Finanial Management-1 (1)
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Transcript of 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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ENVIRONMENTAL FACTORS
• 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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ENVIRONMENTAL FACTORS
• 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
67264.8231200079264.82compounding value at the end of 7
yr
72720.02111200084720.02compounding value at the end of 6
yr
77724.791200089724.79compounding value at the end of 5
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
Capital Market Theory
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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
time period = 4 yrs.
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
time period = 8 yrs.
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= + + + + +
+
+( ) ( ) ... ( )
Valuing Common Stocks
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
Valuing Common Stocks
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.
Capital Market Theory
• 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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