Fundamentals of Financial Management | CMA Inter Syllabus

Table of Content

1. Introduction to Financial management
2. Time value of Money
3. Risk and Return
4. Exercise

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1. Introduction to Financial Management

1.1 Fundamentals

 Finance is called “The science of money”. It studies the principles and the methods of obtaining control of money from those who have saved it, and of administering it by those into whose control it passes. Finance is a branch of economics till 1890. Economics is defined as study of the efficient use of scarce resources. The decisions made by business firm in production, marketing, finance and personnel matters form the subject matters of economics. Finance is the process of conversion of accumulated funds to productive use. It is so intermingled with other economic forces that there is difficulty in appreciating the role of it plays.

 Howard and Upton in their book Introduction to Business Finance define Finance “as that administrative area or set of administrative functions in an organisation which relate with the arrangement of cash and credit so that the organisation may have the means to carry out its objectives as satisfactorily as possible”.

In the words of Parhter and Wert, “Business finance deals primarily with raising, administering and disbursing funds by privately owned business units operating in nonfinancial fields of industry”.

Corporate finance is concerned with budgeting, financial forecasting, cash management, credit administration, investment analysis and fund procurement of the business concern and the business concern needs to adopt modern technology and application suitable to the global environment.

Financial Management is managerial activity which is concerned with the planning and controlling of the firm’s financial resources.

 Howard and Upton define Financial Management “as an application of general managerial principles to the area of financial decision-making”.

Weston and Brigham define Financial Management “as an area of financial decision making, harmonizing individual motives and enterprise goal”.

 According to Van Horne, “Financial management is concerned with the acquisition, financing and management of assets with some overall goal in mind.”

 From the above definitions, two aspects of financial management are quite apparent - (i) procurement of funds and (ii) effective utilisation of funds. Procurement of funds indicates determining the sources of funds, deciding on the methods of raising funds etc. Effective utilisation of funds implies the investment decisions, capital budgeting decisions, working capital management decisions etc.

1.2 Objectives of Financial Management

 Financial management as the name suggests is management of finance. It deals with planning and mobilization of funds required by the firm. There is only one thing which matters for everyone right from the owners to the promoters and that is money. Managing of finance is nothing but managing of money.

 The main objectives of financial management may be classified into: (i) Profit maximization (minimization of loss) and (ii) Value/Wealth maximization.

• (i). Profit Maximization: In the economic theory, the behaviour of a firm is analysed in terms of profit maximization. It implies that a firm either produces maximum output for a given amount of input or uses minimum input for producing a given output. So, profit is considered to be the main driving force in business. A firm should manage all aspects of the business in such a way that revenues are maximised and costs are minimised to obtain maximum profit. Arguments in favour and against of profit maximisation are discussed in subsequent section of this chapter.
• (ii). Value/ Wealth Maximization: The earlier objective of profit maximization is now replaced by value/ wealth maximization. Since profit maximization is a limited one it cannot be the sole objective of a firm. Value creation is the driving force behind financial management. Creating wealth for shareholders by increasing the value for their investment is the key goal of financial management today. Maximising the market value of the firm can be calculated by using the formula

MV+MVE+MVD Where, MV  = Market value of the firm MVE = Market value of equity shares MVD = Market value of debt; if any

 

When the book values and market values of debts are the same, value or wealth maximization essentially reflects maximisation of market value per equity share.

Arguments in favour and against of profit maximisation are discussed in subsequent section of this chapter.

 Another objective of financial management is to trade-off between risk and return. For this, the firm has to make efficient use of economic resources mainly capital.

1.3 Scope and Functions of Financial Management

1. Scope of Financial Management
   Financial management is concerned with managing financial resources in the most optimal manner. 
   Modern financial management focuses three important decisions of a firm. These three decisions are discussed 
   below: 
   
   1. Investment Decision: Investment decision of a firm includes two main aspects- where to invest and how much to invest or the amount of investment. This maximizes the wealth of a firm. There are two basic issues involved in investment decisions: 
      a. Evaluation of alternative investment avenues so as to select the best option.
      b. Monitoring and implementation of the selected investment option. 
       Firms need to focus on optimum utilisation of funds with limited resources. The project with a higher return should be selected for investment. Capital Budgeting decisions helps in selecting the project with higher profitability and feasibility. For short-term investment decisions or the working capital management decisions the firm should ensure that there is neither excessive nor inadequate working capital. 
   2. Financing Decision: The objective of a financing decision of a firm should be to find out the optimum combination of debt – equity, where cost of capital will be minimum and return will be maximum. Financing decision involves decision regarding the financing pattern of the firm. There are mainly two sources of raising funds- internal source and external source. Internal source includes the owned fund of the firm i.e the share capital. Whereas the external source includes the borrowed funds i.e loans from banks and other financial institutions, issuing debentures etc. Risk involved in borrowed funds is higher than the risk involved in owned funds. This is because borrowed funds entail a fixed payment commitment like interest, but the owned funds (equity capital) do not include any such fixed commitment except preference shares. So, reasonable care should be exercised while deciding upon the capital structure.
   3. Dividend Decision: Dividend decision of a firm includes determining how much to distribute as dividend and how much to retain for future expansion programme. The objective of dividend policy is to maximise the market value of the equity shares. If the shareholders’ expectations are not fulfilled, ultimately it will have a negative impact on the market value of shares. On the other hand, if a firm fails to grasp or rather predict the reinvestment opportunities then it will have an impact on the future growth of the firm. So, for deciding on the dividend policy, a firm should strike a proper balance between the shareholders’ (equity) expectation and reinvestment opportunities. 
      So, the scope of financial management is striking a proper balance between all the three decisions of investment, 
      financing and dividend to ensure achieving objective of the firm.
2. Functions of Financial Management
   The functions of financial management involve acquiring funds for meeting short term and long-term requirements of the firm, deployment of funds, control over the use of funds and to trade-off between risk and return.
   The modern approach to the financial management is concerned with the solution of major problems like investment financing and dividend decisions of the financial operations of a business enterprise. Thus, the functions of financial management can broadly be classified into three major decisions, namely: (a) Investment decisions. (b) Financing decisions. (c) Dividend decisions.

Based on the above decisions, functions of financial management are discussed below: 

1. Determining Financial Needs
   One of the most important functions of the financial management is to ensure availability of adequate financing. Financial needs have to be assessed for different purposes. Money may be required for initial promotional expenses, fixed capital and  working capital needs. Promotional expenditure includes expenditure incurred in the process of company formation. Fixed assets need depend upon the nature of the business enterprise – whether it is a manufacturing, non-manufacturing or merchandising enterprise. Current asset needs depend upon the size of the working capital required by an enterprise.
2. Determining Sources of Fund
   The finance manager has to choose sources of funds. He may issue different types of securities and debentures. He may borrow from a number of financial institutions and the public. When a firm is new and small and little known in financial circles, the finance manager faces a great challenge in raising funds. Even when he has a choice in selecting sources of funds, that choice should be exercised with great care and caution.
3. Financial Analysis 
   The Finance Manager has to interpret different statements. He has to use a large number of ratios to analyse the financial status and activities of his firm. He is required to measure its liquidity, determine its profitability, and assets overall performance in financial terms. The finance manager should be crystal clear in his mind about the purposes for which liquidity, profitability and performance are to be measured.
4. Optimal Capital Structure 
   The finance manager has to establish an optimum capital structure and ensure the maximum rate of return on investment. The ratio between equity and other liabilities carrying fixed charges has to be defined. In the process, he has to consider the operating and financial leverages of his firm. The operating activities Leverage exists because of operating expenses, while financial leverage exists because of the amount of debt involved in a firm's capital structure.
5. Cost-Volume-Profit Analysis 
   The finance manager has to ensure that the income of the firm should cover its variable costs. Moreover, a firm will have to generate an adequate income to cover its fixed costs as well. The Finance Manager has to find out the break-even-point-that is, the point at which total costs are matched by total sales or total revenue. He has to try to shift the activity of the firm as far as possible from the break-even point to ensure company’s survival against seasonal fluctuations.
6. Profit Planning and Control 
   Profit planning ensures attainment of stability and growth. Profit planning and control is a dual function which enables management to determine costs it has incurred, and revenues it has earned, during a particular period, and provides shareholders and potential investors with information about the earning strength of the corporation. Profit planning and control are important be, in actual practice, they are directly related to taxation. Profit planning and control are an inescapable responsibility of the management. 
7. Fixed Assets Management
   Fixed assets are financed by long term funds. Finance manager has to ensure that these assets should yield the reasonable returns proportionate to the investment. Moreover, in view of the fact that fixed assets are maintained over a long period of time, the assets exposed to changes in their value, and these changes may adversely affect the position of a firm. 
8. Capital Budgeting 
   Capital budgeting forecasts returns on proposed long-term investments and compares profitability of different investments and their cost of capital. It results in capital expenditure investment. The various proposal assets ranked on the basis of such criteria as urgency, liquidity, profitability and risk sensitivity. The financial analyser should be thoroughly familiar with such financial techniques as pay back, internal rate of return, discounted cash flow and net present value among others because risk increases when investment is stretched over a long period of time. The financial analyst should be able to blend risk with returns so as to get current evaluation of potential investments. 
9. Corporate Taxation 
   Corporate taxation is an important function of the financial management, for the former has a serious impact on the financial planning of a firm. Since the company is a separate legal entity, it is subject to an income-tax structure which is distinct from that which is applied to personal income. 
10. Working Capital Management 
    Working capital is the excess of current assets over current liabilities. This is an important area in the financial management because it is compared to the nervous system of the human body. Current assets consist of cash, inventory, receivables. Current liabilities consist of payables and bank overdraft. A prudent finance manager has to formulate a policy in such a way that there is a balance between profitability and liquidity. 
11. Dividend Policies
    A firm may try to improve its internal financing so that it may avail itself of benefits of future expansion. However, the interests of a firm and its stockholders are complementary, for the financial management is interested in maximizing the value of the firm, and the real interest of stockholders always lies in the maximization of this value of the firm; and this is the ultimate goal of financial management. The dividend policy of a firm depends on a number of financial considerations, the most critical among them being profitability. Thus, there are different dividend policy patterns which a firm may choose to dopt, depending upon their suitability for the firm and its stockholders. 
12. Mergers and Acquisitions
    Firms may expand externally through co-operative arrangements, by acquiring other concerns or by entering into mergers. Acquisitions consist of either the purchase or lease of a smaller firm by a bigger organisation. mergers may be accomplished with a minimum cash outlay, though these involve major problems of valuation and control. The process of valuing a firm and its securities is difficult, complex and prone to errors. The finance manager should, therefore, go through a valuation process very carefully. The most difficult interest to value in a corporation is that of the equity stockholder because he is the residual owner. 

1.4 Profit Optimization and Value Maximization Principle 

Profit maximization or optimization and value/wealth maximization principles of the financial management are basically concerned with procurement and use of funds. Over the time, objectives of the firm have been changed from the profit maximization to value/wealth maximisation. In this section, arguments in favour and against of these two objectives of the firm are discussed. 

A. Profit Maximization: 
Profit maximization is one of the leading goals for all firms as it is reflected in the income statement. If the net operating profits tend to increase consecutively, the firm portrays efficient performance and if the net operating profits tend to decrease consecutively, the firm shows poor financial performance. 
Profit maximization or optimisation is the main objectives of business because: 

1. Profit acts as a measure of efficiency and
2. It serves as a protection against risk. 

Arguments in favour of profit maximization: 

1. When profit earning is the main aim of business the ultimate objective should be profit maximization. 
2. Future is uncertain. A firm should earn more and more profit to meet the future contingencies. 
3. The main source of finance for growth of a business is profit. Hence, profit maximization is required. 
4. Profit maximization is justified on the grounds of rationality as profits act as a measure of efficiency and economic prosperity. 

Arguments against profit maximization: 

1. It leads to exploitation of workers and consumers. 
2. It ignores the risk factors associated with profit. 
3. Profit in itself is a vague concept and means differently to different people. 
4. It is narrow a concept at the cost of social and moral obligations. Thus, profit maximization as an objective of Financial Management has been considered inadequate. 

As it is a short-run concept, so, profit maximization objective many a time fails to exercise any pressure on the management for increasing the future growth rate of the firm. 

B. Value/Wealth Maximization: 

Increasing shareholder value over time is the bottom line of every move we make. - ROBERTO GOIZUETA Former CEO, The Coca-cola Company

 

Value/Wealth maximazation n is considered as the appropriate objective of an enterprise. When the firms maximize the shareholder’s value/wealth, the individual shareholder can use this wealth to maximize his individual utility. Value/Wealth Maximization is the single substitute for a shareholder’s utility.

A shareholder’s wealth or value is shown by:

Shareholder’s value/wealth = No. of shares owned × Current market price per equity share

 

Higher the share price per share, the greater will be the shareholder’s wealth. 

Arguments in favour of Value/Wealth Maximization: 

1. Due to wealth maximization, the short-term money lenders get their payments in time.
2. The long-time lenders too get a fixed rate of interest on their investments. 
3. The employees share in the wealth gets increased. 
4. The various resources are put to economical and efficient use.

 Argument against Value/Wealth Maximization: 

1. It is socially undesirable. 
2. It is not a descriptive idea. 
3. Only stock holders’ wealth maximization does not lead to firm’s wealth maximization. 
4. The objective of wealth maximization is endangered when ownership and management are separated. In 
   spite of the arguments against wealth maximization, it is the most appropriative objective of a firm.

From the above discussion, wealth maximization is a long-term sustainable objective of a firm. Wealth maximization objective of the firm is a better and broader objective compared to the profit maximization objective. Wealth maximization objective considers the following which, profit maximization doesn’t.

There is a conflict goal between the two. 

Why value/wealth maximization objective considers superior than profit maximization, we may put forward some arguments

 These are: 

1. Wealth maximization considers the cash inflows and not the profit figure. 
2. This objective is the long-term objective of a firm.
3. Wealth maximization considers the risk factor, which profit maximization doesn’t.
4. Wealth maximization objective considers the time value of money, so the cash inflows at different points of time are discounted to arrive at present value of cash inflows.
5. This objective takes into account both the qualitative and quantitative aspects i.e cash inflows represent the quantitative aspect and the net present value represents the qualitative aspect, whereas profit maximization objective considers only the quantitative aspect.
6. A firm with wealth maximization pays regular dividend to shareholders whereas those having profit maximization may not pay regular dividend.
7. Wealth maximization objective is preferred by shareholders.
8. This objective takes into account all the factors influencing the market value of shares, which profit maximization doesn’t.

1.5 Dynamic Role of a CFO in Emerging Business Environment

The Finance Manager or the Chief Financial Officer (CFO) plays a dynamic role in a modern company’s development. Until around the first half of the 1900s financial managers primarily raised funds and managed their firms’ cash positions – and that was pretty much it. In the 1950s, the increasing acceptance of present value concepts encouraged financial managers to expand their responsibilities and to become concerned with the selection of capital investment projects. 

The head of finance i.e., CFO is considered to be importantly of the CEO in most organisations and performs a strategic role. The responsibilities of CFO include: 

1. Estimating the total requirements of funds for a given period; 
2. Raising funds through various sources, both national and international, keeping in mind the cost effectiveness; 
3. Investing the funds in both long term as well as short term capital needs;
4. Funding day-to-day working capital requirements of business; 
5. Collecting on time from debtors and paying to creditors on time; 
6. Managing funds and treasury operations;
7. Ensuring a satisfactory return to all the stakeholders; 
8. Paying interest on borrowings;
9. Repaying lenders on due dates; 
10. Maximizing the wealth of the shareholders over the long term;
11. Interfacing with the capital markets; 
12. Awareness to all the latest developments in the financial markets; 
13. Increasing the firm’s competitive financial strength in the market and 
14. Adhering to the requirements of corporate governance. 

Today, external factors have an increasing impact on the finance manager or CFO. These are: 

Heightened corporate competition technological change Volatility in inflamation and interst rates Worldwide economic uncertinity  Fluctuating exchnage Tax law chnages Enviromental issues, and Ethical issues

 

As a result, finance is required to play an ever more vital strategic role within the company. The finance manager has emerged as a team player in the overall effort of a company to create value.

The finance manager or CFO is, therefore, concerned with all financial activities of planning, raising, allocating and controlling the funds in an efficient manner. In addition, profit planning is another important function of the finance manager.

This can be done by decision making in respect of the following areas:

1. Investment decisions for obtaining maximum profitability after taking the time value of the money into account.
2. Financing decisions through a balanced capital structure of Debt-Equity Ratio, sources of finance, EBIT/ EPS computations and Interest Coverage Ratio etc.
3. Dividend decisions, issue of bonus shares and retention of profits with objective of maximization of market value of the equity share.
4. Best utilization of fixed assets.
5. Efficient working capital management (inventory, debtors, cash marketable securities and current liabilities).
6. Taking the cost of capital, risk, return and control aspects into account.
7. Tax administration and tax planning.
8. Pricing, volume of output, product-mix and cost-volume-profit analysis (CVP Analysis).
9. Cost control.
10. Analyse the trends in the stock market and their impact on the price of company’s share and share buy[1]

 Besides, the CFO should comply the regulatory requirements in formulation of financial strategies.

The principal elements of this regulatory framework are: -

1. Different provisions of the Companies Act, 2013.
2. Provisions, guidelines, rules of the Securities and Exchange Board of India Act 1992.
3. Provisions of Foreign Exchange Management Act, 1999.

 If you become a finance manager, your ability to adapt to change, raise funds, invest in assets, and manage wisely will affect the success of your firm and, ultimately, the overall economy as well. In an economy, efficient allocation of resources is vital to optimal growth in that economy; it is also vital to ensuring that individuals obtain satisfac[1]tion of their highest levels of personal wants. Thus, through efficiently acquiring, financing, and managing assets, the financial manager contributes to the firm and to the vitality and growth of the economy as a whole.

Today’s finance manager must have the flexibility to adapt to the changing external environment if his or her firm is to survive. The successful finance manager of tomorrow will need to supplement the traditional metrics of performance with new methods that encourage a greater role for uncertainty and multiple assumptions. These new methods will seek to value the flexibility inherent in initiatives – that is, the way in which taking one step offers you the option to stop or continue down one or more paths. In short, a correct decision may involve doing something today that in itself has small value, but gives you the option to do something of greater value in the future.

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2. Time Value of Money

2.1 Rationale

Most financial decisions, personal as well as business, involve time value of money considerations. Money of the financial problems involves cash flows occurring at different points of the time. For evaluating such cash flows an explicit consideration of the time value of money is required.

 Money has time value. A rupee today is more valuable than a rupee a year hence.

 So, the time value of money is an individual’s preference for possession of a given amount of money now, rather than the same amount at some future date.

Mainly there are three reasons may be attributed to the individual’s time preference for money.

1. Risk: We are not certain about future cash receipts. In an inflationary period, a rupee today represents a greater real Purchasing Power than a rupee a year hence. So, an individual prefers receiving cash now.
2. Preference for consumption: Individuals, in general, prefer current consumption to future consumption.
3. Investment opportunities: Capital can be employed productively to generate positive returns. An investment of one rupee today would grow to (1+r) a year hence (r is the rate of return earned on the investments).

2.2 Techniques

 There are two methods of estimating time value of money which are shown below figure.

Techniques of Time Value of Money

Comparison between Compounding and Discounting

1. Compounding Technique: 
   Compounding is the process of finding future values of cash flows by applying the concept of compound interest. We can calculate the future values (FV) of all the cash flows at the end of the time period at a given rate of interest. 
   Future value = Present value + Interest 
   Compounding technique can be used to the following cases: 
   
   1. Single Flow 
   2. Multiple Flows
   3. Annuity 
2. Discounting Technique 
   Discounting is the process of determining present values of a series of future cash flows. The compound interest rate used for discounting cash flows is also called the discount rate. We determine the time value of money at time “O” by comparing the initial outflow with the sum of thepresent values (PV) of the future inflows at a given rate of interest.
   Discounting technique can be used to the following circumstances. 
   
   1. Single Flow 
   2. Un-even Multiple Flows
   3. Annuity 
   4. Perpetuity 

2.3 Future Value and Present Value of a Single Cash Flow 

i. Future Value of a Single Flow 
Suppose an investor have ` 1,000 today and he deposits it with a financial institution, this pays 10 % interest compounded annually, for a period of 3 years. The deposit would grow as follows: 

 

First year	Principal at the beginning	1000
	Interest for the year (1000 x 0.10)	100
	Principle at the end	1100
Second Year	Principal at the beginning	1100
	Interest for the year (1100 x 0.10)	110
	Principle at the end	1210
Third Year	Principle at the beginning	1210
	Interest for the year (1200 x 0.10)	121
	Principle at the end	1331

 

The general formula for the future value of single flow: 
FV = PV (1+r)n
 
Where FV = Future value n years hence
PV = Amount invested today
r = Interest rate per period 
n = Number of periods of investments

To find out the future value (FV) of a sing;e cash flow, we can use the MS Excel’s built-in function. The FV is given below:   FV (RATE, NPER, PMT, PV, TYPE) RATE is the discount or the interest rate for a period.  NPER is the number of periods.  PMT is the equal payment (annuity) each period  PV is the present value  TYPE indicates the timing of cash flow, occurring either at the beginning or at the end of the period.

 

Illustration 1 

If a person invests ` 1,50,000 in an investment which pays 12% rate of interest, what will be the future value of the invested amount at the end of 10 years? 

Solution: 

The future value (FV) of the invested amount at the end of 10 years will be 

FV = PV (1+r)n
FV = ` 1,50,000 (1+0.12)10
FV = ` 1,50,000 × 3.106 
FV = ` 4,65,900

Doubling Period 

Investor wants to know how long would take to double the investment amount at a given rate of interest. If we look at the future value interest factor table, we find that when the interest rate is 12% it takes about 6 years to double the amount. When the interest rate is 6%, it takes about 12 years to double the amount, so on and so forth. 

There is a thumb rule of 72 that helps to find out the doubling period. According to this rule of thumb, the doubling period is obtained by dividing 72 by the interest rate.

However, an accurate way of calculating the doubling period is the Rule of “69”. 

Under this Rule, doubling period = 0.35 +

Illustration 2 

How long it will take for ` 20,000 to double at a compound rate of 8% per annum (approximately)?

Solution:

The rule of 72 is r/m

Future value of single and multiple cash flows can be calculated by using the following formulae:

ii. Present value of a Single Flow 

Present Value can be calculated by using the following formulas:

.The process of discounting, used for finding present value, is simply the reverse of compounding. The present 
value formula can be readily obtained by manipulating the compounding formula:

FV=PV(1+r)ⁿ

Dividing both sides of above Eq. by (1+r)ⁿ

PV = FV {1/(1+r)ⁿ}

(1/((1+r)ⁿ) in above equation called the discounting factor or the present value interest (PVIF_i,n), the value of (PVIF_i,n) for several combinations of I and n.

To find out the present value (FV) of a single cash flow, we can use the MS Excel’s built-in function. The PV is given below:   PV (RATE, NPER, PMT, FV, TYPE) RATE is the discount or the interest rate for a period.  NPER is the number of periods.  PMT is the equal payment (annuity) each period  FV is the Future value  TYPE indicates the timing of cash flow, occurring either at the beginning or at the end of the period.

 

Illustration 3

Suppose someone promise to give you  ₹1,000 three years hence. What is the present value of this amount if the interest rate is 10%? 

Solution: 

The present value can be calculated by discounting ₹1,000, to the present point of time, as follows:

Value of three years hence = ₹1,000

Value two years hence = ₹1,000 × Value one year hence = ₹1,000 x 1/(1 0.10)

Value one year hence = ₹1,000 x 1/(1+0.10)² 

Value now ( present value) = ₹1,000 x 1/(1+0.10)³ = ₹1,000 x 0.751 = ₹751

2.4 Annunity and Perpetuity

(A) Annuity

An annuity is a series of equal payments or receipts occurring over a specified number of periods. The time period between two successive payments is called payment period or rent period. The word annuity in broader sense includes payments which can be annual, semi-annual, quarterly or any other length of time. For example, when a company set aside a fixed sum each year to meet a future obligation, it is using annuity. 

Future Value of Ordinary Annuity 

In an ordinary annuity, payments or receipts occur at the end of each period. In a ten-year ordinary annuity, the last payment is made at the end of the tenth year.

Future Value of Ordinary Annuity can be calculated by using the following formula:  FVAa = A {((1+r)n – 1/7)}  OR FVAa =A [{(1+r)n -1}/r]

 

Where, 

PVA_n = Present value of an annuity which is the sum of the compound amounts of all payments and a duration of n periods

A = Amount of each instalment or constant periodic flow

r = Discount rate

n = Number of periods

[{1- (1/1+r)n }/r] is called present value interest factor.

(B) Perpetuity: Perpetuity is an annuity that occurs indefinitely. The stream of cash flows continues for an infinite amount of time. Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities. Scholarships paid perpetually from an endowment fund. The value of the perpetuity is finite because r eceipts that are anticipated far in the future have extremely low present value.

By definition, in a perpetuity, time period, n, is so large (i.e., mathematically n approaches infinity) that tends to become zero and the formula for a perpetuity simply becomes

Present value of a perpetuity may be written as follows:

P∞ = A × PVIF Ar,∞

Where,

P∞ = Present value of a perpetuity

A = Constant annual payment PVIF

Ar,∞ = Present value interest factor of perpetuity

 Here, the present value interest factor of perpetuity is simply 1 divided by the interest rate expressed in decimal form. So, the present value of a perpetuity is simply equal to the constant annual payment divided by the interest rate.

So, P∞ = 1/r

Or,

Present value of perpetuity = Perpetuity/Interest rate

2.5 Compound Annual Growth Rate (CAGR)

Compound Annual Growth Rate (CAGR) is the annual growth of investments over a specific period of time. In other words, it is a measure of how much an investor earned from the investments every year during a given interval.

This is one of the most accurate methods of calculating the rise or fall of your investment returns over time.

Steps involved in calculating the CAGR of an investment:

Step 1: Divide the value of an investment at the end of the period by its value at the beginning of that period.

Step 2: Raise the result to an exponent of one divided by the number of years.

Step 3: Subtract one from the subsequent result.

Step 4: Multiply by 100 to convert the answer into a percentage.

The Compound Annual Growth Rate (CAGR) formula is:

CAGR= [(EV/BV)ⁿ -1 × 100

Where,

EV= Ending balance is the value of the investment at the end of the investment period.

BV= Beginning balance is the value of the investment at the beginning of the investment period.

N = Number of years amount invested.

CAGR may be used in the following cases:

1. Calculating and communicating the average returns of investment funds.
2. Demonstrating and comparing the performance of investment advisors. 
3. Comparing the historical returns of stocks with bonds or with a savings account. 
4. Forecasting future values based on the CAGR of a data series. 
5. Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.

For example, X Ltd. had revenues of `100 crore in 2010 which increased to ` 1,000 crore in 2020. What was the compounded annual growth rate? 

Solution:

The Compounded Annual Growth Rate (CGAR) can be calculated as follows:

CAGR =

CAGR = [ ()^1/n-1] x 100

= [(1,000/100)^1/10-1] x 100

= [ (10)^1/10-10] x 100

=26%

2.6 practical Application

An important use of present value concepts is in determining the payments required for an instalment-type loan. The distinguishing feature of this loan is that it is repaid in equal periodic payments that include both interest and principal. These payments can be made monthly, quarterly, semi-annually, or annually. Instalment payments are prevalent in mortgage loans, auto loans, consumer loans, and certain business loans.

The future value of an annuity can be applied in different scenarios by different organisations and individuals such as:

1. One may able to know the accumulated fund at the certain period (i.e., Deposit in Public Provident Fund)
2. How much should one person save annually if his or her savings earn a compound return (i.e., annual savings to buy a house after certain period, deposit in sinking fund).
3. The present value of an annuity can be applied in case of loan amortisation by a borrower.

Illustration 5 

Find the present value of ` 1,000 receivable 6 years hence if the rate of discount is 10%.

Solution:

` 1,000 × PVIF<sub>10%,16</sub>  = ` 1,000 × 0.5645 = ` 564.5

Illustration 6

Find the present value of ` 1,000 receivable 20 years hence if the discount rate is 8%.

Solution:

We obtain the answer as follows:

1,000 x ( 1/1.08)²⁰

= 1,000 x ( 1/1.08)¹⁰ x ( 1/1.08)¹⁰

=` 1,000 × PVIF8%,10 × PVIF8%,10

=` 1,000 × 0.463 × 0.463

=` 214

 Illustration 7

An individual deposited ` 1,00,000 in a bank @ 12% compound interest per annum. How much he would receive after 20 years?

 Given, FVIF_12,20 = 9.646

Solution:

FV= PV (1+r) ⁿ

Or, FV= PV (FVIF_r,n),

Where,

 

PV FV r n	= = = =	Present value or sum invested ` 100,000 Future value Intrest rate i.e 12% or 0.12 Number of years i.e., 20
FV	=	PV (FVIFr,n)
FV	=	`100,000 × 9.646
FV	=	` 9,64,600

 

Illustration 8

Mr. X is depositing ` 20,000 in a recurring bank deposit which pays 9% p.a. compounded interest. How much Amount Mr. A will get at the end of 5^th Year.

Solution:

Formula for calculating future value of annuity FVA_n= A[{(1+r)ⁿ-1}/r]

where,

FVA_n = Future value of an annuity which is the sum of the compound amounts of all payments and a duration of n periods

A = Amount of each instalment or constant periodic flow

r     = Interest rate per period

n = Number of periods

= ` 20,000 ×1 [{(1+0.09)⁵-1}/0.09]

= ` 1,19,694

Illustration 9 

A Person is required to pay annual payments of ` 8,000 in his Deposit Account that pays 10% interest per year. Find out the future value of annuity at the end of 5 years.

Solution:

At the end of	Amount Deposited	Term of the deposit	Future Value
1st year	8,000	4	8,000 x 1.464 = 11,713
2nd year	8,000	3	8,000 x1.331 = 10,648
3rd year	8,000	2	8,000 x1.210 = 9,680
4th year	8,000	1	8,000 x1.110  = 8,800
5th year	8,000	-	8,000 x 1.000 = 8,000
Future value of annunity at the end of 5 years			48,841

Alternatively, the future of annuity can be obtained by using the following formula:

Formula for calculating future value of annuity FVA_n = A[{(1+r)ⁿ-1}/r]

where,

FVA_n = Future value of an annuity which is the sum of the compound amounts of all payments and a duration of n periods

A = Amount of each instalment or constant periodic flow

r     = Interest rate per period

n =   Number of periods

= ` 8,000 × 6.1051 = ` 48,841

Future Value of Annuity at the end of 5 years = ` 48,841.

Illustration 10

Ascertain the future value and compound interest of an amount of ` 75,000 at 8% compounded semi-annually for 5 years.

Solution:

Amount Invested                             = ` 75,000

Rate of Interest                                = 8%

No. of Compounds                          = 2 × 5 = 10 times

Rate of Interest for half year         = 8%/2 = 4%

Compound Value or Future Value = P (1+i)ⁿ

Where,

P = Principal Amount

i = Rate of Interest (in the given case half year interest)

n = No. of years (no. of compounds)

= ` 75,000 (1+4%)¹⁰

= ` 75,000 × 1.4802

= ` 1,11,018

Compound Value = ` 1,11,018

Compound Interest = Compound Value – Principal Amount

= ` 75,000 (1+4%)¹⁰

= ` 75,000 × 1.4802

= ` 1,11,018

Compound Value = ` 1,11,018

Compound Interest = Compound Value – Principal Amount

= ` 1,11,018 – ` 75,000 = ` 36, 018.

Illustration 11

An investor expects a perpetual sum of ` 5,000 annually from his investment. What is the present value of the perpetuity if interest rate is 10%?

Solution:

Present value of a perpetuity = Perpetuity/Interest Rate

PV = A/i = `50,000

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3. Risk and Return

Return and risk are the two critical factors in investment decisions. They are closely linked. If high risk is involved, the required return on the project should also be high. So, the level of risk is measured first and then the level of return.

3.1 Various Connotations of Return

Return is the motivating force and the principal reward in the investment process and it is the key method available to investors in comparing alternative investments. Returns may have different meanings depending upon the investors’ perceptions.

Return on a typical investment consists of two components. The basic component is the periodic cash receipts and (or income) on the investment, either in the form of interest or dividends. The second component is the change in the price of the – commonly known as capital gain or loss.

Realised return is after the fact return -return that was earned or could have been earned. Realised return is

called historical return.

Expected return is the return from an asset that investors anticipate they will earn over future period. It may or may not occur.

The term yield is often used in connection this component of return. Yield refers to the income component in relation to some price for a security.

Some investors may measure return by using financial ratios- Return on Investment (ROI), Return on Equity (ROE) etc. Further, investors may assign more values to cash flows rather than to distant returns such as Internal Rate of Return (IRR).

3.2 Ex-ante and Ex-post Return

Ex-ante Return:

Ex-ante refers to future events. Ex-ante return is the prediction of returns that investor can get from a security or a portfolio.

1. It helps investor to predict future return and to take right decision from investment.
2. Ex-ante predictions help companies to attract investors and raise capital.
3. It helps company to effectively plan inflation, deflation, or serious situations like a

Ex-post Return:

Ex-post means after the event. Ex-post returns are the returns that investor has already got from investment, i.e., historical return.

1. It is useful for prediction of future trend, price.
2. It helps in predicting returns from a security based on actual returns from it over
3. Companies can use historical data to predict future earnings
4. Government and other agencies can use actual results from the past data.

3.3 Types of Risk

According Horne and Wachowicz, risk is the variability of returns from those that are expected. The greater the variability, the riskier the security is said to be.

Risk in an investment asset may be divided into: (i) Systematic Risk and (ii) Unsystematic Risk.

• Systematic Risk: It represents that portion of Total Risk which is attributable to factors that affect the market as a whole. Economic, political and siciological changes are sources of systematic risk. Beta is a measure of Systematic
• Unsystematic Risk: It is the position of total risk that is unique to a firm or industry.

A. Systematic Risk:

It represents that portion of total risk which is attributable to factors that affect the market as a whole. It arises out of external and uncontrollable factors, which are not specific to a security or industry to which such security belongs. It is that part of risk caused by factors that affect the price of all the securities. Beta is a measure of Systematic Risk. It cannot be eliminated by diversification. Systematic risks are discussed below:

1. Market Risk: These are risks that are triggered due to social, political and economic For example, when CBDT issued a draft circular on how to treat income from trading in shares, whether as Capital Receipts or Business Receipts, the stock prices fell down sharply, across all sectors. These risks arise due to changes in demand and supply, expectations of the investors, information flow, investor’s risk perception, etc. consequent to the social, political or economic events.
2. Interest Rate Risk: Uncertainty of future market values and extent of income in the future, due to fluctuations in the general level of interest, is known as Interest Rate Risk. These are risks arising due to fluctuating rates of interest and cost of corporate debt. The cost of corporate debt depends on the interest rates prevailing, maturity periods, credit worthiness of the borrowers, monetary and credit policy of RBI,
3. Purchasing Power Risk: Purchasing Power Risk is the erosion in the value of money due to the effects of inflation.

B. Unsystematic Risk

These are risks that emanate from known and controllable factors, which are unique and / or related to a par-

ticular security or industry. These risks can be eliminated by diversification of portfolio.

1. Business Risk: It is the volatility in revenues and profits of particular Company due to its market conditions, product mix, competition, etc. It may arise due to external reasons or (Government policies specific to that kind of industry) internal reasons (labour efficiency, management, etc.)
2. Financial Risk: These are risks that are associated with the Capital Structure of a Company. A Company with no Debt Financing, has no financial risk. Higher the Financial Leverage, higher the Financial Risk. These may also arise due to short term liquidity problems, shortage in working capital due to funds tied in working capital and receivables, etc.
3. Default Risk: These arise due to default in meeting the financial obligations on Non-payment of finan- cial dues on time increases the insolvency and bankruptcy costs.

3.4 Calculation of Return and Risk

Determination of the acceptability of the investment proposals of a firm involves a trade-off between risks and returns. So, risk -return analysis is used for capital budgeting decisions, purchase of shares, bonds and any readily identifiable capital or financial investments.

Calculation or Measurement of Return:

Returns across time or from different securities can be measured and compared using the total return concept. The total return of a security for a given holding period relates all the cash flows received by an investor during any designated time period to the amount of money invested.

1. Total Return

Total return is calculated as:

Total return = Cash payment received + Price chnage over the period / Purchase price of the asset

The total return is used to measure of return for a specified period of time. Further, this return can be split in two components: dividend and capital gains. The percentage (%) of return can be expressed in mathematical terms.

Assume, P₀ is the initial price, D₁ is the dividend in the period 1, and P₁ is the price at the end of period 1, and the total return for one period as follows:

Total return (%) = Dividend + Capital Gain / Initial Investment

=  D₁ + (P₁ – P₀) / P₀

=  D₁/ P₀  + (P₁ – P₀) / P₀

 However, investing in a particular stock for ten years or a different stock in each ten years could result in 10 total returns which must be calculated separately by using statistical tools.

Illustration 12

The current market price of a share is ` 600. An investor buys 100 shares. After one year he sells these shares at a price of ` 720 and also receives the dividend of ` 30 per share. Find the total return (%) of the investor.

Solution:

Initial investment = ` 600 × 100 = ` 60,000

Dividend earned = ` 30 × 100 = ` 3,000

Capital Gains        = ` (720-600) × 100 = ` 12,000

Total return           = ` 3,000 + ` 12,000 = ` 15,000

Total return (%) = [(` 3,000 + ` 12,000) / ` 60,000] × 100 = 25%

ii. Average Annual Return

There are two commonly methods used in calculating average annual returns: (a) Arithmetic Mean and (b) Geometric Mean.

When an investor wants to know the central tendency of a series of returns, the arithmetic mean is the appro- priate measure. It represents the typical performance for a single period.

If you want to calculate the average compound rate of growth that has actually occurred over multiple periods, the arithmetic mean is not appropriate. Then geometric mean is used.

 iii. Expected rate of Return

The expected return is simply a weighted average of the possible returns, with the weights being the probabil-ities of occurrence. The expected rate of return can be calculated by using the formula given below: 

E(R) = R₁ × P₁+ R₂× P₂+ R₃ × P₃+ R₄ × P₄ +--- + R_n × P_n

R is the rate of returns and

P is the probability

The following table shows how to calculate expected rate of return:

Expected Rate of Return

Economic Conditions (1)	Rate of Return (%)(2)	Probability(3)	Expected Rate of Return (4) = (2) x (3)
Growth	18.0	0.25	4.5
Expansion	11.0	0.25	2.75
Stagnation	1.0	0.25	0.25
Decline	-5.0	0.25	-1.25
Expected Rate of Return			6.25

 

iv. Expected Return on Portfolio

The expected return on a portfolio is the weighted average of the expected returns on the assets comprising the portfolio. When a portfolio consists of two securities, its expected return would be: E(R_P)= w_AE(R_A) + (1-w_B) E(R_B)

where,

E(R_P) = Expected Return of the Portfolio

W_A          = Weight or Proportion of a portfolio invested in Security A

E(R_A) = Expected Return on Security A

1-W_B    = Proportion of a portfolio invested in Security B

E(R_B) = Expected Return on Security B

When a portfolio consists of n number of securities, the expected return of portfolio would be: E(R_P) = ∑w_nE(R_n)

where,

Calculation or Measurment of Risk:

Risk may be defined as the variability of returns from an investment. Since it indicates variation in expected return, therefore statistical techniques may be used to measure risks.

Generally, the following methods are used to measure risk of an investment.

1. Subjective Estimates: Risk analysis is ‘generic’ and may be applied to any situation and any form of decision-making, from determining policy and strategy, through all levels of planning to tactical decision- In different situations, risk may be expressed as low, moderate and high. When variations of returns will not be wide, it may be called low level of risk; when forecast returns are likely to vary widely, it may state as high-risk level and variability of returns is likely to moderate in nature then it may represent as moderate level of risk. This method of risk assessment has its own limitations.
2. Standard Deviation and Variance: The standard deviation is a measure of how each possible outcome deviates from the expected It measures the risk in absolute terms. The higher the value of dispersion, the higher is the risk associated with the Portfolio and vice-versa. Generally, Standard Deviation of a specified security or portfolio is considered to be the Total Risk associated with that security or portfolio.

Standard Deviation is generally considered as the total risk of a particular security. It can be measured as follows:

Where,

x = Expected rate of return = E(R)

x_i = i^th rate of return from an investment proposal

p_i = Probability of occurrence of the i^th rate of return

n = Number of outcomes

Illustration 13 

X Ltd. has forecasted returns on its share with the following probability distribution:

Return (%)	Probability
-20	0.05
-10	0.05
-5	0.10
5	0.10
10	0.15
18	0.25
20	0.25
30	0.05

 

Find out the following: (a) Expected Rate of Return (b) Variance (c) Standard Deviation

Solution:

a. Expected Rate of Return

Expected Return can be calculated by using the following formula:

E(R) = R₁ × P₁ + R₂ × P₂ + R₃ × P₃ + R₄ × P₄ + .....................+ R_n × P_n

= (-20 × 0.05) + (-10 × 0.05) + (-5 × 0.10) + (5 × 0.10) + (10 × 0.15) + (18 × 0.25) + (-20 × 0.05) + (20 × 0.25)

+ (30 × 0.05) = 11%

b. Variance of Return 

Variance can be calculated by using the following formula

σ ² = [R₁-E(R)]² × p₁+ [R₂-E(R)]² × p₂ + [R₃-E(R)]² × p₃+ [R₄-E(R)]² × p₄ ................... [R_n-E(R)]² × p_n

= (-20-11)² × 0.05 + (-10-11)² × 0.05 + (-5-11)² × 0.10 + (5-11)² × 0.10 + (10-11)² × 0.15 + (18-11)² ×

0.25 + (20 – 11)² × 0.25 + (300-11)² × 0.05

= 150%

c. Standard devidation of Return

i.  Coefficient of Variation: Variance or standard deviation are the absolute measure of Standard devia- tion can sometimes be misleading in comparing the risk.

The standard deviation when compared with the expected returns is known as the coefficient of variation

Coefficient of Variation (CV) = Standard deviation / Expected value

Thus, the coefficient of variation is a measure of relative dispersion (risk) – a measure of risk “per unit of expect- ed return.” The larger the CV, the larger the relative risk of the investment.

Illustration 14 

Consider, two securities, A and B, whose normal probability distributions of one-year returns have the following characteristics:

	Section A	Section B
Expected return, [E(R)]	0.08	0.24
Standard deviation, (σ)	0.06	0.08
Coefficent of variation, (CV)	0.75	0.33

 

Comment on the above information.

Solution:

From the above information it is found that the standard deviation of Security B is larger than that of Securty A. So, Security B is the riskier investment opportunity with standard deviation as risk measurement tool.

However, relative to the size of expected return, Security A has greater variation. So, Security A is higher risky investment than Security B.

ii. Beta: The sensitivity of a security to market movements is called beta (β). When an investor wants to invest his money in a portfolio of securities, beta is the proper measure of risk. Beta measures systematic risk i.e., that which affects the market as a whole and hence cannot be eliminated through

Beta depends on the following factor:

1. Standard Deviation (Risk) of the Security or
2. Standard Deviation (Risk) of the
3. Correlation between the Security and

According to the Capital Asset Pricing Model, the required rate of return is equivalent to the risk-free return plus risk premium.

E(R_P) = R_F + { β_P × (R_M –R_F)}

Where,                         

E(R_P) = Expected Return on Portfolio

R_F = Risk Free Rate of Interest/ Return

β_P = Portfolio Beta or Risk Factor

R_M = Expected Return on Market Portfolio Beta is measured as follows:

 β = Cov (A.M.) / 

Cov_(A,M) = Covariance of returns on an individual company’s security (A) with returns for market as a whole (M).

  = Variance of market returns

We know,

Cov_(A,M) = r_(A,M) x  x

r_(A,M)  = Coefficient of correlation between A and M 

= Standard deviation of returns of security A

= Standard deviation of market rate of returns

If the value of changes in different ranges, accordingly, risk of the security would be chnages. Inferences are shown below:

Inferences

Beta Value is	Security is
Less than 1	Less risky than the market portfolio.
Equal to 1	As risky as the market portfolio. normal Beta Security. When security beta = 1 then if market move up by 10% security will move up by 10%. If market fell by 10% security also tend to fall by 10%.
More than 1	More risk than the market portfolio. Termed as Aggressive Security/High beta Security. A Security beta 2 will tend to move twice as much as the market. If market went up by 10% security tends to rise by 20%. If market fall by 10% Security tends to fall by 20%.
Less than 0	Negative Beta. It indicates negative (inverse) relationship between security return and market return. If market goes up security will fall and vice versa. Normally gold is supposed to have negative beta.
Equal to 0	Means there is no systematic risk and share price has no relationship with market. Risk free security is assumed to be zero.

 

illustration 15

From the folowing data, compute the beta of Security X.

= 12%

= 9%

r_(A,M) = +0.72

Solution:

12 x 9 x 0.72 / 9² = 77.76 / 81 = 0.96

Illustration 16

The stock price and dividend history of X Ltd. are given below:

Year	Closing Share Price (`)	Dividend per Share (`)
2015	312	5.50
2016	389	6.75
2017	234	4.60
2018	345	5.90
2019	367	3.78
2020	389	4.10
2021	412	5.98

Using the above data, compute the following:

1. Annual rates of return 
2. Expected average rate of return
3. Variance
4. Standard deviation

Solution:

i. Computation of annual rates of return

Year	Closing Share Price (`) (St)	Dividend per Share (`) (Dt)	Annual rate of return [(St/St-1)-1] + Dt
2015	312	5.50	-
2016	389	6.75	7.00
2017	234	4.60	4.20
2018	345	5.90	6.37
2019	367	3.78	3.84
2020	389	4.10	4.15
2021	412	5.98	6.03
Total			31.58

 

ii. Average rate of return = arthemetic mean of annual rate of return

Total Annual Returns = 31.58

So, Average return = 31.58/6 = 5.27%

iii. Calculation of Variance

Year	Annual Return (Rt)	Average Return (%)(Rm)	(Rt - Rm)	(Rt - Rm)2
2016	7.00	5.27%	1.73	2.89
2017	4.20	5.27	-1.07	1.14
2018	6.37	5.27	1.10	1.22
2019	3.84	5.27	-1.43	2.03
2020	4.15	5.27	-1.11	1.23
2021	6.03	5.27	0.77	0.59
Total				9.20

 

= 9.20 /6-1

=1.84

iv. Standard Deviation (σ) =  =  = 1.35

3.5 Capital Asset Pricing Model

William F. Sharpe and John Linter developed the Capital Asset Pricing Model (CAPM). The model is based on the portfolio theory developed by Harry Markowitz. The model emphasises the risk factor in portfolio theory which is a combination of two risks, systematic risk and unsystematic risk. The model suggests that a security’s return is directly related to its systematic risk which cannot be neutralized through diversification.

CAPM explains the behavior of security prices and provides a mechanism whereby investors could assess the impact of a proposed securities are determined in such a way that the risk premium or excess return are proportion- al to systematic risk, which is indicated by the beta coefficient.

A. Features of CAMP:

1. CAPM explains the relationship between the Expected Return, Non-Diversifiable Risk (Systematic Risk) and the valuation of securities.
2. CAPM is based on the premise that the diversifiable risk of a security is eliminated when more and more securities are added to the Portfolio.
3. All securities do not have same level of systematic risk and therefore, the required rate of return goes with the level of systematic It considers the required rate of return of a security on the basis of its (System- atic Risk) contribution to the total risk.
4. Systematic Risk can be measured by Beta, which is a function of the following:

• 1. Total Risk Associated with the Market Return,
  2. Total Risk Associated with the Individual Securities Return,
  3. Correlation between the two.

B. Assumption

1. With reference to Investors:
   1. Investment goals of investors are They desire higher return for any acceptable level of riskand lower risk for any desired level of return.
   2. Their objective is to maximize the utility of terminal wealth.
   3. Their choice is based on the risk and return of a security.
   4. They have homogenous expectations of risk and return over an identical time horizon.
2. With reference to Market:
   1. Information is freely and simultaneously available to all
   2. Capital Market is not dominated by any individual
   3. Investors can borrow and lend unlimited amount at the risk-free rate.
   4. No taxes, transaction costs, restrictions on short-term rates or other market imperfections.
   5. Total asset quantity is fixed, and all assets are marketable and

We can use CAPM to understand the basic risk-return trade-offs involved in various types of investment decisions. Using Beta as the measure of non-diversifiable risk, the CAPM is used to define the required rate of return on a security

E(Rs) Where,	=	RF + { βs × (RM -RF)}
E(Rs)	=	Expected Return on the Security or Investment
RF	=	Risk Free Rate of Interest / Return
βs	=	Security Beta or Risk Premium
RM	=	Expected Return on all securities or Market return

 

Illustration 17 

the following information is given:

Security Beta: 1.2 

Risk-free rate: 4%

Expected market return: 12%

Calculate expected rate of return on the security.

Solutions:                                                                                           

 E(R_s) = R_F + { β_s × (R_M -R_F)}       

Substituting these data into the CAPM equation, we get

E(R_s) = 4% + [1.20 × (12% - 4%)

= 4% + 9.6% = 13.6%.

Solved Case 1

Compute the future values of (1) an initial ` 100 compounded annually for 10 years at 10% and (2) an annuity of ` 100 for 10 years at 10%.

Solutions:

The future value of an investment compounded annually = F_n = P(1+i)ⁿ = P × FIVF_i,n = F₁₀  = ` 100

(1+0.10)¹⁰ = ` 100 (2.5937) = ` 259.4

The future value of an annuity = A × FVIFA_in = ` 100 × 15.937 = ` 1593.7

Solved Case 2

A note (secured premium note) is available for ` 1,400. It offer, including one immediate payment, 10 annual payments of ` 210. Compute the rate of return (yield) on the note.

Solution:

=>   ₹ 1,400 = ₹ 210 (1 + PVIFA_r,9) 

=> (1 + PVIFA_r,9) =   ₹ 1,400/ ₹ 210  = 6.67

 (1 + PVIFA_r,9) = 6.67 - 1 = 5.67

From the future value table, the closet values are 5.7590 (0.10) and 5.3282 (0.11). By interpolation, r = 10.2%.

The shares of ABC Ltd. are currently selling for ₹ 100 on which the expected dividend is ₹ 4. Compute the total return on the shares if the earnings or dividends are likely to grow at (a) 5 % (b) 10 % and (c) 0 (zero) % (no growth).

Solution:

                  r = (D₁/P₀) + g

a. Rate of growth, 5%:

                    = (₹ 4/₹ 100) + 0.05 = 0.04 + 0.05 = 9%

b. Rate of growth, 10%:

                 r = (₹ 4/₹ 100) + 0.10 = 14%

c. Rate of growth, 0 (zero) % (no growth):

                 r = ₹(4/ 100) = 4 %.

Solved Case 4 

ABC Ltd. is considering a proposal to buy a machine for ₹ 30,000. The expected cash flows after taxes from the machine for a period of 3 consecutive years are ₹ 20,000 each. After the expiry of the useful life of the machine, the seller has guaranteed its repurchase at ₹ 2,000. The firm’s cost of capital is 10% and the risk adjusted discount rate is 18%. Should the company accept the proposal of purchasing the machine?

Solution:

Year	CFAT (₹ )	PV factor (0.18)	Total PV (₹ )
1-3	20,000	2.174	43,480
3	2,000	0.751	1,502
		(As per PVIF Table)	44,982
Less cash outlays			30,000
NPV			14,982

Yes, the company should accept the proposal.

Solved Case 5

The Hypothetical Ltd is examining two mutually exclusive proposals. The management of the company uses certainty equivalents (CE) approach to evaluate new investment proposals. From the following information per- taining to these projects, advise the company as to which project should be taken up by it.

Year	Proposal A		Proposal B
	CFAT (₹)	CE	CFAT (₹)	CE
0	(25,000)	1.0	25,000	1.0
1	15,000	0.8	9,000	0.9
2	15,000	0.7	18,000	0.8
3	15,000	0.6	12,000	0.7
4	15,000	0.5	16,000	0.4

The firm's cost of capital ids 12%, and risk-free borrowing rate is 6%.

Solution:

NPV under CE method: Project A

Year	Expected CFAT (₹)	Certainty Equivalent (CE)	Adjusted CFAT (₹)	PV factor (0.06)	Total PV (₹)
0	(25,000)	1.0	(25,000)	1.000	(25,000)
1	15,000	0.8	12,000	0.943	11,316
2	15,000	0.7	10,500	0.890	9,345
3	15,000	0.6	9,000	0.840	7,560
4	15,000	0.5	7,500	0.792	5,940

NPV under CE method: project B

Year	Expected CFAT (₹)	Certainty Equivalent (CE)	Adjusted CFAT (₹)	PV factor (0.06)	Total PV (₹)
0	(25,000)	1.0	(25,000)	1.000	(25,000)
1	9,000	0.9	8,100	0.943	7,638
2	18,000	0.8	14,400	0.890	12,816
3	12,000	0.7	8,400	0.840	7,056
4	16,000	0.4	6,400	0.792	5,069

The company should take up project A.

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Exercise

A. Theoretical Questions:

• Multiple Choice Questions

1. Time value of money explains that

1. a unit of money received today is worth more than a unit received in future
2. a unit of money received today is worth less than a unit received in future
3. a unit of money received today and at some other time in future is equal
4. none of the above

Answer: a. a unit of money received today is worth more than a unit received in future

2. Time value of money facilities comparison of cash flows occuring at diffrent time periods by

1. compounding all cash flows to a common point of time
2. discounting all cash flows to a common point of time
3. using either (a) or (b)
4. neither (a) nor (b).

Answer: c. using either (a) or (b)

 3. If the nominal rate of interest is 10 per cent per annum and frequency of compounding is 4 e. quarterly compounding, the effective rate of interest will be

1. 25% per annum
2. 38% per annum
3. 10% per annum
4. none of the above

Answer: b. 38% per annum

4. Relationship between annual effective rate of interest and annual nominal rate of interest is, if frequency of compounding is more than 1,

1. Effective Rate < Nominal rate
2. Effective Rate > Nominal rate
3. Effective Rate = Nominal rate
4. none of the above

Answer: b. Effective Rate > Normal rate

5. If annual effective rate of interest is 25 % per annum and nominal rate of return is 10% per annum what is the frequency of compounding

1. 1
2. 3
3. 2
4. 4

Answer: c. 2

6. A student takes a loan of ₹ 50,000 from The rate of interest being charged by SBI is 10% per annum. What would be the amount of equal annual instalment if he wishes to pay it back in five instalments and first instalment, he will pay at the end of year 5?

1. ₹ 11,000

2. ₹ 19,310

3. ₹ 15,000

4. None of the above

Answer: b. ₹ 19,310

7. How much amount should an investor invest now in order to receive five annuities starting from the end of this year of ₹ 10,000 if the rate of interest offered by bank is 10 % per annum?

1. ₹ 40,000
2. ₹ 45,000
3. ₹ 37,910
4. none of the above

Answer: c. ₹ 37,910

8. A bank offers 12% compound interests payable If you deposit ₹2,000 now, how much it will grow at the end of 5 years?

1. ₹3,050
2. ₹3,430
3. ₹3,612
4. ₹3,722

Answer: c. ₹ 3,612

9. A company wants to repay a loan of ₹ 5,00,000, 10 years from What amount should it invest each year for 10 years if the funds can earn 8% per annum. The first investment will be made at the beginning of this year.

1. ₹ 50,000
2. ₹ 31,950
3. ₹ 40,000
4. ₹ 32,950

Answer: b. ₹ 31,950

10. Risk of two securities having different expected return can be compared with

1. standard deviation of securities
2. variance of securities
3. coefficient of variation
4. mean

Answer: c. coefficient of variation

11. A portfolio consists of two securities and the expected return on two securities is 12% and 16% Calculate return of portfolio if first security accounts for 40% of portfolio.

1. 14%
2. 14.4%
3. 16%
4. 12%

Answer: b. 14.4%

12. If the rate of interest is 12%, what are the doubling periods as per the rule 72 and the rule of 69 respectively?

1. 5 Years and 5.2 Years
2. 8 Years and 5.3 Years
3. 6 Years and 6.1 Years
4. 5 Years and 6.6 Years

Answer: c. 6 Years and 6.1 years

13. To create a minimum variance portfolio, in what proportion should the two securities be mixed if the following information is given S1 = 10%, S2 = 12%, P12 = 0.6?

1. 0.72 and 0.28
2. 0.70 and 0.30
3. 0.60 and 0.40
4. 0.50 and 0.40

Answer: a. 0.72 and 0.28

14. A portfolio consisting of two risky securities can be made risk less i.e., Sp = 0, if

1. the securities are perfectly positively correlated
2. the securities are perfectly negatively correlated
3. if the correlation ranges between 0 to 1
4. if the correlation ranges between -1 to +1

Answer: b. the securities are perfectly positively correlated

15. Efficient portfolios are those portfolios, which offer (for a given level of risk)

1. maximum return
2. minimum return
3. average return
4. positive return

Answer: a. maximum return

16. CAPM accounts for -

1. systematic risk
2. unsystematic risk
3. both of the above
4. moderate risk

Answer: a. systematic risk

• State True or False

1. Time value of money signifies that the value of a unit of money remains unchanged during different time periods. False 
2. Time value of a unit of money is different over different periods on account of the reinvestment opportunities with the firms. True
3. Cash flows accruing to the firms at different time periods are directly comparable. False
4. Either compounding or discounting technique can be used, to make heterogeneous cash flows comparable. True
5. Effective and nominal rate of interest remain the same irrespective of the frequency of compounding. False
6. Effective rate of interest is positively correlated with frequency of compounding. True
7. To arrive at the present value of cash flows, discounting is done at the rate which represents opportunity cost of funds. True
8. Present value tables for annuity can be directly applied to mixed stream of cash flows. False
9. To facilitate comparison of cashflows that are occurring at different time periods, the technique of either compounding all cash flows to the terminal year or discounting all cash flows to the time zero period can be adopted. True
10. Return on any finance assest consist of current yield and capital yield. True
11. Risk of an individual financial asses5t refers to variability of its returns around its mean returns. True
12. Return of a portfolio is simply weighted avaerage of returns on individual securities in the portfolio multiplied by their corresponding propotions in the portfolio. True
13. For a given correlation coefficient, a maximum varience portfolio can be created, for which risk of portfolio will be less  than the risk of any security in the portfolio. True
14. Correlation among the securities in the portfolio has nothing to do with the risk of portfolio. False
15. If a portfolio consists of two securities, which are perfectly positively correlated, the risk of portfolio will simply be the weighted average of the standard deviations of individual securities. True
16. A portfolio consisting of two risky securities can be made riskless, if the securities are perfectly negatively correlated. True
17. Efficient frontier consists of those portfolios which offer maximum risk for a given level of expected returns. False
18. In CAPM, Beta represents total risk, i.e., systematic and unsystematic risk. False
19. The point of tangency between the efficient frontier and risk-return indifference curve provides optimal portfolio for the investor concerned. True
20. Security market line (SML) and Capital market line (CML) are the same.  False

• Fill in the Blanks

1. The main objectives of financial management may be classified into: Profit maximization and value/Wealth maximizaion.
2. Higher the stock price per share, the greater will be the shareholder’s wealth.
3. Compound Annual Growth Rate (CAGR) is the annual growth of investments over a specific period of time.
4.  Wealth maximization objective is preferred by shareholders. 
5.  Perpetuity is an annuity that occurs indefinitely.
6. Realised return is after the fact return-return that was earned or could have been earned.
7. Systematic risk represents that portion of Total Risk which is attributable to factors that affect the market as a whole.
8. Purchasing Power Risk is the erosion in the vale of money due to the effects of infaltion.
9. In finance, liquidity risk is the risk that a given security or assest cannot be traded quickly enough in the market to prevent a loss ( or make the required profit).

• Short Essay Type Questions

1. Define financial management and state its objectives.

Answer: 

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2. Narrate the scope of financial

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3. Explain the functions of financial

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4. What do you understand by risk and return?

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5. What are the different measures of return? Compare them. 

Answer: 

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6. What is the Capital Asset Pricing Model?

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7. Write short notes on Future Value and Present Value of a Single Cash Flow.

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8. What do you mean by Ex–ante and Ex–post Return?

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9. Distinguish between Profit Optimization and Value Maximization Principles.

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10. What is Compound Annual Growth Rate (CAGR)?

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11. What do you mean by Annuity and Perpetuity?

Answer:

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• Essay Type Questions

1. Explain the concept of time value of money with appropriate example.

Answer :

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2. Discuss the three broad areas of financial decision making.

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3. Discuss in brief the dynamic role of CFO of a MNC.

Answer:

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4. ‘The basic rationale for the objective of Shareholder Wealth Maximization is that it reflects the most efficient use of society’s economic resources and thus leads to a maximization of society’s economic wealth’ (Ezra Solomon). Comment critically.

Answer:

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B. Numerical Questions:

• Comprehensive Numerical Problems

1. Mrs. P deposited ₹ 1,00,000 on January 2015 in a fixed deposit scheme with a nationlised bank for five years. The maturity value of the fixed deposit is ₹ 2,00,000. Compute the rate of interest compounded annually.

Answer: 14.86%

2. A company has issued debentures of ₹50 lakh to be repaid after 7 How much should the company invest in a sinking fund earning 12 % in order to be able to repay debentures?

Answer: 4.96 lakh

3. XYZ Ltd. has borrowed ₹ 5,00,000 to be repaid in five equal annual payments (interest and principal both). The rate of interest is 16%. Compute the amount of each payment.

Answer: ₹ 1,52,704.39

4. The ABC company expects to receive ₹ 1,00,000 for a period of 10 years from a new project it has just undertaken. Assuming a 10 % rate of interest, how much would be the present value of this annuity?

Answer: ₹ 6,14,500

5. A life insurance company offers a 10-year single premium plan. According to the policy conditions, the investor has to pay ₹ 1,00,000 at the beginning of first year and he will receive a pension of ₹ 16,000 at the beginning of the second year onwards. What will be the yield generated by the investor?

 Answer: 9.60%

6. Share of a company is traded at ₹ An investor expects the company to pay dividend of ₹ 3 per share,form one year now. The expected price one year now is ₹78.50.

a. What is the expected dividend yield, rate of price change and holding period yield?

b. If the beta of the share is 5, risk free rate is 6 % and the market risk premium is 10%, then calculate the required rate of return.

Answer: (a) 5%, 30.83% and 35.83%; (b) 21%

• Unsolved Case(s)

1. You want to borrow ₹ 30 lakh to buy a You approach a bank which charges 13% interest. You can pay ₹ 4 lakh per year towards loan amortisation. What should be loan amortization period?

Answer: 

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2. Mr. X is the Chief Financial Officer (CFO) of ABC Ltd. in Kolkata. His company has performed in line with expectations over the past year. He is currently preparing a financial blue print for the next five years. First, he tried to forecast sales for the next five years. This is so because fixed and working capital needs depend on sales. Therefore, these two items are estimated. He also collected data on possible profits in the coming years. In this way, one can know how much money the company will provide. The remaining funds are arranged externally by the company. He is also considering seeking funding from outside the company.

Identify the concept referred to in the above case and write any two points of importance of the financial concept, so identified.

Answer:

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3. After completing her MBA, Mrs. R. Sharma took over the family food processing business manufacturing pickles, jams and squashes. Started by her grandmother, the company was doing well, but had very high fixed operating costs and poor cash Now, she wants to modernize and diversify it. She approached a financial consultant, who told her that approximately ₹ 50 lakh would be required for modernization and expansion programme. He also informed her that the stock market was going through a bullish phase.

a. After considering the above discussion, name the source of finance Mrs. Sharma should not choose for financing the modernization and expansion of her food processing business. Give one reason in support of your answer.

b. Explain two other factors she should keep in mind while taking this decision.

Answer:  

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Cash Flow Stream

End of Year	A (₹)	B (₹)
1	50,000	10,000
2	40,000	20,000
3	30,000	30,000
4	20,000	40,000
5	10,000	50,000
Total	150,000	150,000

 

Answer the following:

1. Find the present value of each stream, using a 10% discount
2. Compare the calculated present values, and discuss them in light of the fact that the undiscounted total cash flows amount to ₹ 150,000 in each case.