Financial Management Lacture notes, Commerce Department Shah Abdul Latif University, Khairpur, By Sir Anil Kumar

Financial Management

Management Definition: "Coordinating work activities so that they are completed efficiently and effectively with and through other people" (Robbins & Coulter, 2006)

Functions: Basically five functions of management were proposed by a French industrialist named Henri Fayol but now condensed to four functions: namely: Planning, Organizing, Leading, Controlling.

Financial ManagementDefinition: “The process of procurement of funds and the efficient and wise allocation and use of the funds and resources".

Nature of Financial ManagementThe term nature refers to its relationship with the closely related fields of economics and accounting, its functions, scope and objectives.Relationship with the fields of Economics and Accounting

Finance and EconomicsMacro Economics: Overall institutional environment in which a firm operates. It looks at the economy as a whole.Financial managers should understand the economic environment, specifically:

Recognize and understand how monetary policy affects the cost and availability of funds

Be versed in fiscal policy and its effects on the economy Be aware of the various financial institutions and Understand consequences of various levels of economic activity and

changes in economic policy for their decision environment and so on.

Micro Economics: Economic decisions of individuals and organizations. The concepts and theories relevant to financial management are:

Supply and demand relationships and profit maximization strategies. Issues related to the mix of productive factors, optimal sales level and

product pricing strategies. Measurement of utility preference, risk and the determination of value The rationale of depreciating assets. Comparison of marginal revenue and marginal cost.

Finance and Accounting

Accounting provides basic financial input in shape of financial statementsFinancial Management analyses this input to determine past performance and future direction of a firm.

Key Differences between finance and accounting are:

Treatment of fundsIn accounting accrual system is followed.In Financial management Cash flows system is followed.

Decision MakingAn Accountant is primarily concerned with the collection and presentation of data A Financial manger is concerned with the financial planning, controlling and decision making.Thus finance begins where accounting ends

Finance and other related disciplines

Marketing, Production, Quantitative methods etc.

Scope of Financial Management

Approach to the scope is divided into 02 categories.1. Traditional Approach

This approach evolved during 1920’s and continued uptill the early fifties. In initial stages it was known as corporate finance (CF) CF was concerned with procurement of funds externally from capital

market institutions and through various financial instruments and did not consider proper allocation of capital.

Limitations of Traditional Approach Based on outsiders (e.g.: investors, bankers etc.) looking in approach and

insider looking in approach is ignored. Focus was on financing problems of a corporate enterprise and non –

corporate enterprise was outside its scope. More attention was given to episodic events e.g.: promotion,

incorporation, merger, consolidation, reorganization etc and day to day financial problems did not receive much attention.

Focus was on long term financing and working capital management was not in preview of finance function.2. Modern Approach

It views FM in broader sense and covers not only procurement of funds but efficient and wise allocation of funds as well. In modern sense it can be divided into three major decisions as functions of financial management

1. Investment Decision

It relates to the selection of assets in which funds will be invested by a firm. These assets fall into two categories.I. Long term assets or Fixed assets II. Short term assets or Current AssetsIn this regard investment decisions fall into two categories:

I. Capital BudgetingLong term investment decisions regarding the selection of fixed assets or an investment proposal whose benefits are likely to be received in future over the lifetime of a project.The main elements of capital budgeting decisions are: a) the long term assets and their composition (b) the business risk complexion of the firm (c) concept and measurement of the cost of capital

II. Working Capital ManagementMaintaining the proper liquidity position of a firm by achieving trade-off between the profit and risk (liquidity).

2. Financing decisions

Decisions regarding the capital structure (Proportion of debt and equity financing) or leverage of a firm.A reasonable proportion of debt and equity capital is called the optimum capital structure.Financing decisions cover two interrelated aspects.Its one dimension called the capital structure theory is whether there is an optimum capital structure? And in what proportion should funds be raised to maximize the return to the shareholders? Its second dimension called the capital structure decision is to determine an appropriate capital structure, given the facts of a particular case.

3. Dividend Policy Decision

Decisions’ regarding what proportion of the profit is paid to the shareholders as dividend and what is utilized in the investment opportunities available.

Objective of Financial Management

To ensure optimum financial decision through certain financial approaches referred to as decision criterion in respect of three areas namely: investment, financing, dividend is the objective of financial management.

Two widely discussed approaches are:

1. Profit Maximization Decision Criterion

Decisions that increase profit should be undertaken and decisions that decrease profit should be avoided.

The term profit can be used in two senses:

I. As an owner oriented concept it refers to the amount and share of national income which is paid to the owners of business.

II. As profitability it is described as an operational concept. It refers to economic efficiency. A situation where output exceeds input.ORSelect assets, projects, and decisions which are profitable and reject those which are not.

In the current financial literature profit maximization is used in the 2nd sense.

Criticism of Profit Maximization Decision Criterion

The main flaws of this criterion are:

I. Ambiguity of profitIt is not clear which variant of profit to maximize. Variants may be: short term or long term profit, gross profit or net profit etc.

II. Timing of BenefitIt ignores the distinction between the benefits received today or tomorrow while value of a rupee today is worth more than tomorrow.

III. Quality of BenefitIt avoids the degree of certainty with which benefit is received while a consistent benefit is always preferred by investors over ever fluctuating benefit.

2. Wealth Maximization Decision Criterion

It is also known as value maximization or net present worth maximization.

Its operational features satisfy all the requirements lacking in the earlier approach and is considered as universally accepted decision criterion.

It is based on Cash flow generated rather than accounting profit.

The value of a stream of cash flows is calculated by discounting its elements back to the present at a capitalization rate (interest rate) that reflects both time and risk (quality).

As a decision criterion it involves a comparison of value to cost.

An action that has a discounted value that exceeds its cost can be said to create value and should be undertaken.ORThe alternative with the greatest net present value should be selected

The net present worth can be calculated as follows:

W= A1/ (1+K) + A2/ (1+K) 2 + ……+ An/ (1+K)n – C

Where A1, A2, … An represents streams of cash inflows over a period of time.K = Discount rate or interest rate.C = Initial outlay to acquire that asset.

Valuation Concepts

Time Value of Money/ Discounted Cash Flow (DCF) Analysis

Amount that is paid or received at two different points in time is different, and this difference is recognized and accounted for by discounted cash flow (DCF) analysis. ORThe value of a unit of money is different in different time period. The value of a sum of money received today is worth more than tomorrow.

Time Lines

Time: 0 1 2 3 4 10% 20%

Cash Flows: -1000 1100 ? ? ?

Techniques of Time Value of Money Determination

Compounding

The process of determining the future value (FV) of a cash flow or a series of cash flows.

Formula (Single Payment) for Numerical Solutions:

FVn = PV (1+ i)n

Where,PV = Present Value or Beginning AmountI or i = Interest RateINT = Amount of InterestFV = Future Value or Ending Amountn = Number of Years Involved in The Analysis1 = One Rupee

Formula ( Single Payment ) for Tabular Solutions:

FVn = PV (FVIFi, n)

Spread sheet (Excel)

FV (rate, nper, pmt, pv, type)

Discounting

The process of finding the present value (PV) of a future cash flow or a series of cash flows. It is reverse of compounding.

Formula ( Single Payment ) for Numerical Solutions:

FVn PVn =

(1+ i)n

Formula ( Single Payment ) for Tabular Solutions:

PVn = FV ( PVIFi,n )

Annuity

A series of equal periodic payments (PMT) made at fixed intervals for a specified number of periods

An annuity has two categories.

1. Ordinary annuity

An annuity whose payments occur at the end of each period is called an ordinary annuity

2. Annuity Due

An annuity whose payments occur at the beginning of each period is called an annuity due.

Future value of an annuity

Sum of compounded payments

Formula for determining future value of an Ordinary annuity for numerical solutions:

FVAn = PMT (1+ i )0 + PMT (1+ i )1 + PMT (1+ i )2 + . . . . + PMT (1+ i ) n-1

n= PMT ∑ ( 1 + i) n-t

t = 1

Formula for Tabular Solutions: FVAn = PMT (FVIFAi, n)

Example of an ordinary annuity

Suppose: If you deposit Rs.1000 at the end of each year for three years in a bank account @ 10% per annum interest rate, how much will you have at the end of three years.

Annuity DueFormula for Tabular Solutions: FVAn = PMT (FVIFAi, n) (1+i)

Example of an annuity due: Suppose: If you deposit Rs.1000 at the beginning of each year for three years in a bank account @ 10% per annum interest rate, how much will you have at the end of three years.

Present value of an annuity

Sum of Discounted Payments

Present value of an ordinary annuity

Formula for determining Present value of an ordinary annuity for numerical solutions:

PMT PMT PMT PVAn = + + ……. +

(1+i)1 (1+i)2 (1+i)n

= PMT ∑ (1 + i)t

t = 1

Formula for Tabular Solutions: PVAn = PMT (PVIFAi, n)

Example of an ordinary annuitySuppose you were offered a 3 – year annuity with payment of Rs. 100 @ 5% per annum. How large must the lump sum payment today be to make it equivalent to annuity?

Present value of an annuity due

Formula for Tabular Solutions: PVAn = PMT (PVIFAi, n) (1+i)n

Example: In above example if payments are made at the beginning of period, the annuity would have been an annuity due.

Perpetuities

These are the annuities which go on indefinitely or perpetually

Present Value of Perpetuities

Payment PMTPV = =

Interest Rate i

Uneven Cash Flow Streams

A series of uneven (nonconstant) periodic payments made at fixed intervals for a specified number of periods

Present Value of An Uneven Cash Flow Stream

Sum of the present values of the individual cash flows of the stream

If cash flows stream represents an ordinary annuity along with other individual cash flows then these can be determined through the annuity formula.

Formula: 1 2 n 1 1 1

PV = CF1 + CF2 +. ... …+ CFn 1+i 1+i 1+i

tn 1 n∑ CFt = ∑ CFt (PVIF i, t)t = 1 1+ i t = 1

Future Value of An Uneven Cash Flow Stream

Sum of the future values of the individual cash flows of the stream

Formula: n-1 n-2 n-t

FV = CF1 1+i + CF2 1+i +. ... …+ CFn 1+i

n-1n n∑ CFt 1+i = ∑ CFt (FVIF i, n- t)t = 1 t = 1

Different types of interest rates

1. Nominal or quoted rate

It is the interest rate normally quoted by the borrowers or lenders. It is also called annual percentage rate because it is usually interest per year.Suppose: 10% per annum or year.

2. Effective annual rate (EAR)When cash flows are compounded/ discounted frequently( more than once a year ), then to account for this effect, a new interest rate called effective annual rate is determined at which compounding/discounted takes place.Formula to calculate EAR: m

iNom EAR = 1 + 1

m

Where Here i = is the nominal, or quoted rate, while m = number of times compounding / discounting occurs per year

Note: EAR process is not applied in case of annuities.

3. Periodic interest rateThis is the interest rate actually charged by the lender or paid by the borrower each period. It can be annual percentage rate or effective interest rate.

Semi annually, Quarterly, monthly, Daily and other Compounding/Discounting Periods

Semi annually: interest is compounded or discounted twice a year so “n” is multiplied by 2 or (n x 2).ANDInterest rate (i) is divided by 2 or (i / 2)

Quarterly: n x 4 AND i / 4

Monthly: n x 12 AND i / 12

Weekly: n x 52 AND i / 52

Daily: n x 360 or 365 AND i / 360 or 365OR

effective annual rate is determined at which compounding/discounted takes place and then this new interest rate is used in the formulas of compounding and discounting for a lump sum amount.

Or The following general formula can be used for more frequent compounding/ discounting.

More frequent compounding:

Formula: mn i

FVn = PV 1 + m

More frequent discounting: FV

PVn = (1 + i / m)mn

Compounding or Discounting for any fraction of a year period

“n” is determined by dividing the number of months of year by total number of months in a year OR number of days for which amount is compounded or discounted is divided by total number of days in a year.

Suppose total compounding or discounting period is 5 months, then: n = 5/ 12 or 150 / 360

Frequent Compounding/Discounting in case of annuities: i /m; annuity payment /m and resultant new annuity is paid for the nm years.

Amortized Loans

If a loan is to be repaid in equal periodic amounts (monthly, quarterly, or annually), it is said to be amortized loan.

Suppose:A company borrows Rs. 1000 @ 6% interest rate and this load is to be repaid in 3 equal installments at the end of each of the 3 years.

Loan Amortization Schedule Format

Beginning Payment Interest Repayment RemainingAmount of principal balance (1) (2) (3) (2) - (3)=(4) (1) – (4)

Year

01

02

03

Total

Continuous Compounding and Discounting

We can keep compounding or discounting every hour, minute, second and so on continuously.

Continuous Compounding Formula:

FVn = PV ( ein )

Where: e = constant value 2.7183i = interest rate and n = number of years

Example: If Rs.500 is invested for 4 years at an interest rate of 5 percent compounded continuously, then what would be future value?

Continuous Discounting Formula:

FVn PV =

ein

Example: Rs.611 is the value of an investment after 4 years. If this value is discounted continuously at an interest rate of 5 percent, then what would be the present value?

Valuation Models

Securities

Pieces of paper that represent claims against assets such as land, Plants and equipment, commodities or other securities

Types of securities

1. Direct claim securities

Securities which have claims against the cash flows produced by real (tangible) assets

Three primary classes of direct claim securities

1. Bonds 2. Preferred stock 3. Common stock

2. Indirect claim securities or Derivatives

Those securities whose values are derived from the value of some other assets such as goodwill of a company.Example: options, futures etc.

1. Direct claim securities

General Valuation model

CF1 CF2 CFt CFn

V = + + ……… + +……. + (1+k1)1 (1+ k2)2 (1+ kt)t (1+ kn)n

n CFt ∑ t = 1 ( 1+ kt )t

BOND VALUATION

Bond

A bond is a long-term debt contract issued by a business or governmental unit which receives the selling price of bond in exchange for promising to make interest payments and to repay the principal on a specified future date.

Definition of terms frequently used in bond valuation

1. Par ValueThe par value is the stated face value of the bond2. Coupon interest rateIt is the interest rate paid by the issuer of bond to the subscriber of bond every year uptill the maturity of bond. To calculate coupon interest rate the coupon payment (Amount of interest) is divided by the par value.3. Maturity dateThe future date on which the par value is repaid to the subscriber of bond4. Call ProvisionsUsually most of the bonds have the provision whereby the issuer may payoff the par value along with the interest due before the date of maturity.5. New issues versus outstanding bondsNew issueA bond that has just been issued is known as new issueThese are usually issued at par valueOutstanding bondOnce the bond has been on the market for a while, it is an outstanding bondUsually after some period of time bond’s market value becomes much higher than the original par value at which bond was issue.

The basic bond valuation modelINT INT INT M

Bond’s =V = + + ……… + +……. +value (1+kd)1 (1+ kd)2 (1+ kd)N (1+ kd)N

N INT M ∑ + t = 1 ( 1+ kd )t ( 1+ kd )N

Formula for tabular form

VB = INT ( PVIFAkd.N ) + M ( PVIFkd.N )Changes in bond value over time

The following time line is used throughout this topic to analyze the changes in bond value over time.

Time Line:

Time: 0 1 2 3 4 55%

100 100 100 100 100 2000

1. Whenever the going rate of interest, Kd equal to the coupon rate, a bond will sell at its par value. So the value of bond will remain same after one year, two years of issue of bond or throughout the life of bond.

2. Whenever the going rate of interest, Kd falls below the coupon rate, a bond will sell above its par value. Such a bond is called a premium bond.

3. If interest rate, Kd fell below the coupon rate once, twice or many times but then remains constant for the coming years then the value of bond will decrease gradually to the par value of a bond as the maturity date approaches.

4. Whenever the going rate of interest, Kd is greater than the coupon rate, a bond will sell below its par value. Such a bond is called a discount bond.

5. The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt.

Calculation of total rate of return, or yieldA) When the going rate of interest is less than the coupon interest rate

Suppose Mr.X purchased a bond of Rs. 2000 offering Rs. 100 per year coupon interest payment, o1 year after the issue of bond with remaining maturity period of 4 years at going interest rate of 3% per year.

Solution: Now the value of bond 01 year after the issue of bond with 04 year remaining maturity period at an interest rate of 3% would be : 2148.71

Coupon interest payment 100Interest, or current yield = =

Current price of the bond 2148.71

Interest, or current yield = 0.0465 = 0.0465 x 100 = 4.653 %

Suppose Mr.Y purchased a bond of Rs. 2000 offering Rs. 100 per year coupon interest payment, from Mr. X with remaining maturity period of 3 years at going interest rate of 3% per year.

Solution: Now the value of bond after 02 years with remaining maturity period of 03 years would be: 2113.06.

Ending price – Beginning price 2113.06 – 2148.71Capital gains yield = =

Beginning price 2148.71

Capital gains yield =- 35.65 / 2148.71= - 0.0165 = - 0.0165 x 100= - 1.659 %

total return 100 – 35.65 64.35Total rate of return, or yield = = =

Beginning price 2148.71 2148.71

Total return = ( coupon interest payment + capital gain / loss )

Total rate of return, or yield = 0.0299 = 0.0299 x 100 = 2.99 %OR

Total rate of return, or yield = Interest, or current yield + Capital gains yield

Total rate of return, or yield = 4.653 - 1.659 = 2.99 %

B) When the going rate of interest is greater than the coupon interest rate

Suppose:Going rate of interest, Kd is moved to 7 %The Price of bond with 04 years maturity period is: 1864.52The price of bond with 03 years maturity period is: 1895.03

Now the total rate of return or yield is calculated as under:

Coupon interest payment 100Interest, or current yield = =

Current price of the bond 1864.52

Interest, or current yield = 0.0536 = 0.0536 x 100 = 5.3633 %

Ending price – Beginning price 1895.03 – 1864.52Capital gains yield = =

Beginning price 1864.52

Capital gains yield = 30.51 / 1864.52 = 0.01636 = 0.01636 x 100= 1.6363 %

total return 100 + 30.51 130.51Total rate of return, or yield = = =

Beginning price 1864.52 1864.52

Total return = (coupon interest payment + capital gain / loss)

Total rate of return, or yield = 0.0699 = 0.0699 x 100 = 6.999 %OR

Total rate of return, or yield = Interest, or current yield + Capital gains yield

Total rate of return, or yield = 5.3633 + 1.6363 = 6.999 %

Finding the interest rates on a bond

Yield to maturity (YTM)

The expected rate of return earned on a bond held to maturity

The following general bond valuation model can be applied to find the kd

INT INT INT MBond’s =V = + + ……… + +……. +value (1+kd) 1 (1+ kd) 2 (1+ kd) N (1+ kd) N

Yield to call

If a bond can be redeemed before maturity, it is callable, and the return investors will receive if it is called is the yield to call.

Formula:

INT INT INT Call priceBond’s =V = + + ……… + +……. +value (1+kd)1 (1+ kd)2 (1+ kd)N (1+ kd)N

N INT Call price ∑ + t = 1 (1+ kd) t (1+ kd) N

Bond’s value: Price of callable bond

Call Price: It is often equal to the par value plus one year’s interest

Yield to call: Kd

Bond Values with semiannual compounding/discounting

Time line for annual compounding/discounting

Time: 0 1 2 3 4 3%

-2148.71 100 100 100 100 2000

Now above Time line can be converted as under for semi-annual compounding/discounting

0 1 2 3 4 5 6 7 8 1.5%

-2149.71 50 50 50 50 50 50 50 50 2000

Through Financial calculator 1.5

8 -2149.71 50 2000

OR alternatively EAR (Effective annual rate) can be determined and applied to the annual compounding time line to determine the Bond Values with semiannual compounding/discounting.

Interest Rate and Reinvestment Rate Risk

Interest Rate or Price Risk

The longer the maturity of a bond, the more its price will change in response to a given change in interest rates.Suppose Kd, interest rates goes up in the market then the bond having shorter maturity are less risky than bonds having longer maturity.

Reinvestment Rate Risk

Bonds with the short maturities have the risk that the cashflows (interest payments plus maturity value) will be reinvested at lower interest rates. Add figure 7.3, page no. 298

PREFERRED STOCK VALUATION

N I PV PMT FV

Most preferred stocks entitle their owners to regular, fixed dividend payments. These payments usually last forever and if so these are called perpetuities.

Value of preferred stocks is found as under:

Dps

Vps = Kps

Where Vps = Value of preferred stock Dps = Dividend on preferred stock Kps = Required rate of return

If preferred stock is not perpetual ( it has some finite maturity period like bonds ) then it will be valued similar to way a bond is valued after replacing the following bond terms with the preferred stock terms.

VB is replaced to Vps , INT is replace to Dps , Kd is replaced to Kps and Preferred stock par value is equal to Bond’s par value or M (Maturity ).

In case of quarterly or semiannually again same treatment is given as in case of bonds valuation.

COMMON STOCK VALUATION

A Common stock is simply a piece of paper which is expected to provide: a) Dividends and b) Capital Gains

If stock is sold at a price above its purchase price, the investor will receive a capital gain.

Definition of the terms used frequently in stock valuation

Dt = Dividend the stockholders are expected to receive at the end of year t, where t = 1, 2, 3, ….n.

D0 =Most recent dividend which has just been paid and known with certainty

P0 = Actual market price of the stock today.^

Pt = Expected price of the stock at the end of each year t

^

P0 = theoretical or intrinsic value of the stock today according to a particular investor’s analysis based on estimate of stock’s expected dividend stream and riskiness of that stream and it could be above or below P0 . ^

The investor would buy the stock only if his or her estimate of P0 were equal to or greater than P0 .Marginal investors: A group of leading investors whose actions actually determines the market price.g = Expected growth rate in dividends.

Ks = minimum acceptable, or required, rate of return on the stock, considering both its riskiness and the returns.^

Ks = Expected rate of return which an investor expects to receive. ^

An investor would buy the stock only If Ks of a stock is greater than or equal to Ks .

Ks = Actual market or realized rate of return.

Dt / P0 = Expected dividend yield on the stock during the coming year. Suppose if stock is expected to pay a dividend of RS.100 per month for next 12 months and if it’s current price is Rs.1000, then the expected dividend yield is: 100 / 1000 = .10 and in percent .10 x 100 = 10 %

^ P1 – P0

= Expected capital gain yield on the stock during coming yearP0

Suppose if stock sale for 1000 today and if its price is expected to rise to 1050 at the end of 01 year, then: ^Expected capital gain = P1 – P0 = 1050 – 1000 = 50 and expected capital gain yield = 50 / 1000 = .05 and in percent .05 x 100 = 5 % ^Expected total return = Ks = Expected dividend yield (Dt / P0 ) plus expected ^capital gain yield (P1 – P0 / P0 ). 10 % + 5 % = 15 %Common Stock Valuation Models

Usually the investors buy the stocks of a company with the intention of holding it forever so unless a company is liquidated or sold to another concern the cashflows consist only of the dividend streams. Therefore the value of common stock is determined as the present value of the expected dividend streams.

A company may pay their shareholders continuously equal or unequal dividends in different period of time. In this regard valuation of common stock is discussed as under:

Stocks with Zero Growth

The dividends expected to be paid to the shareholders do not grow at all and they are paid an equal constant dividend every year.

Means D1 = D2 = D3, and the equation is given as under:

^ D1 D2 D3

P0 = + + ……… …. + (1+ks)1 (1+ ks)2 (1+ ks)∞

Usually dividends on common stocks are paid for an indefinite period of time so dividend on common stock is considered as perpetuity,

Formula: ^ Dt P0 =

ks

^Example: D = 1.15 , ks = 13.4% then P0 = 8.58

^ Dt 1.15 ks = = = 0.134 = 13.4 % P0 8.58

So expected rate of return can be same as the minimum required rate of return or it may differ.

Normal or Constant Growth Stocks Valuation

The dividends of most companies are expected to grow every year

If the dividends grow at some constant rate then the following valuation model is used:Formula: ^ D0 ( 1 + g ) D1

P0 = = ks – g ks – g

Where: g = Expected constant dividend growth rate every year.And g = Nominal gross domestic product growth rate ( Real GPD + Inflation )

Example: D0 = 100 , ks = 20% , g = 10% then:

Jan,01,08 Jan,01,09 Jan,01,10 Jan,01,11 Jan,01,12 20 %

100 110 121 133.1 144.41

10% 10% 10% 10%

^ 100 (1 + .10) 110 P8 = = = Rs.1100

.20 – .10 0.10While;Expected rate of return = Expected Expected growth

Dividend Yield + rate or Capital Gain yield ^ D1 ks = + g P0

110+ 10 = 10% + 10 %

1100

= 20 %Suppose above analysis has been conducted on January, 01, 2008 when P0 = 1100 is the stock price. And D1 = 110 is the dividend expected at the end of

2008. Now what is the expected stock price at the end of 2008 or beginning of 2009?Solution:

^ D0 ( 1 + g ) D1

P0 = = ks – g ks – g

^ 110 (1 + .10) 121 P9 = = = Rs.1210

.20 – .10 0.10 Expected rate of return = Expected Expected growth

Dividend Yield + rate or Capital Gain yield

^ D2 Ending price - Beginning Price ks = + P0 Beginning Price

121 1210 - 1100 +

1210 1100

1100.10 + = 0.10 + 0.10 = 0.20 = 0.20 x 100 = 20 % 1100 Thus for a constant growth stock following conditions must hold:

1. The dividend is expected to grow forever at a constant rate.

2. The stock price is also expected to grow at this same rate.

3. The expected dividend yield is a constant.

4. The expected capital gains yield is also a constant, and it is equal to g. ^5. The expected total rate of return, ks, is equal to the expected dividend yield ^plus the expected growth rate; ks = dividend yield + g.

Non-Constant Growth Stock’s Valuation

During early part of life a firm’s growth rate is much faster than that of economy, then matches with economy and finally slower than that of economy. These firms are called “Super normal growth firms”.

To calculate value:

Find the PV of the dividends during the period of non-constant growth through following formula:

^ D0 (1 + g) D1 (1 + g) Dm-1 (1 + gm) P0 = + + ……… …. +

(1+ks)1 (1+ ks)2 (1+ ks)m Where m = the length of the supernormal growth period.Suppose total super normal growth period is 3 years then Dm-1 = 3-1= D2

Find the price of the stock at the end of the non-constant growth period, at which point it has become a constant growth stock, and discount this price back to the present. Use the formula of constant growth stock valuation.Formula: ^ Dm ( 1 + g ) Dt

P0 = = ks – g ks – g

^Add these two components to find the intrinsic value of the stock, P0

through the following formula:

^ D0 (1 + g) D1 (1 + g) Dm-1 (1 + gm) Dm (1 + gn) P0 = + + …. + +

(1+ks)1 (1+ ks)2 (1+ ks)m ks – gn

Where gn is the length of the normal or constant growth rate.Example: Snyder Computer Chips inc. is experiencing a period of rapid growth. Earnings and dividends are expected to grow at a rate of 15 percent during the next 2 years, at 13 percent in the third year, and at a constant rate of 6 percent thereafter. Snyder’s last dividend was 1.15 and the required rate of return on the stock is 12 percent. ^ ^Required: calculate the vale of stock today. Calculate P1 and P2 .

Determinants of Market interest rates “K”

K = kRF + DRP + LP + MRPK _ the quoted, or nominal, rate of interest on a given security. There are many different securities, hence many different quoted interest rates.K* _ the real risk-free rate of interest. k* is pronounced “k-star,” and it is the rate that would exist on a riskless security if zero inflation were expected. kRF _ k* _ IP, and it is the quoted risk-free rate of interest on a security such as a U.S. Treasury bill, which is very liquid and also free of most risks.Note that kRF includes the premium for expected inflation, because kRF _ k* _ IP.

IP _ inflation premium. IP is equal to the average expected inflation rate over the life of the security. The expected future inflation rate is not necessarily equal to the current inflation rate, so IP is not necessarily equal to current inflation as reported in Figure

DRP _ default risk premium. This premium reflects the possibility that the issuer will not pay interest or principal at the stated time and in the stated amount. DRP is zero for U.S. Treasury securities, but it rises as the riskiness of issuers increases.LP _ liquidity, or marketability, premium. This is a premium charged by lenders to reflect the fact that some securities cannot be converted to cash on short notice at a “reasonable” price. LP is very low for Treasury securities and for securities issued by large, strong firms, but it is relatively high on securities issued by very small firms.MRP _ maturity risk premium. As we will explain later, longer-term bonds, even Treasury bonds, are exposed to a significant risk of price declines, and a maturity risk premium is charged by lenders to reflect this risk.

More refer P.no. 104 to 109, Brigham, 8th edition.

RISK AND RETURN

Risk

The chances of occurrence of an unfavorable event

Risk can be analyzed in two ways: 1. Stand Alone Risk 2. Portfolio Risk

Stand Alone Risk

Risk is analyzed on an asset in isolation. The risk an investor would face if he or she holds only this one asset

Investment Risk

Probability of actually earning less than the expected return

Probability Distribution

Probability

The probability of an event is the chance that the event will occur

If all possible events or outcomes are listed and if a probability is assigned to each event, the listing is called a probability distribution

Expected Rate of Return ^The k is a weighted average of the possible outcomes (the ki values) with each outcome’s weight being its probability of occurrence.Formula: ^

Expected Rate of Return = k = p1k1 + p2k2 + . . . . . + pnkn

n = ∑ piki t = 1

Example: Suppose there are 30 percent chances of strong demand, 40 percent chances of normal demand and 30 percent chances of week demand of a company’s product. The expected rates of returns during these demands are 20 percent, 15 percent, 10 percent respectively.

Required: Calculate expected rate of return?Measuring Stand-Alone Risk: The Standard Deviation

A common definition of risk is stated as: “the tighter the probability distribution of expected future returns, the smaller the risk of a given investment”.

“Standard Deviation” is the measure used to measure the tightness of the probability distribution of expected future returns.

Smaller the standard deviation, the tighter the probability distribution and accordingly the lower the riskiness of the stock

n ^

Variance = σ2 = ∑ (ki - k)2 Pi t = 1

n ^

Standard Deviation = σ = ∑ (ki - k)2 Pi t = 1

^

Calculation of mean (k) and standard deviation (σ) when only past data regarding the expected rate of return is available: ^

Expected Rate of Return = k = k1 + k2 + . . . . . + kn

n n

∑ ki ^ t = 1

K = N

n Standard Deviation = σ = ∑ ( kt - kAVG )2

t = 1 n – 1

Example: ST – “ a” and “ b”: chap 4, P.no: 181

Empirical rule of variability

This is a rule of thumb used to measure what is the probability of level of spread of the data from mean. Such data follows the mound bell – shaped distribution curve. This rule describes the chances (Probability ) that expected rate of return will fluctuate or vary with a certain range.

_ _General formula: ( k – σ , k + σ )

Its rules are explained as under:

A) Of the area under the curve, 68.26 percent is within + 1σ of the mean, indicating that the probability is 68.26 percent that the outcome will be _ _within the range of k – 1σ , k + 1σ

B) Of the area under the curve, 96 percent is within + 2σ of the mean, indicating that the probability is 96 percent that the outcome will be _ _within the range of k – 2σ , k + 2σ

C) Of the area under the curve, 99 percent is within + 3σ of the mean, indicating that the probability is 99 percent that the outcome will be _ _within the range of k – 3σ , k + 3σ