Financial Management Objectives

FINANCIAL MANAGEMENT
UNIT -1
Financial management – An overview- Time value of money- Introduction to the concept
of risk and return of a single asset and of a portfolio- Valuation of bonds and shares-Option
valuation.
 Meaning
 Definition
 Objectives of Financial Management
 Scope of Financial Management
 Functions of Financial Management
 Importance of Financial Management
INTRODUCTION:
MEANING:
Financial management is that managerial activity which is concerned with the planning
and controlling of the firm’s financial resources.
 It refers to the management of flow funds in the firm.
 It deals with the financial decision making of the firm.
 It is the mainly concerned with the timely procurement of adequate finance from various
resources and its utmost effective utilization for the attainment of organizational
objectives.
 Since raising of funds and their best utilization is the key to success of any firm.
DEFINITION:
“Financial management is concerned with the managerial decisions that result in the
acquisition and financing of short term and long term credits of the firm.”
- Phillippatus
Financial management “as an application of general managerial principles to the area of
financial decision-making.
- Howard and Upton

Financial management “is an area of financial decision-making, harmonizing individual
motives and enterprise goals”.
- Weston and Brigham
Financial management “is the operational activity of a business that is responsible
for obtaining and effectively utilizing the funds necessary for efficient operations.
- Joshep and Massie
Thus, Financial Management is mainly concerned with the effective funds management
in the business. In simple words, Financial Management as practiced by business firms can be
called as Corporation Finance or Business Finance.
OBJECTIVES OF FINANCIAL MANAGEMENT:
The following goals are often considered as the objectives of the financial management.
They are:
 Profit maximization
 Wealth maximization
PROFIT MAXIMIZATION:
The term ‘profit maximization’ implies generation of largest amount of profits over the
time period being analyzed, secondary to Prof. Peter Drucker, business profits play a functional
role in three different ways.
In the words of Peter Drucker.
 Profits indicate the effectiveness of business profits
 They provide the premium to cover costs of staying in business
 They ensure supply of future capital.
Profits are source of funds from which organizations are able to defray certain expenses
like replacement, obsolescence, marketing etc.
Maximization of profits for a long term is desirable and appreciable. The tendency to
maximize profits in the short run may invite innumerable problems to the organization
concerned. In fact, maximization of profits in the short run may give an impression of being
exploitative. The extent of uncertainty in business increases the appreciation of proprietor /
partner / company and hence many prefer short-run profit maximization to long –run profit
maximization.
The underlying basic of profit maximization is efficiency. It is assumed that profit
maximization causes the efficient allocation of resources under the competitive impact
conditions and profit is regarded as the most appropriate measure of a firm’s performance.

Arguments in favour of profit maximization
Arguments in favor of profit maximization as the objective of business are enumerated
below:
1. Profits are the major source of finance for the growth and development of its business.
2. Profitability serves as a barometer for measuring efficiency and economic prosperity of a
business entity.
3. Profits are required to promote socio-economic welfare.
Criticisms leveled against profit maximization:
However, profit maximization objective has been criticized on innumerable grounds.
Under the changed economic and corporate environment, profit maximization is regarded as
unrealistic, difficult, and inappropriate and socially not much liked goal for business
organizations. Profit maximization as an objective of financial management has been considered
inadequate and rejected because of the following drawbacks.
1. There are several goals towards which a business firm / organization should direct
themselves profit – maximization is one of the goals of the organization and not the only
goal.
2. Maintenance of firm’s share in the market, development and growth of the firm,
expansion and diversification are other goals of business concern.
3. Rendering social responsibility
4. Enhancing the shareholders’ wealth maximization.
As Solomon opines, profit maximization has been rejected as an operational criterion for
maximizing the owner's economic welfare as it cannot help us in ranking alternative courses of
action in terms of their economic efficiency.
 Criteria:
 Ambiguity
 Time value of money
 Risk factor
Profit maximization is considered as an important goal in financial decision-making in an
organization. It ensures that firm utilizes its available resources most efficiently under conditions
of competitive markets. Profit maximization as corporate goal is criticized by scholars mainly on
following grounds:
i) It is vague conceptually.
ii) It ignores timing of returns.
iii) It ignores the risk factor.
iv) it may tempt to make such decisions which may in the long run prove disastrous.
v) Its emphasis is generally on short run projects.
vi) It may cause decreasing share prices.

vii) The profit is only one of the many objectives and variables that a firm considers.
WEALTH MAXIMIZATION:
Wealth maximization is one of the modern approaches, which involves latest innovations
and improvements in the field of the business concern. The term wealth means shareholder
wealth or the wealth of the persons those who are involved in the business concern.
Wealth maximization is also known as value maximization or net present worth
maximization. This objective is a universally accepted concept in the field of business.
Favorable Arguments for Wealth Maximization:
i. Wealth maximization is superior to the profit maximization because the main aim of
the business concern under this concept is to improve the value or wealth of the
shareholders.
ii. Wealth maximization considers the comparison of the value to cost associated with
the business concern. Total value detected from the total cost incurred for the
business operation. It provides extract value of the business concern.
iii. Wealth maximization considers both time and risk of the business concern.
iv. Wealth maximization provides efficient allocation of resources.
v. It ensures the economic interest of the society.
Unfavorable Arguments for Wealth Maximization:
i. Wealth maximization leads to prescriptive idea of the business concern but it may not
be suitable to present day business activities.
ii. Wealth maximization is nothing, it is also profit maximization, it is the indirect name
of the profit maximization.
iii. Wealth maximization creates ownership-management controversy.
iv. Management alone enjoys certain benefits.
v. The ultimate aim of the wealth maximization objectives is to maximize the profit.
vi. Wealth maximization can be activated only with the help of the profitable position of
the business concern.
 There are two important issues are related to the value/share maximization. They
are
 Economic value added
 Focus on stakeholders
Other objectives are:
 Return maximization
 Provide support for decision making

 Manage risk
 Use resources as efficiently, effectively and economically
 Provide a supportive control environment
 Comply with authorities and safeguard assets
SCOPE OF FINANCIAL MANAGEMENT:
Firm creates manufacturing capacities for production of goods; some provide services to
customers. Thus, there are three important activities of a business firm are:
 Production
 Marketing
 Finance
Financial management is one of the important parts of overall management, which is
directly related with various functional departments like personnel, marketing and production.
Financial management covers wide area with multidimensional approaches. The following are
the important scope of financial management.
 Financial Management and Economics
 Financial Management and Accounting
 Financial Management or Mathematics
 Financial Management and Production Management
 Financial Management and Marketing
 Financial Management and Human Resource
ROLE OF FINANCIAL MANAGEMENT:
REAL AND FINANCIAL ASSETS:
A firm requires real assets to carry on its business.
 Tangible real assets:
 These are physical assets that include plant, machinery, office, factory, furniture
and building.
 Intangible real assets:
PRODUCTION FINANCE
MARKETING

 It includes technical know-how, technological collaborations, patents and
copyrights.
 Financial assets:
 It is also called as securities, are financial papers or instruments such as shares
and bonds or debentures.
 Firms issue securities to investors in the primary capital markets to raise necessary funds.
 The securities issued by firms are traded – bought and sold – by investors in the
secondary capital markets, referred to as stock exchanges.
 Financial assets also include lease obligations and borrowing from banks, financial
institutions and other resources.
 In a lease, the lessee obtains a right to use the lessor’s asset for an agreed amount of
rental over the period of lease.
 Funds applied to assets by the firm are called capital expenditures or investment.
 The firm expects to receive return on investment and might distribute return (or profit) as
dividends to investors.
EQUITY AND BORROWED FUNDS:
 There are two types of funds that a firm can raise. They are
 Equity funds(equity)
 Borrowed funds(debt)
 A firm sells shares to acquire equity funds
 Shares represent ownership rights of their holders. Buyers of shares are called share
holders or stockholders and they are the legal owners of the firm whom they hold the
shares.
 Shareholders invest their money in the shares of a company in the expectation of a return
on their invested capital.
s.no
Ordinary shareholders Preference shareholders
1.
The dividend rate over for the shareholders
is not fixed, and it can vary from year to year
depending on the decision of board of
directors.
The preference shareholder receive the dividends
at a fixed rate, and they have priority over the
ordinary shareholders
2
The payment of dividends received by the
shareholder after meeting the obligations of
others, they are generally called owners of
residue.
The payment of dividend to shareholders is not a
legal obligation; it depends on the discretion of
the board of directors

 The return of the shareholders consists of dividend and capital gain. Share holders make
their capital gain or loss by selling their shares.
 Shareholders can be of two types. They are
 Ordinary shareholders
 Preference shareholders
 Dividends paid by a company are not deductible expenses for calculating corporate
income taxes.
 As per the current laws in India, a company is required to pay 12.5% tax on dividends.
 A company can also obtain equity funds by retaining earnings available for shareholders.
 Retained earnings, which could be preferred to as internal equity, are undistributed profits
of equity capital.
 The retention of earnings can be considered as a form of raising new capital.
 If a company distributes all earnings to shareholders, then it can acquire new capital from
the same sources by issuing new shares called right shares.
 Also a public issue of shares may be made to attract new shareholders to contribute
equity capital.
 Another important source of securing capital is creditors or lenders.
 Lenders are not the owners of the company.
 Loans are generally furnished for a specific period at a fixed rate of interest.
 For lenders, the return on loans or debt comes in the form of interest paid by the firm.
 Interest is a cost of debt to the firm. Payment of interest is a legal obligation.
 The amount of interest paid by a firm is a deductible expense for computing corporate
income taxes. Thus, interest tax shield is valuable to a firm.
 The firm may borrow funds from a large number of sources, such as banks, financial
institutions, public or by issuing bonds or debentures.
 A bond or debentures is a certificate acknowledging the amount of money lent by a
bondholder to the company.
 It states the amount, the rate of interest and the maturity of the bond or debenture.
 Since bond or debenture is a financial instrument, it can be traded in the secondary capital
market.
FINANCE MANAGEMENT FUNCTIONS:
 The functions of raising funds, investing them in assets and distributing returns earned
from assets to shareholders are respectively known as follows:
 Financing decision
 Investment decision
 Dividend decision

 A firm attempts to balance cash inflows and outflows while performing these functions.
This is called as liquidity decision, and may add it to the list of important finance
decisions or functions.
 Thus, finance functions include:
 Long-term asset-mix or investment decision
 Capital mix or financing decision
 Profit allocation or dividend decision
 Short-term asset-mix or liquidity decision
Investment Decisions:
A firm’s investment decisions involve capital expenditures. They are therefore referred as
capital budgeting decisions. There is a broad agreement that the correct cut-off rate or the
required rate of return on investments is the opportunity cost of capital. The opportunity cost
of capital is the expected rate of return that an investor could earn by investing his or her
money in financial assets of equivalent risk.
Financing Decisions:
A financing decision is the second important function to be performed by the financial
manager. He or she must decide when, where from and how to acquire funds to meet the
firm‟s investment needs. The mix of debt and equity is known as the firm‟s capital
structure. The financial manager must strive to obtain the best financing mix or the optimum
capital structure for his or her firm.
Dividend Decisions:
A dividend decision is the third major financial decision. The financial manager must
decide whether the firm should distribute all profits or retain them or distribute a portion and
retain the balance. The proportion of profits distributed as divided is called the dividend-
payout ratio and the retained portion of profits is known as the retention ratio.
Liquidity Decision:
Investment in current assets affects the firm’s profitability and liquidity. Management of
current assets that affects a firm liquidity is yet another important finance function. A proper
trade-off must be achieved between profitability and liquidity. The profitability-liquidity
trade-off requires that the financial manger should develop sound techniques of managing
current assets.
 The finance manager has to focus his attention on
i. Procuring the received quantum of funds as and when necessary, at the lowest cost
ii. Investing the funds in various assets in most profitable way, and
iii. Distributing returns to the shareholders in order to satisfy their expectations.
The three functions of the finance manager encompass most of the financial events in any
firm. Thus, the functions of a finance manager may be summarized to include the followings:
 Overall financial planning and control

 Raising funds from different sources
 Selection of fixed assets
 Evaluating financial performance
 Financial negotiation
 Keeping touch with stock exchange quotations
 Keeping touch with the behavior of share prices
 Management of working capital, and
 Any other individual financial event.
ROLE OF FINANCIAL MANAGER AND TWO-WAY CASH FLOWS TO CAPITAL
MARKET
Finance manager performs the following major functions:
 Forecasting Financial Requirements
 Acquiring Necessary Capital
 Investment Decision
 Cash Management
 Interrelation with Other Departments
CAPITAL MARKET
AND
FINANCIAL ASSETS
CASH INFLOWS IN
TERMS OF FUNDS
CASH OUTFLOWS IN TERMS OF
DIVIDENDS
PROFITS GENERATED
PROFITS REINVESTED
REAL ASSETS
ACQUIRED BYTHE FIRM
ON THE BASIS OF
DECISION BY THE
FINANCE MANAGER
FIRM
OR
FINANCIAL MANAGER

IMPORTANCE OF FINANCIAL MANAGEMENT
Finance is the life blood of business organization. It needs to meet the requirement of the
business concern. Each and every business concern must maintain adequate amount of finance
for their smooth running of the business concern and also maintain the business carefully to
achieve the goal of the business concern. The business goal can be achieved only with the help of
effective management of finance. We can’t neglect the importance of finance at any time at and
at any situation. Some of the importance of the financial management is as follows:
Financial Planning:
Financial management helps to determine the financial requirement of the business
concern and leads to take financial planning of the concern. Financial planning is an important
part of the business concern, which helps to promotion of an enterprise.
Acquisition of Funds:
Financial management involves the acquisition of required finance to the business
concern. Acquiring needed funds play a major part of the financial management, which involve
possible source of finance at minimum cost.
Proper Use of Funds:
Proper use and allocation of funds leads to improve the operational efficiency of the
business concern. When the finance manager uses the funds properly, they can reduce the cost of
capital and increase the value of the firm.
Financial Decision
Financial management helps to take sound financial decision in the business concern.
Financial decision will affect the entire business operation of the concern. Because there is a
direct relationship with various department functions such as marketing, production personnel,
etc.
Improve Profitability:
Profitability of the concern purely depends on the effectiveness and proper utilization of
funds by the business concern. Financial management helps to improve the profitability position
of the concern with the help of strong financial control devices such as budgetary control, ratio
analysis and cost volume profit analysis.

Increase the Value of the Firm
Financial management is very important in the field of increasing the wealth of the
investors and the business concern. Ultimate aim of any business concern will achieve the
maximum profit and higher profitability leads to maximize the wealth of the investors as well as
the nation.
Promoting Savings:
Savings are possible only when the business concern earns higher profitability and
maximizing wealth. Effective financial management helps to promoting and mobilizing
individual and corporate savings. Nowadays financial management is also popularly known as
business finance or corporate finances. The business concern or corporate sectors cannot
function without the importance of the financial management.
TIME VALUE OF MONEY:
The concept of TVM refers to the fact that the money received today is different in its
worth from the money receivable at some other time in future. In other words, the same principle
can be stated as that the money receivable in future is less valuable than the money received
today.
For example, if an individual is given an option to receive Rs.1000 today or to receive the
same amount after one year, he will definitely choose to receive the amount today.
The obvious reason for this reference for receiving money today is that the rupee received
today has a higher value than the rupee receivable in future. This preference for current money as
against future money is known as the time preference for money or simply time value of money.
Cash flows can be either positive or negative; positive cash flows are called cash inflows
and negative cash flows are called cash outflows.
Time Preference for Money:
If an individual behaves rationally, he or she would not value the opportunity to receive a
specific amount of money now, equally with the opportunity to have the same amount at some
future date. Most individuals value the opportunity to receive money now higher than waiting for
one or more periods to receive the same amount. Time Preference of Money or Time Value of
Money (TVM) is an individual‟s preference for possession of a given amount of money now,
rather than the same amount at some future time.
Three reasons may be attributed to the individual’s time preference for money.
 Risk

 Preference for consumption
 Investment opportunities
REASONS FOR TIME VALUE OF MONEY:
Money has time value because of the following reasons:
Risk and Uncertainty:
 Future is always uncertain and risky. Outflow of cash is in our control as payments to
parties are made by us.
 There is no certainty for future cash inflows. Cash inflows are dependent out on our
Creditor, Bank etc.
 As an individual or firm is not certain about future cash receipts, it prefers receiving cash
now.
Inflation:
 In an inflationary economy, the money received today, has more purchasing power than
the money to be received in future.
 In other words, a rupee today represents a greater real purchasing power than a rupee a
year hence.
Consumption:
Individuals generally prefer current consumption to future consumption.
Investment opportunities:
An investor can profitably employ a rupee received today, to give him a higher value to
be received tomorrow or after a certain period of time.
Eg 1:
A project needs an initial investment of ` 1,00,000. It is expected to give a return of`
20,000 per annum at the end of each year, for six years. The project thus involves a cash outflow
of ` 1,00,000 in the ‘zero year’ and cash inflows of ` 20,000 per year, for six years. In order to
decide, whether to accept or reject the project, it is necessary that the Present Value of cash
inflows received annually for six years is ascertained and compared with the initial investment of
` 1,00,000. The firm will accept the project only when the Present Value of cash inflows at the
desired rate of interest exceeds the initial investment or at least equals the initial investment of `
1,00,000.

TECHNIQUES OF TIME VALUE OF MONEY:
There are two techniques for adjusting time value of money.
They are:
1. Compounding Techniques/Future Value Techniques
2. Discounting/Present Value Techniques
The value of money at a future date with a given interest rate is called future value.
Similarly, the worth of money today that is receivable or payable at a future date is called Present
Value.
COMPOUNDING TECHNIQUES/FUTURE VALUE TECHNIQUE:
In this concept, the interest earned on the initial principal amount becomes a part of the
principal at the end of the compounding period.
Future Value of a Single Cash Flow
FOR EXAMPLE: Suppose you invest ` 1000 for three years in a saving account that
pays 10 per cent interest per year. If you let your interest income be reinvested, your investment
will grow as follows
First year :
Principal at the beginning 1,000
Interest for the year (` 1,000 × 0.10) 100
Principal at the end 1,100
Second year :
Principal at the beginning 1,100
Interest for the year (` 1,100 × 0.10) 110
Principal at the end 1210
Third year :
Principal at the beginning 1210
Interest for the year (` 1210 × 0.10) 121
Principal at the end 1331
 This process of compounding will continue for an indefinite time period.
 The process of investing money as well as reinvesting interest earned there on is called
Compounding.
 But the way it has gone about calculating the future value will prove to be cumbersome if
the future value over long maturity periods of 20 years to 30 years is to be calculated.
 A generalized procedure for calculating the future value of a single amount compounded
annually is as follows:
FVn = PV(1 + r) n

In this equation (1 + r)n is called the future value interest factor (FVIF).
where,
FVn = Future value of the initial flow n year hence
PV = Initial cash flow
r = Annual rate of Interest
n = number of years
By taking into consideration, the above example, we get the same result.
FVn = PV (1 + r) n
= 1,000 (1.10)3
FVn = 1331
To solve future value problems, we consult a future value interest factor (FVIF) table.
The table shows the future value factor for certain combinations of periods and interest rates. To
simplify calculations, this expression has been evaluated for various combination of ‘r’ and ‘n’.
Exhibit 1.1 presents one such table showing the future value factor for certain combinations of
periods and interest rates.
Future Value of an Annuity:
Annuity is a fixed payment (or receipt) each year for a specified number of years. If you
rent a flat and promise to make a series of payment over an agreed period, you have created an
annuity. The equal-installment loans from the house financing companies or employers are
common examples of annuities. The compound value of an annuity cannot be computed directly
from the previous equation as shown above.
The computations can be expressed as follows:
For example, a constant sum of Re1 is deposited in a savings account at the end of each
year for four years at 6 percent interest. This implies that Re1 deposited at the end of the first
year grow for 3 years, Re1 at the end of second year for 2 years, Re1 at the end of the third year
for 1 year and Re1 at the end of the fourth year will not yield any interest.
Using the concept of the compound value of a lump sum, we can compute the value of
annuity. The compound value of
Re1 deposited in the first year will be: 1*1.063 = 1.191
Re1 deposited in the second year will be: 1*1.062 = 1.124
Re1 deposited in the third year will be: 1*1.061 = 1.060
Re1 deposited at the end of fourth year will be: 1 = 1.000
Total = 4.375
Sinking Fund:
 Sinking fund is a fund which is created out of fixed payments each period to acculmulate
to a future sum after a specific period.
F4 = A(1+i)3 +A(1+i)2 + A(1+i) + A

 For eg, companies generally create sinking funds to retire bonds(debentures) on maturity.
 The factor used to calculate annuity for a given future sum is called the sinking fund
factor(SFF)
Eg:
DISCOUNTING/PRESENT VALUE TECHNIQUES:
 Present value of a future cash flow (inflow or outflow) is the amount of current cash that
is of equivalent value to the decision maker.
 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.
Present Value of a Single Cash Flow:
 Formulate to calculate the present value of a lump sum to be received after some future
periods:

 The term is parenthesis is the discount factor or present value factor (PVF), and it is
always less than 1.0 for positive i, indicating that a future amount has a smaller present
value.
PV=Fn x PVF n,i
 In excel,
PV(rate,nper,pmt,fv,type)
Eg:
Suppose that an investor wants to find out the present value of Rs. 50,000 to be received
after 15 years. Her interest rate is 9%. First, we will find out the present value factor (PVF),
which is 0.275.
PV = 50,000 x PVF15, 0.09
= 50,000 x 0.275
= Rs. 13,750
Present value of an annuity:
 The present value of an annuity can be written in the following general form:
 The term within the parenthesis is the present value factor of an annuity of Re. 1, which
would call PVFA, and it is a sum of single-payment present value factors.
P = A x PVAF n,i
 In excel,
PMT(rate,nper,pv,fv,type)
Eg:
An investor, who has a required interest rate as 10 percent per year, may have an
opportunity to receive an annuity of Rs.1 for four years.
The present value of Rs.1 received
After one year is, P = 1/(1.10) = Rs.0.909,
After two years, P = 1/(1.10)2 = Rs.0.826,
After 3 years, P = 1/(1.10)3 = Rs.0.751 and
After four years, P = 1/(1.10)4= Rs.0.683.
Thus the total present value of an annuity of Rs.1 for four years is Rs.3.169 as shown

below.
P = [1/(1.10) + 1/(1.10)2 +1/(1.10)3 +1/(1.10)4]
= [0.909 + 0.826 + 0.751 + 0.683 = Rs.3.169
For example, assume that a person receives an annuity of Rs.5000 for four years. If the
rate of interest is 10 percent, the present value of Rs.5000 annuity is calculated as follows:
P = 5000 [1/0.10 − 1/0.10 (1.10)4]
= 5000 * (10 − 6.830)
= 5000 * 3.170
= Rs.15,850
We can also calculate the present value factor of an annuity of Rs.1 for n periods at i rate
of interest, by the formula and using the table (factor) value as shown below:
PV = 5000 * (PVFA 4,0.10)
= 5000 * 3.170 = Rs.15,850
Present Value of an Uneven Periodic Sum:
 In most instances the firm receives a stream of uneven cash flows. Thus the present value
factors for an annuity cannot be used.
 The procedure is to calculate the present value of each cash flow and aggregate all
present values.
Eg:
Consider than an investor has an opportunity of receiving Rs.1000, Rs.1500, Rs.800,
Rs.1100 and Rs.400 respectively at the end of one through five years. Find out the present value
of this stream of uneven cash flows. If the investor‟s required interest is 8 percent, what will be
the present cash flow?
Solution:
The present value is calculated as follows:
Present value = 1000+ 1500+ 800+ 1100+ 400
(1.08) (1.08)2 (1.08)3 (1.08)4 (1.08)5
The complication of solving this equation can be resolved by using the calculated table.
We can find out the appropriate present value factors (PVFs) either from the calculated table or
by using calculator land multiplying them by respective amount.
The present value calculation will be as follows:
PV =1000 * PVF1.08 + 1500 * PVF2.08 + 800 * PVF3.08 + 1100 * PVF4.08+ 400 * PVF5.08
= 1000*0.926 + 1500*0.857 + 800*0.794 + 1100*0.735 + 400*0.681
= Rs.3, 927.60

MULTI-PERIOD COMPOUNDING:
In practice, cash flows could occur more than once a year. For example, banks may pay
interest on savings account quarterly. On bonds or debentures and public deposits, companies
may pay interest semi-annually. Similarly, financial institutions may require corporate borrowers
to pay interest quarterly or half-yearly.
o The interest rate is usually specified on an annual basis, in a long agreement or
security (such as bonds) and is known as the nominal rate of interest.
o If compounding is done more than once a year, the actual annualized rate of
interest would be higher than the nominal interest rate and it is called the effective
interest rate.
Problem:
You can get an annual rate of interest of 13 percent on a public deposit with a company.
What is the effective rate of interest if the compounding is done (a) halfyearly, (b) quarterly, (c)
monthly and (d) weekly? Calculate EIR.
Solution:
The general formula for calculating EIR can be written in the following general form:
where
i - The annual nominal rate of interest,
n - The number of years and
m- The number of compounding per year.
In annual compounding, m = 1, in monthly compounding, m = 12 and in weekly
compounding m = 52.
Effective Interest Rate (EIR):
(a) EIR = [1+0.13/2]1*2 – 1 = (1.065)2 – 1 = 1.1342 – 1 = 0.1342 or 13.42%
(b) EIR = [1+0.13/4]1*4 – 1 = (1.0325)4 – 1 = 1.1365 – 1 = 0.1365 or 13.65%
(c) EIR = [1+0.13/12]1*12 – 1= (1.01083)12 – 1 = 1.1380 – 1 = 0.1380 or 13.80%
(d) EIR = [1+0.13/52]1*52 – 1= (1.0025)52 – 1 = 1.1386 – 1 = 0.1386 or 13.86%
Problem: (Multi-period Compounding):
Find out the compound value of Rs.1000, interest rate being 12 percent per annum if
compounded annually, semi-annually, quarterly and monthly for 2 years.
 Annual compounding

Fn = 1000[1+0.12/1]2*1 = 1000(1.12)2 = 1000*1.254 = Rs.1254
 Half-yearly compounding
Fn = 1000[1+0.12/2]2*2 = 1000(1.06)4 = 1000*1.262 = Rs.1262
 Quarterly compounding
Fn = 1000[1+0.12/4]2*4 = 1000(1.03)8 = 1000*1.267 = Rs.1267
 Monthly compounding
Fn = 1000[1+0.12/12]2*12 = 1000(1.01)24 = 1000*1.270 = Rs.1270
INTRODUCTION TO THE CONCEPT OF RISK AND RETURN OF A SINGLE
ASSET AND OF A PORTFOLIO
RISK:
The risk simply means the possibility of loss or damage, the degree or probability of such
loss. Risk is composed of the demand that bring in variations in return of income. The main
forces contributing to risk are price and interest. All investments are risky, whether in stock or
capital market or banking and financial sector, real estate, bullion gold, etc
DEFINITION OF RISK:
According to Fischer and Jordon, “Risk is the variability of return around the expected
average is thus a quantitative description of risk”.
According to Cornelius Keating, “Risk is the unwanted subset of a set of uncertain
outcomes”.
CAUSES OF RISK:
 Wrong Decision: Wrong decision of what to invest in.
 Wrong Timing: Wrong timing of investments.
 Nature of Instruments: Nature of instruments invested such as shares or bonds, chit
funds, benefit funds are highly risky than bank deposits or postal certificates, etc.
 Creditworthiness of Issuer: Securities of government and semi-government bodies are
more creditworthy than those issued by the corporate sector.
 Maturity Period (or) Length of Investment: Longer the period, the more risky is the
investment normally.
 Amount of Investment: Higher the amount invested in any security the larger is the risk.
 Method of Investment: Method of investment, namely, secured by collateral or not.
 Terms of Lending: Terms of lending such as periodicity of servicing, redemption
periods, etc.
 Nature of Industry: Nature of industry or business in which the company is operating.
 National and International Factors: The factors prevailing in the nation and abroad in
terms of acts of goods, etc.

TYPES OF RISK:
There are different types of risk. They are:
DIAGRAMMATIC REPRESENTATION OF TYPES OF RISK
TYPES OF RISK:
 Systematic Risk
 Marketing Risk
 Interest Rate Risk
 Purchasing Power Risk
RISK
SYSTEMATIC RISK UNSYSTEMATIC
RISK
Interest Rate Marketing Risk
Purchasing
Power Risk
Business Risk Finacial Risk
Internal Risk External Risk

 Unsystematic Risk
 Business Risk
o Internal Risk
o External Risk
 Financial Risk
MEASURES OF RISK:
Risk refers to the possibility that the actual outcome of an investment will refer from the
expected outcome. Put differently, risk refers to variability or dispersion. If an asset’s return has
no variability, it is risk-less. The risk can be measured by variance and standard deviation.
RATES OF RETURN AND HOLDING PERIODS:
Investors may hold their investment in shares for longer periods than for one year. How
do we calculate holding-period returns?
For example, you invest Rs.1 today in a company’s share for five years. The rates of
return are 18 percent, 9 percent, 0 percent, −10 percent and 14 percent. What is the worth of your
shares?
You hold the share for five years; hence, you can calculate the worth of your investment
assuming that each year dividends from the previous year are reinvested in shares. The worth of
your investment after five years is:
Investment worth after five years
= (1+0.18) × (1+0.09) × (1+0.0) × (1−0.10) × (1+0.14)
= 1.18 × 1.09 × 1.00 × 0.90 × 1.14 = Rs.1.32
Your one rupee investment has grown to Rs.1.32 at the end of five years. Thus your total
return is: 1.32 – 1 = 0.32 or 32 percent. Your total return is a five-year holding period return.
Problem: Variance and Standard Deviation
The shares of Hypothetical Company Limited have the following anticipated returns with
associated probabilities. What is the expected rate of return?
Return (%): −20 −10 10 15 20 25 30
Probability: 0.05 0.10 0.20 0.25 0.20 0.15 0.05
Solution
The expected rate of return is:
E(R) =(−20 ×0.05) + (−10 ×0.10) + (10 ×0.20) + (15 ×0.25) +
(20 ×0.20) + (25 ×0.15) + (30 ×0.05)
= 13%
The risk, measured in terms of variance and standard deviation, is:

σ2 = [(−20– 13)]20.05 + [(−10– 13)]20.10 + [(10– 13)]20.20 + [(15–13)]20.25 + [(20–13)]20.20
+ [(25–13)]20.15 + [(30–13)]20.05
= 156
σ = √156 = 12.49%
RISK PREFERENCE:
 A risk-averse investor will choose among investments with the equal rates of return, the
investment with lowest standard deviation and among investments with equal risk she
would prefer the one with higher return.
 A risk-neutral investor does not consider risk, and would always prefer investments with
higher returns.
 A risk-seeking investor likes investments with higher risk irrespective of the rates of
return. In reality, most (if not all) investors are risk-averse.

RISK-RETURN TRADE-OFF:
 Financial decisions of the firm are guided by the risk-return trade-off.
 The return and risk relationship:
Return = Risk-free rate + Risk premium
 Risk-free rate is a compensation for time and risk premium for risk.
MEANING OF RETURN:
The objective of any investor is to maximize expected returns from his investments,
subject to various constrains, primarily risk. Return is the motivating force, inspiring the investor
in the form of rewards for undertaking the investment. The importance of returns in any
investment decision can be traced to the following factors.
 It enables investors to compare alternative investments in terms of what they have to
offer the investor.
 Measurement of historical or past returns enables the investors to assess how well they
have done.
 Measurement of historical returns also helps in estimation of future returns.
TYPES OF RETURN
There are two types which are as follows:
 Realized return
 Expected return

Realized Return:
This is ex-post (after the fact) return, or return that was or could have been earned. For
example, a deposit of Rs.1000 in a bank on January 1, at a stated annual interest rate of 10% will
be worth Rs.1100 exactly a year later. The historical or realized return in this case is 10%.
Expected Return:
This is the return from an asset that investors anticipate or expect to earn over some
future period. The expected return is subject to uncertainty or risk and may or may not occur.
The investor compensates for the uncertainty in returns and the timing of those returns by
requiring an expected return that is sufficiently high to offset the risk or uncertainty.
COMPONENTS OF RETURN:
The return of an investment consists of two components.
Current Return:
The first component that often comes to mind when one is thinking about return is the
periodic cash flow (income), such as dividend or interest generated by the investment. Current
return is measured as the periodic income in relation to the beginning price of the investment.
Capital Return:
The second component of return is reflected in the price change called the capital return.
It is simply the price appreciation (or depreciation) divided by the beginning price of the asset.
For assets like equity stocks, the capital return predominates.
MEASURE OF RETURN
1) Traditional Method
2) Modern Method
Traditional methods:
Computation of yield to measure a financial asset’s return is the simplest and oldest
technique of measurement. Yield can be found out by the following ways:
Estimated Yield = Expected Cash Income / Current Price of Assets
Actual Yield = Cash Income / Amount Invested
Problem
An investor buys a bond in 2010 maturity in 2012 at Rs.900. It has a maturity value
of 10 years and par value of Rs.1000. It fetches Rs.90 every year. Calculate yield.
Solution
Current Yield = Annual Cash Price / Purchase Price
90 / 900 = 10%
Yield to Maturity = Average Annual Return / Average Investment
= 100 / 950 = 0.105 or 10.5%
C = Annual Coupon
M = Maturity of par value of bond
P = Purchase Price

N = Number of years remaining to maturity
Average Annual Return = C +[(M−P)/N]
= 90 + [1000−900)/10]
= 90 + 10 = 100
Average Investment = (M+P)/2
= (1000+900)/2
= 1900/2 = 950
The return of stock or share is measured by finding out dividend yield. Dividend yields
can be estimated on expected yields as well as actual yields.
Estimated Yield = Expected Cash Dividend / Current Share price
Actual Yield = Dividend Received / Price of the share in the beginning
(or)
Earning Yield = Earning / Price of Share
Problem:
A stock that is selling for Rs.36 and earns Rs.3 annually has an E/P ratio of what?
Solution
Earning Yield = Earning / Price of Share
= 3/36 =0.083 or 8.33%
RISK AND RETURN:
Financial decisions incur different degree of risk. Your decision to invest the 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 the money in shares, as return
is not certain. However, you can expect a lower return from government bond and higher from
shares. Risk and expected return move in tandem; the greater the risk, the greater the expected
return. The following figure shows this risk-return relationship.
Overview of Financial Management:

Risk-free rate is a rate obtainable from a default-risk free government security. An
investor assuming risk from her investment requires risk premium above the risk-free rate. Risk-
free rate is a compensation for time and risk premium for risk. Higher the risk of action, higher
will be the risk premium leading to higher required return on that action. A proper balance
between return and risk should be maintained to maximize the market value of a firm’s shares
VALUATION OF BONDS AND SHARES:
A bond is a contract that requires the borrower to pay the interest income to the lender. It
resembles the promissory note issued by the government and corporate. The par value of the
bond indicates the face value of the bond i.e. the value stated on the bond paper. Generally, the
face values of bonds are Rs.1000, Rs.2000, Rs.5000 and alike. Most of the bonds are make fixed
interest payment till the maturity period.
Thus, security can be valued in the following form;
1) Bond
2) Equity Shares
3) Preference Shares
4) Derivative Instrument like Option
Features of a Bond:
 Long-term debt instrument or security.
 Can be secured or unsecured.
 Interest Rate or coupon rate is fixed
 Face Value or par value of Rs 100 or Rs 1,000, and interest is paid on face value.
 Maturity is fixed.
 Redemption value - may be redeemed at par or premium.
 Market Value- may be different from par value or redemption value as it is traded in
the market.
VALUATION OF BOND:
Present Value of Bond
The value of a bond – or any asset, real or financial – is equal to the present value of the
value of cash flows expected from it. So determining the intrinsic value of a bond requires:
a. An estimated of expected cash flow,
b. An estimate of the required return.
The value of the bond is calculated as:

n
P = Σ [C÷(1+r)t] + [M÷(1+r)n]
t=1
Where,
P = value (in rupees)
n = number of years
C = annual coupon payment (in rupees)
r = periodic required return rate
M = maturity value
t = time period when the payment is received
We can also apply the formula by using present value of an ordinary annuity.
P = C × PVIFA r,n + M × PVIF r,n
For example, consider a 10 year, 12 percent coupon bond with a par value of Rs.1000.
The required yield on this bond is 13 percent. The cash flows for this bond are as follows:
 10 annual coupon payment of Rs.120
 Rs.1000 principal repayment 10 years from now
 The value of the bond is:
P = C × PVIFA13%,10yrs + M × PVIF13%,10yrs
= 120 × 5.426 + 1000 × 0.295
= 651.1 + 295 = Rs.946.1
TYPES OF BONDS:
 Bonds with maturity
 Pure discount bonds -The bond discount is the difference between the par value
and the selling price.
 Perpetual bonds
BOND WITH MATURITY:
Eg:
Bond Value = Present value of Interest + Present value of maturity value

Yield to Maturity:
The Yield-to-maturity (YTM) is the measure of a bond's rate of return that considers both
the interest income and any capital gain or loss. YTM is bond's internal rate of return.
A perpetual bond yield to maturity
Current Yield:
 Current yield is the annual interest divided by the bond's current value.
 Current yield does not account for the capital gain or loss
Eg:
The annual interest is Rs.60 on the current investment of 883.40. Therefore, the current rate
of return or the current yield is 60/883.4 = 6.8 percent.
Yield to Call:
The call period would be different from the maturity period and the call (or redemption)
value could be different from the maturity value.
Eg:
Suppose the 10% for 10 year Rs.1000 bond is redeemable (callable) in 5 years at a call price
of Rs. 1050. The bond is currently selling for Rs. 950. The bond's yield to call is 12.7%
PURE DISCOUNT BONDS:
 Pure discount bonds do not carry an explicit rate of interest.
 It provides for the payment of a lump sum amount at a future date in exchange for the
current price of the bond.
 The difference between the face value of the bond and its purchase price gives the return
or YTM to the investor.
Eg:
A company may issue a pure discount bond of Rs. 1000 face value for Rs. 520 today for a
period of five years. The rate of interest can be calculated as follows:

 Pure discount bonds are called deep-discount bonds or zero-interest bonds or zero-
coupon bonds.
 The market interest rate, also called the market yield, is used as the discount rate.
 Value of a pure discount bond = PV of the amount on maturity:
Consider the IDBI bond with a face value of Rs. 500000 with a maturity of 30 years.
Suppose the current market yield on similar is 9 percent. The value of the IDBI pure-discount
bond today is as follows:
PERPETUAL BONDS:
 Perpetual bonds are also called as Consol’s, has an indefinite life and therefore, it has no
maturity value. Perpetual bonds or debentures are rarely found in practice.
 Suppose that a 10% of Rs.1000 bond will pay Rs.100 annual interest into perpetuity.
What would be its value of the bond if the market yield or interest rate were 15%?
 The value of the bond is determined as follows:
VALUATION OF SHARES:
 A company may issue two types of shares:
 Ordinary shares
 Preference shares

 Features of Preference and Ordinary shares:
 Claim
 Dividend
 Redemption
 Conversion
VALUATION OF PREFERENCE SHARES:
 The valuation of the preference shares would be the sum of the present values of
dividends and the redemption value
 A formula similar to the valuation of bond can be used to value preference shares with a
maturity period:
VALUATION OF ORDINARY SHARES:
 The valuation of ordinary shares or equity shares is relatively more difficult.
 The rate of dividend on equity shares is not known; also, the payment of equity
dividend is discretionary.

 The earnings and dividends on equity shares are generally expected to grow, unlike
the interest on bonds and preference dividend.
SINGLE PERIOD VALUATION:
The valuation of ordinary shares or equity shares is determined by capitalizing the future
dividend stream at the opportunity cost of capital.
 If the share price is expected to grow at g percent, P1
P1+P0(1+g)
 To obtain formula for the share valuation as follows:
Eg:
 An under-valued share has a market price less than the share's present value.
 An over-valued share has a market price higher than the shares present value.

MULTIPLE PERIOD VALUATION:
The following is the general formula for calculating the value of a share.
Growth in dividends:
 Normal Growth
Growth= Retention ratio x Return on equity
g=b x ROE
 Super-normal Growth:
Share value = PV of dividends during finite super-normal growth period +
PV of dividends during indefinite normal growth period
Eg:

Present value of dividends and future share price:
Growth in dividends:
 Earnings and dividends of most companies grow over time, at least, because of their
retention policies.
 If total equity financed firms retains a constant proportion of its annual earnings (b) and
reinvests it at its internal rate of return, which is its return on equity (ROE), then it can be
shown that the dividends will grow at a constant rate equal to the product of retention
ratio and return on equity; that is,
b=b x ROE
Eg:

Perpetual Growth Model:
The present value of the share is equal to the dividend after a year, DIV1, is divided by
the difference of the capitalization rate (ke) and the growth rate(g);
i.e: (ke – g)
It is based on the following assumptions:
 The capitalization rate or the opportunity cost of capital must be greater than the growth
rate, (ke > g), otherwise absurd results will be attained. If ke = g, the equation will yield an
infinite price and if ke < g, the result will be a negative price.
 The initial dividend per share, DIV1 must be greater than zero (i.e. , DIV1 > 0).
 The relationship between ke and g is assumed to remain constant and perpetual.
Eg:
Super-normal Growth:
 The dividends of a company may not grow at the same constant rate indefinitely. It may
face a two-stage growth situation.
 In the first stage, dividends may grow at a super-normal growth rate when the company is
experiencing very high demand for its products are able to extract premium from
customers.
 Afterwards, the demand for the company products may normalize and therefore, earnings
and dividends may grow at a normal growth rate.
 The share value in a two stage growth situation can be determined in two parts.
 First, we can find the present value of constantly growing dividend annuity for a
definite super-normal growth period.

 Second, we can calculate the present value of constantly growing dividend,
indefinitely (in perpetuity), after the super-normal growth period.
Eg:

(iii) Value of the share today:
P0 = 19.10+32.19= 51.29
Constant Growth Model (Gordon Model):
One of the most popular dividend discount models, called the Gordon model as it was
originally proposed by Myron J Gordon assumes that the dividend per share grows at a constant
rate (g). The value of a share, under this assumption is:
P0 = [D1/(1+r)] + [D1(1+g) /(1+r)2] + . . . . . . + [D1/(1+g)n /(1+r)n+1]
P0 = [D1/(r−g)]
For example,
Ramesh Engineering Limited is expected to grow at the rate of 6 percent per annum. The
dividend expected on Rajesh’s equity share a year hence is Rs.2.00. What price will you put on
it if your required rate of return for this share is 14 percent?
Solution:
The price of Rajesh’s equity share would be:
P0 = [D1/(r−g)]
= [2.00 /(0.14−0.06)]
= Rs.25.00

Zero Growth Model:
The most basic of all the DDMs is the zero growth models. This model assumes that
dividend will be constant over time, so that growth is zero and that the investor’s required rate of
return is constant. This model is:
P0 = [D /(1+r)] + [D /(1+r)] + ….. + [D /(1+r)] + [D /(1+r)∞
]
Above equation can be simplified as:
P0 = D/r
Ratio Approach:
The ratio approach to the valuation of equity shares includes
 Price-Earnings Ratios and
 Earnings Multiplier Approach.
Price-Earnings Ratios:
Despite the inherent sensibility of dividend discount models, many security analysts
follow a much simpler procedure to value equity by using Price-Earnings (P/E) ratios. The P/E
ratio indicates the price being paid for each rupee of a firm’s earnings.
The ratio of equity is equal to its current market price divided by some measure of
earnings per share, that is:
P/E Ratio = Market Price / Earnings per share
Earnings Multiplier Approach:
The P/E ratio is a commonly utilized tool for equity analysts. The Earnings Multiplier
Approach is a means to forecast future earnings of a company and consequently the estimated
P/E ratio. To calculate the earnings multiplier, multiply the aggregate earnings by the P/E to
market value.
To derive the P/E estimate, the dividend discount model is used as:
(P0)/(E1) = (D1/E1) /(Ke – g)
Where,
P0 = Price of security
E1 = Project earnings in the next year
D1 = Dividend estimated for the next year
Ke = Required return on equity capital
g = Growth rate
Earnings Multiplier = P/E ratio × Aggregate Earnings

OPTION VALUATION
Options are derivatives contracts that give the buyer the right to buy or sell an underlying
asset at a certain price within a specified time period. Selling or buying options involves two
parties, namely a buyer and a seller. The strategy of selling options is popular mostly with traders
who are capable of meaning the element of risk that is inherent in such transactions.
An option is a type of a contract between two parties where one person grants the other
person the right, but not the obligation, to buy a specific asset at a specific price within a specific
time period. Alternatively, the contract may grant the other party the right, but not the obligation,
to sell a specific asset at a specific price within a specific time period.
TYPES OF OPTIONS:
There are two types of options. They are:
(i) Call Options and
(ii) Put Options.
Before commodity options were banned in India in 1952, the same two types of options
were traded as “teji” (call) and “mandi” (put) in the security market.
Call Options:
 In Call Option, the option buyer has the right, but not the obligation, to buy the
commodity at the predetermined price.
 For example, A enters into a contract with B whereby A has the right to purchase 100
ounces of gold from B for Rs.400 per ounce at any time prior to August 1. For granting
this option A pays B an option premium of Rs.5 per ounce. This is a call option.
Put Option:
 In Put Option, the option buyer has the right, but not the obligation, to sell the commodity
at a specified price.
 For example, X enters into a contract with Y whereby X has the right to sell 100 ounces
of gold from Yat a price of Rs.400 at any time before August 1. For granting this option
X pays YRs.6 per ounce as premium. This is a put option.
OPTION TERMINOLOGY:
 Index Options
 Stock Options
 Buyer of an Option
 Writer of an Option
 Expiration Date

 Strike Price
 In-the-Money
 At-the-Money
 Out-of-the-Money
Index Options:
These options have the index as the underlying. Some options are European while others
are American. Like index futures contracts, index options contracts are also cash settled.
Stock Options:
Stock options are options on individual stocks. A contract gives the holder the right to
buy or sell shares at the specified price.
Buyer of an Option:
The buyer of an option is the one who by paying the option premium buys the right but
not the obligation to exercise his option on the seller/writer.
Writer of an Option:
The writer of a call/put option is the one who receives the option premium and is thereby
obliged to sell/buy the asset if the buyer exercises his right.
Expiration Date:
The date specified in the option contract is known as the expiration date, the exercise
date, the strike date or the maturity.
Strike Price:
The price specified in the options contract is known as the strike price or the exercise
price.
In-the-Money:
An ITM option is an option that would lead to a positive cash flow to the holder if it were
exercised immediately. A call option on the index is said to be in-the-money when the current
index stands at a level higher than the strike price (i.e. spot price > strike piece). In case of put
option, the put is ITM if the index is below the strike price.
At-the-Money:
An ATM option is an option that would lead to zero cash flow if it were exercised
immediately. An option on the index is at-the-money when
the current index equals the strike price (i.e. spot price = strike piece).
Out-of-the-Money:
An OTM option is an option that would lead to a negative cash flow if it were exercised
immediately. A call option on the index is out-of-the-money when the current index stands at a
level lesser than the strike price (i.e. spot price < strike piece). In case of put option, the put is
OTM if the index is above the strike price.
Problem

Jerry House paid a premium of Rs.4 per share for one 6-month call option contract (total
of Rs.400 for 100 shares) of the Mahony Corporation. At the time of the purchase, Mahony stock
was selling for Rs.56 per share and the exercise price of the call option was Rs.55.
1. Determine Jerry’s profit or loss if the price of Mahoney‟ stock is Rs.54 when the option
is exercised?
2. What is Jerry’s profit or loss if the Mahony‟s stock is Rs.62 when the option is
exercised?
3. Ignore taxes and transaction cost.
Solution:
Cost of call = (Rs.4 premium)×100 = Rs.400
Ending value = (−Rs.400 cost) + (0 gain) = Rs.400 loss
The option was worthless because the stock’s price is less than the exercise price at
maturity.
Cost of call = 400
Ending value = −Rs.400 + (Rs.62−55)×100
= −400 + 700 = Rs.300 gain
FACTORS DETERMINING OPTION PRICE:
In purchasing an option the amount the buyer pays for the option privilege is called the
premium, or sometimes the option money. In most option transactions the contract price is the
stock market price prevailing at the time the option is written and the premium becomes the
variable over which buyer and seller bargain.
 Volatility
 Expiration Date
 Striking Prices
 Stock Price
 Dividends
 Interest Rates
BLACK-SCHOLES OPTION PRICING MODEL (BSOPM):
Option pricing theory also called Black-Scholes theory or derivatives pricing theory
traces its roots to Bachelier who invented Brownian motion to model options on French
government bonds. This work anticipated Einsten’s independent use of the Brownian motion in
physics by five years. The Black-Scholes model is used to calculated a theoretical call price
(ignoring dividends paid during the life of the option) using the five key determinants of an

option‟s price; stock price, strike price, volatility, time to expiration and short-term (risk-free)
interest rate.
The original formula for calculating the theoretical Option Price (OP) is as follows:
C = SN(d1) – Ee−rt N(d2)
Where,
d1 = In[S/E] + [r+(1/2)σ2]t and
σ√t
d2 = In[S/E] + [r−(1/2)σ2]t
σ√t
The variables are:
S = Stock price
E = Strike price
t = Time remaining until expiration
r = Risk free interest rate
σ = Annual volatility of stock price (standard deviation)
In = Natural logarithm
e = Exponential function
N = Standard normal cumulative distribution function
The Black-Scholes model gives theoretical value for European put and call options on
non-dividend paying stocks. The key argument is that traders could riskless hedge a long options
position with a short position in the stock and continuously adjust the hedge ratio (the delta value
– one of the option sensitivities known as „greeks”) as needed. Assuming that the stock price
follows a random walk, and using the methods of stochastic calculus, a price for the option can
be calculated where there is no arbitrage profit.
Assumptions of Black and Scholes Model
 Stock Pays no Dividends during the Option‟s Life
 European Exercise Terms are Used
 Markets are Efficient
 No Commissions are Charged
 Interest Rates remain Constant and Known
 Returns are Long-normally Distributed
Advantages of Black & Scholes Model
 The main advantage of the Black & Scholes model is speed.
 It helps to calculate a very large number of option prices in a very short time.

Disadvantages of Black & Scholes Model
 It cannot be used to accurately price options with an American-style exercise.
 It is limited to exercise only to the European options which can only be exercised at
expiration.

Financial Management Objectives

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Financial Management Objectives