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FINANCIAL MANAGEMENT :INTRODUCTION

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An Introduction to the

Ten Basic Principles

CORPORATE FINANCE

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Foundation of Finance

Finance fundamentals spring from 10simple principles that dont requireknowledge of finance to understand.

However, while it is not necessary tounderstand finance in order to understandthese principles, it is necessary tounderstand these principles in order tounderstand finance.

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PRINCIPLE 1

The Risk-Return Trade-Off

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PRINCIPLE 2

The Time Value ofMoney

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PRINCIPLE 3

Cash Not Profit isKing.

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PRINCIPLE 4

Incremental Cash Flows

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PRINCIPLE 5

The Curse of CompetitiveMarkets

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PRINCIPLE 6

Efficient Capital Markets

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PRINCIPLE 7

The Agency Problem

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PRINCIPLE 8

Taxes Bias BusinessDecisions.

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PRINCIPLE 9

All Risk is Not Equal

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1-13

PRINCIPLE 10

Ethical behaviour isdoing the right thing,and ethical dilemmas areeverywhere in finance.

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1-14

FINANCIAL MANAGEMENT

Financial Management is concerned with the acquisition,

financing and management of assets with some overall goal in

mind

-J.C.VANHORNE

"Financial Management is an area of financialdecision making, harmonizing individual motives

and enterprises goals

-Weston and Brigham

Financial Management is that managerial activity

which is concerned with the planning and controlling

of the firms financial resources.

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1-15

Financial Management: Defined

This is the business management function that is

concerned with managing abusiness finances

It refers to the application of financial management

tools and techniques to coordinate all the financial

functions in the business

Management of funds is a critical aspect offinancial management. Management of funds actas the foremost concern whether it is in a businessundertaking or in an educational institution.Financial management, which is simply meant

dealing with management of money matters.

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1-16Management

By Financial Management we mean efficient use of

economic resources namely capital funds. Financial

management is concerned with the managerial

decisions that result in the acquisition and financing of

short term and long term credits for the firm.

Here it deals with the situations that require selection

of specific assets, or a combination of assets and the

selection of specific problem of size and growth of anenterprise.

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1-17Management

Sound financial management is essential in all types of

organizations whether it be profit or non-profit. Financialmanagement is essential in a planned Economy as well as in a

capitalist set-up as it involves efficient use of the resources.

From time to time it is observed that many firms have been

liquidated not because their technology was obsolete or because

their products were not in demand or their labour was not skilled

and motivated, but that there was a mismanagement of financial

affairs. Even in a boom period, when a company make high

profits there is also a fear of liquidation because of bad financial

management.

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1-18

Contd..

Financial management optimizes the output from the given input of

funds. In a country like India where resources are scarce and thedemand for funds are many, the need of proper financial

management is required. In case of newly started companies with a

high growth rate it is more important to have sound financial

management since finance alone guarantees their survival.

Financial management is very important in case of non-profit

organizations, which do not pay adequate attentions to financial

management.

How ever a sound system of financial management has to be

cultivated among bureaucrats, administrators, engineers,

educationalists and public at a large.

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1-19Management

Profit Maximization:

The objective of financial management is the same as the objective of a

company which is to earn profit. But profit maximization alone cannot be

the sole objective of a company. It is a limited objective. If profits are

given undue importance then problems may arise, so profit maximization

objective is justified on the following grounds:

Rationality

Maximization of Social Benefit

Efficient allocation and uses of resources

Measurement of success of decisions

Sources of incentive

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Profit Maximization contd.

Profit Maximization objective is considered to be a very limited objective,

because it has a number of drawbacks, which render this objective as anineffective decisional criterion. These drawbacks (limitations) are as under:

Ambiguity / Loose expression of the term profit: The term profit is vague and

it involves much more contradictions.

Profit Maximization objective ignores timing of benefit (time-value-money):

Profit Maximization fails to take into account the time pattern of returns. Profitmaximization does not take into account the social considerations

Profit Maximization objective fails to recognize quality of benefits (risk

factor): Profit maximization must be attempted with a realization of risks

involved. A positive relationship exists between risk and profits. So both risk

and profit objectives should be balanced.

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1-21Objectives of Financial Managementcontd..

Wealth Maximization:

The value of a firm is represented by the market price of the company's

stock (equity share). by Van Horne.

The market price of a firm's stock represents the assessment of all market

participants as to what the value of the particular firm is.

It takes in to account present and prospective future earnings per share,

the timing and risk of these earning, the dividend policy of the firm and

many other factors that bear upon the market price of the stock. Market

price acts as the performance index or report card of the firm's progress

and potential.

It is based on the concept of cash flows. It also signifies the net worth of the enterprise measured in terms of net

present value (NPV) i.e., the difference between Gross Present Value and

the Cost of Capital Investments required for achieving the benefits.

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1 22

Wealth Maximization contd.

Wealth maximization as a decision criterion isused in the context of three important areas of

financial management:

In case of investment decision, the value of firm is

maximized when projects with higher NPV areaccepted

In case of financing decision, it may be stated that

when the return is maximized with the minimum risk,

market value per share will be maximized. In case of dividend decision, the optimum dividend

policy is one that maximizes the market value for share.

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1 23

Functions of a Financial Manager

Financial Forecasting: It requires the applications of various statistical,

mathematical & accounting techniques.

Financial Planning: It is done under three distinct sub-activities Formulation of financial objectives Framing the financial policies Developing financial procedures

Financial Decisions: It involves the determination of financial sources,comparative study of their cost of capital, examining the impact on shareholdersequity, etc.

Financial Negotiations

Investment Decisions: It is function of financial management to determine the

volume of investments in fixed and current assets.

Management of Cash Flows

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1 24Functions of a Financial Managercontd

Management of Income: It comprises correct measurement of

income, distribution of income in correct proportion andfollowing the appropriate dividend policy.

Appraisal of Financial Performance: This function analyze andevaluate the financial performance of the business concern aftera definite interval and to communicate the results to top

management.

Understanding Capital Market: Financial Manager should knowhow risk is measured and how to cope with it in investment andfinancing decisions.

To make efforts for Increasing the Productivity of the Capital: Itis done by discovering the new opportunities of investments.

To Advise the top Management: Financial Manager advise inrespect of proper diagnosis of the problem, alternative solutions

to the problem and selection of the best solutions.

1-25Importance of Proper Financial

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1 25Importance of Proper FinancialManagement

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6

Importance of FM Contd

Maximize use of financial resources

FM allows you to identify and plan for the useof your financial resources.

It provides information for financial decisionmaking.

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Evaluate new business opportunities

FM provides the key information and answerquestions of whether to exploit such

opportunities or not.

That is, entrepreneurs can effectively analyze abusiness opportunity and determine whether it

is worthwhile or not.

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Measuring business performance

FM helps the investor to monitor the

progress of their business towards

achieving business goals and to take

corrective action where necessary.

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Making sound business decisions The financial information systems provides

a wide range of information that can beused to make better decisions.

This is done using financial ratios, breakeven analysis etc.

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MAJOR FINANCIAL MANAGEMNET

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MAJOR FINANCIAL MANAGEMNETDECISIONS

Investment decision

Working capital decision

Financing decision

Earnings management decision

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1. Investment decision

This is also known as the Capital budgeting, and it

refers to the decision to invest in long term assets.

The assets are expected to be used over a long

period of time e.g. when a firm acquires plant and

equipment or replaces an old equipment or when

you invest in research and development.

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Importance of Capital Budgeting

It determines the asset mix and hencethe business risk.

It involves heavy initial outlays of the

business resources.

Benefits accrue in future which future is

associated with risk and uncertainty.

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2. Working capital decision

This is the decision concerned with the short termassets/resources an organization uses to meet its day

to day obligations.

Such assets include:

Cash reserves of the organisation

Funds collected from debtors of the organization.

Inventories

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3. Financing decision This is the decision concerned with the sourcing of funds that are

utilized under the investment decision.

Much management time and effort is devoted to trying to ensurethe adequacy of the company's profit flow.

However, it is just as important that a company has an adequateflow of funds if it is to remain in business and very much less

management time and effort is devoted to this need. As companies expand, they require growing amounts of cash to

finance acquisitions of fixed assets. They also require growingamounts of cash to finance their growing working capitalrequirements.

Some of this funding requirement will come from INTERNALsources, whilst some will need to come from EXTERNALsources.

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4. Earnings Management Decision

The Financial Manager has to decide on what to

do with the earnings once they have been

realised. There are three options,

To declare and pay all dividends to shareholders

To retain all the earnings and hence declare and

pay no dividends

To decide on what proportion to be paid and what

to be retained.

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DECISIONS RETURN RISK

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DECISIONS, RETURN, RISK,

AND MARKET VALUE

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TIME VALUE OF MONEY

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The Time Value of Money

Would you prefer to have Rs. 1million now or Rs. 1 million 10years from now?

Of course,Of course, we would allwe would all

prefer the money now!prefer the money now!

This illustrates that thereThis illustrates that thereis an inherent monetaryis an inherent monetary

value attached to time.value attached to time.

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Money?

A rupee received today is worth more thana rupee received tomorrow This is because a rupee received today can be

invested to earn interest

The amount of interest earned depends on therate of return that can be earned on theinvestment

Time value of money quantifies the valueof a rupee through time

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Uses of Time Value of Money

Time Value of Money, or TVM, is a concept that is

used in all aspects of finance including:

Bond valuation

Stock valuation

Accept/reject decisions for project management

Financial analysis of firms

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Types of TVM Calculations

There are many types of TVMcalculations

The basic types will be covered areinclude: Present & Future value of an investment Future value with compounding Future value with continuous compounding

Present value ofperpetuity Present value ofgrowingperpetuity Present & Future value ofannuities

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Present Value of an Investment

Present value calculations determine what the valueof a cash flow received in the future would be worth

today (time 0)

The process of finding a present value is called

discounting (hint: it gets smaller)

The interest rate used to discount cash flows isgenerally called the discount rate

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Investment

General Present ValuePresent Value Formula:

PV = CFt/ (1+r)t

or PV = FVt/ (1+r)t

or PVPV = FVFVtt (PVIFPVIFr,t) -- See Table ISee Table I

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PVIFPVIFr,t is found on Table I at the end of the book.

Period 6% 7% 8%

1 .943 .935 .926

2 .890 .873 .857

3 .840 .816 .794

4 .792 .763 .735

5 .747 .713 .681

Valuation using Table I

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Example of PV of an Investment

How much would Rs. 10,000 received five years from now be

worth today if the current interest rate is 10%?

1. Draw a timeline

The arrow represents the flow of money and the numbers underthe timeline represent the time period.

Note that time period zero is today.

0 1 2 3 4 5

Rs. 10,000?r = 10%

PVPV

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Calculation based on general formula: PVPV = FVFVtt / (1+r)

t PVPV = 10,00010,000 / (1+

0.10)5 = Rs. 6,209.21Rs. 6,209.21

Calculation based on Table I:

PVPVtt = 10,00010,000 (PVIFPVIF10% , 5) = 10,00010,000(.621) =

Rs. 6,210.00Rs. 6,210.00 [Due to Rounding]

Example of PV of an Investment

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Future Value of an Investment

You can think of future value as theopposite of present value

Future value determines the amount that a

sum of money invested today will grow toin a given period of time

The process of finding a future value iscalled compounding (hint: it gets larger)

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FVIFFVIFr,t is found on Table II at the end of the book.

Valuation using Table II

Period 6% 7% 8%

1 1.060 1.070 1.080

2 1.124 1.145 1.166

3 1.191 1.225 1.260

4 1.262 1.311 1.360

5 1.338 1.403 1.469

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Example of FV of an Investment

How much money will you have in 5 years if you invest Rs.

10,000 today at a 10% rate of return?

1. Draw a timeline

00 11 22 33

Rs. 10,000Rs. 10,000 ??r = 10%r = 10%

44 55 FVFV

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Example of FV of an Investment

Calculation based on general formula:

FVFVnn = CFt * (1+r)t

FVFV55 = 10,000 (1+ 0.10)5

= Rs. 16,105.106,105.10

Calculation based on Table I:

FVFV55 = 10,000(FVIFFVIF10%, 5)

= 10,000(1.611)

= Rs. 16,110Rs. 16,110 [Due to Rounding]

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Some Things to Note

In both of the examples, note that if you were to

perform the opposite operation on the answers(i.e., find the future value of Rs. 6210 or the

present value of Rs. 16105) you will end up withyour original investment of Rs. 10,000.

This illustrates how present value and future valueconcepts are intertwined. In fact, they are thesame equation . . .

Take PV = FVt/ (1+r)t and solve for FV

t. You will get

FVt= PV * (1+r)t.

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Compounding Periods

Compounding an investment m times a year forTyears provides for future value of wealth:

Tm

m

r

CFV

+= 10For example, if you invest Rs. 50 for 3years at 12% compounded semi-

annually, your investment will grow to

93.70.)06.1(502

12.150 6

32

RsFV ==

+=

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(Ad d)

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(Advanced)

The general formula for the future value of an investment compoundedcontinuously over many periods can be written as:

FV= C0erT

WhereC0 is cash flow at date 0,

ris the stated annual interest rate,

T is the number of periods over which the cash is

invested, and

e is a transcendental number approximately equal to

2.718. ex is a key on your calculator.

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P i

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Perpetuity

A constant stream of cash flows that lasts forever.

0

1

C

2

C

3

C

The formula for the Present Value of a perpetuityis:

++

++

++

=32

)1()1()1( r

C

r

C

r

CPV

r

CPV =

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Perpetuity Example

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Perpetuity: Example

Q.What is the value of a British consol that promises to pay 15each year, every year until the sun turns into a red giant and

burns the planet to a crisp?

The interest rate is 10-percent.

0

1

15

2

15

3

15

15010.

15==PV

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Growing Perpetuity

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Growing Perpetuity

A growing stream of cash flows that lasts forever.

0

1

C

2

C(1+g)

3

C (1+g)2

The formula for the Present Value of a growing perpetuity is:

++

++

+

++

+=

3

2

2 )1(

)1(

)1(

)1(

)1( r

gC

r

gC

r

CPV

gr

CPV

=

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Growing Perpetuity: Example

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Growing Perpetuity: Example

Q. The expected dividend next year is $1.30 and dividends areexpected to grow at 5% forever.

If the discount rate is 10%, what is the value of this promiseddividend stream?

0

1

$1.30

2

$1.30(1.05)

3

$1.30 (1.05)2

00.26$05.10.

30.1$=

=PV

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A iti

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Annuities

An annuity is a cash flow stream in which

the cash flows are all equal and occur at

regular intervals.

Note that annuities can be a fixed amount,

an amount that grows at a constant rate

over time, or an amount that grows at

various rates of growth over time. Wewill focus on fixed amounts.

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T f A iti

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Types of Annuities

An Annuity An Annuity represents a series of equal payments (or receipts) occurring over aspecified number of equidistant periods.

Ordinary AnnuityOrdinary Annuity: Payments orreceipts occur at the end of each period.Annuity DueAnnuity Due: Payments or receipts

occur at thebeginning of each period.

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Examples of Annuities

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Examples of Annuities

Student Loan Payments Car Loan Payments

Insurance Premiums

Mortgage Payments

Retirement Savings

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PV f A it

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PV of an AnnuityA constant stream of cash flows with a fixed maturity.

The formula for the Present Value of an annuity is:

++

++

++

+= Tr

CrC

rC

rCPV

)1()1()1()1( 32

),(*

)1(

11

trPVIFACPV

or

rr

CPV

T

=

+=

0 1

C

2

C

3

C

T

C

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E l f PV f A it

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Example of PV of an Annuity

Q. Assume that Mr. X owns an investment that will pay her

Rs. 100 each year for 20 years. The current interest rateis 15%. What is the PV of this annuity?

1. Draw a timeline

00 11 22 33 .. 1919 2020

100100 100100 100100 100100 100100

??

r = 15%r = 15%

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E ample of PV of an Annuit

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Example of PV of an Annuity

2. Write out the formula using symbols:

PVA = C * {[1-(1+r)-t]/r}

3. Substitute appropriate numbers:

PVA = 100 * {[1-(1+.15)-20 ]/.15}

4.

Solve for the PVPVA = 100 * 6.2593

PVA = Rs. 625.93

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FV of an Annuity

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FV of an AnnuityA constant stream of cash flows with a fixed maturity.

The formula for the Future Value of an annuity is:

),(*

1)1(

trFVIFACFV

or

rr

rCFV

T

=

+=

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Example of FV of an Annuity

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Q. Assume that Mr. X owns an investment that will pay her

Rs. 100 each year for 20 years. The current interest rateis 15%. What is the FV of this annuity?

1. Draw a timeline

00 11 22 33 .. 1919 2020

100100 100100 100100 100100 100100

r = 15%r = 15%

??

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2. Write out the formula using symbols:

FVAt = C* {[(1+r)t 1]/r}

3. Substitute the appropriate numbers:

FVA20 = 100 * {[(1+.15)20 1]/.15

4. Solve for the FV:

FVA20 = 100 * 102.4436

FVA20 = Rs. 10,244.36

1-68Formula for Ordinary Annuity & AnnuityD

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Due

ForForPresent ValuePresent Value CalculationCalculation

Formula for Ordinary AnnuityFormula for Ordinary Annuity

PVAPVAtt = CFt *(PVIFAr% ,t)

Formula for Annuity DueFormula for Annuity Due

PVADPVADtt = CFt *(PVIFAr% ,t)(1+r)

ForForFuture ValueFuture Value CalculationCalculation Formula for Ordinary AnnuityFormula for Ordinary Annuity

FVAFVAtt

= CFt

*(FVIFAr% ,t

)

Formula for Annuity DueFormula for Annuity Due

FVADFVADtt = CFt *(FVIFAr% ,t)(1+r)

Where CFt= Cash Flow

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RISK AND RETURNANALYSIS

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Risk Defined

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Risk Defined

There is no universally agreed-upon definition of risk.

In the context of business and finance, risk is defined as

the chance of suffering a financial loss.

Assets (real or financial) which have a greater chance ofloss are considered more risky than those with a lower

chance of loss.

Risk may be used interchangeably with the term

uncertainty to refer to the variability of returns associated

with a given asset.

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Return Defined

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Return Defined

Total Returnrepresents the total gain or loss on an

investment over a given period of time

Total return can be expressed either in rupee terms

or inpercentage terms.

Componentsof the total

return

Income stream from theinvestment

Capital gain or loss due tochanges in asset prices

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Rupee Returns

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Rupee Returns

The sum of the cash received and the change in

value of the asset, in rupees.

Time 0 1

Initialinvestment

Ending market

value

Dividends

Rupee Return = Dividend + Change in Market Value

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Percentage Return

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Percentage Return

The sum of the cash received and the change in

value of the asset divided by the original

investment.

Initial investment

Rupee ReturnPercentage Return =

Initial investment

Dividend + Change in Market ValuePercentage Return =

Capital gain yieldDividend Yield +=

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Returns: Example

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Returns: Example

Suppose you bought 100 shares of Infosys one year agotoday at Rs. 25. Over the last year, you received Rs. 20

in dividends (= 1 rupee per share 100 shares). At the

end of the year, the stock sells for Rs. 30. How did you

do? Quite well. You invested 25 100 = Rs. 2,500. At the

end of the year, you have stock worth Rs. 3,000 and cash

dividends of Rs. 100. Your rupee gain was Rs.600 = 100+ (3,000 2,500).

Your percentage gain for the year is = 24.0 %

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Average Rate of Return

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Average Rate of Return

The average rate of return is the sum of the

various one-period rate of return divided by

the number of periods.

Average rate of return,

T

RRR T

)( 1 ++=

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Holding Period Returns

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Holding-Period Returns

The holding period return is the return that

an investor would get when holding an

investment over a period of n years, when

the return during yeari is given as ri:

1)1()1()1(

returnperiodholding

21+++=

=

nrrr

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Holding Period Return: Example

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Suppose your investment provides thefollowing returns over a four-year period:

Year Return

1 10%

2 -5%

3 20%

4 15% %21.444421.

1)15.1()20.1()95(.)10.1(

1)1()1()1()1(

returnperiodholdingYour

4321

==

=++++=

=rrrr

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So, our investor made 9.58% on his money for fouryears, realizing a holding period return of 44.21%So, our investor made 9.58% on his money for fouryears, realizing a holding period return of 44.21%

An investor who held this investment would haveactually realized an annual return of 9.58%:

Year Return

1 10%2 -5%

3 20%

4 15%%58.9095844.

1)15.1()20.1()95(.)10.1(

)1()1()1()1()1(

returnaverageGeometric

4

43214

==

=

++++=+

=

g

g

r

rrrrr

4)095844.1(4421.1 =


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The Variability of Stock Returns

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Variance (2

) a measure of volatility in units of percentsquared

Standard deviation ( ) a measure of volatility in percentage

terms

1

)(

Variance 1

2

2

==

=N

RRN

t

t

The Variability of Stock Returns

VariancedeviationStandard =

1-80Individual Securities or Single FinancialAssets

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Assets

The characteristics of individualsecurities that are of interest are the:

Expected Return Variance and Standard Deviation

Covariance and Correlation

1-81Single Financial Assets:: Expected Return &Risk

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Risk

Investors and analysts often look at historical returns as

a starting point for predicting the future.

However, they are much more interested in what the

returns on their investments will be in the future.

For this reason, we need a method for estimating future

returns.

One way of doing this is to assign probabilities for

future states of nature and the returns that would be

realized if a particular state of nature would occur.

1-82Return Measurement for a SingleAsset E pected Return

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Asset: Expected Return

The most common statistical indicator of an assets risk is thestandard deviation,

k, which measures the dispersion

around the expected value.

The expected value of a return, k-bar, is the most likely

return of an asset.

1-83

Example : Expected Return,Variance & Standard Deviation

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Consider the following two risky asset world.

There is a 1/3 chance of each state of the

economy and the only assets are a stock fund anda bond fund.

Rate of ReturnScenario Probability Stock fund Bond fund

Recession 33.3% -7% 17%

Normal 33.3% 12% 7%

Boom 33.3% 28% -3%

Variance & Standard Deviation

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Stock fund Bond Fund

Rate of Squared Rate of Squared

Scenario Return Deviation Return Deviation

Recession -7% 3.24% 17% 1.00%Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%

Expected return 11.00% 7.00%

Variance 0.0205 0.0067

Standard Deviation 14.3% 8.2%


1-85


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Recession -7% 3.24% 17% 1.00%

Normal12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


%11)(

%)28(3

1%)12(3

1%)7(3

1)(

=

++=

S

S

rE

rE


1-86


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Recession -7% 3.24% 17% 1.00%

Normal12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


%7)(

%)3(3

1%)7(3

1%)17(3

1)(

=

++=

B

B

rE

rE


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Recession -7% 3.24% 17% 1.00%

Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


%24.3%)7%11(2 =


1-88


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Recession -7% 3.24% 17% 1.00%

Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


%01.%)12%11(2 =


1-89


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Recession -7% 3.24% 17% 1.00%

Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


%89.2%)28%11(2 =


1-90


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Recession -7% 3.24% 17% 1.00%

Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


%)89.2%01.0%24.3(3

1%05.2 ++=


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Recession -7% 3.24% 17% 1.00%

Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


0205.0%3.14 =


1-92

Portfolio Risk and Return

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An investment portfolio is any collection or combination of

financial assets.

If we assume all investors are rational and therefore risk averse,that investor will ALWAYS choose to invest in portfolios ratherthan in single assets.

Investors will hold portfolios because he or she will diversifyaway a portion of the risk that is inherent in putting all your eggsin one basket.

If an investor holds a single asset, he or she will fully suffer the

consequences of poor performance.

This is not the case for an investor who owns a diversifiedportfolio of assets.

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Risk of a Portfolio

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Risk of a Portfolio

Diversification is enhanced depending upon the extent to

which the returns on assets move together. This movement is typically measured by a statistic known

as correlation as shown in the figure below.

1-94

Risk of a Portfolio (cont.)

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s o a o o o (co )

Even if two assets are not perfectly negatively

correlated, an investor can still realize diversificationbenefits from combining them in a portfolio as shown in

the figure below.

1-95

Portfolios

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Recession -7% 3.24% 17% 1.00%

Normal 12% 0.01% 7% 0.00%

Boom 28% 2.89% -3% 1.00%


Variance 0.0205 0.0067


Note that stocks have a higher expected return than bonds andhigher risk. Let us turn now to the risk-return tradeoff of a portfolio

that is 50% invested in bonds and 50% invested in stocks.

1-96

Portfolios

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Rate of Return

Scenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%

Normal 12% 7% 9.5% 0.003%

Boom 28% -3% 12.5% 0.123%

Expected return 11.00% 7.00% 9.0%

Variance 0.0205 0.0067 0.0010

Standard Deviation 14.31% 8.16% 3.08%

The rate of return on the portfolio is a weighted average of the

returns on the stocks and bonds in the portfolio:

SSBBP rwrwr +=

%)17(%50%)7(%50%5 +=

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Portfolios

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Rate of Return


Normal 12% 7% 9.5% 0.003%

Boom 28% -3% 12.5% 0.123%


Variance 0.0205 0.0067 0.0010




%)7(%50%)12(%50%5.9 +=

SSBBP rwrwr +=

1-98

Portfolios

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Rate of Return

Scenario Stock fund Bond fund Portfolio squared deviation

Recession -7% 17% 5.0% 0.160%

Normal 12% 7% 9.5% 0.003%

Boom 28% -3% 12.5% 0.123%

Expected return 11.00% 7.00% 9.0%Variance 0.0205 0.0067 0.0010




%)3(%50%)28(%50%5.12 +=

SSBBP rwrwr +=

1-99

Portfolios

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Rate of Return


Normal 12% 7% 9.5% 0.003%

Boom 28% -3% 12.5% 0.123%


Variance 0.0205 0.0067 0.0010


The expectedrate of return on the portfolio is a weighted average

of the expectedreturns on the securities in the portfolio.

%)7(%50%)11(%50%9 +=

)()()( SSBBP rEwrEwrE +=

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Portfolios

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Rate of Return


Normal 12% 7% 9.5% 0.003%

Boom 28% -3% 12.5% 0.123%


Variance 0.0205 0.0067 0.0010


The variance of the rate of return on the two risky assets portfolio is

BSSSBB2

SS2

BB2

P ))(w2(w)(w)(w ++=

where BS is the correlation coefficient between the returns on the

stock and bond funds.

1-101

Portfolios

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Rate of ReturnScenario Stock fund Bond fund Portfolio squared deviation

Recession -7% 17% 5.0% 0.160%

Normal 12% 7% 9.5% 0.003%

Boom 28% -3% 12.5% 0.123%


Variance 0.0205 0.0067 0.0010


Observe the decrease in risk that diversification offers.

An equally weighted portfolio (50% in stocks and 50% in bonds)

has less risk than stocks or bonds held in isolation.

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A measure of the degree to which two variables move together

relative to their individual mean values over time

The Covariance between the returns on two stocks can becalculated as follows:

N

Cov(RA,RB) = A,B = pi(RAi - E[RA])(RBi - E[RB]) i=1

Where: , = the covariance between the returns on stocks A and B

N = the number of states

pi = the probability of state i R

Ai= the return on stock A in state i

E[RA] = the expected return on stock A

RBi

= the return on stock B in state i

E[RB] = the expected return on stock B

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The correlation coefficient is obtained by standardizing (dividing) the

covariance by the product of the individual standard deviations

The Correlation Coefficient between the returns on two stocks can be

calculated as follows:

A,B Cov(RA,RB)

Corr(RA,RB) = A,B = A B = SD(RA)SD(RB)

Where:

A,B

=the correlation coefficient between the returns on stocks A and B

A,B

=the covariance between the returns on stocks A and B,

A=the standard deviation on stock A, and

B=the standard deviation on stock B

1-104Two-Security Portfolios with VariousCorrelations

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100%

bonds

re

turn

100%

stocks

= 0.2

= 1.0

= -1.0

Relationship depends on correlation coefficient

-1.0 < < +1.0

If = +1.0, no risk reduction is possible

If = 1.0, complete risk reduction is possible

1-105Portfolio Risk as a Function of the Numberof Stocks in the Portfolio

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Nondiversifiable risk;

Systematic Risk;Market Risk

Diversifiable Risk;

Nonsystematic Risk;

Firm Specific Risk;Unique Risk

n

In a large portfolio the variance terms are effectively

diversified away, but the covariance terms are not.

Thus diversification can eliminate some, but not all of the risk of

individual securities.

Portfolio risk

1-106Risk Diversification: Systematic &Unsystematic Risk

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Asystematic riskis any risk that affects a large number of assets,

each to a greater or lesser degree.

It arises on account of economy wide uncertainties and the

tendency of individual securities to move together with changes

in the market. It is also known as Market risk.

Examples of systematic risk include uncertainty about general

economic conditions, such as GNP, interest rates or inflation.

This part of risk cannot be reduced through diversification.

1-107Risk Diversification: Systematic &Unsystematic Risk

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An unsystematic riskis a risk that specifically affects a single

asset or small group of assets.

It arises from the unique uncertainties of individual securities. It

is also called unique risk.

These uncertainties are diversifiable if a large number ofsecurities are combined to form well-diversified portfolios. Thus

unsystematic risk can be totally reduced through diversification.

Announcements specific to a company, such as a gold miningcompany striking gold, the government increases custom duty,

are examples of unsystematic risk.

Unsystematic Risk

1-108Relationship between Risk andExpected Return (CAPM)

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p ( )

Expected Return on the Market:

Expected return on an individual security:

PremiumRiskMarket+=F

M RR

)( FMiFi RRRR +=

Market Risk Premium

This applies to individual securities held within well-diversified portfolios.

1-109Expecte Return on an In v uaSecurity

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This formula is called the Capital Asset PricingModel (CAPM)

)( FMiFi RRRR +=

Assume i = 0, then the expected return isRF. Assume i = 1, then Mi RR =

Expectedreturn on

a security

=Risk-

free rate+

Beta of the

security

Market risk

premium

1-110Capital Asset Pricing Model (CAPM):Assumptions

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Market efficiency: The Capital Market efficiency implies that

share prices reflect all available information. Also, individual arenot able to effect the prices of securities. This means that there

are large number of investors holding small amount of wealth.

Risk aversion and mean-variance optimization: Investors are

risk-averse. They evaluate a securitys return and risk in terms of

expected return and variance or standard deviation respectively.

They prefer the highest expected returns for a given level of

risks. This implies that investors are mean-variance and they

form efficient portfolios.

1-111

CAPM Assumptions contd.

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Homogeneous Expectations: All investors have the

same expectations about the expected returns andrisk of securities.

Single Time period: All investors decisions arebased on single time period.

Risk-free rate: All investors can lend and borrow at

a risk-free rate of interest. They form portfoliosfrom publicly traded securities like shares and

bonds.

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Capital Market Line

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The capital market (securities markets) is the market for securities

The capital market includes the stock market and the bond market.

CML is used to illustrate all of the efficient portfolio combinations

available to investors.

The CML is derived by drawing a tangent line from the intercept

point on the efficient frontier to the point where the expected return

equals the risk-free rate of return.

1-113

Capital Market Line

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The Capital Market Line

Expected Return onthe Portfolio

Standard Deviation of thePortfolio

0%

0% 10%

4%

8%

20% 30% 40%

12%

Risk-freerate

Capital

MarketLine

1-114

Capital Market Line

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The Capital Market Line and Iso Utility Curves

Expected Return onthe Portfolio

Standard Deviation of thePortfolio

0%

0% 10%

4%

8%

20% 30% 40%

12%

Risk-freerate

CapitalMarket

Line

HighlyRisk

AverseInvestor

A risk-taker

1-115

The Security Market Line

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Portfolio E(R) Beta

Risk-free asset Rf 0

Market portfolio E(Rm) 1

Consider a portfolio composed of the following two assets:

An asset that pays a risk-free return Rf, , and

A market portfolio that contains some of every risky asset inthe market.

Security market line: the line connecting the risk-free

asset and the market portfolio

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The Security Market Line shows how an investor can construct a

portfolio of T-bills and the market portfolio to achieve the

desired level of risk and return.

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In equilibrium, all assets lie on this line.

If individual stock or portfolio lies above the line:

Expected return is too high stock is undervalued.

Investors bid up price until expected return falls.

If individual stock or portfolio lies below SML:

Expected return is too low stock is overvalued.

Investors sell stock driving down price until expected

return rises.

Plots relationship between expected return and betas.

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i

E(RP)

RF

SML

Slope = (y2-y1) / (x2-x1)

= [E(RM) R

F] / (M-0)

= [E(RM) RF] / (1-0)

= E(RM) RF

= Market Risk Premium

A - Undervalued

RM

M =1.0

B

A

B - Overvalued

1-119

Capital Market Line v/sSecurity Market Line

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The capital market line (CML) is a line used in the capital asset

pricing model to illustrate the rates of return for efficient whilethe security market line (SML) is a line that graphs the

systematic, or market, risk versus return of the whole market at

a certain time and shows all risky marketable securities.

The CML is derived by drawing a tangent line from the

intercept point on the efficient frontier to the point where theexpected return equals the risk-free rate of return while the

SML essentially graphs the results from the capital asset

pricing model (CAPM) formula. The x-axis represents the risk

(beta), and the y-axis represents the expected return. Themarket risk premium is determined from the slope of the SML.

1-120

Capital Market Line v/sSecurity Market Line

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What is plotted CML plots efficient portfolios, i.e. combinations

of the risky portfolio and the risk-free asset (it is

not valid for individual assets)

SML plots individual assets and portfolios

Measure of risk

for CML standard deviation (because welldiversified portfolios)

f SML b (b i di id l )

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