Lecture 2 15Feb2011

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LEC

Master in

Corpora

URE 2

Business Administration (M.B.A.)

e Finance

Dr Andry Rakotovololona

[email protected]

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Time: 10.00 11.30 or 14.00 15.30

1. Arbitrage & Law of One Price

2. Risk and Return

3. Interest Rates

4. Time Value for Money

CONTENTS

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February 15, 2011 2February 15, 2011

. . .

5. DDM, CAPM & Cost of Equity

6. Valuing Bonds & Cost Of Debt

7. WACC

7. Debt and Taxes

8. Q & A

9. Thank You !

2

.

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1. ARBITRAGE & LAW O

Arbitrage

The practice of buyinggoods in different maa price difference.

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An arbitrage opportpossible to make arisk or making any i

Normal Market

A competitive marketarbitrage opportunitie

February 15, 2011 4

ONE PRICE

and selling equivalentkets to take advantage of

unity occurs when it isprofit without taking anynvestment.

n which there are nos.

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Law of One Price

If equivalent investmesimultaneously in diffthen they must trade f

markets. Determining the No-A

Unless the rice of the s

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value of the securitys caopportunity will appear.

No-Arbitrage Price of a S

February 15, 2011

Price(Security) (All cPV=

5

t opportunities traderent competitive markets,or the same price in both

bitrage Price.

curit e uals the resent

h flows, an arbitrage

curity:

sh flows paid by the security)

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2. RISK AND RETURN

The higher the risk of an in

the return required by the

Impacts on the cost of c

company only invests in

roviders of ca ital a u

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February 15, 2011

capital, then the cost of

would be low.

Conversely, for higher ri

capital to the company

the investors for the ad

6

vestment, the higher will be

roviders of the capital:

apital Put simply, if a

safe projects or offers the

aranteed return on their

such capital to the company

sk investments the cost of

ill be high to compensate

itional risk.

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Elements Of Return

Return Required is a com

for a given financial instru

1. Risk-free return: levelinvestment with zero ri

2. Risk remium: return

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the risk-free rate for aninvest in the company.

Risk Free Return

Risk-free rate is normaloffered by short-dated

treasury bills (gilts).

7

bination of two elements

ment:

of return expected of ansk to the investor.

re uired above and be ond

investor to be willing to

ly equated to the returngovernment bonds or

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Pecking Order Theory

Risk FreeRate of

Return

Risk FreeRate of

Return

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Government

Debt

Secured

Loan Notes

U

L

Hierarchy of ranking/authority

Effort or L

8

& Degree Of Risk

Higher RiskInvestment

Mezzanine

Finance

nsecured

an Notes

derived from the Principle of Least

ast Resistance.

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Government debt is the le

repaid.

Short term debt is generalrather than long term gov

Although the long terinvestors could lose oucapital value ifeconom

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.

Secured loan notes are cothe companys assets withspecific assets) or a floati

assets):

Sometimes referred tocomponents: the loan i

assets.9

ast risky as it will always be

ly regarded as risk freernment debt: Why?

debt can be repaid,t on the return and theic conditions change

porate debts: Secured oneither a fixed charge (ong charge (over all the

as debentures with twotself and the charge on the

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Unsecured loan notes: Dewithout any security, thercarries significant risk.

Mezzanine finance: Broad

financial instruments Tybe subordinated to other lunsecured), so less likely

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.

Very high risk and ranshare capital in terms

Ordinary shares: Most risin both the order of theirreturn (dividend) or the pcase of bankruptcy.

1

t that the company sellsfore not protected and

name for a variety of

ically unsecured, and mayoans (secured oro be repaid if the company

just above the ordinaryf risk.

y investments and rank lastolders receiving an annualyment of their capital in

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Price of Risk

Risky vs. Risk-free Cash

Cash Flows & MaComparison between a Risk-Free B

Market

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lows

rket Prices (in $):ond (4%) and an Investment in theortfolio

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Assume there is an eq

weak economy or stro

Price(Risk-free Bond) PV(Cash Fl

($1100 in o

$1058 toda

=

=

=

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($800) + ($140

Although both invest

expected value, the mvalue since it has a gr

February 15, 2011 1

ual probability of either a

ng economy.

ws)

e year) (1.04 $ in one year / $ today)

0) = $1100

ents have the same

rket index has a lowerater amount of risk.

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Risk Aversion & Risk Pr

Risk Aversion

Investors prefer to hathan a risky one of the

Risk Premium

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p

earn to compensate th

When a cash flow is rivalue we must discou

on average at a rate thinterest rate plus an a

February 15, 2011 1

mium

e a safe income rathersame average amount.

em for a securitys risk.

ky, to compute its presentt the cash flow we expect

at equals the risk-freepropriate risk premium.

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(1400 1100) / 11

Market return if the ec

Expected return of a risky invest

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(800 1000) / 100

Expected market retur

(40%) + (20%)

February 15, 2011 1

nomy is strong

0 = 40%

nomy is weak

Expected Gain at end of year

ent = Initial Cost

= 20%

10%

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3. INTEREST RATES

The Effective Annual Rat

Indicates the total amearned at the end of o

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Also referred to as the(EAY) or Annual Perce

February 15, 2011 1

(EAR)

unt of interest that will bene year.

.

Effective Annual Yieldtage Yield (APY)

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Adjusting Discount Rat

Time Periods

Earning a 5% return annuearning 2.5% every six m

General Equation for DisConversion:

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(1.05)0.5 1= 1.0247

Note: n = 0.5 sincsix month (

February 15, 2011

Equivalent n-Period Di

1

to Different

ally is not the same asonths.

ount Rate Period

1 = 0.0247 = 2.47%.

e we are solving for ther 1/2 year) rate.

n

count Rate = (1 + r) - 1

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Annual Percentage Rate

APR indicates the amount oyear.

Simple interest is the awithout the effect of c

The APR is typically less tha

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The APR itself cannot be us

The APR with kcompoundinof quoting the actual intere

compounding period:

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Interest Rate per Compoundin

1

simple interest earned in one

mount of interest earnedmpounding.

the EAR.

d as a discount rate.

g periods is a wayt earned each

APRg Period =

k-Periods / year

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Converting an APR into a

The EAR increases wit

APR1 + EAR = 1 +

k

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Continuous compouninstant.

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n EAR

the frequency of

k

ing is compounding every

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Example

Effective Annual Rates foCompounding Periods:

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A 6% APR with continuouan EAR of approximately

February 15, 2011 1

r a 6% APR with Different

s compounding results in6.1831%.

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U.S. Interest Rates and I

19602009

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February 15, 2011

Source: US Treasury and Us Bureau of Labour Statistics.

2

nflation Rates,

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4. TIME VALUE OF MON

The Three Rules of Time

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Y

Travel:

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Example: The Rules of

Suppose we plan to saveat the end of each of the

If we can earn a fixed 10savings, how much will

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February 15, 2011

to ay? The time line would look

2

ime Travel

$1000 today, and $1000next two years.

interest rate on oure have three years from

like this:

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FUTURE VALUING a Stre

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m of Cash-Flows

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PRESENT VALUING a Str

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am of Cash-Flows

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Present Value of a Cash Flo

0

( )

=

= =N

n

n

PV PV C

2

Stream:

0

(1 )=+

N

n

n

C

r

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Annuities

When a constant cash flointervals for a finite num

called an annuity.

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February 15, 2011

Present Value of an Annu

2

C CPV = + +

(1+r) (1+r) (1+

2

w will occur at regularer ofNperiods, it is

ity

N

3 N nn=1

C C+...+ =

r) (1+ r) (1+ r)

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Perpetuities

When a constant cash flointervals forever it is call

Investment = $100 rei

Interest er ear = 5%.

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3

w will occur at regulard a perpetuity:

nvested every year.

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Growing Perpetuities

Assume you expect the apayment to increase at a

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Present Value of a Growi

PV (growing perp

3

mount of your perpetualconstant rate g.

g Perpetuity

Cetuity) = r - g

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5. COST OF EQUITY

Definition:

The rate of return required

This may be calculated in o

1. Dividend-Discount Mod

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2. Capital Asset Pricing M

3

by a shareholder.

ne of two ways:

l (DDM).

del (CAPM).

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DIVIDEND DIS

To understand how to cal

start with the closely relat

companys share price: Calculation = dividend

the share rice to the

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February 15, 2011

by the shareholders. Cash-Inflow from the d

reflects the permanent

3

OUNT MODEL

ulate the cost of equity, we

ed calculation of the

valuation model equates

V of the dividends received

ividends a perpetuity that

nature of the share capital.

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Applying the Dividend

What is the price if we planyears?

1 20 2

E E

1 (1 )

= +

+ +

Div DivPr r

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February 15, 2011

This is known as the Divi rE : Equity cost of capi

Note: the above equat

horizon N. Thus all investors (wit

the same value to the

investment horizons.3

iscount Model

n holding the stock for N

E E

(1 ) (1 )

+ +

+ +

N N

N N Div P

r r

end Discount Model.al.

ion holds for any

h the same beliefs) will attachstock, independent of their

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The price of any stock is eqex ected future dividends it

1 20 2

E E

1 (1 )

= + +

+ +

Div DivP

r r

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February 15, 2011

3

al to the present value of thewill a .

3

31E E

1 ) (1 )

=

+ =

+ + n nn

Div Di

r r

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Constant Dividend Growth

The simplest forecast forstates that they will grow

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the firms future dividendsat a constant rate g, forever.

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Constant-Dividend Growth

10

E

=

DivP

r g

1 =Div

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The value of the firm delevel, the cost of equity,

0

P

,

3

odel

ends on the current dividendnd the growth rate.

.

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0

E

Div $2.P = =

r - g 0.075 -

Solution:

3

6= $39.33

0.015

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Estimating Growth Of D

The first method of deter

0n

n

Dg = -1D

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Where D0 = current dividend

Dn = dividend n-years

4

ividends

ining growth g is:

ago.

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The GORDONS GROWTH

estimating the growth of Two ways of writing th

which both mean exac

g = r

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ere r = e urn on e nves

b = Proportion of Fun

41

ODEL is another way of

ividends:formula for this model

ly the same thing,

e un s.

s Retained.

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In the exam formula sheet tslightly different version:

where rE = Return on Eq

b = Proportion o

Eg = r b

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The rationale behind the monly occurs if a company rereinvest in the business.

Ifcompany paid out all its e

growth as no new investmegenerate the additional prof

Thus, profits would be thdividends would also be

4

e examiner might give you a

uity

Funds Retained

del = growth of dividendsains some of its earnings to

rnings as dividends = no

ts or projects which wouldits,

e same and thereforehe same every year.

CAPITAL ASSET

RICING MODEL

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CAPITAL ASSET

Definition:

The Capital Asset Pricing

that values shares by meaparticular share against th

in all shares.

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It can also be applied tothan shares.

The basic idea There is

and return: All investors have a ge

that they collectively ereturn for all shares

4

RICING MODEL

odel (CAPM) is a model

suring the risk of ae risk of the overall market

inancial instruments other

a relationship between risk

eral idea of the trade-offspect between risk andsort of average.

Are the in estors in the ma

rket acting rationall ?

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Are the investors in the m

If we can understand/qrelationship between rimarket Knowing theassociated with a parti

price. By acting rationally inv

adjustment to a partic

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ncrease or ecrease

share.

There are two stages to thCAPM:

a) Systematic and unsystb) The CAPM formula.

4

arket acting rationally ?

uantify the generalsk and return for the wholerisks and returnsular share will drive to its

stors require anlar share price to reflect ther s assoc a e w a

e full explanation of the

matic risk.

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Systematic & Unsystem

Definition of Systematic Ri

Risk affecting all the comp(the stock market).

Caused by economy-widecaused by factors specific

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share prices. Similarly, a recession w

prices.

Definition of Unsystematic Risk associated with intrin

associated with individual

4

tic Risk

k:

any shares in the market

onsiderations but noto particular shares,

ll also depress all share

Risk:ic and specific parameters

companies.

Di ifi ti

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Diversification

Constructing a portfol

gradually adding othe

reduce the total risk o Example: if you buy

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should also buy sh

manufacturers so y

the risks posed by t

4

io with one share and

shares will tend to

the portfolio.shares in ice cream

,

res in umbrella

u balance and reduce

he weather.

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In theory, if you buy s

the shares in the mar

market capitalizations

is referred to as a ma

would have diversified

specific or unsystema

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However, even if youdiversified portfolio sdiversified away all th

will still be left with th

4

ares representing all

et in proportion to their

, you would have what

ket portfolio and you

away all the company

ic risks.

ave a very wellch that you haveunsystematic risk you

e systematic risk.

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Most of the unsystematic riskis e

30 differ

4

iminated with a portfolio of about

nt shares.

P tf li I li ti

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Portfolio Implications

To avoid risk altogetherin a portfolio consistingsecurities such as gover

A balanced portfolio oin the stock market will

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in the market. Individual shares will ha

characteristics which ar

market average, Their risk will be det

sector and gearing. S

risky and some less.4

, an investor must investentirely ofrisk-freenment debt.

all the stocks and sharessuffer systematic risk

ve systematic riskdifferent from this

rmined by the industryome shares will be more

(Beta) Factors

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(Beta) Factors

The factor was devisedsystematic risk of a singleportfolio.

The market portfolio isand is given a factor

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greater or smaller thansystematic risk which itheir required returns:

If factor of 0.5 moves in line with thalf as much.

If factor of 2 Sh

moves in line with tas much. 5

s a means to measure thecompany share or a

taken to be the benchmarkf 1.

1 depending on theirmeasured by considering

hare or portfolio returne market return but only

are or portfolio return

e market return but twice

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Example: Suppose the ret

tend to vary twice as muc

as a whole,

So that if market retur

returns would go up b

If market returns fell b

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February 15, 2011

would fall by 8%. Then, ABC would be sa

The factor is thus the m

in terms of the markets s

51

rns on shares in ABC plc

as returns from the market

s went up by 6%, ABCs

12%.

4% then ABCs returns

id to have a factor of 2.

asure of a shares volatility

stematic risk.

Return Calculations Inv lving CAPM

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Return Calculations Inv

From CAPM, we can derive tformula for the required ret

Where KE = Required (Expected) Re

=

E F(K - R )= .(

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RF = Risk-free Rate of InteresRM = Return on Market Portf

This means that the expectparticular share over the ris

shares times the expectemarket over the risk free ra

The return of a particular sh

the return required on the5

lving CAPM

he following mathematicalrn for a particular share:

urn from Individual Share.

M F- R )

.

t.lio

d excess return of thefree rate equals the

excess return of thee.

are is the shares times

arket.

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The difference between theportfolio and the risk free r

as the market risk premiu

(ERP).

The risk free rate is the ra

are effectively risk free.

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The above equation can b

E F M K = R + .(R - R

5

return on the marketeturn (RM RF) is referred to

or the equity risk premium

te on short term gilts which

re-written as:

) This is the Cost of Equity

Criticisms of CAPM

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Criticisms of CAPM

1. CAPM = single period model

valid for a finite period of time

or updated at regular intervals.

2. CAPM assumes no transaction csecurities.

3. Any beta value calculated will b

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not e appropriate current y

changed the capital structure o

4. Market return may change cons

time.

5. CAPM assumes an efficient inve

possible to diversify away risk

some unsystematic risk may re

6. Additionally the idea that all un

will not hold true if stocks cha5

the values calculated are only

and will need to be recalculated

osts associated with trading

based on historic data and may

particu ar y so i t e company as

r their type of business.

iderably over short periods of

stment market where it is

Not necessarily the case as

main.

ystematic risk is diversified away

ge in terms of volatility.

6 VALUING BONDS

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6. VALUING BONDS

Understanding bonds an

The prices of risk-free

used to determine the

Firms often issue bon

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,

is one factor in deter Bonds provide an opp

securities can be price

February 15, 2011 5

their pricing is useful:

government bonds can be

risk-free interest rates,

s to fund their own

ining the cost of capital,rtunity to know how

d in a competitive market.

Bond Cash Flows Prices and Yields

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Bond Cash Flows, Prices

Bond Terminology

Bond Certificate: State Maturity Date: Final re

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erm: e me rema

date.

Coupon: Promised int

Face Value: Notional athe interest payments.

February 15, 2011 5

, and Yields

s the terms of the bond.payment date.

ng un e repaymen

rest payments.

mount used to compute

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Coupon Rate: Determi

coupon payment, exp

Coupon Payment:

Coupon RNumber of Cou

=CPN

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nes the amount of each

essed as an APR.

ate Face Valuepon Payments per Year

Zero-Coupon Bonds

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Zero Coupon Bonds

Zero-Coupon Bond

Does not make coupo Always sells at a disco

face value so the ar

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bonds. Treasury Bills are U.S.

bonds with a maturity

February 15, 2011 5

payments.unt (a price lower than

also called ure discount

government zero-couponofup to one year.

Yield to Maturity

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Yield to Maturity

The discount rate thatthe promised bond pacurrent market price o

Price of a Zero-Coupo

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Yield to Maturity of an

(1=

+

PYT

1

=

n

n

FVYTM

P

February 15, 2011 5

sets the present value ofments equal to the

f the bond.

bond:

n-Year Zero-Coupon Bond

)nn

1

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Coupon Bonds

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Coupon Bonds

Yield to Maturity

The YTM is the single

the present value of tflows to its current pri

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Yield to Maturity of a1

1(1

=

P CPN

y


iscount rate that equates

e bonds remaining cashce.

oupon Bond:1

) (1 )

+

+ +N N

FV

y y

Discounts & Premiums

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Bond Prices Immediate

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y After a Coupon Payment

The Effect of Time on B nd Prices

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Revert to Par

Yield to Maturity & Bon Price Fluctuations

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y

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7. COST OF DEBT

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The cost of debt is the ratproviders require on the f

We would expect this t

equity because the riskassociated with equity.

The market value of debt

MBA

Co

rp

February 15, 2011

present value of its future

To calculate the marke

Determine all the cthe debt (typically t

the final value at whredeemed),

Discount them at athe present value of

market value). 6

e of return that debtnds that they provide:

be lower than the cost of

is lower than the risk

s assumed to be thecash flows:

value of debt

sh flows associated withe interest payments and

ich the debt will be

appropriate rate to givethe debt (i.e. the current

Terminology

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rateFina

nce

1. Loan notes, bonds and debentu

by a company. Gilts and treasur

government.

2. Traded debt is always quoted in

3. Interest paid on the debt is stat

MBA

Corp

February 15, 2011

va ue as state . s s

not the same as the cost of debt

4. Debt can be:

a) Irredeemable never paid b

b) redeemable at par (nominal

c) or redeemable at a premium

5. Interest can be either fixed or fl

6

es are all types of debt issued

bills are debt issues by a

$100 nominal units or blocks

d as a percentage of nominal

own as t e coupon rate. t s

.

ck

value)

or discount (for more or less).

ating (variable).

Irredeemable Debt With Tax

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rateFina

nce

The calculation is based onseen above, but we calculagiven market price.

D

i.(1-K =

MBA

Corp

February 15, 2011

Where i = Interest Paid

T = Marginal Tax Rate

P0 = Market Price excl. int

(similar to excl. dividendf

6

the PV of a perpetuity ase the return on the debt for a

)

reston the loan stock

r shares).

Cost Of Redeemable Debt with Tax

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rateFina

nce

The KD for a redeemable derelevant cash flows:

The relevant cash flows

The market value of t

The interest payment

MBA

Corp

February 15, 2011

e re emp on va ue

Annual interest payments fo Discount each cash-flow (@

coupon rate).

6

t is given by the IRR of the

ould be:

e debt/bond.

per period.

o e e on .

r year-1 to year-n = i(1 - T).rate above or below the

Interpolate the IRR using th following formula:

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rateFina

nce

p g

If the current market value asame the irredeemable debt

Low

Interpolation Low

R

NP IRR = R +

NPV

MBA

Corp

February 15, 2011 6

g

d the redemption value are theformula can be used.

( )LowHigh

R

High Low

R

Vx R - R

- NPV

Cost of Redeemable De t Evaluation

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rateFina

nce COST OF BOND CAPI

Bond Current Market V

Maturit before Redem

MBA

Corp


Tax rate = 25%

Redemption Price = 1

Net Interest Payable =

7

AL

lue = 98

tion = 3 Years

0

6 * (1 - 0.25) = 4.5

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rateFina

nce

Year Description Cash-Flow * (1-t)

0 Market Value -98

1 Interest 4.5

2 Interest 4.5

3 Interest + Par Value 104.5

Cost of Bond

MBA

Corp


NPV

IRR 5.26%

Kd = IRR 5.24%

5.24% = IRR(CF0 : CF3 ; 6%)

71

CF1 - 6% PV1 DCF2 - 4% PV2

1.000 -98.00 1.000 -98.00

0.943 4.25 0.962 4.33

0.890 4.00 0.925 4.16

0.840 87.74 0.889 92.90

-2.01 3.39

IRR = LR + [NPV LR / (NPV LR NPV HR)] * (HR - LR)

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Example

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rateFina

nce

General information:

Taxation Rate = 30%

Convertible Debt Informatio

MBA

Corp

February 15, 2011

Debt Book Value = 110

Debt Market Price = 11

Treasury Bond (Risk-Fre

Redemption at Par (10

7February 15, 2011 7

n:

,000,000

) Rate = 3.5%

) = 8 years

Year Description Cash flo

Cost of Convertible Debt

w *(1 t) DCF 1 8% PV1 DCF 2 2% PV2

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rateFina

nce


0 Market Value -1

1 Interest 5.

2 Interest 5.

3 Interest 5.

4 Interest 5.

5 Interest 5.

6 Interest 5.

7 Interest 5.

MBA

Corp

February 15, 2011

n eres + ar

NPV

IRR 4.4

Kd = IRR 4.1

7February 15, 2011

4.11% = IRR ( CF0 : CF8 ; 8%)

-23,79IRR = LR + [NPV LR / (NPV LR NPV HR)] * (HR - LR)

7

w *(1-t) DCF 1 - 8% PV1 DCF 2 - 2% PV2

0 1.000 -110.000 1.000 -110.000

6 0.926 5.185 0.980 5.490

6 0.857 4.801 0.961 5.383

6 0.794 4.445 0.942 5.277

6 0.735 4.116 0.924 5.174

6 0.681 3.811 0.906 5.072

6 0.630 3.529 0.888 4.973

6 0.583 3.268 0.871 4.875

. . . . .

-23.792 16.372

%

%

= Sum (Market Value & InterestPV1)

16,372 = Sum (Market Value & InterestPV2)

Bank Debt (Non Tradea le Debt)

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rateFinance

A substantial proportion of

not traded.

Bank loans and other non-tr

debt equal to the coupon ra

MBA

Corp

February 15, 2011

LoanK =Interest (Cou

7

he debt of companies is

aded loans have a cost of

te adjusted for tax:

on) Rate (1-T)

Example

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rateFinance

Bank Loan information:

Loan Interest Rate = 1

Loan Book Value = 1

MBA

Corp

February 15, 2011

Interest on Loan

kL (After-Tax) = 10% * (1-0.

Cost o Ban Loan

7

0%

0,000,000

10.0%

0) 7.0%

Preference Shares

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rateFinance

Definition:

A preference share is a fixed

in the form of a dividend rat Preference shares are normal

equity but they are not tax d

MBA

Corp

February 15, 2011

not deduct the tax in calculat

They can be treated using thwith no growth:

PS0

DK =

P

7

rate charge to the company

er than in terms of interest.ly treated as debt rather thanductible. Therefore, we doing the cost.

dividend-discount model

8. WEIGHTED AVERAGE(WACC)

COST OF CAPITAL

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rateFinance

WACC is the average offinancing (equity, loan n

preference shares) weigproportion each elemen

MBA

Corp

.

February 15, 2011 7

ost of the companysotes, bank loans,

ted according to thebears to the total pool

Example

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rateFinance

General information:

Taxation Rate = 30%

Equity information:

Ordinar Shares issue

MBA

C

orp

February 15, 2011

Ordinary Share price

Equity Beta = 1.3

Market Return (Expec

14%


= 140,000,000

8.50

ed by Equity Investors) =

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rateFinance

Convertible Debt Informati Interest Rate on Debt =

Debt Book Value = 11

Debt Market Price = 1

Treasury Bond (Risk-Fre

MBA

C

orp

February 15, 2011

Redemption at Par (10

Bank Loan information:

Loan Interest Rate = 1

Loan Book Value = 1


n:8%

,000,000

0

e) Rate = 3.5%

0) = 8 years

0%

0,000,000

WACC Calculations

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rateFinance Rf

Beta ()

RM

RM- Rf

-

Cost of Equity

MBA

C

orp


Interest on Loan

kL (After-Tax) = 10% * (1-0.30)

Cost of Bank Loan

81

3.5%

1.3

14%

10.5%

10.0%

7.0%

.


Cost of Convertible Debt

w *(1-t) DCF 1 - 8% PV1 DCF 2 - 2% PV2

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rateFinance

0 Market Value -1

1 Interest 5.

2 Interest 5.

3 Interest 5.

4 Interest 5.

5 Interest 5.

6 Interest 5.

7 Interest 5.

MBA

C

orp

February 15, 2011

n eres + ar

NPV

IRR 4.4

Kd = IRR 4.1

8February 15, 2011

4.11% = IRR ( CF0 : CF8 ; 8%)

-23,79IRR = LR + [NPV LR / (NPV LR NPV HR)] * (HR - LR)

8

0 1.000 -110.000 1.000 -110.000

6 0.926 5.185 0.980 5.490

6 0.857 4.801 0.961 5.383

6 0.794 4.445 0.942 5.277

6 0.735 4.116 0.924 5.174

6 0.681 3.811 0.906 5.072

6 0.630 3.529 0.888 4.973

6 0.583 3.268 0.871 4.875

. . . . .

-23.792 16.372

%

%

= Sum (Market Value & InterestPV1)

16,372 = Sum (Market Value & InterestPV2)

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Use Of WACC

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rateFinance

WACC = cost of capital

Can be used to evaluate the coconditions apply.

Main thing to be considered: Averagcapital is appropriate:

1. WACC appropriate if the compa

MBA

C

orp

The company will maintain

run (i.e. same financial risk

The project has the same dthe company has now.

2. WACC also appropriate if the pr

of the company.3. However, if funds are to be rais

funds raised matched to the prmay be more appropriate

February 15, 2011 8

panys investment projects if certain

e cost of capital or Marginal cost of

ny adopts a pooled funds approach to

its existing capital structure in the long

);

egree of systematic (business) risk as

oject is insignificant relative to the size

d specifically for a project with theject, then the marginal cost of capital

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Example

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rateFinance

Consider Safeway, Inc. winterest and taxes of app

2008, and interest expeSafeways marginal corp

MBA

C

orp

February 15, 2011 8

ich had earnings beforeroximately $1.85 billion in

ses of about $350 million.rate tax rate was 35%.

Interest Tax Deduction

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rateFinance

Safeways debt obligatioequity. But the total amo

investors was higher wit

MBA

C

orp

February 15, 2011 8

s reduced the value of itsnt available to all

leverage.

Interest Tax Shield

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rateFin

ance

The reduction in taxesdeductibility of interes

Interest Tax Shield Corpora=

MBA

C

orp

,

reduction in taxes wit $648 million $52

The interest payme

of 35% $350 milli

February 15, 2011 8

paid due to the taxt

te Tax Rate Interest Payments

leverage:million = $123 million.

ts provided a tax savings

n = $123 million.

Cash Flows of the Unlevered and Levered Firm

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rateFin

ance

MBA

C

orp

February 15, 2011 8

The WACC with and wit out Corporate Taxes

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rateFin

ance

MBA

C

orp

February 15, 2011 9

6. Questions & Answer

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rateFin

ance

Q

MBA

C

orp


& A

DOMINUS I LUMINATIO MEA

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rateFin

ance

MBA

C

orp


Than

9

You !

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Lecture 2 15Feb2011