

Compound and Simple Interest :When money is invested at compound interest which means that each interest payment is reinvested to earn further interest in future periods. By contrast, if no interest is earned on interest the investment earns only simple interest. In such a case the invest grows, grows as follows.

Future Value = Present Value [ 1+ Number of years X Interest rate]

Doubling Period :How long would it take to double the amount at a given rate of interest ? For this we will look at the future value interest factor we find when the interest rate is 12% it takes about 6 years and when the interest rate is 6% it takes about 12 years. To simplify the calculation there is a rule of 72.

The doubling period is obtained by dividing 72 by the interest rate. For example if the interest rate is 8 percent, the doubling period is about 9 years (72/8).To calculate the doubling period, a more accurate rule is the rule of 69, according to this rule, the doubling period is equal to

0.35 + 69/Interest rate

Illustrartion : Interest Rate Doubling Period 10% 0.35 + 69/10

0.35 + 6.97.25 years.

Present Value of Single Amount :Suppose someone promises to give you Rs.1,000 three year hence what is the present value of this amount if the interest rate is 10% ? The present value can be

calculated by discounting Rs.1000, to the present point of time as follows.The process of discounting used for calculating the present value is simply the inverse of compounding. The present value formula can be obtained by manipulating the compounding formula.

FVn = PV (1+r)n ………………Equ. 1

Dividing Equ. 1 by (1+r)n we get

PV = FVn [ 1/(1+r)n ]

The Factor [ 1/(1+r)n ] is called the discounting factor or the present value interest factor (PVIFn)

Illustration : What is the present value of Rs.1,000 receivable 16 years hence if the discounting rate is 10%.

PV = FVn [ 1/(1+r)n ]

= 1,000[ 1/(1+.10)16 ]

= 1,000[ 1/(1.10)16 ]= 1,000 [0.218] = Rs.218

Graphic View :

Present Value of an uneven Series :In financial analysis we often come across uneven cash flow streams. For example, the cash flow stream associated with a capital investment projected in typically uneven. Likewise, the dividend stream associated with an equity share is usually uneven and perhaps growing.

The present value of a cash flow stream- uneven or even- may be calculated with the help of the following formula :

PVn = present value of a cash flow stream.At= cash flow occurring at the end of year t.n = duration of the cash flow stream.

Future Value of Annuity : An annuity is a stream of constant cash flow (payment or receipt) occurring at regular intervals of time. The premium payments of life insurance policy, are an annuity. When the cash flows at the end of each period, the annuity is called an ordinary annuity or a deferred annuity. When the cash flows occur at the beginning of each period, the annuity is called an annuity due.Suppose you deposit Rs. 1,000 annually in a bank for 5 years and your deposits earn a

compound interest of 10 %. What will be the value of their series of deposit (an annuity) at the end of 5 years ?

FVAn = Rs.1,000 (1.10)4 + Rs.1,000 (1.10)3 + Rs.1,000 (1.10)2 + Rs.1,000 (1.10) + Rs.1,000

= Rs. 1,000(1.464) + Rs.1,000 (1.331) + Rs.1,000 (1.21) + Rs.1,000 = Rs.6,105

FormulaThe future value of an annuity.

FVAn = A [(1+r)n-1] r

Applications

Knowing what lies in store for you :

Suppose you have decided to deposit Rs. 30,000 per year in your public provident

fund A/c for 30 years. What will be the accumulated amount in your public provident fund A/c at the end of 30 years if the interest rate is 11%

The accumulated sum will be = Rs. 30,000 (FVIFA 11%, 30yrs)= Rs. 30,000 [(1+.11)30-1] .11

= Rs. 30,000 [(1.11)30-1] .11= Rs. 30,000 (199.02)= Rs. 59,70,600.

How much should you save annually:You want to buy a house after 5 years when it is expected to cost Rs. 2 million. How much should you save annually if your savings earn a compound retrun of 12% ?

FVIFAn=5,r=12% = [(1+0.12)5-1] 0.12 = 6.353

The annual savings should be

Rs.20,00,000/6.353= Rs.3,14,812

Sinking Fund

It is a kind of reserve by which a provision is made to reduce a liability,e.g., redemption of debentures or repayment of a loan. A sinking fund of specific reserve set aside for the redemption of a long-term debt. The main purpose of creating a sinking fund is to have a certain sum of money to accumulated for a future date by setting aside a certain sum of money every year. It is a kind of specific reserve. Every year a certain sum of money is invested in such a way that will compound interest, the exact amount to wipe off the liability or replace the wasting asset or to meet the loss, will be available. The amount to be invested every year can be known from the compound interest annuity tables.

Finding the interest Rate A finance company advertises that it will pay a lump sum of Rs. 8,000 at the end of 6 years to investors who deposit annually Rs,1,000 for 6 years. What interest rate is implicit(suggested) in this offer ?

Find the FVIFAr,6

Rs.8,000 = Rs.1,000 X FVIFAr,6

FVIFAr,6 = Rs.8,000/Rs.1,000

Look at the FVIFAr,n table and read the row corresponding to 6 years until you find a value close to 8.000. Doing so, we find thatFVIA12%,6 is 8.115 So we conclude that the interest rate is slightly below 12%.

How Long should you wait :You want to take up a trip to the moon which costs Rs 10,00,000 the cost is

expected to remain unchanged in nominal terms. You can save annually Rs.50,000 to fulfill your desire. How long will you have to wait if your savings earn an interest of 12% ?

50,000 X FVIAn=?,12%, = 10,00,00050,000 X {1.12n-1/0.12} =1,00,0001.12n-1 = 2.4

1.12n = 2.4 +1= 3.4n log 1.12 = log 3.4n X 0.0492 = 0.5315n = 0.5315/0.0492n = 10.8 yearsyou will have to wait for about 11 years

Present Value of an Annuity :Suppose you expect to receive Rs.1,000 annually for 3 years, each receipt occurring at the end of the year. What is the present value or this stream of benefits if the discount rate is 10% ? The present value of

this annuity is simply the sum of the present values of all the inflow of this annuity :

Rs 1,000 (1/1.10) + Rs. 1,000 (1/1.10)2 + Rs. 1,000 (1/1.10)3

= Rs.1,000 X 0.9091 + Rs.1,000 X 0.8264 + Rs.1,000 X 0.7513

= Rs.2,478.8

Formula

PVAn = A [{1-(1/1+r)n}/r] A = Constant Periodic flow

Present Value interest factor for an annuity is

Applications

How much can you borrow for a car :After reviewing your budget, you have determined that you can afford to pay Rs.12,000 per month for 3 years toward a new car. You call a finance company and learn that the going rate of interest on car finance is 1.5% month for 36 months . How much can you borrow ?

To determining the amount of borrowing, we have to calculate the present value of Rs.12,000 per month for 36 months at 1.5% per month.

= [{1-(1/1+r)36}/r] = [{1-(1/1.015)36}/0.015] = 27.70Hence the present value of 36 payments of Rs.12,000 each is :

Present value=Rs.12,000 x 27.70 = Rs.3,32,400

You can, therefore, borrow Rs.3,32,400 to buy the car.

Period of loan Amortisation(the process of paying back a debt by making a small regular payments over

a period of time) : You want to borrow Rs10,80,000 to buy a flat. You approach a housing finance company which charges 12.5% interest. You can pay Rs. 1,80,000 per year toward loan amortization. What should be the maturity period of the loan ?

The present value of annuity of Rs1,80,000 is set equal to Rs.10,80,000.

1,80,000 x PVIAn,r = 10,80,000

1,80,000 x PVIAn=?,r=12.5% =

10,80,000

1,80,000x[{1-(1/1.125)n}/0.125] = 10,80,000

[{1-(1/1.125)n}/0.125] = 10,80,000/1,80,000

= [{1-(1/1.125)n}/0.125] = 61/(1.125)n = 0.251.125n = 4n log 1.125 = log 4n x 0.0512 = 0.6021n =0.6021/0.0512 = 11.76 years

you can perhaps request for a maturity of 12 years.

Determining the periodic withdrawal: If we make an investment today for a given period of time at a specified rate of interest, we may like to know the annual income. Capital recovery is the annuity of an investment made today for a specified period of time at a given rate of interest. The reciprocal of the present value annuity factor

is called the capital recovery factor (CRF).

Your father deposits Rs.3,00,000 on retirement in a bank which pays 10% interest. How much can he withdraw annually for a period of 10 years.

A = Rs.3,00,000 x 1/PVIFA10%,10

= Rs.3,00,000 x 1/6.145 = Rs.48,819

Present Value of a Growing Annuity :

The cash flow that grows at a constant rate for a specified period of time is a growing annuity.

The above formula can be used when the growth rate is less than the discount rate (g<r) as well as when the growth rate is more than the discount rate (g>r). However, it does not work when the growth rate is equal to the discount rate (g = r) in this case, the present value is simply equal to nA.

For example , Suppose you have the right to harvest a teak(a kind of asian tree) plantation for the next 20 years over which you expect to get 1,00,000 cubic feet of teak per year. The current price per cubic feet of teak is Rs. 500, but it is expected to increase at a rate of 8% per year. The discount rate is 15%. The present value of the teak that you can harvest from the teak forest can be determined as follows:

A Note on Annuities Due :

Ordinary Annuity is the annuity in which cash flows occur at the end of each period. But in which cash flow occurs at the beginning of each period is called an annuity due.

For example : When you enter into a lease for an apartment, the lease payments are due at the beginning of the month. The first lease payment is made at the beginning of the month. the second lease payment is due at the beginning of the second month, so on and so forth.

Since the cash flow of an annuity due occurs one period earlier in comparison to the cash flows on an ordinary annuity, the following relationship holds :

Annuity Due Value = Ordinary annuity value x (1+r)

Present Value of a perpetuity :

A Perpetuity is an annuity of infinite duration. The present value of a perpetuity may be expressed as follows

P = A x PVIFA r,infinite

A = constant annual paymentPVIFA r,infinite = present value interest factor for a perpetuity (an annuity of infinite duration)The value of PVIFA r,infinite equal to :

.

Intra-Year Compounding and Discounting:

So far we assumed that compounding is done annually. Now we consider the case where compounding is done more frequently. Suppose you deposit Rs.1,000 with a finance company which advertises that it pays 12% interest semi-annually- this means that the interest is paid every six months. The general formula for the future value of a single cash flow after n years when compounding is done m times a year is :

FVn = PV [1+(r/m)]mxn

Effective Versus Stated Rate :

Rs. 1,000 grows to Rs,1,123.6 at the end of a year if the stated rate of interest is 12% and compounding is done semi-annually.This means that Rs.1,000 grows at the rate of 12.36% per annum. The figur12.36 % is called the effective interest rate.

The relationship between the effective interest rate and the stated annual interest rate is as follows :

Effective interest rate = [1+ (Stated annual interest rate/m)]m -1

Shorter Discounting periods :Sometimes cash flows have to be discounted more frequently than once a year- Semi annually, quarterly, monthly, or daily. As in the case of intra-year compounding , the shorter discounting period implies that (i) the number of periods in the analysis increases and (ii) the discount rate applicable per period decreases.

Formula

PV = FVn [1/1+(r/m)]mn