financial management - class ppt[1]

Financial Management

Introduction

Barter Non-Barter

What role money plays? Money has two roles to play

As a Measure Estimating cash flow Valuing the assets and liabilities Financial & Cost Accounting

As a Resources Planning of Spending Planning of Investment Allocation of Money (capital) as resources

Money as a Measure…

• Cash flows happens over a period of time• Value of same amount of cash flow will be different at different time

– Rs. 1000 now is not same as Rs. 1000 one year from now because• Same money can be invested and positive return can be generated• Present is certain and future in uncertainty• Inflation reduces purchasing power of money

• One need to estimate the value of all the cash flows– Need to express all the cash flows into one time dimension

• Present Value• Future value

Study of Time Value of Money Helps in Consistent Measurement…Study of Time Value of Money Helps in Consistent Measurement…

Learning from Economic Theory Money As a Resource…

What is price of Capital? Interest Rate Dividend Yield Expected Capital Appreciation Bond/Debenture Yield

Who Provides Capital? Individual Financial Institutions

Input OutputProcess

Product Services

Labor Capital Raw

Material

Financial Market Provides Capital for a Price and Firms Create

Assets with the Help of Capital to Generate Wealth…

Financial Market Provides Capital for a Price and Firms Create

Assets with the Help of Capital to Generate Wealth…

Understanding the Financial Market

Surplus BusinessUnit (SBU)

(Households, Corporate)

Deficit BusinessUnit (DBU)

(Government, Corporate)

funds

claim

Create Assets for DBU Creates Liabilities for DBUClaims of SBU can be debt claims or equity claims

Assets Liabilities

CLAIMSor

DEBT or borrowed capitalor

EQUITY or owners capital

FUNDS

Total Assets = Total Liabilities

Understanding the Firm

What is a firm?

A firm is an organization that combines inputs and follows some process to produce some forms of output

What are the goals of a firm?• Should a firm maximize the welfare of employees, or customers, or supplier• Should it maximize shareholders wealth, profits, EPS, return on investment?

A Firm Need to Use its Scare Resources (Capital) Optimally to

Achieve the Goal…

A Firm Need to Use its Scare Resources (Capital) Optimally to

Achieve the Goal…

Firms Operates in Markets

• What goods and services to produce?

• What are the target market?

Finance Manager Plays an Important Role to Make Sure the Firm Meets the

Goal it has Aimed for…

Finance Manager Plays an Important Role to Make Sure the Firm Meets the

Goal it has Aimed for…

What are the questions Financial Mangers deal with?

• How big the firm should be?

• How fast it should grow?

• Where should it invest?

• What should be the composition of its assets?

• How should the assets be financed?

• How should the returns to be distributed?

• How to get the best return from the investment?

• How to minimize the expenditure without affecting the growth of the firm?

Finance Strategy is Driven by Objective of the Firm, Business

Opportunity, Cost of Capital for the Firm…

Finance Strategy is Driven by Objective of the Firm, Business

Opportunity, Cost of Capital for the Firm…

Organization StructureCEO

CFO

Treasurer Controller

• Manages the cash• Planning and capital budgeting• Raising the money• Managing the external relationship• Managing the credit and fraud issues

• Prepare the accounts• Manage the expenditure• Internal audit• Reporting and preparing balance sheet and P&L

Financial Management Objective is to Maximize Value of the Firm by Balancing Between Risk and Reward..

Financial Management Objective is to Maximize Value of the Firm by Balancing Between Risk and Reward..

Complexity of role of finance manager is a function of type of firm

Types of firm:• Sole proprietorship• Partnership• Cooperative society• Private company• Public limited company

How does external environment affect financial management?

External factors that affects most of the financial decision can be broadly divided into:

• Regulatory Framework• Taxes• Financial system

Financial decisions of a firm depends on legal forms of the organization which is an internal matter with in the frame work of the external environment

Financial Management maximizes value with the external regulatory environment…

Financial Management maximizes value with the external regulatory environment…

How regulatory framework affects financial decisions?

Principal elements of regulatory framework are:• Industrial policy• Companies act• Securities and Exchange Board of India Guidelines

How does taxes affects financial decisions?

• Corporate income tax• Depreciation• Interest expenses vis-à-vis dividend payment• Exemptions and deductions• Dividend distribution tax• Capital gain tax• Sales tax• Customs duty

Financial Institution• Commercial Banks• Insurance Companies• Mutual Funds• Provident Funds• Non Banking Financial Companies

Supplier Of Funds• Individual• Business• Government

Funds

Deposits/Shares

PrivatePlaceme

nt

Purchaser of Funds• Individual• Business• Government

Financial Markets• Money Market• Capital Market

Funds Funds

Funds

How financial framework affects financial decisions?

Interest Rate&

Time Value of Money

Interest Rate

Introduction• Most of us would have either paid and/or received

interest if… – We have taken loans and have paid interest to the lender.

• Student loan• Auto loan• Personal loan• Mortgage loan

– We have invested have received interest from the borrower. • Saving account deposits• Fixed deposits• Infrastructure bonds• Bonds Debentures of companies

Introduction (Cont…)• What is interest?

– Compensation paid by the borrower of capital to the lender

• Rent paid by the borrower of capital to the lender. The rent is for permitting the borrower to use funds of lender

• How is interest rate determined?– Depends on the market for capital

• In a free market it is determined by demand and supply of capital• In a controlled market, regulator can specify the interest rate• In a regulated market, market can determine the interest rate but

regulator can intervene if it fills that market is not functioning optimally

Real vis-à-vis Nominal Interest Rate…• What is real interest rate?

– Compensation paid by the borrower of capital to the lender when lender has zero risk and inflation rate is zero

• Loans to government when there is no inflation

• What are the implication of no inflation?– If one lends Rs. 100 at 10% for a year

• Assuming that the Rs. 100 can buy 100 mangoes• Next year the Rs. 110 can buy 110 mangoes• If there is positive inflation then next year Rs. 110 will able to buy

less that 110 mangoes• This implies that in case of inflation the real interest rate would be

less than 10%

Real vis-à-vis Nominal Interest Rate…• Most people who invest do so by acquiring financial assets such as

– Shares of stock – Shares of a mutual fund– Or bonds/debentures– deposits with commercial bank

• Financial assets give returns in terms of money without any assurance about the investor’s ability to acquire goods and services at the time of repayment

• Financial assets therefore give a NOMINAL or MONEY rate of return.– In the example, the GOI gave a 10% return on an investment of Rs 100.– Let us say inflation rate is 5%– The # of mangoes that can be bought is 110/1.05 = 104.74– The real rate of return is 4.76% which is different from 10% nominal return– The relationship between the nominal and real rates of return is expressed in

the FISHER hypothesis;• “Nominal Return” = “Real Return” + Inflation Rate (Approximate)

Interest Rate and Uncertainty…• In FISHER equation it is assumed that the rate of inflation is known with

certainty. – In real life inflation is uncertain and is random– In the case of random variables exact outcome is not known in

advance– Agents would have expected value of inflation

• Which is a probability weighted average of the values that the variable can take.

• Therefore in real life a default free security will not give an assured real rate.– It will give an assured nominal rate – The real rate will depend on the actual rate of inflation

There is Uncertainty (Risk) over the Real Rate of Return even if the Nominal Return is Certain due to Uncertainty over Inflation…

There is Uncertainty (Risk) over the Real Rate of Return even if the Nominal Return is Certain due to Uncertainty over Inflation…

Uncertainty and Risk Aversion…• Majority of investors are characterized by Risk Aversion.

– What is risk aversion?• It does not mean that investor would not take risk• It means that investor would expect higher return to take higher risk.• Given a choice between two investments with the same expected rate of

return the investor will choose the less risky option• In the case of existence of positive inflation

– The investor will not accept the expected inflation as compensation– To tolerate the inflation risk the investor will demand a POSITIVE risk premium– Compensation over and above the expected rate of inflation

• Why?– The actual inflation could be higher than anticipated resulting in actual

real rate lower than anticipated.– The Fisher equation need to be modified to take into risk aversion nature of the

investor• The Fisher equation may be restated as

– Nominal Return = Real Return + Expected Inflation + Risk Premium

What Drives Interest Rate…• From the discussion so far with zero default the interest rate would depends on

– The real rate– The expected inflation– The risk premium of the investor

When we relax the assumption of zero default risk the interest rate would depends• Credit risk involved with the borrower, which would vary from individual to individual

– The risk of non-payment of interest rate– The risk of non-payment of principal– Higher the risk of default higher would be expected interest rate

• Tenure of the investment– Higher the tenure higher could be credit risk– The lender would prefer to lend for short-term and borrower would prefer to borrow for long-

term for a given rate of interest rate– Lender would demand higher interest rate to lend for long tenure

Nuances of Calculating Interest Income…• Simple interest rate vis-à-vis compound interest rate

– When interest is calculated on interest income generated during the previous period

– They will differ when the interest conversion period is different from the measurement period

– What is interest conversion period?• The unit of time over which interest is paid once and is reinvested to earn

additional interest is called interest conversion period– What is measurement period?

• The unit on which the time is measured is called measurement period• The interest conversion period is typically less than or equal to the

measurement period.• Nominal interest rate vis-à-vis effective interest rate

– The quoted interest rate per measurement period is called the nominal interest rate

– The interest that a unit of currency invested at the beginning of a measurement period would have earned by the end of the period is called the effective rate

Using the Right Rate for Measurement…• Effective rate is what one gets and nominal rate is what one sees• Compounding yields greater benefits than simple interest

– The larger the value of N the greater is the impact of compounding. Thus, the earlier one starts investing the greater are the returns.

• If the length of the interest conversion period is equal to the measurement period– The effective rate will be equal to the nominal rate

• If the interest conversion period is shorter than the measurement period– The effective rate will be greater than the nominal rate

• If the interest conversion period is longer than the measurement period– The effective rate will be lower than the nominal rate

• If we are comparing two alternative investment opportunity, first thing we need to do is convert the rate of return into effective rate of return

Effective Rate is Appropriate Rate to Measure…Effective Rate is Appropriate Rate to Measure…

Future & Present Value

Future Value of MoneyQ1. Rs. 10,000 is invested and the investor gets 10% return every year for three years.

What would be the future value of the money invested?

Ans: Present Value (PV) = Rs. 10,000 Rate of Return (r) = 10% = 10/100 = 0.10 Number of Years (N) = 3

Future Value (FV) at the end of first year = Rs. 10,000 + 0.10*Rs. 10,000

FV at the end of second year = Rs. 10,000 + 0.10*Rs. 10,000 + 0.10*Rs. 10,000

FV at the end of third year = Rs. 10,000 + 0.10*Rs. 10,000 + 0.10*Rs. 10,000 + 0.10*Rs. 10,000

= Rs. 10,000 (1 + 0.10 + 0.10 + 0.10)= Rs. 10,000 (1 + 3 * 0.10)

If we generalize: FV = PV ( 1 + Nr) when return is simple return


What would be the future value of the money invested if the compounding of return happens at the end of every year?

Ans: Present Value (PV) = Rs. 10,000 Rate of Return (r) = 10% = 10/100 = 0.10 ; Number of Years (N) = 3

Future Value (FV) at the end of first year = Rs. 10,000 + 0.10*Rs. 10,000

FV at the end of second year = (Rs. 10,000 + 0.10*Rs. 10,000) + 0.10* (Rs. 10,000 + 0.10*Rs. 10,000)= Rs. 10, 000 (1+0.10) + 0.10 * Rs. 10, 000 ( 1 + 0.10)= Rs. 10,000 (1+0.10) ( 1 + 0.10) = Rs. 10, 000 ( 1 + 0.10)²

FV at the end of third year = Rs. 10, 000 ( 1 + 0.10)² + Rs. 10, 000 ( 1 + 0.10)² * 0.10= Rs. 10, 000 ( 1 + 0.10)² ( 1 + 0.10)= Rs. 10, 000 ( 1 + 0.10)³

If we generalize the formula: FV = PV ( 1 + r)N

Calculative Simple and Compound Interest…

Simple interest can be calculated by using the formula;

P(1+rN)

Compound interest can be calculated by using the formula;

P(1+r)N

Where;

• P principal invested at the outset• N # of measurement periods for which the investment is being made• r nominal rate of interest per measurement period


What would be the future value of the money invested if the compounding of return happens at the end of every six month?

Ans: Present Value (PV) = Rs. 10,000 Rate of Return (R) = 10% = 10/100 = 0.10 Number of Years (N) = 3 Number of compounding per year (k) = 2

Future Value (FV) at the end of first year = Rs. 10,000 + (0.10/2)*Rs. 10,000

+ (Rs. 10,000 + (0.10/2)*Rs. 10,000) * (0.10/2)= Rs. 10,000 ((1 + (0.10/2)) + Rs. 10,000 ((1 + (0.10/2)) * (0.10/2)= Rs. 10,000 ((1 + (0.10/2)) ( (1 + (0.10/2)) = Rs. 10,000 ((1 + (0.10/2))1*2

Contd…

Future Value of MoneyFuture Value (FV) at the end of second year = [Rs. 10,000 ((1 + (0.10/2))1*2 + Rs. 10,000 ((1 + (0.10/2))1*2 * (0.10/2)]+ [Rs. 10,000 ((1 + (0.10/2))1*2 + Rs. 10,000 ((1 + (0.10/2))1*2 * (0.10/2)] * (0.10/2)

= Rs. 10,000 ((1 + (0.10/2))1*2 * ((1+(0.10/2))+ Rs. 10,000 ((1 + (0.10/2))1*2 * ((1+(0.10/2)) * (0.10/2) = Rs. 10,000 ((1 + (0.10/2))1*2 * ((1+(0.10/2)) ((1 + (0.10/2))= Rs. 10,000 ((1 + (0.10/2))2*2

Future Value (FV) at the end of third year = [Rs. 10,000 ((1 + (0.10/2))2*2 + Rs. 10,000 ((1 + (0.10/2))2*2 * (0.10/2)]+ [Rs. 10,000 ((1 + (0.10/2))2*2 + Rs. 10,000 ((1 + (0.10/2))2*2 * (0.10/2)] * (0.10/2)= Rs. 10,000 ((1 + (0.10/2))2*2 (( 1 + (0.10/2))+ Rs. 10,000 ((1 + (0.10/2))2*2 (( 1 + (0.10/2)) * (0.10/2)= Rs. 10,000 ((1 + (0.10/2))2*2 (( 1 + (0.10/2)) * ((1 + (0.10/2))= Rs. 10,000 ((1 + (0.10/2))3*2

If we generalize the formula; FV = PV ( 1 + r/m)Nm

Calculative Effective Interest Rate…The effective rate i can be calculated by using the formula when theNominal rate is r and m # of interest conversion periods per measurement period.

Conversely the nominal rate r can be calculated if we know i and m And N=1

Two Nominal Rates Compounded at Different Intervals are Equivalent if they

Yield the Same Effective Rate …Two Nominal Rates Compounded at Different Intervals are Equivalent if they

Yield the Same Effective Rate …

Continuous Compounding • Consider Rs P is invested for N periods at r per cent per period and the

interest is compounded m times per period, the terminal value will be

If # of compounding very large and approaches infinite; as m the terminal value will be

Effective Rate is Nothing But Compounding Rate When Interest Rate Conversion Period is Different From Measurement Period…

Effective Rate is Nothing But Compounding Rate When Interest Rate Conversion Period is Different From Measurement Period…

Future Value of Money• When an amount is deposited for a time period at a given rate of

interest – The amount that is accrued at the end is called the future value of the

original investment– So if Rs P is invested for N periods at r% per period

( 1 + r/m)Nm is the amount to which an investment of Rs 1 will grow at the end of N periods.

It is called FVIF – Future Value Interest Factor. It is a function of r and N. It is given in the form of tables for integer values of r and N If the FVIF is known, the future value of any principal can be found by

multiplying the principal by the factor.

FV = PV ( 1 + r/m)Nm

Present Value of Money• When an amount is expected to come in a future date it would be

important to know what would the amount be worth at present – The worth of the a certain cash flow at present is called the present value of

the future cash flow– So if Rs FV is expected cash flow at the end of period N the PV is

Where r is interest rate and m is the # of times interest is accessed per

measurement period. 1 / [( 1 + r/m)Nm] is the amount that need to be invested to get Rs 1 at

the end of N periods. It is called PVIF – Present Value Interest Factor.

It is a function of r and N. It is given in the form of tables for integer values of r and N If the PVIF is known, the present value of any amount can be found by

multiplying the future value by the factor.

PV = FV / [( 1 + r/m)Nm]

Future & Present ValueIllustrations

Illustration - 1• Pritam has deposited Rs 20,000 with SBI for 4 years• The bank pays simple interest at the rate of 15% per annum• What is amount Pritam is going to receive at the end of 4th

year• FV = P(1+rN) • FV = 20000 (1+0.15*4) = 20000 (1+.6) = Rs. 32,000• What is amount Pritam is going to receive at the end of 4.5

years (every thing else remain the same)?• FV = 20000 (1+0.15*4.5) = 20000 (1+.675) = Rs. 33,500

Illustration - 2• Pritam has deposited Rs 20,000 with SBI for 4 years• The bank pays 15% per annum interest rate compounded annually

• What is amount Pritam is going to receive at the end of 4th year• FV = P(1+r)N • FV = 20000 (1+0.15)4 = 20000 * 1.749 = Rs. 34,980

• What is amount Pritam is going to receive at the end of 4.5 years (every thing else remain the same)?

• FV = 20000 (1+0.15)4.5 = 20000 (1+.975) = Rs. 37,512

• What amount Pritam is going to receive at the end of 4.5 years if he gets compounding rate till the 4th year and simple rate for the next 6 months (every thing else remain the same)?

• FV = 34980 + 34980 * (0.15/2) = 34980 + 2623.5 = Rs. 37,603

Illustration - 3• ICICI Bank is quoting 9% per annum compounded

annually and HDFC Bank is quoting 8.75% per annum compounded quarterly.

• Where would you invest?• In the case of ICICI

– The nominal rate is 9% per annum– The effective rate is also 9% per annum

• In the case of HDFC– The nominal rate is 8.75% per annum– The effective rate is (1+0.0875/4)4 = 9.0413% per annum

Illustration - 4

• Suppose HDC Bank wants to offer an effective annual rate of 10% with quarterly compounding – What should be the quoted nominal rate

ICICI Bank is offering 9% per annum with semi-annual compounding.

What should be the equivalent rate offered by HDFC Bank if it intends to compound quarterly.

Illustration - 5• Pritam has deposited Rs 10,000 with SBI for 5 years at 10%

per annum compounded continuously.• What is the amount Pritam is going to get after 5 years• FV = 10000 * e (r*N) = 10000 * (2.7206)0.1*5 = 10000 * 1.649

= Rs. 16,490

Illustration - 6• Pritam has deposited Rs 10,000 for 5 years at 10% compounded annually.• What is the Future Value?

Thus F.V. = 10,000 x 1.6105 = Rs 16,105

Pritam has deposited Rs 10,000 for 4 years at 10% per annum compounded semi-annually.

What is the Future Value? 10% for 4 years is equivalent to 5% for 8 half-years

Thus F.V. = 10,000 x 1.4775 = Rs 14,775

Illustration - 7• LIC has collected a one time premium of Rs 10,000 from Pritam

and has promised to pay her Rs 30,000 after 10 years.• The company is in a position to invest the premium at 10%

compounded annually. • Can LIC meet its obligation?• The future value of Rs 10,000 after 10 years is• FV = 10,000 x FVIF (10,10) = 10000 * (1.1)10 = 10000 * 2.5937 =

Rs 25,937 • The FV is lesser than the liability of Rs 30,000

• Therefore LIC can not meet its commitment, and to meet its commitment it has to either increase the premium or increase the effective rate of return

Illustration -8• Syndicate Bank is offering the following scheme

– An investor has to deposit Rs 10,000 for 10 years– Interest for the first 5 years is 10% compounded annually – Interest for the next 5 years is 12% compounded annually – What is the Future Value?

The first step is to calculate the future value after 5 years:

The next step is to treat this as the principal and compute its terminal value after another 5 years

Illustration - 9• Pritam would like to have Rs. 12000 after 4 years• What amount Pritam need to invest if he gets a 10%

simple rate of return• PV = FV / (1+rN) = 12000 / [1+0.1*4] = Rs. 8571

• What amount Pritam need to invest if he gets a 10% return compounded quarterly

• PV = FV / (1+r)N = 12000 / (1+0.1/4)16 = Rs. 8084

• SBI is offering an instrument that will pay Rs 10,000 after 5 years.

• The price that is quoted is Rs 5,000.• If the investor wants a 10% rate of return,

should he invest. The problem can be approached in three ways.

Illustration – 10: Evaluating an Investment

The Future Value Approach• Assume that the instrument is bought for

5,000. • If the rate of return is 10% the future value is

5,000 x FVIF (10,5) = 5000 * 1.6105 = Rs 8,052.50

• Since the instrument promises a terminal value of Rs 10,000 which is greater than the required future value, the investment is attractive.


The Present Value Approach• The present value of Rs 10,000 using a discount rate of 10% is;

10,000 * PVIF(10,5) = 10000 * 0.6209 = Rs 6,209• Therefore to get a 10% return over 5 years the

investor would have to pay Rs 6,209• In this case the investment is Rs 5,000 which is less

than Rs 6,209• The investment is attractive


The Rate of Return Approach • The investor invest Rs 5,000 and receive Rs 10,000 after 5

years.• What is the rate of return?• The rate of return can be calculated by:


The rate of return that would equal LHS with RHS is 14.87%

In this case the actual rate of return is 14.87% and the required rate for the investor is 10%

Therefore the investment is attractive.

Illustration - 11: The Internal Rate of Return• Let us assume that an investment of Rs 18,000 will

entitle us to the following cash flows for the next 5 years. – What is the rate of return of this investment?

Illustration - 11: The Internal Rate of Return

• The rate of return is the solution to the following equation:

The solution to this equation is called the Internal Rate of Return (IRR)

It can be obtained using the IRR function in EXCEL. In this case, the solution is 14.5189%

Annuities

Understanding Annuities• What is an annuity?

– Annuity is a series of equal payments made/received at equally spaced time intervals

– Annuity are of two types• Ordinary annuity: When payment made/received at the end of first period• Annuity Due: When payment made/received at the beginning of the first

period– Examples of annuity

• House rent and monthly salary till it is revised – Ordinary Annuity• Insurance premium: Annuity Due• EMIs on housing/automobile loans: Ordinary Annuity

The interval between successive payments/receipt is called the payment/receipt period

We will assume that the payment/receipt period is the same as the interest conversion period for valuation purpose The assumption implies that is, if the annuity paid/received

annually/semi-annually, we will assume annual/semi-annual compounding

Future Vale of Annuity

11

11

111

11

11111

1111

11111

111

2

2

32

12

N

N

N

N

N

N

N

N

rr

AFV

rAFVr

rAFVrFV

ArAFVrFV

ArArarArAArFV

AArArArArFV

rArArArArFV

rArArAAFV

WhereA = Regular Annuityr = interest rate

Present Vale of Annuity

N

N

N

N

NNN

N

N

r

A

r

APV

r

AAPVr

r

AAPVrPV

r

APVArPV

r

A

r

A

r

A

r

A

r

AArPV

r

A

r

A

r

AArPV

r

A

r

A

r

A

r

APV

11

11

11

11

111111

1111

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32

WhereA = Regular Annuityr = interest rate

Understanding Annuities

• PVIFA is the present value of an annuity that pays Rs 1 per period for N period.– We can calculate the present value by multiplying the annuity with the PVIFA

• FVIFA is the future value of an annuity that pays Rs 1 per period for N period.– We can calculate the future value by multiplying the annuity with the FVIFA

Present Value Interest Factor of Annuity(PVIFA)

Future Value Interest Factor of Annuity(FVIFA)

Relationship Between PVIFA and FVIFA

Present Value of Annuity Due

The present value of an annuity due is greater than that of an ordinary annuity that makes N payments Why?

Each cash flow has to be discounted for one period less.

Future Value of Annuity Due

The future value of an annuity due is greater than that of an ordinary annuity that makes N payments Why?

Each cash flow will get one period more to yield return.

Perpetuities An annuity that pays forever is called a perpetuity. The future value of a perpetuity has a finite present

value.

Illustration - 12• LIC is offering an instrument that will pay Rs 10,000 per year for next 20

years, beginning one year from now.• If the rate of interest is 10%, what is the present value?

– PV = 10,000xPVIFA(10,20) = 10,000 x 8.5136 = Rs 85,136• If the rate of interest is 10%, and payment is for 25 years what is the

present value?– PV = 10,000xPVIFA(10,20) = 10,000 x 9.0770 = Rs 90,770

• If the rate of interest is 8%, what is the present value?– PV = 10,000xPVIFA(10,20) = 10,000 x 9.8181 = Rs 98,181

• If the rate of interest is 8%, and payment is for 25 years what is the present value?– PV = 10,000xPVIFA(10,20) = 10,000 x 10.6748 = Rs 106,748

The Present Value of Annuity would Decrease if the Interest Rate

Goes Up and Increases with the # of Years of Payment

The Present Value of Annuity would Decrease if the Interest Rate

Goes Up and Increases with the # of Years of Payment

Illustration - 13• Pritam is expecting to receive Rs 10,000 per year for next 20 years,

beginning one year from now.• If the cash flow can be invested at 10%, what is the future value?

– FV = 10,000xFVIFA(10,20) = 10,000 x 57.275 = Rs 572,750• If the rate of interest is 10%, and Pritam is going to receive the payment for

25 years, what is the present value?– FV = 10,000xFVIFA(10,25) = 10,000 x 98.3471 = Rs 983,471

• If the rate of interest is 8%, what is the present value?– FV = 10,000xFVIFA(8,20) = 10,000 x 45.7620 = Rs 457,620

• If the rate of interest is 8%, and Pritam is going to receive the payment for 25 years, what is the present value?

• PV = 10,000xPVIFA(10,20) = 10,000 x 73.1059 = Rs 731,059

The Future Value of Annuity would Increase if the Interest Rate Goes

Up and Increases with the # of Years of Payment

The Future Value of Annuity would Increase if the Interest Rate Goes

Up and Increases with the # of Years of Payment

Illustration - 14• Pritam bought a insurance policy, which requires him to pay Rs. 10,000 per

year as insurance premium for next 20 years.• If the rate of interest is 10%, what is the present value?

– PV = 10,000xPVIFAAD(10,20) = 10,000 x 9.3649 = Rs 93,649– Which is equal to Rs. 85,136 * (1+r) = Rs. 93,649

• Pritam bought a insurance policy, which requires him to pay Rs. 10,000 per year as insurance premium for next 20 years.

• If Pritam would have invested the amount he would have got 10% per annum, what is the future value of the cash he invested in the insurance policy?– FV = 10,000xFVIFAAD(10,20) = 10,000 x 63.0025 = Rs 630,025– Which is equal to Rs. 572,750 * (1+r) = Rs. 630,025

Illustration - 15• A financial instrument promises to pay Rs 10,000 per year forever. • If the investor requires a 10% rate of return, how much should he be willing

to pay for it?• The value of the perpetuity is: 10,000 / 0.1 = 100,000• If the investor requires a 20% rate of return, how much should he be willing

to pay for it?• The value of the perpetuity is: 10,000 / 0.2 = 50,000• If the payment from the instrument increases to Rs.12,000 and investor

requires a 10% rate of return, how much should he be willing to pay for it?• The value of the perpetuity is: 12,000 / 0.1 = 120,000

The Value of the Perpetuity would Decrease if the Required Rate of

Return Increases and Value would Increase if the Payment Increases

The Value of the Perpetuity would Decrease if the Required Rate of

Return Increases and Value would Increase if the Payment Increases

Amortization

Understanding Amortization• The amortization is a process of repaying an installment loan by

means of equal installments at periodic intervals. • Each of the installments paid can be seen in form of an annuity.

– Logically speaking the present value of the annuity discounted at the loan interest rate would be equal to the loan amount

• Each equal installment would consists of two component– A Portion of the principal amount– Interest on the outstanding loan amount

• An amortization schedule would show the payment that goes into principal component and payment that goes into interest component, together with the outstanding loan balance after the payment is made.

Estimating the Amortization Schedule• Consider a loan which is repaid in N installments of Rs A each.• The original loan amount is Rs L, and the periodic interest rate is r.

Estimating the Amortization Schedule

Illustration - 16

• Pritam has borrowed Rs 10,000 from SBI and has to pay it back in five equal annual installments.

• The interest rate is 10% per annum on the outstanding balance.

• What is the installment amount?

Illustration – 16: Amortization Schedule

At time 0, the outstanding principal is 10,000 After one period an installment of Rs 2,637.97 is made.

The interest due for the first period is 10% of 10,000 or Rs 1,000 So the excess payment of Rs 1,637.97 is a partial repayment of principal. After the payment the outstanding principal is Rs 8,362.03 After another period a second installment is paid. The interest for this period is 10% of 8,362.03 which is Rs 836.20. The balance of Rs 1,801.77 constitutes a partial repayment of principal.

The value of the outstanding balance at the end should be zero. After each payment the outstanding principal keeps declining. Since the installment is constant

The interest component steadily declines While the principal component steadily increases

Amortization with a Balloon Payment

• Pritam has taken a loan of Rs 100,000 from SBI. • She has to pay in 5 equal annual installments along with a terminal

payment of Rs 25,000• The terminal payment which has to be made over and above the

scheduled installment in year 5– Is called a BALLOON payment.

• If the interest rate is 10% per annum, the annual installment may be calculated as

Amortization Schedule

Types of Interest Computation• Financial institutions employ a variety of different techniques to calculate the interest on the loans made by

them. The interest that is effectively paid on the loan may be very different from the rate that is quoted. Thus what you see is not what you get.

The Simple Interest Method• In this technique, interest is charged for only the period of time that a borrower has actually used the funds.

– Each time principal is partly repaid, the interest due will decrease.The Add-on Rate Approach• In this case interest is first calculated on the full principal.• The sum of interest plus principal is then divided by the total number of payments in order to determine the

amount of each payment.• In Alfred’s case if he repays in one annual installment, there will be no difference with this approach as

compared to the simple interest approach.The Discount Method Approach• In this approach the total interest is first computed on the entire loan amount.• This is then deducted from the loan amount.• The balance is lent to the borrower.The Compensating Balance Approach• Many banks require that borrowers keep a certain percentage of the loan amount with them as a deposit.• This is called a Compensating Balance.• It raises the effective interest rate

– Since the borrower cannot use the entire amount that is sanctioned

Illustration – 17: Simple Interest Method• Pritam has borrowed 5,000 from the bank for a year.• The bank charges simple interest at the rate of 8% per annum.

• If the loan is repaid at the end of one year:– Interest payable = 5000x0.08 = 400– Total amount repayable = 5,400

• Assume the loan is repaid in two equal semi-annual installments.– After six months principal of 2,500 is repaid.– Interest will however be charged on 5,000.– Amount repayable = 2500 + 5000x0.08x.5 = 2700

• For the next six months interest will be charged only on 2,500.– The amount payable at the end of the second six-monthly period

= 2500 + 2500x0.08x.5 = 2,600– Total outflow on account of principal plus interest = 2700 + 2600 = 5300– Obviously the more frequently the principal is repaid the lower is the interest.

Illustration – 18: Add-on Rate Approach• What if he repays in two installments?

– Interest for the entire year = 400– This will be added to the principal and divided by 2.– Thus each installment = (5000 + 400) / 2 = 2700

• The quoted rate is 8% per annum.• But the actual rate will be higher.• The actual rate is given by

The solution is i = 10.5758% This is of course the nominal annual rate. The effective annual rate is 10.8554%

Illustration – 19: The Discount Method Approach

• Prtam borrows 5000 at 8% for a year.• The interest for the year is 400.• So Pritam will be given 4600 and will have to repay

5000 at the end.• The effective rate of interest

= [(5000 – 4600) / 4600 ] * 100 = 8.6957%

Illustration – 20: The Compensating Balance Approach

• Pritam is sanctioned 5,000 at the rate of 8%.• But he has to keep 10% of the loan amount with the bank for

the duration of the loan.• So while he pays an interest of 400, the usable amount is only

5000x0.9 = 4500• The effective interest cost is [400 / 4500] * 100 =

8.8889%• Quite obviously

– The higher the compensating balance, the greater will be the effective interest rate.

Annual Percentage Rate (APR)• The effective rate of interest that is paid by a borrower is a

function of the type of loan that is offered to him.• Since different lenders used different loan structures,

comparisons between competing loan offers can be difficult. • To ensure uniformity the U.S. Congress passed the

– Consumer Credit Protection Act– This is commonly known as

• The Truth-in-Lending Act• The law requires institutions extending credit to use a

prescribed method for computing the quoted rate.• Every lending institution is required to compute the APR and

report it before the loan agreement is signed.• The most accurate way to compute the APR is by equating the

present value of the repayments made by the borrower to the loan amount.

Valuation of Assets(Debt & Equity)

Valuation of Debt

Understanding the Debt Instrument• What is debt and who issues it?

– It is a financial claim issued by borrower of funds for whom it is a liability.• Who holds it?

– The lender of funds for whom it is an asset• What is the difference between debt and equity?

– Equity confer ownership rights where as debt does not.– Debt promises to pay interest at periodic intervals and to repay the principal

itself at a pre-specified maturity date, where as equity gives right to the surplus generated by the organization without any promise

– Debt usually has a finite life span where as equity has infinite life– The interest payments are contractual obligations borrowers are required to

make payments irrespective of their financial performance• In the event of liquidation

– The claims of debt holders must be settled first, Only then can equity holders be paid.

Terminology Associate with Debt InstrumentFace Value• It is the principal value and the amount payable by the borrower to the lender

at maturity.• Periodic interest payments are calculated on this amount

Term to Maturity• It is the time remaining for the bond to mature and time remaining for which

interest has to be paid as promised.

The Coupon Rate and the Coupon Value • Periodic interest rate (coupon rate) need to paid by the borrower.• The value of the coupon can be calculated by multiplying the face value with

the coupon rate.

Yield to Maturity (YTM)• YTM is the rate of return an investor will get if held to maturity and all coupon

received before maturity must be reinvested at the YTM

Terminology Associate with Debt InstrumentDiscount Bonds• If the price of the bond is less than the face value at the time of issue then it is a

discount bond• If the bond is trading at lower than face value then also is called discount bond

– This will happen when the YTM is higher than the coupon rate.Par Bonds• If the price of the bond is equal to the face value at the time of issue then it is a par

bond• If the bond is trading at face value then also is called par bond

– This will happen when the YTM is equal to coupon rate.Premium Bonds• If the price of the bond is more than the face value at the time of issue then it is a

premium bond• If the bond is trading at higher than face value then also is called discount bond

– This will happen when the YTM is lower than the coupon rate.A Zero Coupon Bonds• In a zero coupon bond coupon rate is zero• It is issued at a discount and repays the principal at maturity. The difference

between the offer price and the face value is the return received by the investor.

Valuing Debt: Discounted Cash-flow Method• Value of a bond is derived from the stream of cash flows that the bond holders have

the right to receive at periodic interval.• How would we derive the value when the cash-flows are received at different time

intervals?– All future cash flows including the payment of principal at maturity needs to be

discounted to the present to derive the value of the cash flows• Value of bond is a function YTM which is determined by;

– The face value or the maturity amount – The coupon rate– The term to maturity– The market price of the bond

• The valuation can be arrived by treating periodic cash flows as annuity and the terminal face value is a lump sum payment.

– If the coupon is paid more often than once per year then the coupon amount needs to calculated accordingly

• Nuances of Valuing bonds– If the investor know the yield that is required by him, then he can calculate the price that

would give him the expected yield.– Conversely, if the investor buys the bond at a certain price, he could calculate the yield he

would receive from the investment.– Therefore the yield and price is dependent on each other and need to be determined

simultaneously

Valuing Debt: Example• Let us take following example;

– Tata Motors were to issue a bond with 10 years to maturity.– The maturity amount at the end of 10 year is Rs.1000– The coupon rate is 8%, and coupon amount is Rs. 80.– The coupon is paid at the end of the year

• The company is going to pay 10 coupons which can be treated as annuity and the present value of the annuity would be

– (R80 / 0.08) * [1 - 1 / (1+0.8)10] = 1000 * [1 – 1 / 2.1589] = 1000 * 0.53681 = Rs.536.81

• The company is going to pay Rs.1000 at the end of 10th year. The present value of the maturity amount would be

– 1000 / (1+0.08)10 = 1000 / 2.1589 = Rs.463.19

• The two parts can be added to get the value of the bond – Rs.536.81 + Rs.463.19 = Rs.1000

• The bond is selling at its face value. Given the coupon rate is 8% and coupon amount is Rs.80, the bond will be valued at Rs.1000

Valuing Debt: Example of Change in Interest rate• Let us a year has gone by and the interest rate has changed to 10%;

– Tata Motors bond has 9 years to maturity.– The maturity amount at the end of 9 year is Rs.1000– The coupon rate is 8%, and coupon amount is Rs. 80.– The coupon is paid at the end of the year


– (R80 / 0.1) * [1 - 1 / (1+0.1)9] = 800 * [1 – 1 / 2.3579] = 800 * 0.57590 = Rs.460.72• The company is going to pay Rs.1000 at the end of 9th year. The present value of the maturity

amount would be– 1000 / (1+0.1)9 = 1000 / 2.3579 = Rs.424.10

• The two parts can be added to get the value of the bond – Rs.460.72 + Rs.424.10 = Rs.884.82

• The bond would sell at Rs.885 after one year when the interest rate is 10%– Given the going interest rate is 10%, the YTM has to be 10%. The investor would only get

YTM of 10% on 8% coupon rate bond only if the investor get the bond at discount– Loss in interest rate of 2% will compensated by the difference in value at maturity and

market price– Rs.1000 – Rs. 884.82 = Rs.115.18 is nothing but the present value of difference in coupon

value at 8% and 10% coupon rate which is value of annuity of Rs.20 for 9 years discounted at 10%.

– (R20 / 0.1) * [1 - 1 / (1+0.1)9] = 200 * [1 – 1 / 2.3579] = 200 * 0.57590 = Rs.115.18

Valuing Debt: Example of Change in Interest rate• Let us a year has gone by and the interest rate has changed to 6%;

– Tata Motors bond has 9 years to maturity.– The maturity amount at the end of 9 year is Rs.1000– The coupon rate is 8%, and coupon amount is Rs. 80.– The coupon is paid at the end of the year


– (R80 / 0.06) * [1 - 1 / (1+0.06)9] = 1333.333 * [1 – 1 / 1.6895] = 1333.333 * 0.40810 = Rs.544.14

• The company is going to pay Rs.1000 at the end of 9th year. The present value of the maturity amount would be

– 1000 / (1+0.06)9 = 1000 / 1.6895 = Rs.591.89• The two parts can be added to get the value of the bond

– Rs.544.14 + Rs.591.89 = Rs.1,136.03• The bond would sell at Rs.1,136 after one year when the interest rate is 6%

– Given the going interest rate is 6%, the YTM has to be 6%. The investor would only get YTM of 6% on 8% coupon rate bond only if the investor get the bond at premium

– Gain in interest rate of 2% will compensated by the difference in value at maturity and market price

– Rs.1136.03 – Rs. 1000 = Rs.136.03 is nothing but the present value of difference in coupon value at 8% and 6% coupon rate which is value of annuity of Rs.20 for 9 years discounted at 10%.

– (R20 / 0.06) * [1 - 1 / (1+0.06)9] = 333.33 * [1 – 1 / 1.6895] = 333.33 * 0.40810 = Rs.136.03

Valuing Debt: Generalizing• Based on the learning from the examples we can generalize the formula for valuing

the bond• V = [C/r] * [1 – 1/(1+r)t] + [F/(1+r)t, where

– V is the price of the bond– C is the coupon amount– r is the yield required from the bond– F is the face value or the amount received at the maturity– t is the time term left to maturity

• In case the coupon is paid more than once in a year, we need to change the r and t accordingly, for example; – If the coupon is paid twice in a year then the appropriate yield would be r/2– The time left to maturity would be 2t

Valuing Debt: Risk Associated with Bonds• All bonds are exposed to one or more sources of risk.

– Credit risk: This risk refers to the possibility of default on payment of principal or the periodic interest payments.

– Interest rate risk: This risk refer to change in value of bonds due to change in interest rate and risk of re-investment return due to change in Change in interest rate.

– Liquidity risk: This risk refers to not able to sell the bond– Inflation risk: This refers to risk associated with inflation– Foreign exchange risk: This risk involved only if bond is issued in foreign currency

• The potential investor need to evaluate the risk associated with the bond– At the time of issue, it is the issuer’s responsibility to provide accurate information about his

financial soundness and creditworthiness, which is provided in the offer document or the prospectus.

– Given the complexity of offer document, a general investor may not able to evaluate the bond issuer’s credibility

– This work is generally done by credit rating agencies– This agencies take all available information and provide ratings in simple terms so that the

investor can understand the risk associated with the bond• Higher the risk associate with the bonds higher would be the yield

– If the risk change before the maturity period then it can be reflected on the price of the bond

– Credit rating agencies provide rating updates to help the investors to make appropriate decisions

Understanding Complex BondsFloaters• Floaters is a types of bond where the coupon rate can that can change over

time instead of a fixed coupon in case of plain vanilla bond – Floaters can be linked to a benchmark rate like LIBOR or government

treasury bonds.– The coupon rate would be Benchmark Rate +/- x%– The difference between the benchmark and coupon rate is call the

spread– The spread can be positive as well as negative

Inverse Floater• In the case of an inverse floater the coupon varies inversely with the

benchmark.– For instance the rate on an inverse floater may be specified as 10% - LIBOR.– In this case as LIBOR rises, the coupon will decrease, whereas as LIBOR falls, the

coupon will increase.• In case of inverse floater a a floor has to be specified for the coupon because

if the in the absence of a floor the coupon can become negative

Callable Bonds• In the case of callable bonds the issuer has the right to call back the bond

before the maturity of the bond by paying the face value.– When the yield is falling the issuer would be better of calling back the bond if

he has the option– On the other hand the buyer would like to hold on to the bond because he is

getting higher yield, and he has a re-investment risk– The call option always works in favor of the issuer

• Buyers of callable bonds would like to expect a higher yield because he faces uncertainty over the cash flow– To compensate for the risk the buyer would demand higher coupon rate or

lower price of the bond.

• Freely callable bonds can be called at any time and hence offer the lender no protection. On the other hand deferred callable bonds can be called after some pre-specified time

• In some cases some premium is paid (one years coupon) at the time of calling the bond, which is called the call premium

Putt-able Bonds• In the case of putt-able bonds the subscriber has the right to return the

bond before the maturity and collect the face value.– When the yield is rising the subscriber would be better of surrendering the bond

if he has the option– On the other hand the issuer would like the lender to hold on to the bond

because the issuer would have to pay higher yield, and he has a re-issuance risk– The put option always works in favor of the lender

• Seller of putt-able bonds would like to provide a lower yield because the issuer faces uncertainty over the withdrawal of bond– To compensate for the risk the issuer would demand a premium resulting in

lower coupon rate or higher price of the bond.

• Freely putt-able bonds can be returned at any time and hence offer the issuer no protection. On the other hand deferred putt-able bonds can be returned after some pre-specified time

• In some cases some premium is paid (one years coupon) at the time of returning the bond, which is called the put premium

Convertible and Exchangeable Bonds• A convertible bond is right for the bond holder to convert the bond into

common stocks of the issuing corporation.– The conversion ratio (# of common stock per bond) is predetermined. – The conversion can be made after the a pre-specified time or over a pre-

specified period.– The stated conversion ratio may also decline over time depending on the

provision– The conversion ratio generally adjusted proportionately for stock splits

and stock dividends.• Exchangeable bonds are a category of convertible bond, that grants the

holder a privilege to gets the shares of a different company.– Exchangeable bonds may be issued by firms which own blocks of shares

of another company and intend to sell them eventually by doing in a exchangeable bond way is to defer the selling decision because

• The expectation that the price of the exchangeable stock will rise• Tax benefit involved

Valuation of Equity

Introduction• Valuation of an equity would depend on the required return the investor

would demand to invest in the equity.• What are the factors that determine the required rate of return on an

investment?– Risk associated with the investment. The greater the risk, greater will be

the required return.– The size of the cash flows received from it. Greater the cash flow

greater would be the valuation– The timing of the cash flows.

• How do we define and measure risk of an investment and what do we mean when we say that investment in asset A is riskier than the investment in asset B?– What is the relationship between an asset’s risk and its required return?

• Risk associated with an asset can be of two types– Systematic risk: The risk contributed by the factors that affect all the

assets. For example decline in growth rate of the economy.– Unsystematic risk: The risk contributed by the factors that affect only

the asset under consideration. For example decline in growth rate of the company where the investment has been made.

Valuation of Equity: Cash Flow Method• What are the cash flows from an equity investment?

– Dividend for each holding period – Inflow from sale of the stock at the end of investment horizon.

• Consider the case of an investor who plans to hold the stock for one period– Price of the equity can be expressed by

Generalization of the Cash Flow Equation• If we assume that the person who buys the stock after one period also has

a one period investment horizon, then:

Extending the same logic for t period would give us

Therefore value of any equity share is the present value expected stream dividends expected to be paid over infinite period

Equity Valuation: The Constant Growth Model• It is extremely difficult to forecast an infinite stream of dividends, which is

required to derive the valuation of equity. • To make it simple we can assume that the dividends are going to grow at a

constant rate over the infinite period– Let us assume dividends is going to grow at g% per year and the declared

declared dividend now is d0

– The value of the equity is

Equity Valuation: Solving for r• The cash flow method would require us to use the most appropriate value

for r (the discount rate)• The discount rate would depend on risk associated with the equity in

question• To derive the value of r we need know the risk associated with the equity,

and the relationship between risk and expected return• The relationship between risk and return can be derived if we know the risk

premium market would pay to take an extra unit of risk• This relationship is described in Capital Asset Pricing Model (CAPM)• The CAPM would help us determine the expected return from a asset.• The CAPM only provides incremental return for taking systematic risk

because the unsystematic risk can be eliminated through diversification

Equity Valuation: Role of Diversification• When an investor makes an investment he takes two kind of risk

– One that is specific to the equity – Other that is related to the macro economic factor, which would affect all

equities • If two equities are co-related with each other by combining these two

equities one can reduce the risk associated with individual equities.• If we take a very large number of equities and the investors will allocate

the invest able fund across all these equities then the portfolios will not have any equity specific risk (unsystematic risk)

• The portfolio would only have systematic risk, and market would only provide incremental return for taking the systematic risk.

• This has an important implication– To a diversified investor only systematic risk matters – The investment decision would depend on individual assets contribution to the

systematic risk

Understanding Systematic Risk • There is a reward on an average for bearing incremental risk and the

reward depends only on the systematic risk of the investment • Why?

– Unsystematic risk can be eliminated by diversification, hence no reward for taking the risk. Market will not reward for taking unnecessary risk.

• Only systematic risk is relevant for determining the expected return and the risk premium of an asset

• Systematic risk is measured by the BETA of an asset - (Beta)• Beta measures the systematic risk of an asset relative to market portfolio.

By definition market portfolio has a beta of 1.0– So an asset with a beta of 0.50 has half as much systematic risk as the

market portfolio– An asset with a beta of 2.0 has twice as much systematic risk as the

market portfolio • The larger the beta, the higher the systematic risk and the greater will be

the expected return• Security A may have higher unsystematic risk than security B, if security B

has more systematic risk then the expected return on security B would be higher than security A

Understanding the Portfolio Return and Risk• Portfolio return can be calculated by taking a weighted average of expected

return of all assets that constitute the portfolio.• Risk of an asset can be measured by calculating the standard deviations of

returns of the asset.• Calculation of portfolio risk is more complex because of interaction among

assets• The portfolio risk is measured by summing of all the co-variances• A well diversified portfolio has only systematic risk. Therefore we can calculate

the contribution of an individual asset to the portfolio risk by measuring the co-variances between the asset and well diversified portfolio (market portfolio)

• The Beta which measure the systematic risk of an asset is nothing but the co-variance between the asset and a market portfolio (well diversified portfolio)

• A security would enter a portfolio only when its contribution towards portfolio return is higher in comparison to its contribution towards portfolio risk

Risk Premium & CAPM• A risk averse investor demands risk premium if he is taking incremental

risk• If Ri is the return from an asset i and risk-free rate is Rf then the risk

premium of the asset I is Ri – Rf

– Is the risk premium (Ri – Rf) adequate for the asset i– How would we know adequacy of risk premium of an asset?

• First we need to calculate the risk premium market demand for a market portfolio, which is (Rm – Rf) where Rm is the expected return from the market

• Multiply (Ri – Rf) with the quantity of risk associate with the asset I, which is measure by Beta

• Once we know the risk premium of the asset i we can easily calculate the expected return from the asset I

• The expected return from asset i is described in the form CAPM

Deriving the CAPM• Let us take an asst i

– Asset i’s contribution to risk premium is Ri – Rf– Asset i’s contribution to risk is Cov(Ri, Rm)– Risk premium per unit of risk is = (Ri – Rf)/ Cov(Ri, Rm)

• Let us take the market portfolio m– The risk premium in the market is Rm – Rf

– The risk of the market portfolio is Cov(Rm, Rm) = σm2

– Risk premium per unit of risk is = (Rm – Rf)/ σm2

• In the equilibrium the risk premium per unit of risk for the asset I will be equal to the risk premium per unit of risk for the market portfolio

• Therefore (Ri – Rf)/ Cov(Ri, Rm) = (Rm – Rf)/ σm2

– (Ri – Rf) = (Rm – Rf) * [Cov(Ri, Rm)/ σm2]

– Ri = Rf + Cov(Ri, Rm)/ σm2] * (Rm – Rf)

– Ri = Rf + βi * (Rm – Rf) where β = Cov(Ri, Rm)/ σm2]

• Now we have equation which would help us in calculating the expected return for an asset

Using CAPM• The CAPM can be used for many purpose

– Pricing of risky assets• If the expected return is higher then the asset is over priced• If the expected return is lower then the asset is under priced• As a investor one is always looking for under priced asset

– Calculating the cost of equity• The CAPM equation would help us in calculating the cost of equity

by giving the return that an investor is looking from the specific equity investment

– Calculating the risk premium• CAPM gives us the frame work to calculate the market price for risk• It would help us to calculate the incremental return that is required

to take an unit of incremental risk• Establishes the relationship between risk and return

Cost of Capital

Understanding Cost of Capital• Firms need capital for creating assets that would generate return for the

owners of firm• The capital is provided by organizations that have surplus capital

– Capital can have two types of claim• Debt• Equity

• The SBU demand a return to provide capital– The expected return demanded by the SBU is the cost of capital for the firm,

the DBU– The expected return would be a function of types of capital

• The firm’s overall cost of capital will reflect the required return on the firms composition of types of capital – Overall cost of capital will be a mixture of the returns required by the creditors

(debt capital provider) and the returns required by the shareholders (equity capital provider)

– The cost of capital is related to the expected return required by the provider of both of capital

– A firm’s cost of capital is nothing but the weighted average cost of debt and equity

– COST OF CAPITAL= REQUIRED RETURN ON THE INVESTMENT

Required Return vis-à-vis Cost of Capital• What is required rate of return?

– Required rate of return is the rate of return above which the investor would be better of

– For example • If the required rate of return on a investment is 10%, the investor would be better of

if the return is more than 10%• On the other hand the investor would not invest if the rate of return is below 10%• In this specific example the cost of capital for the investment would be 10%

• The required return would be a function of the risk associated with the project– Let us evaluate a risk-free project

• How would we determine the required rate of return for the risk-free project?• Required return for a risk free project is nothing but the return an investor gets when

the investor invest in risk free instrument, which is nothing but return available on government bonds

– Let us evaluate a risky project• Required return would be higher for a risky project and will depend on the risk-free

rate and the risk premium demanded by the investor• The cost of capital associated with an investment depends on the risk of the

investment • Cost of capital primarily depends on the use of funds

Understanding Cost of Equity• Cost of equity of firm is the expected return form the firm’s

equity• How would we know the firm’s cost of equity?

– This is a difficult question • Why?

– There is no way of directly measuring the expected return of the investor in the firm’s equity.

– Therefore the cost of equity of firm need to be estimated.• We will discuss four approaches for estimating the cost of

equity– The dividend growth model approach– The security market line (SML) approach– Bond yield plus risk premium approach– Earning-Price ratio approach

The Dividend Growth Model Approach• Let us assume that;

– A firm is currently paying D0 dividend– The dividend is expected to grow at a constant rate g– The required return on equity is RE

• From our valuation of equity classed we know that: – P0 = D0x(1+g) / RE – g = D1 / RE – g

– By rearranging we will get RE = [D1 / P0] + g– Given that RE is the required rate of return on firm’s equity, it would be the cost

of equity capital for the firm

• To estimate the RE we need to know P0, D1, and g

• It would be easy to get P0 and D1 for listed firm, but estimating the g would a challenge

Pros & Cons of the Dividend Growth Model Approach

• It is a simple model• There are some practical difficulties we would face when we

are calculating the cost of equity for firms– Who does not pay any dividends– Even if companies pay dividends there is no guaranty that it would grow

at a constant rate– Importantly the estimated cost of equity is very sensitive to the

estimated growth rate “g”• Conceptually this approach excludes risk associated with the

firms business – Investors expected return would increase if the risky-ness of investment

increases• However, there is no direct adjustment for the risky-ness of an investment

in this model• There is no allowance for the degree of uncertainty associate with the

estimated growth rate of the dividend payout

The SML Approach• From our valuation of equity classed we know that

– Ri = Rf + βi * (Rm – Rf)– Where;

• Ri is the expected return from the firm i (which is nothing but the cost of equity for firm i)

• Rf is the risk free rate of return• βi is mthe risk associate with the firm I• Rm is the market return from equity investment

• To use the SML approach for estimating the cost of equity we would require – The available risk-free rate, which can be easily found by considering 1

year return from investment in government security– Estimate for the market return, which can be calculated by considering

the return from the investment in the equity index fund (in case of India it can be return from NIFFTY or SENSEX)

– Estimate of the risk associated with the company, which can be estimated from the historical data of the firms equity

Pros & Cons of the SML Approach• What are the advantages?

– The SML approach has two distinctive advantages• It explicitly quantifies risk associate with the investment• It can be estimated for the firms that do not pay any dividends

• What are the disadvantages?– The SML approach has two distinctive disadvantages

• It is quite difficult to estimate the risk associate with the firm and the market return

• Estimates dependent• We would be using few estimates to estimate cost of equity. Therefore if our

estimates are poor then the cost of equity will be inaccurate

• The dividend growth as well as the SML approach uses the past data to predict the future– Economic conditions can change quickly and the past may not be the best

guide to the future– The cost of equity can be sensitive to change is economic conditions

Bond Yield Plus Risk Premium & Earning-Price Ratio Approach

Bond Yield Plus Risk Premium Approach• In case of this approach

– The cost of equity = Yield on long term yield bonds + Risk-premium• The logic of this approach is simple

– The firm which is risky will have higher cost of equity – The cost of equity is linked to cost of debt

• However, this approach is silence on how one should calculate the risk premium, the calculation is subjective approach by analysts

Earning-Price Ration Approach• In case of this approach

– The cost of equity = E1 / P0, where• E1 = E0 (1+growth of earning for equity share)• P0 is the current price of the equity

• This approach is quite useful when the firm is not listed• This approach would provide appropriate cost of equity, when;

– The EPS is expected to be constant and the dividend pay-out is 100%– Retained earnings are expected to generate rate of return equal to cost of equity

• Both the conditions are rare occurring all the time, making it a weak approach

Understanding Cost of Debt• The cost is debt of firm is the return that the firm’s lenders demand • The cost of debt unlike the cost of equity can be observed either directly

or indirectly– The cost of debt is the interest rate that the firm must pay on new borrowings– Interest rates can be observed from the financial market

• Let us take the case of a firm that has already issued bonds– The YTM of the outstanding bonds is the required rate of return on the firm’s

debt– Cost of debt in case of such firms is equal to the YTM of existing bonds– The coupon rate of the existing bonds is irrelevant to cost of debt for new debt

• Let us say the firm is going to issue new bonds– The bond needs to be rated by the credit rating agencies– The rating of bonds would provide the benchmark rate for the bond– In case of first time bond offerings the cost of debt would be equal to the

YTM of the bonds corresponding to the same risk category

Understanding Cost of Preferred Stock• Some times firms raise capital by using hybrid form of capital

– This hybrid form of capital having some characteristics of debt and equity

• The debt characteristic– It pays fixed amount– It has higher rights than equity in case of insolvency

• The equity capital– It is for perpetuity – It has lower rights than the debt in case of insolvency

– This type of hybrid capital is called preferred stock• The cost of preferred stock is given by:

Rp = D/P0 where– Rp expected return from the preferred stock– D is the fixed annual dividend– P0 is the current price per share

• Thus the cost of preferred stock is equal to the dividend yield on the equity

Weighted Average Cost of Capital• We have discussed the three types of capital employed by a firm.• How would we calculate the cost of capital for the firm?

– First estimate the share of each type of capital– Calculate cost of each types of capital– Calculate the weighted average costs of capital where the weights are the shares of each

type of capital• Let us take a hypothetical example where E is the market value of a firm’s equity, D is

the market value of a firm’s debt, and P is the market value of firms preferred stock– Total value of the firm is (V); V = E + P + D– Therefore E/V is the share of equity, P/V is the share of preferred stock and D/V is the

share of debt.– E/V + P/V + D/V = 100%

• We need to calculate the value of equity, preferred stock, and debt– The market value of equity = market price per share * the number of shares outstanding. – The market value of debt = market value of a bond * the number of bonds outstanding.

• If there are multiple bond issues repeat the calculation of D for each bond issue and add up the values.

• What is some of the debt is not publicly traded?– We must estimate the yield from similar debt that is publicly traded and this yield should be used to price

the privately held debt.– The market value of preferred stock is=(D/r)*no of preferred stock; D=fixed annual

dividend

Weighted Average Cost of Capital – Tax Implications

• The firm is always concerned with after-tax cash flows • Therefore the cost of capital should incorporate the

effect of tax– This has implications for cost of debt because debt gives the

firm a tax shield • If T is the tax rate the effective cost of debt is RD*(1-T)

• Therefore;– WACC = RE x E/V + P/V x RP + D/V x RD(1-T)

Divisional and Project Costs of Capital• What would be cost of capital for a new project, will it be same as before

the new project?– A manufacturer company is thinking of expanding production by setting up a

new plant– A manufacturing company is thinking of expanding to retail business– There will be situations where the cash flows from the new project could have

different risk from the risk with the current cash flows of the overall firm.

• Let us assume that the riskless rate is 8%, and the market risk premium is 10%. If the firm is an all-equity firm with a beta of 1.2– The cost of equity = WACC = 21.6%=(Rf+Risk premium)*beta– If the firm has to evaluate new projects using this cost of capital, it would

accept project that would provide return in excess of 21.6%.

• If the risk of the new project is lower then the risk premium required for the same project would be lower than 10%, hence the cost of capital would be less than 21.6%.– Use of same cost of capital could reject project that are relatively safe– Therefore, if the new project risk is different from the risk of the existing

business then using the same cost of capital to would result in sub-optimal investment decision

Divisional and Project Costs of Capital• The same type of error can arise if a company has multiple lines of business.

– Assume a corporation has two business divisions • A grocery retail business • An electronics manufacturing operation

– The first has relatively low risk– The second has relatively high risk

• The corporation’s cost of capital is a mixture of the costs of capitals of two distinct business– It is natural to say that both of these divisions would be competing for capital

• The retail business wants to expand to new cities• Manufacturing unit wants to set up a new plant

– What happen if we use WACC as a tool to allocate capital?• The manufacturing division would get more capital

– The cost of capital is same for both the division– It would provide more return in comparison to retail business because the

business has more risk– The less risky retail division may have great profit potential, but it would not get capital

for expansion • Therefore WACC may not be suitable criterion for evaluating project with different levels of

risk.• Ideally the cost of capital needs to estimated for not only for new projects but also for the

different divisions with in an existing business conglomerate– This can be done by following the same method we have discussed before with minor

modifications

Illustration - 21• A company has 2MM shares outstanding • The stock price is Rs.40……..rs 20• The debt is quoted at 90% of face value and the face value of debt is 10

MM, it might be single debt therefore value of debt= market value of bond x no of bonds= 90% of 10 * 1=9

• The YTM for the debt is 10%= cost of debt RD

• The risk-free rate is 5%• The market risk premium is 10% and the beta is .75• The tax rate is 30%• RE = 5 + .75 x 10 = 12.5% and RD = 10% • The value of equity is 2 x 40 = 40MM • Value of debt is 0.90 x 10 = 9MM• Total value V = 49MM• WACC = 40/49 x 12.5 + 9/49 * 10 x (1-0.3) = 11.49%

Capital Budgeting

3 layers of efficient capital market

• Total or realized return= expected return + error(systematic and unsystematic risk)

• 3 layers depends on how we define available• First weak form efficient- available means

historically available• Second semi strong form efficient- publically

available(includes historically available)• Third strong form efficient- privately (including

publically available.)

Introduction• Capital budgeting addresses the following questions;

– What new projects the firm should invest?• Should it expand to new market?• Should it launch new products?• Should it increase the production by setting up new plants?• And many more questions that would require the firm to invest in physical (new

technology, new factory) or intangible assets (increase the marketing expenses to increase the brand value)

• Capital budgeting decision would affect the firms growth, profitability, and competitiveness in the long-run– Why?

• Fixed assets created through investment will have long life• The long-tern investment is generally not easily reversible

• The firm will have many alternative where investment can be made, and capital budgeting process helps the financial managers to make the appropriate choice.

• There are a number of techniques for capital budgeting like;– Net Present Value (NPV) method– Internal Rate of Return (IRR) method

• Modified Internal Rate of Return (MIRR) method– Pay-back period method– Benefit-cost ratio method

Net Present Value (NPV)• When should one make an investment?

– If the investment creates value after taking care of the cost– The value is net of cost and therefore called Net Present Value (NPV)

• How do we create value? Let us take an example;– An individual has a house valued at Rs. 25 Lakhs– If he renovates it can be sold at Rs. 30 Lakhs– The cost of renovation is Rs. 3 Lakhs– The owner of house can create value of Rs. 2 Lakhs by investing Rs. 3 Lakhs– Therefore the renovation project would yield a NPV of Rs. 2 Lakhs

• The challenge any investor faces is is to identify in advance that an investment would generate positive NPV, which is the subject matter of capital budgeting

• The capital budgeting process is nothing but a search for project that would generate positive NPV project for investment

• In the case of the house that we considered there is a ready market from where an estimate of the sales proceeds can be obtained, which simplifies the investment decision making process

• Capital budgeting becomes more difficult when we cannot observe the market value of at least comparable investments, which is more realistic

Net Present Value (NPV)• Let us assume that we are planning to set up an dairy firm.

– We can estimate what would it cost to set up the dairy firm – However, would not know the revenue stream from this project– We have to make an estimate of the revenues that would be generated from the diary

project?• Once we have an estimate of the cash flow from the estimate we would have to

calculate the present value of the cash flows• Difference between the investment and the present value of the future cash-flow of

the project will give us the NPV of the project. The cost of setting up the project is Rs. 30,000

• Assume that the cash flows from investment will be Rs. 20,000 per year with a operating expenses of Rs. 14,000 per year.

• The net cash inflow from the project is 20,000 – 14,000 = 6,000 per annum. The business will be wound up in 8 years.

• The salvage value of plant and machinery will be Rs. 2,000 after 8 years. • We will use a 15% discount rate on new projects. • Thus we have an 8 year annuity of Rs. 6,000 per annum plus one lump sum inflow of

Rs. 2,000 after 8 years. • The PV of the cash flows = Rs. 27,578 and the NPV = -30,000+27,578= -Rs. 2422• Since the NPV is negative, this project is not worth undertaking. If the NPV is positive

accept the project and If the NPV is negative reject the project

Internal Rate of Return (IRR)• IRR is the discount rate that equates the present value of cash out-flows

with the cash in-flows of a project.– Present value of cash out-flow will be equal to cash in-flow when the NPV of the

project is equal to zero• The IRR can be calculated if we set the NPV equation equal to zero

– Consider a simple project; Invest 500 today Get back 550 next year. – The NPV of the project = -100 + 110/(1+r)– Equating the NPV to zero would imply 110/(1+r) - 100 = 0 r = 10%– Therefore the IRR is 10%

• IRR of a project is the required return from an investment that would make the NPV of the investment equal to zero

• Let us take an example– A project costs 4000 and the required return from the project is 15%– The cash inflows are 1000, 2000, and 3000 in the first, second, and third year

respectively– The IRR can calculated by making the NPV = 0, in this case it is 19%.– Given that IRR is greater than the required rate of return the project should be

accepted• Therefore investment in a project is acceptable when IRR exceeds the

required rate from the project

NPV vis-à-vis IRR• Calculation of NPV and IRR seems similar!

– Does it mean that use of NPV and IRR would lead to the same decisions about the investment proposal?

• The answer is yes as long as two conditions are met– The project’s cash flows must be conventional

• The first cash flow is negative and all the rest are positive– The project must be independent

• That is the decision taken with respect to this project does not affect the decision to accept or reject another

– If two investments are mutually exclusive then• Accepting one would mean rejecting another

• If we have two or more mutually exclusive projects which is the best– The answer is, the one with the largest NPV– Is it necessarily the one with the highest IRR– The answer is NO– Let us take an example to show this

NPV vis-à-vis IRR - Illustrations• Let us look at two projects; project A and project B, whose cash flows are

given below

Year Project A Project B0 -1000 -10001 550 3502 655 4653 405 7504 355 600

The project A has an IRR of 38% and Project B has an IRR of 35%. if use IRR as the tool project A is better

Let use NPV as a tool to evaluate the projects If our required rate is 15%, the NPV method would identify the project B to be

better If our required rate is 25%, the NPV method would identify the project A to be better

NPV vis-à-vis IRR – Learning from Illustrations• The NPV method is sensitive to the required rate of return

– What should be the appropriate required return?• It should be at least the cost of capital

• NPV and IRR method may result in different choices• It can be misleading to evaluated two projects and rank them on the basis of

IRR to determine which is the best project• Thus if we have mutually exclusive projects we should not rank then based

on their returns • Therefore to compare two projects we should look at the NPV because it

provides an estimate of contribution of the project towards the value of the firm

• However IRR is very popular in practice in comparison to NPV method• It is simple to understand in terms returns than value creation from a project

• IRR is a simple way of communicating about the contribution of a project• The IRR may have a practical advantage because to estimate NPV we need to

know the cost of capital but IRR can be estimated without knowing the cost of capital

Modified Internal Rate of Return (MIRR)• To address the shortcomings of IRR, MIRR is use

– The MIRR can be calculated by;• Calculate the present value of the costs (PVC)• Calculate the terminal value of the cash inflows expected from the

project (TV)• Conceptually PVC = TV / (1+MIRR)n-1

• We can easily solve for the MIRR from the equation• Cost of capital is used as the discount rate.

• Let us take an example– The project cash flows are -120, -80, 20, 60, 80, 100, 120 and cost of

capital is 15%– The PVC = 120 + 80 / 1.15 = 189.6– The TV = 20(1.15)4 + 60(1.15)3 + 80(1.15)2 + 100(1.15) +120= 467– 189.6 = 467 / (1+MIRR)6– The MIRR = 0.162 = 16.2%– The IRR of the same project is 16.81%

• In this case the differences is small but this need not always be the case

Payback Period Method• Payback is the length of time taken to recover the investment amount• Let us understand the payback method through this example.

Time Cash Flow of a Project

Cumulative Cash Flow the Project

0 (155,000) (155,000)

1 55,000 (100,000)

2 75,000 (25,000)

3 25,000 0

4 25,000 25,000

The project recovers the initial investment amount by 3rd year Therefore for this project the payback period is 3 years. The payback period rule would be

If required payback is higher than the actual payback period then accept the project else reject it

Payback Period Method• The payback period method has some shortcomings.

– Firstly to compute the payback period we simply add up the cash flows– Secondly there is no discounting – Time Value of Money is totally ignored.

• Payback period method does not factor in risk differences– In practice a more risky project would be evaluated using a higher

discount rate– Since the payback criterion ignores discounting it analyzes projects with

different risk profiles without factoring in the risk differences.• A major issue is how do we choose a cutoff period

– What is the basis for stating that we will accept projects with a payback of say 3 years or less

– In practice the cutoff has to be arbitrarily decided• The criterion totally ignores cash flows arising after the initial

investment is recovered.

Benefit Cost Ratio Method (BCR)• The benefit cost ratio is defined as the ration of

the present value of all the benefits (PVB) that is going to occur (positive cash inflows) and the initial investment (I)

• Let us take an example – A projects initial investment is Rs. 200– The present value of future cash flows is 250– The BCR = PVB / I = 250 / 200 = 1.25– What does BCR of 1.25 means

• It means per Rs. 1 invested we get Rs. 1.25• The BCR rule would be;

– If the project has a BCR of greater than 1 then accept the project

Capital Budgeting in Practice• NPV is the most appropriate methods for capital budgeting

decisions?– When the NPV can be computed, why look at other methods?

• Investment decision making process needs to take care of uncertainties regarding the future

• Real NPV is unknown and the NPV calculated is an estimate.– Let us assume a project has a positive NPV; short payback and a high IRR

• The information about the project suggests one should proceed with the project

– On the other hand if the NPV is positive; payback is long and IRR is low • The information suggests one should be careful• Verify the estimates• Do further analysis

• Therefore though NPV is technically is the best method it can be used in conjunction with other method to make a better decision

Project Cash Flow Analysis

Understanding the Cash Flows• Why should firm go for new projects?

– To increase the future cash flow, which would increase the value of the firm in future

– To invest the surplus generated productively to increase the value of the firm in future.

• To evaluate an investment, we need to consider:– The changes in the firm’s cash flows due to the investment – The change in cash flow need to increase the value of the firm– The relevant cash flow for a investment would be the incremental cash

flow because of the direct consequence of the decision to take up the new project.

– Therefore the existing cash flow of the firm has now relevant on the investment decision.

• What are incremental cash flows?– The incremental cash flows for a project is any changes in the firm’s

future cash flows that can be exclusively attributed to the investment in new project.

Understanding the Cash Flows• The incremental cash flow is based on the stand alone principle• The stand alone principle treats the investment as;

– The project is like a small firm – The projects has its own futures revenues and costs associated with it

like any other firm – The project can generate its own assets – The project can have its own liabilities– The assets will generate cash flows from the assets it creates and pay

back the liabilities– At the end the project should have the surplus that would increase the

value of the firm• The investment amount on the new project is like acquiring the

cash flows from the small firm.– It is easy to make errors while deciding what cash flows are incremental.– We will discuss some of the potential pitfalls and how to avoid them

Understanding the Cash Flows• A project could have externalities: positive as well as

negatives – A negative externalities would negatively affect the existing

cash flow, which is called value erosion– A positive externalities would positively affect the existing

cash flow, which is called value addition

• In accounting for erosion – it is important to recognize that sales that would have been lost because of future competition should not be attributed to the project– Erosion is relevant only when the sales would not otherwise

be lost

Understanding the Cash Flows• Evaluation of an investment proposal should not include the cost of capital• Why?

– The goal in project evaluation is to compare the cash flows from a project to the cost of acquisition – the NPV

• The mix of debt-equity used is a managerial variable that determines how cash flows will be divided between owners and creditors

• The cash flow of the new investment should take into account the effect of tax

• The capital budgeting process would involve in preparing one pro-forma or projected financial statements

• To prepare a pro-forma statement we need estimates of quantities like:– # of unit of sales– Selling price per unit – Variable cost per unit– Fixed costs – Total investment required Including investment in NWC–

Understanding the Cash Flows – The Sunk Cost• What is a sunk cost of a project?

– The sunk cost is the cost that has already being incurred– It is the cost that the firm has to make whether it takes up the project or

not• The sunk cost can not be changed the decision of accepting or rejecting the

project• It is not relevant for the decision making process

• Therefore the sunk cost principle is not to include it on the cost side of the project cash flow

• For example;– A diary firm evaluating whether to lunch butter as a product in market– To evaluate the proposal it hires a consultant– The consulting fee should not be considered as a cost in incremental cash

flow method• The firm any way has to be paid whether or not the product is launched

Understanding the Cash Flows – Opportunity Costs• What is opportunity cost of a project?

– An opportunity cost of a project is the benefit it has to sacrifice to take up the project

• A firm is thinking of using an ideal piece of land for building multiplex– To build a multiplex the firm has to buy the land– In this case there is no cash out flow for the purchase of the land

because the firm already own it – For the multiplex project what should be the cost of land

• Is it a free given that there is no cash out flow?– The principle of opportunity cost would say it is not because it is a valuable

resource that can be used by other competing project s or at the least it can be sold and money can be used for other purpose as well

• Therefore when we are estimating the cash flows for a project we need to take into account all the possible opportunity costs of the assets that are going to be used in the project, which is currently owned by the firm

Understanding the Cash Flows: Effect on Working Capital

• A new project would require incremental working capital– New project would need cash on hand to pay expenses– Cash needed to finance the inventories of inputs, and outputs– Some of the cash requirement can be financed through account

payables– The balance has to be generated– The balance cash required in termed as Net Working Capital

• As the project is wound up– Inventories will be sold – Receivables will be collected– Bills will be paid – Cash balances will be utilized – These activities will free up the NWC that was initially invested

• While estimating the cash flows of a project we need to account for net working capital expenses

Risk Analysis in Capital Budgeting

Sources of Risk for Capital Budgeting• Most of the capital budgeting decision involves risk

– Risk of increase in expenses to execute the project– Risk of non-realization of expected revenue from the project

• Sources of risk for a project– Project specific risk– Competitive risk– Industry specific risk– Market risk– International risk

Techniques of Risk Analysis• Risk analysis for capital budgeting is complex• The techniques of risk analysis can be broadly divided into two

types– Analysis of standalone risk– Analysis of contextual risk

• The analysis of standalone risk can be done in many different ways– Breakeven analysis– Scenario analysis– Sensitivity analysis– Hiller model– Simulation analysis– Decision tree analysis

• The analysis of contextual risk can be done in many different ways– Corporate risk analysis– Market risk analysis

Break-even analysis• In sensitivity and scenario analysis we attempt to estimate the

effect of changes in certain factors on the project viability• In case of break-even analysis we attempt to estimate the

minimum amount of sales that would make sure that the project does not loose money– The process of estimating the break-even point is called break-even

analysis• The break-even analysis is of two types

– Accounting break-even analysis: In this case the analysis would involve to identifying the sales amount that would result in zero cash profit

– Financial break-even analysis: In this case the analysis would involve to identifying the sales amount that would result in zero NPV

• Accounting break-even point = (Fixed cost + depreciation) / Gross Margin or contribution margin ratio

• Financial break-even point = contribution/1-variable cost %

Scenario Analysis• In scenario analysis, several factors are changed simultaneously

to understand the risk involved in a given project• Typically three case are considered

– Normal– Pessimistic– Optimistic

• Scenario analysis is an improvement over sensitivity analysis with respect to variability of factors happening simultaneously

• However, in case of scenario analysis there is no well defined scenarios, the project manager has to create hypothetical cases by using his/her experiences

• The project managers estimate of different scenario would affect the assessment of risk involved in a project

Sensitivity Analysis• Identify the factors that can change the cash flow of the project

in question• Change one factor at a time by fixing all other factors

– This would help us in identifying the most sensitive factor– Once the most sensitive factor is identified we can take necessary

measures to reduce the risk involved in that factor– This would also help in monitoring the performance of the project

• The sensitivity analysis is very subjective and requires good understanding of the project

• Two individuals may decide differently depending on the prospective

• Sensitivity analysis only changes one factor at a time where as in real world variables tend to change simultaneously

An Example…Data on Investment• Low-cost Housing Project requires an investment of 530,000 in fixed-assets (machinery) and

60,000 (at t=0) in NWC (net working capital)• The machine can be sold off for 30,000 at the end of its five-year life• So, DPY (Depreciation per Year) = (530,000 – 30,000)/5 = 100,000

Data on Income and expenses• Base Figures and Maximum Expected Variations:

– Apartments per Year= 25 units give & take 4%– Price per Apartment = 70,000 give & take 5%– “Variable cost to Price” Ratio = 80% give and take 8%– Fixed Cost = 150,000 give and take 12%– We can compute that DTS (Depreciation Tax Shield) = $100,000 x 34% (tax rate) = 34,000

• WACC is given to be 15%

Lower Bound Base Case Upper Bound

Number of Apartments Sold 24 25 26

Price per Apartment 66,500 70,000 73,500

Variable Cost as % of Revenue 88% 80% 72%

Fixed Costs 168,000 150,000 132,000

An Example…Revenue (70,000 x 25) 1,750,000

Variable Costs (80% of Revenue) 1,400,000

= Contribution 350,000 Fixed Cost (excluding Non-Cash Charges) 150,000 Non-Cash Charges (like Depreciation) 100,000

= EBIT 100,000 Interest 0= Taxable Income 100,000 Taxes @34% 34,000

= NI (Net Income) 66,000+ Non-Cash Charges (like Depreciation) 100,000

= OCF 166,000OCF= NI+ DEP + INT= TR- FC-VC-TAX- INT., exclude non cash

charges.

An Example…At what price (per apartment) Operating CF is zero?

Þ Net Income = OCF – Non-Cash Charge = 0 - 100,000 = -100,000Þ EBIT = Taxable Income = -100,000 /(1-34%) = -151,515Þ Contribution = -151,515 + Non-Cash Charge + Fixed Cost = 98,485Þ Breakeven Revenue = Contribution / (1-80%) = 492,424Þ Breakeven Price (per apartment) = 492,424 / 25 = 19,697(assuming that 25 apartments are sold annually)

AND Breakeven Number of Apartments = 492,424 / 70,000 ≈ 7(assuming that each apartment is sold for 70,000)

Caveat: Breakeven is often measured by the number of units to be sold

This is referred as Cash Breakeven Point

An Example…

At what price (per apartment) Revenue just covers actual costs (excludes non-cash charges)? Therefore, contribution= dep + FC + EBIT, here EBIT=0 AND dep is excluded.

Requires that Contribution = Fixed Cost = 150,000

=> Breakeven Revenue = Contribution / (1-80%) = 750,000

Þ Breakeven Price (per apartment) = 750,000 / 25 = 30,000

AND Breakeven Number of Apartments = 750,000 / 70,000 ≈ 11

This is also referred as Cash Breakeven Point

If there were no taxes, Breakeven Points 1 and 2 would be the same. Because then

contribution= EBIT + FC + dep = -100000 + 150000 + 100000= 150000= FC , it is the tax

rate which is making difference between the ocf=o and just covered cost method cash

break even point.

An Example…

At what price (per apartment) Net Income is zero?

Þ Taxable Income = 0 => EBIT = 0Þ Contribution = 0 + Non-Cash Charge + Fixed Cost = 250,000Þ Breakeven Revenue = Contribution / (1-80%) = 1,250,000Þ Breakeven Price (per apartment) = 1,250,000 / 25 = 50,000AND Breakeven Number of Apartments = 1,250,000 / 70,000 ≈ 18

This is the Accounting Breakeven Point

At this point, Operating Cash Flow equals DepreciationDepreciation is taken here as the Recovery of Investment in Fixed Assets(clearly ignores time value of money)

Estimating the Cash Flows – Base Case Net Sales OR Revenue 1,750,000

- Variable Costs and Fixed Costs 1,550,000(Exclude Non-Cash Charges)

- Actual Taxes 34,000(This has to be known or given)

= Operating CF 166,000

NI (Net Income) 66,000

+ Non-Cash Charges 100,000

+ Interest 0

= Operating CF 166,000

The top-down approach

The bottom-up approach

Estimating the Cash Flows – Base CaseThe tax-shield approach

Revenue ($70,000 x 25)1,750,000

Variable Costs (80% of Revenue)1,400,000

= Contribution 350,000 Fixed Cost (excluding Non-Cash Charges)

150,000= Taxable Income without Non-Cash Charges & Interest

200,000 Taxes @34% 68,000= EAT 132,000+ DTS (Depreciation Tax Shield)

34,000

= OCF (Un-levered) 166,000

Scenario Analysis: Base-Case NPVProject-LcH Special CF CFs at Special CF

at t =0 t=1 t=2 … t=5 at t= 5

-530,000 +30,000 -60,000 +60,000

OCF OCF … OCF

TOTAL -590,000 OCF OCF … OCF 90,000

NPVLcH = -590,000 + OCF x PVIFA15%,5 +

= -545,254 + 166,000 x PVIFA15%,5

= -545,254 + 556,458

= 11,204

5%)151(000,90

Scenario Analysis: Worst-Case NPVProject-LcH Special CF CFs at Special CF

at t =0 t=1 t=2 … t=5 at t= 5

-530,000 +30,000 -60,000 +60,000

OCF OCF … OCF



= -545,254 + 49,523* x PVIFA15%,5

= -379,245

*Derive this under most unfavorable figures for units sold, price, variable cost, and fixed cost

5%)151(000,90

Scenario Analysis: Best-Case NPVProject-LcH Special CF CFs at Special CF

at t =0 t=1 t=2 … t=5 at t= 5

-530,000 +30,000 -60,000 +60,000

OCF OCF … OCF



= -545,254 + 300,033* x PVIFA15%,5

= 460,502

*Derive this under most favorable figures for units sold, price, variable cost, and fixed cost

5%)151(000,90

Thank You

MM Hypothesis

• Capital structure does not matters investors can lend and invest their own.

• Thus whatever the capital structure the stock prices will remain the same

• When taxes =0 then,• WACC= E/V*Re + D/V *Rd• Re= WACC+ (WACC-Rd)* D/E

M &M

• The cost of equity depends on• Wacc• Rd• D/E ratio• The cost of equity given by a straight line with

a slope of WACC- Rd• According to MM hypothesis cost of equity

does not depend on the D/E ratio

• The fact that debt is cheaper than equity will be offset by the rise in cost of equity

• The net result is what WACC remain the same

MM hypothesis and implication of tax and bankrutptcy

• Debt has two features• Interst on debt is tax deductible• Bankruptcy: one limiting factor affecting the

amount of debt a firm can raise is bankruptcy cost.

bankruptcy

• When this happen the ownership of firm get transferred to the debt holders

• When the value of assets becomes equal to the value of debt the firm is called bankrupt

• Then value of equity becomes 0.• And the debt holders holds the asset equals to

the value of debt provided there is no transactional cost involved.

• In the real world it is expensive to be get bankrupt

• The cost associated with bankruptcy may offset the tax benefit due to leveraging

Direct cost of bankruptcy

• Legal and administration cost• A fraction of asset get disappeared(bankruptcy

tax)• This cost is incentive for debt financing

Indirect cost of bankruptcy

• Time• Strain• Financial distress• Profitable projects may be get terminated

Conclusion of bankruptcy

• The tax benefit from leveraging is important to firms that are in tax paying condition

• Firm with high dep tax shield will get less benefit from leveraging• Firm with substantial accumulated loss will get little value form

tax shield• Greater the volatility less a firm should borrow• Borrowing depends on asset quantity• Financial distress is more costly for some firm• The cost of bankruptcy depends on asset and easiness of transfer

of the asset• The firm will greater risk of facing financial distress will borrow

less

Dividend policy

• The connecting link between owner and management is dividend policy which a manager decides

• Residual dividen policy: growth and capital appreciation driven

• Managed dividend policy: under managed dividend policy manager attempts to reduce the variablity of pay out of dividend

• It is constant, increasing or predictable cash outflow• Mutual funds: dividend & growth

agency problem &Dividend policy

• Dividend stripping• cash flow is shared by debt and equity holders• Debtors get assured when company has liquidable

assets• Shareholders enjoy upside potential• Debtholders enjoy downside risk with equity holders• How I can get my money back quicky in case of equity

holdr- by getting more and large dividend paid• To reduce the conflict between debt and stock holders

there is need of managed dividend policy

Leveraging and dividend policy

• Higher the leverage more the divident paid is incentive for the equity holders

• In case of levereged firm payment of divident increase the default

• In low levereged firm dividend payment will have very low impact on value of debt

• Dividend payment makes debt more risky• Low the debt low is the chances of default

Pricing mechanism and repurchase vis-vis cash dividend

• Assymetry of info arises when two individual have different set of info.

• Manager tries to reduce it through the divident policy• The signal will be credible and believable only when it can’t be

mimiced• Pricing mechanism must separate the firm with favourable

information with the firm with less fabourable information based on the dividend signal

• When prices of the share is low what managers perceived what it should be, then mangers go for buy back, the manger will be benefit more than paying dividend provided company has money to buy back.

Working capital management

• Deals with short term mangement of assets and liability• Gross wc• Net wc• Wcm involve• Cash and liquidity mangement• Account receivable and payable management• Formulate credit policy and negotiate favourable credit

terms• Estimates working capital need• Monitoring the inventories

Factor influencing working cap requirement

• Nature of business• Cycle of business• Seasonality of business• Market condition• Supplier condition

Level of WC & CA requirement

• Less CA – shortage cost• More CA – carrying cost• In order to balance these two cost we need

optimum working capital

Level of working capital depends on

• Operating cycle• - inventory period( inventory supplied – goods

finished and sold)• - account receivable period(sale- cash

received)• Cash cycle• - operating cycle• - account payable period( bill received to paid)

• OC= INVENTORY PERIOD + ARP• CC= OC- APP• LEVEL OF CA AND WC REQUIREMENT• Inventory period= avg inventory/ (cogs/365)• ARP = avg account receivable/ (sale/365)• APP = avg account payable period / (cogs/365)

Cash and liquidity management

• Why do firm need cash• Transaction motive• Precautionary motive• Speculative motive

• Collection float, disbursement float and net float• The firm objective is to • Maximize the float to increase the cash balance• Speeding the collection• Delaying the payment• Concentration banking

Investing the surplus fund

• Criteria for evaluating the investment requirement

• Safety• Liquidity• Maturity period and • yield

Understanding the need to decide on the portfolio investment

• Ready cash segment: cash needed to meet un anticipated operational requrirement. Safety & liquidity

• Controable cash segment: cash requied for planned investments. Safety, size and maturity period of instrument

• Free cash segment: amount or cash which must be invested. Safety & yield.

Investing options

• Bill discounting• Inter corporation deposit• Mutual fund schemesEquity, debt and balanced.• Treasurey bills• CD, CP and FD with banks

Credit management

• Credit payment: credit period, billing & payment conditions, cash discount

• Credit policy variables: cash discount, collection efforts, credit period and credit standard

• Credit evaluation• Credit granting decision• Credit monitoring

financial management - class ppt[1]

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