Finanial Management-1 (1)

8/18/2019 Finanial Management-1 (1)

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Firm & Financial Management

Covers chp. 1


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The Firm

• Association of people for the provision of

goods and services with an intention ofmaking a profit.

• Legal forms are:- – Sole Proprietorship

– Partnership

– corporations


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Corporate Structure

Sole Proprietorships

Corporations

Partnerships

Limited Liability

Corporate tax on profits +

Personal tax on dividends

Unlimited Liability

Personal tax on profits


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ENVIRONMENTAL FACTORS


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What can go wrong ….


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The counter reaction


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• Important for Financial Manager to

understand the External Environment inwhich he has to operate.

• Some of the dominant factors are :- – Government/Financial Market Regulations

– Forms of Business organisation.

– Taxation etc.


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• Regulatory Framework

– FERA/FEMA

– MRTP/COMPETION POLICY

– COMPANY’S ACT ( salient features)


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FEMA• FEMA was introduced in 1998, with a

motive to “facilitate exchange market inIndia”.

• There was a regime shift from “exchange

control to exchangemanagement”.

• 1993,exchange rate of rupee was made

market determined. 1994, accepted articleVIII of IMF.


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Objective/ goal


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Role of The Financial Manager

Financial

manager

Firm's

operations

Financial

markets

(1) Cash raised from investors

(1)

(2) Cash invested in firm

(2)

(3) Cash generated by operations

(3)

(4a) Cash reinvested

(4a)

(4b) Cash returned to investors

(4b)


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The Goal of Financial

Management

• What are firm decision-makers hired to do?

“ General Motors is not in the business of makingautomobiles. General Motors is in the business

of making money.”-- Alfred P. Sloan


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Goal Of FinancialManagement• What should be the goal of a corporation?

–Maximize profit?

–Minimize costs?

–Maximize market share?

–Maximize the current value of the company’sstock?


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The Goal• Maximize profit – Are we talking about long-runor short-run profits? Do we mean accountingprofits or some measure of cash flow?

• Minimize costs – We can minimize costs todayby not purchasing new equipment or delayingmaintenance, but this may not be in the best

interest of the firm or its owners.• Maximize market share – This has been astrategy of many of the dotcom companies. Theyissued stock and then used it primarily for

advertising to increase the number of “hits” totheir web sites. Even though many of thecompanies have a huge market share (i.e. Amazon) they still do not have positive earnings

and their owners are not happy (1996).


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Maximize the current value of the

company’s stock• There is no short run vs. long run here. The stock

price should incorporate expectations about the

future of the company and consider the trade-offbetween short-run profits and long-run profits.• The purpose of a for-profit business should be to

make money for its owners. Maximizing the

current stock price increases the wealth of theowners of the firm.• This is analogous to maximizing owners’ equity

for firms that do not have publicly traded stock.• Non-profits can also follow the same principle, but

their “owners” are the constituencies that theywere created to help.


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Manager’s dilemma


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Indian Financial System• Topics to be covered …

– Capital market

– Money Market

– Banking / developmental Institutions.


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Common Stock

• Ownership in a Corporation

• One vote per share.

• Have a residual (last) claim on income

and assets in liquidation, thus ariskier position than bonds andpreferred stockholders.

• Shareholders’ liability for the debtsof the corporation is limited to theirinvestment in the common stock.


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Common Stock(concluded)

• Shareholders’ return is derived from dividends

declared by the board of directors and frommarket appreciation in the value of the stock.

• Common shareholders may vote their shares to

elect the members of the board of directors.• Members of the board of directors can be

elected by cumulative voting or straight voting.


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Preferred Stock

• A Preferred or prior claim on earnings and

assets compared to common stock

• Dividends paid ahead of common if declared.

• Preferred stockholders are usually excludedfrom voting for board of directors and

shareholder issues.

• Many corporations buy preferred stock.


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Convertible Securities• Convertible preferred stock -- convertible to

common stock at specific common price ornumber of shares (conversion ratio). – Dividends received until conversion

– Investor may participate in growth of firm.

• Convertible bonds -- convertible to commonstock at specific common price or number ofshares (conversion ratio).

– Pays fixed bond rate until conversion. – Provides potential for higher returns for investors.


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Primary Market for Equities

• The first time shares are sold in the market is an

unseasoned offering or an initial public offering(IPO); additional shares may be sold later as aseasoned offering.

• Equities may be: – Sold directly to investors by the firm.

– Purchased and sold at a higher price (underwriter’sspread) by investment bankers in an underwritten

offering. – Sold to existing shareholders in a rights offering.


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Primary Market for Equities(concluded)

• The size of the underwriter’s spreaddepends on the underwriter’s level ofuncertainty concerning the shares’ marketprice.


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The Secondary Market forEquity Securities

• Subsequent Trading in Securities after

primary issue• Stock may trade on:

– Exchanges.

– Over the counter

• Provides investor liquidity


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The Secondary Market forEquity Securities (concluded)

• Stable prices are related to the extent of: – Breadth of the market or the number of varied traders

of the stock.

– Depth of the market or the extent to which there are

conditional orders to buy and sell below and abovethe current price, respectively.

– Resiliency of the market or the ability of the market toattract buyer/sellers when the stock pricesdecreases/increases, respectively.


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Secondary Markets• Bring Buyers/ Sellers Together Four Ways:

– A buyer may incur search costs and find a seller

on their own, called a direct search. – A broker may bring buyer and seller together,

charging a commission.

– A dealer may sell/buy (bid/ask) securities from aninventory of securities, reducing search costs.The dealer’s return is the bid/ask spread.

– An auction market allocates the selling shares tothe highest bidder, providing a buyer/seller.


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The Size of Dealer Bid/askSpreads:

• are proportionately higher for low priced

stocks due to fixed costs of operations.• are higher for trades of a few shares.

• are higher for a large block trade; a liquidity

service is performed.• are narrower with more frequent trading,

where the costs of providing liquidity are less.

• are wider with traders with insider information,where the dealer may have to incur the costof price discovery, or buying high, selling low!


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Inventory model


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Capital Market• Defined as : the market of financial assets

that has long or indefinite maturity.• Nerve centre of the industrial development

of any economy.

• SEBI regulates it.


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Composition/Structure of Capital

Market

VC

FIIs

CB MF

IFI

DFI

P & S

CM

HEREHERE:

P & S : Primary/sec.marketsDFI:developmentfinancial inst.IFI:Investment fin. Inst.MF: Mutual FundsCB: commercial Banks


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Transactions


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Challenges & SEBI• SEBI was set up in 1988, but was given a

statutory recognition in 1992 on therecommendation of the Narasimhan Committeereport.

• The ‘Strategic action plan’ has identified 4 key

spheres• Investors – firms-market-regulations• The Sebi Act(1992) was amended at oct 02.• Sebi Appellate Tribunal (SAT).• Penalty Max of 5 lacs.• Board must comprise of : a chairman, 2 Min. of

Fin,1 from RBI,5 others (3 whole time Director)


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Hiccups• Efficiency

• Insider trading / information efficiency• Volatility

• Liquidity• Reach


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Rs

. 1

Billion

etan Parekh (K10 stocks)2001

Rs

. 0.77

Billion

BPL

,Videocon

,Sterlite1998

Rs

. 7

Billion

CRB Group

:C

.R

.Bhansali1997

Rs

. 61.8

Million

Sesa Goa

,Rupangi Impex

&Magan Industries Ltd

1995

Rs

. 170

Million

M

.S

.Shoes

: ( Pawan Sachdeva

)manupulated the

share prices before a Rights issue

1994

Rs

. 54

Billion

Harshad Mehta

:the market went up by 143

between Sept 91 & Apr 92

1992

Amount

involved Events ( stock market crisis ) Date


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Electronic Communication Networks

Nasdaq

Reuters

Instinet

Strike

REDIBook

Archipelago

BRUT

NextTrade

TradeBook

ISLAND

Attain

JP Morgan

Goldman Sachs

Merrill Lynch

Sal Smith Barney

Heine

Herzog

DLJ

Lehman

PaineWeber

Bear Stearns

SLK

TD WaterhouseFidelity

Schwab

Townsend

South Western SecGary Putnam

E-Trade

CNBC

Morgan stanley Dean Witter

ASC Sunguard

Knight Trinkmark

Bloomberg

PIM

All Tech

TA Associates

LVMH

Datek

Platforms for Internalizationby Broker/Dealer and Banks


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Daily Returns on BSE Sensex(1995-2004)

-15

-10

-5

0

5

10

3-

Jun-

96

25-

Oct-

96

21-

Mar-

97

19-

Aug-

97

12-

Jan-

98

9-

Jun-

98

2-

Nov-

98

24-

Mar-

99

17-

Aug-

99

10-

Jan-

00

7-

Jun-

00

31-

Oct-

00

26-

Mar-

01

20-

Aug-

01

17-

Jan-

02

13-

Jun-

02

8-

Nov-

02

4-

Apr-

03

29-

Aug-

03

20-

Jan-

04

5-

Jul-

04

25-

Nov-

04

Date

D a i l y R e t u r n s ( % )

BSE

Volatility clustering

Volatility


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14th – 17th May’04

10:19 PM 17/05/2004

INDIAN STOCK MARKET CRASH (Times of India)

Indian stocks were in virtual free-fall on Monday, wiping out 40 billion dollars

in market value, amid frenzied selling on fears a new Congress-ledgovernment will slow the pace of reform in Asia's fastest-growing economy.

The Bombay Stock Exchange and National Stock Exchange suspended

trading after their benchmark indices fell 15.5 percent and 17.5 percent,respectively. Both racked up their biggest point drop ever and sank to their

lowest levels since the Big Bull crisis.


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To conclude…• Financial management is more influence

by external factors than firm specificproblems

• CFOs/CEOs are expected to add value tothe investments trusted upon them ratherthan just showing profits .

• Capital market in India is volatile andshows seasonality.


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Time Value of Money (contd.)

Session # 3

Financial Management - I


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Problem set #1 : solutions1. Determine the future values utilizing a time preferencerate of 9 %:

(i) The future value of Rs. 15,000 invested now for a period

of 4 yrs.

(ii) The future value at the end of 5 yrs of an investment ofRs 6000 now and of an investment of Rs. 6000 one

year from now.(iii) The future value at the end of 8 years of an annualdeposit of Rs.18,000 each year.

(iv) The future value at the end of 8 years of an annualdeposit of Rs. 18000 at the beginning of each year.

(v) The future value at the end of 8 years of a deposit of Rs18000 at the end of the first four years and withdrawalof Rs.12, 000 per year at the end of year five throughseven.


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Solution # 1• (i) time preference (discount rate) = 9%

investments = 15,000

time period = 4 yrs.

CVF(4,9%) = 1.4116 (appox.)

FV = 15,000*(1.09)4 = 15,000* 1.4116

= 21,173.72(ii) Investments = 6000 (now) & 6000( 1 yr after)

period (eoy) = 5 yrs

compouning period = 5 & 4 yrsCVF = 1.5386 & 1.4116

FV = 9231.74 & 8469.49


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Solution # 1• (iii) Annual investments (eoy) = 18,000

time period = 8 yrs.CVAF = 11.0285 (appox.)

FV = 18,000* 11.0285 = 198,513

(iv) Investments (b0y)= 18000

period = 8 yrs

CVAF (annuity due) = 12.0210FV = 18000 * 12.0210 = 216378


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Solution # 1• (v)

73318.65707073318.66compounding value at the end of 8

yr


yr


yr


yr

82316.32compounding value at the end of 4

yr

18000annual investment for 4 yrs

Balancewithdrawal


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Solution#2• Rate of interest = 15 %

sum received now = 100period = 10 yr

PVAF = 5.0188

therefore 1/ PVAF = 0.1993100 = 5.0188A

Hence A = .1993*100= 19.93

For Annuity due , PVAF(1+.15) = 5.7716Hence A = 100/5.7716 = 17.33


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Solution#3• Needed future sum after 15 yr= 300,000

periods = 15 yrsinterest rate = 12%

CVAF = 37.28Therefore , A*37.28 = 300000

A = 8047.22


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Solution#4

Price of the house = 500,000Cash payment = 100,000Balance = 400,000Installment period = 20 yrsInterest rate = 12%PVAF = 7.4694 A*7.4694 = 400,000

A = 53551.51 (appox)

RepaymentinterestInstallmentBalanceyear


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47,813.835737.6853,551.510.1520

42,690.9210860.5953,551.5147813.9819

38,116.8915434.6253,551.5190504.9018

34,032.9419518.5753,551.51128621.7917

30,386.5623164.9553,551.51162654.7416

27,130.8526420.6653,551.51193041.2915

24,223.9829327.5353,551.51220172.1414

21,628.5531922.9653,551.51244396.1213

19,311.2134240.3053,551.51266024.6712

17,242.1536309.3653,551.51285335.8711

15,394.7738156.7453,551.51302578.0210

13,745.3339806.1853,551.51317972.809

12,272.6241278.8953,551.51331718.138

10,957.7042593.8153,551.51343990.757

9,783.6643767.8553,551.51354948.456

8,735.4144816.1053,551.51364732.105

7,799.4745752.0453,551.51373467.514

6,963.8146587.7053,551.51381266.983

6,217.6947333.8253,551.51388230.802

5,551.5148000.0053,551.51394448.491

400000.000


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Solution # 5• Answer??


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Other forms of Annuity• Perpetuity: it is an Annuity that occurs

indefinitely. (i.e. without a maturity)P = A/I

E.g. , an investor expects a perpetual sum ofRs 500 annually from his investments.What is the present value of this perpetuity

if the interest rate is 10%.soln : P = 500/0.10 = Rs 5000.


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Other forms of AnnuityPresent value of a growing Annuity: the

periodic cash flows grow at a compoundingrate. E.g. Arun gets an annual salary of Rs1,00,000 with the provision for an annual

increment of 10%.P = A/(1+g)[ ( 1-(1+i*)-n) /i*]

Where, i* = (i-g)/(1+g)


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An Example…• A dividend stream commencing one year

hence at Rs 66 is expected to grow at10% annum for 15 Yrs and then ceases. Ifthe discount rate is 21%, what is the PV of

the expected series.soln: P = A/(1+g)[ ( 1-(1+i*)-n) /i*]

Where, i* = (i-g)/(1+g)

i* =(0.21-0.10)/1.10 = 0.10 A/(1+g) = 66/1.10 = 60


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Example (contd.)• Refer to table of PVAF (15,10%)= 7.606

P = 60 * 7.606 = Rs 456.36


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Some terms• Capital Recovery: it is the annuity of an

investment for a specified time at agiven rate.

• If you make an investment today for a

given period of time at a specified rateof interest you may like to know theannual income generated from it.

• The reciprocal of PVAF is CRF ( capitalrecovery factor).


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An Example…• If you plan to invest Rs 10,000 today for a period

of 4 years. The interest rate is 10%. How mushincome per year should you receive to recoveryour investment?

• Soln : PV = A (PVAFn,i) A = PV (CRFn,i) A = 10,000 (0.3155) = Rs 3155


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problems• PV = A (PVAF n,i)

using the given values, we obtain..10000 = A (2.531)

A = Rs 3951i.e. paying Rs 3951 each year, for three yrs ,

you shall completely pay off your loan with

9% interest rate.


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problems• Exactly ten yrs from now Sri Chand will

start receiving a pension of Rs 3000 ayear. The payment will continue for 16 yrs.How much is the pension worth now, if Sri

Chand’s interest rate is 10%?


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problemsSoln: Sri Chand will receive the first payment atthe end of 10th Year and last payment at the endof 25th year.

Assuming an Annuity for 25 yrs @ 10%, PVAF25= 9.077 but we know that he will not receive

anything till the end of 9th yr. therefore wesubtract PVAF @ 10% for 9 yrs.

i.e. PVAF25 – PVAF9 = 9.077 – 5.759 =3.318

Therefore, the present value of the pension will be= 3.318* 3000 = Rs 9954


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problems• How long will it take to double your money

if it grows at 12% annually ?• If a person deposits Rs 1000 on an

account that pays him 10% for the first 5

yrs and 13% for the following eight yrs,what is the annual compound rate ofinterest for the 13 yr period?


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problems• Amount = 1000

interest rate for (1-5)yr = 10%interest rate for (6-13) yrs = 13%

compound value for 13 yr period= 1000 * (1.15)5 * (1.13)8 = 4281.45

the compound interest rate will be

= [ ( 4281.45/1000)1/13 – 1 ] = 11.84%


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problems• A finance company makes an offer to

deposit a sum of Rs 1100 and thenreceive a return of Rs 80 p.a. perpetually.Should this offer be accepted if the rate of

interest is 8% ? Will the decision change ifthe rate of interest is 5%?


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Problems• The person should accept the offer if the

present value (PV) of the perpetuity ismore than the initial deposit of Rs 1100

If the rate of interest is 8%

PV = A/i = 80/.08 = RS 1000 ( reject)

If the rate of interest is 5 %

PV = 80/.05 = Rs 1600( accept)


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problems• What is the minimum amount which a

person should be ready to accept todayfrom a debtor who otherwise has to pay asum of Rs 5000 today, Rs 6000, Rs 8000

and Rs 9000 and Rs 10000 at the end ofyr 1,2,3,4 respectively from today. Therate of interest is 14%.

problems


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• Soln : the minimum amt. is the PV of the series of amt.due ,discounted at 14% , as follows:

28409

59200.592100004

60750.67590003

61520.76980002

52620.87760001

5000150000

PVPVF(n,14%) Amt dueyear


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problems• A company is expected to declare a

dividend of Rs2 at the end of first yearfrom now and this dividend is expected togrow 10% every year . What is the PV of

this stream of dividends if the rate ofinterest is 15%?


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problems• Soln : PV = A /(i - g)……………. Eqn #1

it is a perpetuity which is growing @ 10% p.a.The formula

P = A/(1+g)[ ( 1-(1+i*)-n) /i*]

Here, n = ∞ , hence we get Eqn # 1Solving for PV we obtain,

PV = 2/(0.15-0.10) = Rs 40


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summary• The concept of TVM refers to the fact that

the money received today is different in itsworth from the money receivable sometime in the future.

• Some business & personal decisions likeCapital recovery, Loan Amortization ,returns from bonds etc can be effectivelydetermined using TVM.


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Risk & Returns


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Topics

• Concept of Risk & Return•Sources of risk

•Portfolio and risk•CAPM ( Capital Asset Pricing Model)


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Concept of returns

•Required Returns (Ex post) arestatistically derived from historicalobservations.

•Expected Returns (Ex ante) are

statistically derived expected values fromfuture estimates of observations.


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Probability & Returns

•In the world of uncertainty , the expectedreturns may or may not materialize.

• The expected rate of return for anyasset is the weighted average rate ofreturn using the probability of each rate of

return as the weight.

•E.g.:- consider the range of returns under thepossible states of economic conditions. What


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prate of return can you expect ?

6.00

-1.500.25-6.0Decline

0.250.251.0Stagnation

2.620.2510.5Expansion

4.630.2518.5Growth

E(R)

(4)=(2)*(3)

Probability

(3)

Rate of

Return( )

(2)

Economic

conditions (1)


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Risk & Returns

• Risk : the chance that the actualoutcome from an investment will differfrom the expected outcome.

•Investment decisions always involve atrade off between risk & return.


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Sources of Risk

• Factors which make any financialasset risky are:

1. Business Risk: industry/environmental factors involved.

2. Market Risk: variability in returns due

to the fluctuations in the securitiesmarket.


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Sources of Risk

3. Liquidity Risk: ease with which asecurity can be bought or sold withoutmuch transaction cost.

4. Financial Risk: influenced by the

degree of financial leverage


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Sources of Risk

5. Interest Rate Risk: changes in theinterest rates.

6. Inflation Risk: change in the inflationinfluences the purchasing power of

the investors.


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•E.g. :- Jenson & Nicholson, a paint company,has the following dividend per share (DIV) and


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the market price per share (AMP) for the period87-92

154.002.01992

100.002.01991

67.002.01990

30.881.531989

20.751.531988

31.251.531987

AMP (Rs)IV (Rs)ear

Calculate the annual returns(5yrs).how risky is theshare?

solution


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Expected Return = = + −r Div

P

P P

P

1

0

1 0

0

R88 = [1.53 + 20.75-31.25]/ 31.25 = -0.287

Similarly,

R89 = 56.2%,R90 = 123.4%,R91 = 52.2%,R92 = 57%

Rm = 1/5 {-28.7+56.2+123.4+52.2+57} = 52%

To determine the riskness of the share, we calculate the

variation of the returns :

σ2 =1/5{ (-28.7-52)2 + (56.2-52)2 + (123.4 – 52)2 + (52.2-52)2 +(57-52)2} = 2330.63 or S.D = 48.28

Probability distributions (Rev.)


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• A listing of all possible outcomes, and the

probability of each occurrence.• Can be shown graphically.

Expected Rate of Return

Rate of Return (%)100150-70

Firm X

Firm Y

Investment alternatives


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43.0%30.0%-20.0%50.0%8.0%0.1Boom

29.0%45.0%-10.0%35.0%8.0%0.2 Above avg

15.0%7.0%0.0%20.0%8.0%0.4 Average

1.0%-10.0%14.7%-2.0%8.0%0.2Below avg

-13.0%10.0%28.0%-22.0%8.0%0.1Recession

MP ACCHNCHLLGOIProb.Economy

Return: Calculating the expected return


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for each alternative

17.4%(0.1)(50%) (0.2)(35%)(0.4)(20%)

(0.2)(-2%)(0.1)(-22.%)k

Pk k

returnof rateexpectedk

HT

^

n

1i

ii

^

^

=+ ++

+=

=

=

∑=

Summary of expected returns for


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all alternativesExp return

HLL 17.4%Market 15.0% ACC 13.8%

GOI 8.0%HNC. 1.7%

HLL has the highest expected return, and appearsto be the best investment alternative, but is itreally? Have we failed to account for risk?

Risk: Calculating the standard deviation

f h lt ti


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for each alternative

deviationStandard=σ2 Variance σ==σ

i

2n

1ii

P)k ̂k (∑=

−=σ

Standard deviation calculation


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σGOI = 0%

σHLL = 20%

σHNC = 13.4%

σ ACC = 18.8%

σM =15.3%

Comparing standard deviations


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ACC

Prob. GOI

HLL

0 8 13.8 17.4 Rate of Return (%)

Comments on standard deviation

f i k


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as a measure of risk• Standard deviation (σi) measures total, or stand-

alone, risk.

• The larger σi is, the lower the probability thatactual returns will be closer to expected returns.

• Larger σi is associated with a wider probability

distribution of returns.• Difficult to compare standard deviations, becausereturn has not been accounted for.

Comparing risk and return


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15.3%15.0%Market

18.8%13.8% ACC*

13.4%1.7%HNC*

20.0%17.4%HLL

0.0%8.0%GOIs

Risk, σExpected returnSecurity

Coefficient of Variation (CV)


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A standardized measure of dispersion about theexpected value, that shows the risk per unit of

return.

^

k

MeandevStd CV σ ==

Risk rankings,

b coefficient of ariation


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by coefficient of variationCV

GOI 0.000HLL 1.149HNC. 7.882 ACC 1.362

Market 1.020

HNC has the highest degree of risk per unit ofreturn.

HLL, despite having the highest standarddeviation of returns, has a relatively average CV.

Illustrating the CV as a measure

of relative risk


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of relative risk

σ A = σB , but A is riskier because of a larger

probability of losses. In other words, the sameamount of risk (as measured by σ) for less returns.

0

A B

Rate of Return (%)

Prob.

ACC Ltd courtesy: J P Morgan

300 ACC Ltd (250.800, 255.100, 248.300, 253.250, +3.20000)


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2002O N D 2003 M A M J J A S O N D 2004 M A M J J A

0000

000000000000

x100

150

200

250

Capital Market Theory


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Capital Market Theory• Dominant principle

• Markowitz’s Portfolio theory• Two asset portfolio

• Efficient frontier

• The CAPM

The Dominance Principle


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The Dominance Principle• States that among all investments with a

given return, the one with the least risk isdesirable; or given the same level of risk,the one with the highest return is most

desirable.

Dominance Principle Example


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Dominance Principle Example• Security E(Ri) σ

ATW 7% 3%GAC 7% 4%YTC 15% 15%

FTR 3% 3%HTC 8% 12%• ATW dominates GAC

• ATW dominates FTR



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Capital Market TheoryMarkowitz Model

Markowitz model generates an efficient

frontier,which is a set of efficient portfolios.

• A portfolio is said to be efficient if it offers the

maximum expected return for a given level ofrisk or minimum risk for a given level of expectedreturns.

Markowitz Diversification


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Markowitz Diversification• Although there are no securities with

perfectly negative correlation, almost allassets are less than perfectly correlated.Therefore, you can reduce total risk (σp)

through diversification. If we considermany assets at various weights, we cangenerate the efficient frontier.

Risk revisited


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Risk revisited• Unsystematic Risk

– ... is that portion of an asset’s total risk whichcan be eliminated through diversification

• Systematic Risk

– ... is that risk which cannot be eliminated – Inherent in the marketplace

Diversification


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Diversification

Unsystematic

Risk

1 5 10 20 30

Risk

Systematic Risk

No. of Assets

75% of Co.

Total Risk

25% of Co.Total Risk

Efficient Frontier


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Efficient Frontier • The Efficient Frontier represents all the

dominant portfolios in risk/return space.

• There is one portfolio (M) which can beconsidered the market portfolio if we

analyze all assets in the market. Hence,M would be a portfolio made up of assetsthat correspond to the real relative weights

of each asset in the market.

Efficient Frontier (continued)


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Efficient Frontier (continued)• Assume you have 20 assets.

• you can calculate all possible portfoliocombinations.

• The Efficient Frontier will consist of those

portfolios with the highest return given thesame level of risk or minimum risk giventhe same return (Dominance Rule)

Expected

PortfolioReturn, kp Efficient Set


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, p

Risk, p

Feasible Set

Feasible and Efficient Portfolios

• The feasible set of portfolios represents allportfolios that can be constructed from a


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p pportfolios that can be constructed from agiven set of stocks.

• An efficient portfolio is one that offers:

– the most return for a given amount of risk, or

– the least risk for a give amount of return.

• The collection of efficient portfolios is calledthe efficient set or efficient frontier .

IB2 IB1

ExpectedReturn, k

p


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I A2I A1

Optimal PortfolioInvestor A

Optimal PortfolioInvestor B

Risk pOptimal Portfolios

Selection of the Optim al Portfolio


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p

H ow w ill the investor go about selecting theoptimal portfolio?

Investors will have to consider theirindifference curves… .

Put the investor’s indifference curves andthe efficient frontier and go for the portfolioon the farthest northw est indifference curve,w here the indifference curve is tangent to theefficient frontier.


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Indifference Curves for a Risk-Averse Investor


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σ

1 I 2

I

E(R)

3 I

4 I

Tangent Portfo l io

Portfolio Selection for a Highly Risk-Averse

Investor


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σ

1 I

2 I E(R)

3 I 4

I

Tangent Portfo lio

e opt ma port o os p otte a ong t e curve ave t e

highest expected return possible for the given amount

of risk. (source:investopedia.com)


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What is the CAPM?


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The CAPM is an equilibrium model that

specifies the relationship between risk andrequired rate of return for assets held in well-diversified portfolios.

Derived using principles of diversification withsimplified assumptions

Markowitz, Sharpe, Lintner and Mossin are

researchers credited with its development.

Slope and Market Risk Premium


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M = Market portfolior f = Risk free rateE(r M) - r f = Market risk premium

= Slope of the CAPMM

E(r) = r f + (E (r M) – r f )ß

What are the assumptionsof the CAPM?


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• Investors all think in terms of a single holding period.

• All investors have identical expectations.

• Investors can borrow or lend unlimitedamounts at the risk-free rate.

(More...)

• There are no taxes and no

What are the assumptions

of the CAPM?


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• There are no taxes and notransactions costs.

• All investors are price takers, that is,investors’ buying and selling won’t

influence stock prices.• Quantities of all assets are given and

fixed.

What impact does kRF

have onthe efficient frontier?


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• When a risk-free asset is added to thefeasible set, investors can createportfolios that combine this asset with a

portfolio of risky assets.• The straight line connecting kRF with M,

the tangency point between the line and

the old efficient set, becomes the newefficient frontier.

Efficient Set with a Risk-Free Asset


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M

Z

. AkRF

M Risk, p

The Capital MarketLine (CML):

New Efficient Set

. .B

kM^

ExpectedReturn, kp

What is the Capital Market Line?


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• The Capital Market Line (CML) is all

linear combinations of the risk-free assetand Portfolio M.

• Portfolios below the CML are inferior.

– The CML defines the new efficient set. – All investors will choose a portfolio on the

CML.

The CML Equation


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kp = kRF +

SlopeIntercept

^ p.

kM - kRF^

M

Riskmeasure

What does the CML tell us?


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• The expected rate of return on any

efficient portfolio is equal to the risk-free rate plus a risk premium.

• The optimal portfolio for any investor isthe point of tangency between the CMLand the investor’s indifference curves.

II2

CML

ExpectedReturn, kp


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kRF

MRisk, p

I1

R = OptimalPortfolio

.R .M

kR

kM

R

^

^

What is the Security Market Line (SML)?


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• The CML gives the risk/returnrelationship for efficient portfolios.

• The Security Market Line (SML), also

part of the CAPM, gives the risk/returnrelationship for individual stocks.

• The measure of risk used in the SML isThe SML Equation


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• The measure of risk used in the SML isthe beta coefficient of company i, ß.

• Where,

β = [COV(r i,r m)] / σm2

Slope, SML = E(r m) - r f = market risk premium

SML = r f + [E(r m) - r f ]


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• CAPM/SML concepts are based onexpectations, yet betas are calculated


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p , yusing historical data. A company’s

historical data may not reflect investors’expectations about future riskiness.

• Other models are being developed thatwill one day replace the CAPM, but itstill provides a good framework forthinking about risk and return.


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Cost of Capital

Cost of capital

• Returns from the firms perspective


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p p

• Firm raises money from both equity investors

and lenders. Both group of investors make theirinvestments expecting to make a return .

• Firm’s average cost of funds, which is the

average return required by firm’s investors

• What must be paid to attract funds

What sources of long-term

capital do firms use?


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LongLong--TermTerm

CapitalCapital

Preferred StockPreferred Stock Common StockCommon StockLongLong--TermTerm

DebtDebt

New CommonNew Common

StockStock

Retained

Earnings

Cost of equity/debt

• Expected returns for the equity investors


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• Expected returns for the equity investors,

would include a premium for the risk in theinvestment….. Cost of equity

• Expected returns the lenders hope tomake on their investments, includes apremium for default risk ….. Cost of debt.

Weighted Average Cost of

Capital, WACC


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sspspsdTd k

w

k

w

k

w

equitycommon

of Cost

equitycommonof

Proportion

stockpreferred

of Cost

stockpreferredof

Proportion

debt of cost

tax- After

debtof

Proportion

×+×+=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ×

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ×

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ×

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ =

• A weighted average of the componentcosts of debt, preferred stock, and

common equity

The Logic of the Weighted Average

Cost of Capital


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•The use of debt impacts the ability to useequity, and vice versa, so the weightedaverage cost must be used to evaluate

projects, regardless of the specific financingused to fund a particular project.

Basic Definitions

C it l C t


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• Capital Component

–Types of capital used by firms to raisemoney

• kd = before tax interest cost

• kdT = kd(1-T) = after tax cost of debt

• kps = cost of preferred stock

• ks

= cost of retained earnings

• ke = cost of external equity (new stock)


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Cost of Preferred Stock


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• Rate of return investors require on thefirm’s preferred stock

• The preferred dividend divided by the

net issuing price

)F1(P

D

costsFlotationP

D

NP

Dk

0

ps

0

ps ps

ps −=

−==

Cost of Retained Earnings

• Rate of return investors require on the


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sk ˆ g 0

P

1D̂

RP RFk sk =+=+=

firm’s common stock


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Three ways to determine cost of

common equity, ks


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1. CAPM: ks = kRF + (kM – kRF)b.

2. DCF: ks = D1/P0 + g.3. Own-Bond-Yield-Plus-Risk

Premium: ks = kd + RP.

What’s the cost of commonequity based on the CAPM?


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kRF = 7%, RPM = 6%, b = 1.2.

ks = kRF + (kM – kRF )b.

= 7.0% + (6.0%)1.2 = 14.2%.

What’s the DCF cost of commonequity, ks? Given: D0 = Rs 4.19;

P0 = Rs 50; g = 5%.


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D1P0

D0(1 + g)P0

Rs 4.19(1.05)Rs 50

ks = + g = + g

= + 0.05

= 0.088 + 0.05= 13.8%.

0 ; g

Suppose the company has

been earning 15% on equity(ROE = 15%) and retaining


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(ROE 15%) and retaining

35% (dividend payout = 65%),and this situation is expected

to continue.

What’s the expected future g?

Retention growth rate:


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g = (1 – Payout)(ROE) = 0.35(15%)= 5.25%.

Here (1 – Payout) = Fraction retained.

Could DCF methodology be appliedif g is not constant?


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• YES, nonconstant g stocks areexpected to have constant g atsome point, generally in 5 to 10years.

• But calculations get complicated.

Find ks using the own-bond-yield-

plus-risk-premium method.(kd = 10%, RP = 4%.)


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• This RP ≠ CAPM RP.

• Produces ballpark estimate of ks.

ks = kd + RP

= 10.0% + 4.0% = 14.0%

What’s a reasonable final estimate

of ks?

M th d E ti t


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Method Estimate

CAPM 14.2%

DCF 13.8%kd + RP 14.0%

Average 14.0%


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Why is the cost of retained earnings

cheaper than the cost of issuing newcommon stock?


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1. When a company issues newcommon stock they also have to pay

flotation costs to the underwriter.2. Issuing new common stock may

send a negative signal to the capital

markets, which may depress stockprice.

Suppose new common stock had a

flotation cost of 15%. What is ke?

D0(1 + g)


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ke = + g

0( g)

P0(1 – F)

= + 5.0%

= + 5.0% = 15.4%.

Rs 4.19(1.05)

Rs 50(1 – 0.15)

Rs 4.40Rs 42.50

What’s the firm’s WACC(ignoring flotation costs)?


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WACC = wdkd(1 – T) + wpkp + wcks

= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)

= 1.8% + 0.9% + 8.4% = 11.1%.

What factors influence a company’s

composite WACC?

• Market conditions


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• Market conditions.

• Level of interest rates

• Tax rates

• The firm’s capital structure and dividendpolicy.

• The firm’s investment policy. Firms with

riskier projects generally have a higherWACC.

Should the company use the composite

WACC as the hurdle rate for each of itsprojects?*


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• NO! The composite WACC reflects therisk of an average project undertaken bythe firm. Therefore, the WACC only

represents the “hurdle rate” for a typicalproject with average risk.

• Different projects have different risks. The

project’s WACC should be adjusted toreflect the project’s risk.

Risk and the Cost of Capital

Rate of Return(%)

WACC

Accep tance Reg ion


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WACC

Rejection Regio n

Risk

L

B

A

H12.0

8.0

10.010.5

9.5

0 Risk L Risk A RiskH

Divisional Cost of Capital

Rate of Return(%)

WACCDivision H’s WACC

13.0


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Project H

Risk

Project LCompos ite WACCfor Firm A

13.0

7.0

10.0

11.0

9.0

Division L’s WACC

0 RiskL Risk Av erage RiskH

Take note

• Use of current cost of debt : the interestrate the firm would pay if it issues the debt


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p y

today.• when determining the market risk

premium, use current rate in both thecases . i.e. current risk free rate & currentexpected rate of return on the stock.

Revision session


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• Intro to FM

•Time value of Money•Valuation of securities

•Risk & return

•Cost of capital

Introduction to FM

• Three basic principles

1. Financing principle


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g p p

2. Investment principle

3. Dividend principle.

Introduction to FM

• What should be the goal of acorporation?


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– Maximize profit? – Maximize the current value of the company’s

stock?

i.e PROFIT MAXIMISATIONOR

VALUE MAXIMISATION ??

THE FIRM


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Topics under TVM

• Introduction

• Future value of a single cash flow


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g

• Present value of a single flow

• Multiple flows and Annuity

Introduction

• The most important concept in finance

• Time preference for money


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y

– Risk or uncertainty of future cash flows

– Preference for present consumption (PPP)

– Investment opportunities• Time preference rate is generally

expressed by an interest rate.

What is the PV of Rs100 due in

3 years if k = 10%?


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100

0 1 2 310%

PV = ?

Future Value of an Annuity

• Annuity: A series of payments of equal


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amounts at fixed intervals for a specifiednumber of periods.

• Ordinary (deferred) Annuity: An annuitywhose payments occur at the end of eachperiod.

• Annuity Due: An annuity whosepayments occur at the beginning of each

period.

Ordinary Annuity Versus Annuity Due

Ordinary Annuity


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PMT PMTPMT

0 1 2 3k%

PMT PMT

0 1 2 3

k%

PMT

Annuity Due

What’s the FV of a 3-year

Ordinary Annuity of Rs100 at10%?


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100 100100

0 1 2 310%

110

121

FV = 331

What is the PV of this

Uneven Cash Flow Stream?


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0

100

1

300

2

300

310%

-50

4

What is the PV of this

Uneven Cash Flow Stream?


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0

100

1

300

2

300

310%

-50

4

90.91

247.93

225.39-34.15

530.08 = PV

Mathematical expressions: simplified

• Fn = P ( 1+i )n

the term ( 1+i )n is the CVF ( compound


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value factor) .We can make use of the tables for easy

reference. ( Formula Book – only for part-

B & C)Eg: for i = 4% and n= 5 yrs , refer to 6th

column and the row corresponding to 5

years, the CVF/FVF is 1.217

Mathematical expressions: simplified

• Compound value of an annuity

Fn = A (FVAFn,i)


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Present value of an annuity

PV = A ( PVAFn,i)

Compound value of an annuity dueFn = A ( FVAFn,i)(1+i)

• Present value of an annuity duePV = A ( PVAFn,i)(1+i)

Problems

1. Mahesh deposits $5,000 in a savingsaccount earning 8% interest annually.


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(a) How much will be in the account at theend of the twelfth year?

(b) How many years would be required toaccumulate $20,000 under the sameassumptions?

solution

(a) Future valueFV = PV(1 + i)n

FV = $5,000(1 + .08)12

FV $5 000(2 518)


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FV = $5,000(2.518)FV = $12,590

(b) $20,000 = $5,000(1 + .08)n

4 = (1.08)n

Read down the 8% column of the future value table untilthe value 4 is found. The value 4 is not found exactly,but it can be determined that N is approximately 18years.

Problem set #1 : solutions1. Determine the future values utilizing a time preferencerate of 9 %:(i) The future value of Rs. 15,000 invested now for a period

of 4 yrs.


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(ii) The future value at the end of 5 yrs of an investment ofRs 6000 now and of an investment of Rs. 6000 oneyear from now.

(iii) The future value at the end of 8 years of an annualdeposit of Rs.18,000 each year.

(iv) The future value at the end of 8 years of an annualdeposit of Rs. 18000 at the beginning of each year.

(v) The future value at the end of 8 years of a deposit of Rs

18000 at the end of the first four years and withdrawalof Rs.12, 000 per year at the end of year five throughseven.

Solution # 1

• (i) time preference (discount rate) = 9%

investments = 15,000


CVF(4 9%) 1 4116 ( )


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CVF(4,9%) = 1.4116 (appox.)

FV = 15,000*(1.09)4 = 15,000* 1.4116

= 21,173.72

(ii) Investments = 6000 (now) & 6000( 1 yr after)period (eoy) = 5 yrs & 5yrs

compounding period = 5 & 4 yrs

CVF = 1.5386 & 1.4116

FV = 9231.74 & 8469.49

Solution # 1

• (iii) Annual investments (eoy) = 18,000


CVAF 11 0285 (appo )


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CVAF = 11.0285 (appox.)FV = 18,000* 11.0285 = 198,513

(iv) Investments (b0y)= 18000period = 8 yrs

CVAF (annuity due) = 12.0210

FV = 18000 * 12.0210 = 216378


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problems

• A company is expected to declare adividend of Rs2 at the end of first year

from now and this dividend is expected to


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from now and this dividend is expected togrow 10% every year . What is the PV ofthis stream of dividends if the rate of

interest is 15%?

problems

• Soln : PV = A /(i - g)……………. Eqn #1

it is a perpetuity which is growing @ 10% p.a.

The formula


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The formulaP = A/(1+g)[ ( 1-(1+i*)-n) /i*]Here, n = ∞ , hence we get Eqn # 1

Solving for PV we obtain,

PV = 2/(0.15-0.10) = Rs 40

Other forms of Annuity

• Perpetuity: it is an Annuity that occursindefinitely. (i.e. without a maturity)

P = A/I


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P = A/IE.g. , an investor expects a perpetual sum of

Rs 500 annually from his investments.What is the present value of this perpetuityif the interest rate is 10%.

soln : P = 500/0.10 = Rs 5000.

Other forms of Annuity

Present value of a growing Annuity: theperiodic cash flows grow at a compounding

rate E g Arun gets an annual salary of Rs


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rate. E.g. Arun gets an annual salary of Rs1,00,000 with the provision for an annualincrement of 10%.

P = A/(1+g)[ ( 1-(1+i*)-n) /i*]

Where, i* = (i-g)/(1+g)

An Example…

• A dividend stream commencing one yearhence at Rs 66 is expected to grow at

10% annum for 15 Yrs and then ceases Ifth di t t i 21% h t i th PV f


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10% annum for 15 Yrs and then ceases. Ifthe discount rate is 21%, what is the PV ofthe expected series.

soln: P = A/(1+g)[ ( 1-(1+i*)-n

) /i*]Where, i* = (i-g)/(1+g)

i* =(0.21-0.10)/1.10 = 0.10

A/(1+g) = 66/1.10 = 60

Valuation of Securities

• Bond valuation

• Equity valuation


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Concepts of valuation

• In general, the value of an asset is theprice that a willing and able buyer pays to

a willing and able seller


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a willing and able seller • Note that if either the buyer or seller is not

both willing and able, then an offer doesnot establish the value of the asset

Intrinsic ValueIntrinsic Value - The present value of the

expected future cash flows discounted at thedecision maker’s required rate of return

• The size and timing of the expected future


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• The size and timing of the expected futurecash flows

• The individual’s required rate of return• Note that the intrinsic value of an asset can be,

and often is, different for each individual (that’s

what makes markets work)


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Calculating the Value of a Bond

NdNd1d

B

)k(1

M

)k(1

INT ...

)k(1

INT V

++

+++

+=

The value of the bond can be expressed as :


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)k (1)k (1)k (1 +++Where,INT = annual coupon paymentKd = req. rate of return/discount rateN = time period.

VB = INT *PVAFn,i + M* PVFn,i

Yield To Maturity

Yield to maturity (YTM) : rate of return earned onbond held until maturity

The IR when:

Price of the bond = PV of all cash flowreceivables


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Eg : par value : Rs 1000, CI = 9%,time to maturity= 8and currently priced at Rs 800. what will be

the yield to maturity?sol: An appox.

= INT + (M-P)/n

0.4M + 0.6 P= 13.06%

examples

#1: the govt. is proposing to sell a 5-yearbond of Rs 1000 @ 8% IR per annum. The

bond amount will be amortized equallyit lif If i t h i i


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bond amount will be amortized equallyover its life. If an investor has a minimumrequired rate of return of 7%, what is the

bonds present value for him?

solution

Sol #1:the amt of interest will go on reducingbecause of amortization. The amount of

interest for five years will be :


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te est o e yea s beRs 1000 * 0.08 = Rs 80

Rs (1000 – 200)*.08 = Rs 64

P = 280/(1+0.07) +264/(1+0.07)2

…+216/(1+0.07)5

= Rs 1025.66

Valuing Common Stocks

Dividend Discount Model - Computation of today’sstock price which states that share value equalsthe present value of all expected futuredividends.


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dividends.

H - Time horizon for your investment.

P

Div

r

Div

r

Div P

r

H H

H 0

1

1

2

21 1 1= + + + + +

+

+( ) ( ) ... ( )


ExampleCurrent forecasts are for XYZ Company to pay

dividends of Rs3, Rs3.24, and Rs3.50 over the

next three years, respectively. At the end of threeyears you anticipate selling your stock at a market


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years you anticipate selling your stock at a market

price of Rs94.48. What is the price of the stock

given a 12% expected return?

PV =

+

+

+

++

+

3 00

1 12

3 24

1 12

350 94 48

1 121 2 3

.

( . )

.

( . )

. .

( . )

PV = Rs 75


Constant Growth DDM - A version of the dividendgrowth model in which dividends grow at aconstant rate (Gordon Growth Model).

Di


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Given any combination of variables in theequation, you can solve for the unknown

variable.

P Div

r g

01=

−

Concept of returns

•Mean Returns (Ex post) are statistically

derived from historical observations.


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•Expected Returns (Ex ante) arestatistically derived expected values fromfuture estimates of observations.

Sources of Risk

• Factors which make any financial

asset risky are:


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y

1. Business Risk: industry/

environmental factors involved.2. Market Risk: variability in returns due

to the fluctuations in the securities

market.

Sources of Risk

3. Liquidity Risk: ease with which a

security can be bought or sold without


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much transaction cost.

4. Financial Risk: influenced by thedegree of financial leverage

Sources of Risk

5. Interest Rate Risk: changes in the

interest rates.


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6. Inflation Risk: change in the inflationinfluences the purchasing power ofthe investors.

Measuring Risk

•Risk of an asset can be measured in

terms of its variance.


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•More the deviation from the expectedvalue , more riskier the asset.


• Dominant principle

• Markowitz’s Portfolio theory

• Two asset portfolio


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• Efficient frontier

• The CAPM

Diversification

Risk

75% of Co


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UnsystematicRisk

1 5 10 20 30

Systematic Risk

No. of Assets

75% of Co.

Total Risk

25% of Co.

Total Risk

Probability distributions (Rev.)

• A listing of all possible outcomes, and theprobability of each occurrence.

• Can be shown graphically.


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Expected Rate of Return

Rate of Return (%)100150-70

Firm X

Firm Y

e opt ma port o os p otte a ong t e curve ave t ehighest expected return possible for the given amount

of risk.


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M

Z

Efficient Set with a Risk-Free Asset

. .B

k̂

ExpectedReturn, kp


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. AkRF

M Risk, p

The Capital Market

Line (CML):New Efficient Set

. .kM

• The Capital Market Line (CML) is alllinear combinations of the risk-free asset

and Portfolio M.• Portfolios below the CML are inferior

What is the Capital Market Line?


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• Portfolios below the CML are inferior. – The CML defines the new efficient set.

– All investors will choose a portfolio on theCML.

kp = kRF +^ p.

The CML Equation

kM - kRF^


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p

SlopeIntercept

p

M

RiskMeasure

I1I2

CML

R

M

kR

kM^^

ExpectedReturn, kp


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kRF

MRisk, p

R = Optimal

Portfolio

. .R

R

• The CML gives the risk/returnrelationship for efficient portfolios.The Security Market Line (SML) also

What is the Security Market Line (SML)?


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• The Security Market Line (SML), alsopart of the CAPM, gives the risk/returnrelationship for individual stocks.

• The measure of risk used in the SML isthe beta coefficient of company i, ß.

• Where,β = [COV(r r )] / σ 2

The SML Equation


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β = [COV(r i,r m)] / σm2

Slope, SML = E(r m) - r f = market risk premium

SML = r f + [E(r m) - r f ]

• If beta = 1.0, stock is average risk.

• If beta > 1.0, stock is riskier than

average.• If beta < 1.0, stock is less risky than

ABOUT BETA …..


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If beta 1.0, stock is less risky thanaverage.

• Most stocks have betas in the range of0.5 to 1.5.

• Betas of individual securities are notgood estimators of future risk.

• Betas of portfolios of 10 or morerandomly selected stocks are

BETA FOR Portfolios….(?)


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randomly selected stocks arereasonably stable.

• Past portfolio betas are good estimatesof future portfolio volatility.

Question # 3

• The risk free rate is 8%. The expectedreturn on the market portfolio is 16%.

Calculate the expected return on thefollowing securities.


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2.0D2.6C

1.0B

0.4 A

betasecurity

Solution # 3

• Given, risk free rate8%. … R(f)

• The expected returnon the marketportfolio 16% R(m)

16.00%1B

11.20%0.4 A

R ( f ) + beta *( R ( m ) –R ( f ))

ßsecurity


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portfolio 16%... R(m)

24.00%

2D

28.80%

2.6C

Question # 4

• Calculate the betafactor of the followinginvestments. Isacceptance of theinvestment worthwhile

30%12%1/3

6%9%1/3

Invest.MarketProb.


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investment worthwhilebased upon its level

of risk? The risk freerate = 6%. 18%18%1/3

30%12%1/3


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Question # 5

• The std. deviation of returns of thesecurity ‘s’ 20% & that of the market

portfolio is 15%.calculate beta . When,1. Cor (s,m)=0.7


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2. Cor (s,m)=0.4

3. Cor (s,m)= -0.25


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Question # 6

• The expected return on the market portfolio & therisk free rate of return are estimated to be 13% &9% resp. ABC Ltd. Has Just paid a dividend of Rs.2per share with annual growth rate of 7%. The

sensitivity index (beta) of ABC has been found to be1.2

1. Find out the equilibrium price for the shares of ABC


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q pLtd.

2. Examine the change in the price if (i) risk premium increases by 2%

(ii) expected growth rate of dividends increases to10%

(iii) market sensitivity index becomes 1.3 for thescript.

Solution # 6

• Using CAPM, R(i) = R(f) +ß*(R(m) – R(f))the req. rate of return(R) = 9% +1.2*(13-9)=13.8%

Now , R = 13.8%D = Rs. 2g = 7%


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g = 7%1. The equilibrium price (P) = D(1+g)/ (R-g)…Annuity

dueor, P = 2.14/ .068 = Rs. 31.47

Solution # 6

2. Effect on price :

(i) if the risk premium increases by 2%,Then R = 13.8% +2%

Therefore the equilibrium price (P) = Rs. 24.32

(ii) g=10%


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(ii) g 10%We obtain, P =Rs. 57.9

(iii) Beta = 1.3 then, R = 14.2%Hence , P = Rs. 29.72

Multiple choice

• If the market return is below the risk freerate, then the stocks which possess highsystematic risk gives returns which _________ as compared to the stockswhich have a low systematic risks.


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y

1. Are lower

2. Are higher

3. Cannot be determined

4. None of the above

Multiple choice

• Of the following, the systematic riskencompasses:

1. Business risk2. Financial risk


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3. Interest rate risk

4. Inflation risk

Multiple choice

• A stock will not have a finite Beta if

1. Its correlation with the market is –ve

2. The stock is highly volatile3. The market index is stagnant


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g

4. Both (2) & (3)5. None of the above.


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Multiple choice

• An economic surveysuggests that aneconomic boom is inoffering. The followingdata are available with

regards to asset A and B20 10 1B

60.91.5 A

Residual

variance

(%

squared)

Correlation

with market

returns

Beta Asset


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20.10.1B

1. Buy A

2. Sell A

3. Invest half of funds in A & other half in B

4. Buy B

• Individual investors are price takers.

• Single-period investment horizon.

• Investments are limited to traded financialassets.

CAPM-Assumptions


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• No taxes and transaction costs.

• Information is costless and available to allinvestors.

• Investors are rational mean-varianceoptimizers.

Th h t ti

Assumptions (cont’d)


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• There are homogeneous expectations.

• Recent studies have questioned itsvalidity.

• Investors seem to be concerned with

What are our conclusions

regarding the CAPM?


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• Investors seem to be concerned with

both market risk and stand-alone risk.Therefore, the SML may not produce acorrect estimate of ki.

(More...)

Cost of capital

• Returns from the firms perspective

• Firm raises money from both equity investorsand lenders. Both group of investors make theirinvestments expecting to make a return .

• Firm’s average cost of funds, which is the


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average return required by firm’s investors

• What must be paid to attract funds

What sources of long-termcapital do firms use?

LongLong--TermTermCapitalCapital

Preferred StockPreferred Stock Common StockCommon StockLongLong--TermTermD bD bt


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DebtDebt

New CommonNew CommonStockStock

RetainedEarnings


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Basic Definitions

• Capital Component

–Types of capital used by firms to raise

money

• kd = before tax interest cost


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• kdT

= kd(1-T) = after tax cost of debt

• kps = cost of preferred stock

• ks = cost of retained earnings

• ke = cost of external equity (new stock)


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k̂g1D̂

RPkk =+=+=

Cost of Retained Earnings

• Rate of return investors require on thefirm’s common stock


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s

k g

0P

RP

RF

k

s

k ++


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Three ways to determine cost ofcommon equity, ks

1. CAPM: ks = kRF + (kM – kRF)b.

2. DCF: ks = D1/P0 + g.


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s 1 0

3. Own-Bond-Yield-Plus-RiskPremium: ks = kd + RP.

Cost of Capital and Firm Value


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A Pictorial View


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WACC lowest

What factors influence a company’s

composite WACC?

• Market conditions.

• Level of interest rates• Tax rates

• The firm’s capital structure and dividend


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The firm s capital structure and dividendpolicy.

• The firm’s investment policy. Firms withriskier projects generally have a higherWACC.

mistakes to avoid

• Use of current cost of debt : the interestrate the firm would pay if it issues the debt

today.• when determining the market riskpremium, use current rate in both the


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cases . i.e. current risk free rate & currentexpected rate of return on the stock.

Important !!!

• Group A – Money Market in India (**)• Group B – Indian F/O Market ()

• Group C – Trading & Exchange (*)

• Group D – listing in foreign Exchanges ()

• Group E - FOREX Market (**)

• Group F – financial Institutions- developmental/NBFC


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Group F financial Institutions developmental/NBFC(***)

• Group G – Function of RBI (***)

• Group H – financial sector reforms (***)

• Group I – Indian Banking System (***)

Important!!

• See problem number 64 and 71 of

workbook . (page # 583 and page# 585)


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