Time preferences suggest a positive component to all discount rates Call this the risk-free rate...

• Time preferences suggest a positive component to all discount rates • Call this the risk-free rate (remember the last lecture?!?)

• Risk aversion suggests an additional component representative of the asset’s risk• Call this the risk premium

• Variation in discount rates across assets is really variation in risk premia (the second component)• Riskier assets should have a higher risk premium• In capital budgeting (discussed a couple of lectures from now),

riskier projects should be valued with a higher discount rate

Two Basic Components of Discount rate

• Expected rate of return (ex ante):• Calculated by multiplying each possible outcome by its

probability of occurrence and then summing these products • Weighted average of outcomes where the weights are the

probabilities and weighted average is the expected rate of return

• Realized rate of return (ex post):• Actual rate of return earned during some past period • Can be considered the “after-the-fact” rate of return

• Realized rate of return is often different from the expected rate of return• However, on average, these two tend to be fairly close!

Expected Versus Realized Rates of Return

• Let us first consider an example of expected rate of return (or ex ante returns):

• Calculated by multiplying each possible outcome by its probability of occurrence and then summing these products

• Weighted average of outcomes where the weights are the probabilities and weighted average is the expected rate of return

• Let us also consider risk in our example

Expected Returns and Risk: An Example

• Risk means uncertainty about what an investor’s realized holding period return will be • i.e., that realized returns will differ from expected returns

• We can quantify the uncertainty using probability distributions

• Example (Stock Fund or SF): • Assume there is considerable uncertainty with respect to the

end of year price of an index stock fund, which is currently selling for $100

• Also, the investor expects a dividend of $4

Holding Period Returns (HPR)

Holding Period Returns (HPR): SF Example

Holding Period Return Formula

Holding Period Return: Boom

Holding Period Return: Normal

Holding Period Return: Recession

iceBeginning

ndsCashDivideiceBeginningiceEndingHPR

Pr

PrPr

%44100$/)100$4$140($

%14100$/)100$4$110($

%16100$/)100$4$80($

Expected Returns: SF Example

Expected Return Equation

• The expected return (mean) is the probability weighted average of all possible outcomes

i

N

iirPr

1

%14%)16(25.%)14(5.%)44(25.

r

• Variance = average squared deviation from the mean• Represents the dispersion of a given distribution• Variance is a natural measure of risk

• Standard deviation = square root of variance

• Higher variance (or standard deviation) represents greater dispersion and, hence, greater risk

Measuring Risk

Computing Standard Deviation: SF Example

•The standard deviation is the square root of the variance

•The equation is:

•The standard deviation of our example follows:

N

iii rrP

1

2)(

%21.21)14.16.(25.)14.14(.5.)14.44(.25. 222

• What is the average realized rate of return for Stock A and Stock B using the sample data?

Average (Mean) Realized Returns: Example

520072006200520042003 AAAAA

AvgStockArrrrr

r

520072006200520042003 BBBBB

AvgStockBrrrrr

r

02.05

04.0)04.0(08.0)02.0(04.0

AvgStockAr

03.05

08.0)04.0(06.003.002.0

AvgStockBr

• Consider our two stocks again: Stock A and Stock B

• Note: As we will see, covariance is a very important concept!

Realized Returns and Risk: Example

Covariance: New Concept in Risk Measurement

1

))((1

,,

N

rrrrCovEstimated

N

tAvgBBAvgAA

BABA

15

)03.04)(.02.04(.)03.04.)(02.04.()03.06)(.02.08(.)03.03)(.02.02.()03.02)(.02.04(.,

BACov

0017.0, BACov

• Consider our two stocks again: Stock A and Stock B

Realized Returns and Risk: Example

Correlation: New Concept in Risk Measurement

BA

BA

StockBStockA

BABABA SS

Covrho

,,,,

7727.00458.00490.0

0017.0,,

BA

BABA

• Stand-alone risk is the risk an investor faces if he holds a single asset in isolation• i.e., rather than as part of a portfolio of assets

• Stand-alone risk can be measured as the coefficient of variation (CV)• Coefficient of variation is the standard deviation divided by the

expected return• Coefficient of variation (CV) shows the risk per unit of return• CV is used by investors to compare two or more alternative

investments

What is Stand-Alone Risk?

How is Stand-Alone Risk Measured?

• Stand-alone risk can be measured as the coefficient of variation (CV)

• Coefficient of Variation equation follows:

Coefficient of Variation (CV)

r

CV

• Assume you have the following three investment options:

• (1) A T-bill with the following attributes:

• (2) A Bond with the following attributes:

• (3) A Stock with the following attributes:

Coefficient of Variation (CV): Example

%95.1Re

rturnExpected %8.2tan iondardDeviatS

%35.5Re


%11.10Re


• Portfolio Returns:

• To compute the return on a portfolio, first compute the return on each single asset making up the portfolio

• The return on the portfolio is the weighted average of the individual security returns

• The historical (ex post) average return is often used as a proxy for the expected (ex ante) returns

• Example: Assume we have a portfolio made up of 40% of Stock A and 60% of Stock B

Portfolio Return

• Consider our example of Stock A and Stock B again:

Portfolio Return: Example

1

1

At

AtAtAtA

P

DPPr

1

1

Bt

BtBtBtB

P

DPPr

04.01

12007

At

AtAtAtA P

DPPr

08.01

12007

Bt

BtBtBtB P

DPPr

200720072007 BBAAP rwrwr

064.0)08.06.0()04.04.0(2007 Pr

• Which will have a higher standard deviation – an individual asset (i.e., stand-alone asset) or a portfolio of assets?

• Assume returns of different assets are not perfectly correlated• Gains in some of the portfolio’s assets will offset losses in

other assets• End result: Return variability (i.e., variance or standard

deviation) is reduced when assets are combined in a portfolio

Risk in a Portfolio Context

• Assume an investor owns an asset and wishes to add another asset to create a portfolio

• Question: What risk should the investor consider?

• Answer: Fundamental principle of finance is that investor cannot assess the riskiness of an investment by examining only its own standard deviation!

• Risk must always be considered in a portfolio context• i.e., taking into account the standard deviation of the entire

portfolio after adding the asset in question

Risk in a Portfolio Context continued…

• Your $500,000 home will burn down with probability equal to 0.002 (i.e., 0.2%)

• Your expected loss (due to your home burning down) is: 0.002 x $500,000 = $1,000

• An insurance policy (no deductible) costs $1,100

• (1) What is expected profit of investment in the policy?

• (2) What is expected return of investment in the policy?

• (3) What is standard deviation of profit of an investment in the policy?

Risk in a Portfolio Context: New Example

• (1) What is the expected profit of investment in the policy?

• (2) What is the expected return on the policy?


000,1$)0$998.0()000,500$002.0(1

i

N

iirPr

100$100,1$000,1$)(Pr

CostrrEofitExpected

%09.9100,1$

100$PrRe

Cost

ofitExpectedturnExpected

• (3) What is the standard deviation of profit of an investment in the policy?

• If your house burns down you get $498,900 (i.e., $500,000 - $1,100)• If your house doesn’t burn down you get -$1,100


N

iii rErP

1

2)]([ 100$100,1$000,1$)(

CostrrE

22 ])100[]100,1([998.])100[]100,1000,500([002.

31.338,22000,000,499

• Who wants to buy an asset with a negative expected return and a high level of risk (as measured by standard deviation)?

• Let’s see a show of hands! Raise your hand if you would purchase this asset!!


31.338,22%09.9Re turnExpected

• In fact, this may be a valuable addition to a portfolio because of its impact on portfolio risk

• What is the standard deviation of the value of the complete portfolio, which consists of the following two assets?

• Asset 1: Your House• Asset 2: The Insurance Policy


• Diversification is a strategy designed to reduce risk by spreading a portfolio across many assets

• The riskiness of a portfolio is usually smaller than the average of the assets’ riskiness (i.e., average of assets’ σs)

• This is true as long as the returns on the assets making up the portfolio are not perfectly correlated with one another

Diversification

• The experiment’s results:

Diversification…More Generally

• Portfolio standard deviation falls to about 20% when 20 stocks are added to the portfolio

• Some risk is diversifiable (i.e., it can be eliminated in a portfolio context) and is known as…• …Firm-specific risk, also known as…• …Idiosyncratic risk, also known as…• …Diversifiable risk, also known as…• …Unsystematic risk

• Other risk is not diversifiable even in a portfolio…• …Market risk, also known as…• …Systematic risk, also known as…• …Nondiversifiable risk

Risk and Diversification

Risk and Diversification

• An investor is only concerned with the risk of his overall portfolio

• Implication: To a well-diversified investor, only systematic risk matters

• On the risk-return tradeoff:• Since idiosyncratic risk can be freely diversified away,

investors cannot expect to be compensated for bearing it• Investors only expect compensation for bearing systematic risk

Risk and a Diversified Investor

Returns

• Return on investment– Gain or loss from an investment– Two components include:

• (1) Income component (dividend or interest)• (2) Price change (capital gain or loss)

Stock Returns • Dollar Return

– Measure of how much money you make on investment

• Capital Gain (Loss) is price appreciation (depreciation) on the stock

• Percentage Return– Rate of return for each dollar invested

)(Re LossnCapitalGaicomeDividendInturnDollar

arketValueBeginningM

LossnCapitalGaicomeDividendIn


turnDollarturnPercentage

)(ReRe

YieldLossnsCapitalGaieldDividendYiturnPercentage )(Re

Example: Calculating Stock Returns • It appears you did quite well!• Dollar Return

• Percentage Return

)(Re LossnCapitalGaicomeDividendInturnDollar

520$500$20$Re turnDollar


LossnCapitalGaicomeDividendInturnPercentage

)(Re

%8.20500,2$

500$20$Re

turnPercentage

Holding Period Returns • The holding period return is the return that

an investor would get when holding an investment over a period of t years, when the return during year i is given as Ri:

1)1(...)1()1(Re 21 nRRRturniodHoldingPer

Example: Holding Period Returns • Suppose your investment provides the

following returns over a four-year period:

1)1()1()1()1(Re 4321 RRRRturniodHoldingPer

Year Return

1 10%2 -5%3 20%4 15%

1)15.1()20.1()95.0()10.1(Re turniodHoldingPer

%21.444421.0Re turniodHoldingPer

Return Statistics • The history of capital market returns can be

summarized by describing the following:– Average Return

– Standard Deviation of Returns

– Frequency Distribution of Returns

T

RRRR T

...21

1

)(...)()( 222

21

T

RRRRRRVARSD T

Average Stock Returns and Risk-Free Returns

• The Risk Premium– The added return (over and above the risk-free rate)

resulting from bearing risk– One of the most significant observations of stock

market data is the long-run excess of stock return over the risk-free return

• Average excess return from large company common stocks for the period 1926 through 2005 was:

• Average excess return from small company common stocks for the period 1926 through 2005 was:

%8.3%3.12%5.8

%8.3%4.17%6.13

Risk Premia

• Suppose that The Wall Street Journal announced that the current rate for one-year Treasury bills (T-bills) is 5%

• What is the expected return on the market of small-company stocks?– Recall the average excess return on small company

stocks for the period 1926 through 2005 was 13.6%– Given a risk-free rate of 5%, we have an expected

return on the market of small-company stocks of:

%0.5%6.13%6.18

Risk Statistics • There is no universally accepted definition

of risk

• A useful construct for thinking rigorously about risk is the probability distribution

– Provides a list of all possible outcomes and their probabilities

Risk Statistics • Calculating sample statistics

– Mean, or Average, Return

– Sample Variance

– Sample Standard Deviation

T

RRRR T

...21

1

)(...)()( 222

212

T

RRRRRRVar T

1

)(...)()( 222

21

T

RRRRRRSD T

More on Average Returns • Arithmetic Average

– Return earned in an average period over multiple periods

• Geometric Average– Average compound return per period over multiple

periods

• The geometric average will be less than the arithmetic average unless all the returns are equal

Forecasting Return

• Blume’s formula– Arithmetic average overly optimistic for long horizons– Geometric average overly pessimistic for short horizons– Blume’s formula is a simple way to combine both!

• Where T is the forecast horizon and N is the number of years of historical data we are working with

• T must be less than N

Forecasting Return• Example: Blume’s formula

– Suppose from 25 years of data we calculate arithmetic average of 12% and geometric average of 9%

– From these averages, we can make 1-year, 5-year, and 10-year average return forecasts:

%5.11%12125

525%9

125

15)5(

R

%12%12125

125%9

125

11)1(

R

%875.10%12125

1025%9

125

110)10(

R

What is Investment Risk

• Risk, in general, refers to the chance that some unfavorable event will occur

• Investment risk pertains to the probability of realized (actual) returns being less than expected returns

– The greater the chance of low or negative returns, the riskier the investment

Types of Risk

• Stand-alone risk– Riskiness of an asset held in isolation

• Portfolio risk– Riskiness of an asset held as one of a number of assets

in a portfolio– In a portfolio context, risk can be divided into two

components• Diversifiable (firm-specific) risk• Market (non-diversifiable) risk

Individual Securities

• The characteristics of individual securities that are of interest are the:– Expected Return: Return on a risky asset expected in the future

– Variance and Standard Deviation: Measures of dispersion of an asset’s returns around its expected, or mean, return

S

stateaa stateRstatepRE

1

)()()(

S

stateaaaa REstateRstatepRVar

1

22 )]()([)()(

S

stateaaaa REstateRstatepRSD

1

2)]()([)()(

Expected Return, Variance, Standard Deviation, and Covariance

• Consider the following two risky asset world– There is a 1/3 chance of each state of the economy– The only assets are a stock fund and a bond fund

Rate of ReturnScenario Probability Stock Fund Bond FundRecession 33.3% -7% 17%Normal 33.3% 12% 7%Boom 33.3% 28% -3%

Expected Return

Stock Fund Bond Fund

Rate of Squared Rate of Squared

Scenario Return Deviation Return Deviation Recession -7% 0.0324 17% 0.0100Normal 12% 0.0001 7% 0.0000Boom 28% 0.0289 -3% 0.0100Expected return 11.00% 7.00%Variance 0.0205 0.0067Standard Deviation 14.3% 8.2%

Expected Return




%11)(

%)28(31%)12(3

1%)7(31)(

S

S

RE

RE

Variance




0324.%)11%7( 2

Variance




)0289.0001.0324(.3

10205.

Standard Deviation




0205.0%3.14

Covariance

– Deviation compares return in each state to the expected return

– Weighted takes the product of the deviations multiplied by the probability of that state

Stock Bond

Scenario Deviation Deviation Product WeightedRecession -18% 10% -0.0180 -0.0060Normal 1% 0% 0.0000 0.0000Boom 17% -10% -0.0170 -0.0057 Sum -0.0117 Covariance -0.0117

Correlation

998.0)082)(.143(.

0117.

),(

ba

ba RRCov

Return and Risk for Portfolios

– Note that stocks have a higher expected return than bonds and higher risk

– Now turn to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks




Portfolios

– The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio

Rate of ReturnScenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.0016Normal 12% 7% 9.5% 0.0000Boom 28% -3% 12.5% 0.0012

Expected return 11.00% 7.00% 9.0%Variance 0.0205 0.0067 0.0010Standard Deviation 14.31% 8.16% 3.08%

SSBBP RwRwR

%)17(%50%)7(%50%5

Portfolios• Covariance

• Correlation

)]()([)]()([)(),(1

SS

S

stateBBSB REstateRREstateRstatepRRCov

006.0%]0.11%0.7[%]0.7%17[)( 31

000.0%]0.11%0.12[%]0.7%7[)( 31

005667.0%]0.11%0.28[%]0.7%3[)( 31

011667.0),( SB RRCov

999.01431.00816.0

011667.0),(

SB RRCorr

SB

SBSB

RRCovRRCorr

),(),(

Portfolios

– Observe the decrease risk that diversification offers• Particularly when the two assets are almost perfectly

negatively correlated!!!

– An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than either stocks or bonds held in isolation

Rate of ReturnScenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.0016Normal 12% 7% 9.5% 0.0000Boom 28% -3% 12.5% 0.0012

Expected return 11.00% 7.00% 9.0%Variance 0.0205 0.0067 0.0010Standard Deviation 14.31% 8.16% 3.08%

The Efficient Set for Many Securities

– Consider a world with many risky assets– We can still identify the opportunity set of risk-return

combinations of various portfolios

retu

rn

P

Individual Assets

The Efficient Set for Many Securities

– The section of the opportunity set above the minimum variance portfolio is the efficient frontier

retu

rn

P

Individual Assets

efficient frontier

minimum variance portfolio

Diversification and Portfolio Risk

• Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns

– This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another asset

– However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion

Portfolio Risk and Number of Stocks– In a large portfolio, the variance terms are effectively

diversified away, but the covariance terms are not!

n

Nondiversifiable risk; Systematic Risk; Market Risk

Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk

Portfolio risk

What is Diversifiable Risk?• Caused by company specific events (e.g.,

lawsuits, strikes, winning or losing major contracts, etc.)– Risk factors that affect a limited number of assets– Also known as unique risk or unsystematic risk– Risk that can be eliminated by combining assets into a

portfolio• Effects of such events on a portfolio can be eliminated by

diversification

– If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

What is Market Risk?• Stems from such external events as war,

inflation, recession, changes in GDP and/or interest rates – Risk factors that affect a large number of assets– Also known as non-diversifiable risk or systematic risk

• Known as systematic risk since it shows the degree to which a stock moves with other stocks

– Because all firms are effected simultaneously by these factors, market risk cannot be eliminated by combining assets into a portfolio

• Effects of such factors on a portfolio cannot be eliminated by diversification

What is Total Risk?

• Total risk = systematic risk + unsystematic risk

– The standard deviation of returns of an individual asset is a measure of total risk

– For well-diversified portfolios, unsystematic risk is very small

– Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

Stock Prices and Information

• Actual (realized) return = expected return + unexpected return (surprise)– Surprise is risk of investment (what we couldn’t

forecast prior to buying the asset)

• General diversification information– Most stocks are positively correlated:– Average stand-alone risk:– Average portfolio risk:– Combining stocks in a portfolio lowers risk

• Except when :

65.0, yxCorr

%24.49x

%20P

0.1Corr

Risk Free Assets• Assume there is a risky asset, x, and a risk

free asset, f• Risky Asset:• Risk Free Asset:

– You have $100, you put $50 in x and $50 in f (i.e., lending $50 at the risk free rate)

– The weights are:

,16.0)( xRE %8x

,06.0)( fRE %0f

50.0100$

50$

lthInitialWea

AmountInXwx

50.0100$

50$

lthInitialWea

AmountInFw f

%11%)6(5.0%)16(5.0)()( ffxxp RwREwRE

%4%)8(5.0)( xxp wRSD

Riskless Borrowing and Lending• The Capital Market Line (CML)

– Expected Portfolio Return:

– Slope = Market Price of Risk:

– Any portfolio on CML is a combination of M and f

– If we invest in the risk-free asset, f, and in M:

– If we borrow money at the risk-free rate and invest in M

pfp SlopeRRE ][)(

M

fM RRESlope

)(

fMMMp RwREwRE )1()()(

MMp w

Mp

Mp

Riskless Borrowing and Lending• The Capital Market Line (CML)

– With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope

– This is the Capital Market Line (CML)

retu

rn

P

Rf

CML

efficient frontier

Market Equilibrium

– With the optimal capital allocation line (i.e., the CML) identified, all investors choose a point along the line

• i.e., some combination of the risk-free asset and the market portfolio, M

– In a world with homogeneous expectations, M is the same for all investors

retu

rn

Rf

P

M

efficient frontierCML

The Systematic Risk Principal

• Risk when holding the Market Portfolio, M– Researchers have shown that the best measure of the

risk of a security in a large portfolio is the beta (β) of the security

– Beta measures the responsiveness of a security to movements in the market portfolio, i.e., systematic risk

• The reward for bearing risk depends only upon systematic risk since unsystematic risk can be diversified away

)(

),(2

M

Mii R

RRCov

Portfolio Betas (βp)

• Portfolio Betas– While portfolio variance is not equal to a simple

weighted sum of individual security variances, portfolio betas are equal to the weighted sum of individual security betas

• Where w is the proportion of security i’s market value to that of the entire portfolio, and N is the number of securities in the portfolio

N

iiip w

1

Relationship between Risk and Expected Return (CAPM)

• Beta and the Risk Premium• A risk-free asset has a beta of zero• When a risky asset is combined with a risk-free asset, the

resulting portfolio expected return is a weighted sum of their expected returns and the portfolio beta is the weighted sum of their betas

• Reward-to-Risk Ratio• We can vary the amount invested in each type of asset and

get an idea of the relationship between portfolio expected return and portfolio beta

p

fp RRERatiowardToRisk

)(

Re


• What happens if two assets have different reward-to-risk ratios?

• Since systematic risk is all that matters in determining expected return, the reward-to-risk ratio must be the same for all assets and portfolios in equilibrium

– If not, investors would only buy the assets (or portfolios) that offer a higher reward-to-risk ratio

• Because the reward-to-risk ratio is the same for all assets, it must hold for the risk-free asset as well as for the market portfolio

• Result:

b

fb

a

fa RRERRE

)()(


• The Security Market Line (SML)– The security market line is the line which gives the

expected return – systematic risk (beta) combinations of assets in a well functioning, active financial market

• In an active, competitive market in which only systematic risk affects expected return, the reward-to-risk ratio must be the same for all assets in the market

• The slope of the SML is the difference between the expected return on the market portfolio and the risk-free rate (i.e., the market risk premium)

• Result:fM

i

fi RRERRE

)()(


• Expected Return on the Market

• Expected Return on an individual security

– Or

• This applies to individual securities held within well-diversified portfolios

fMi

fi RRERRE

)()(

PremiumRisk Market )( fM RRE

])([)( fMifi RRERRE

Market Risk Premium


• Capital Asset Pricing Model (CAPM)

])([)( fMifi RRERRE

Exp

ecte

d re

turn

)( MRE

fR

bβM =1.0

The Capital Asset Pricing Model• The Capital Asset Pricing Model (CAPM)

– An equilibrium model of the relationship between risk and required return on assets in a diversified portfolio

– What determines an asset’s expected return?• The risk-free rate: the pure time value of money• The market risk premium: the reward for bearing systematic

risk• The beta coefficient: a measure of the amount of systematic

risk present in a particular asset

– The CAPM: ])([)( fMifi RRERRE

The Capital Asset Pricing Model• Example: Capital Asset Pricing Model

– Suppose a stock has 1.5 times the systematic risk as the market portfolio

– The risk-free rate as measured by the T-bill rate is 3% and the expected risk premium on the market portfolio is 7%

– What is the stock’s expected return according to the CAPM?

])([)( fMifi RRERRE

%5.13%]7[5.1%3)( iRE

The Capital Asset Pricing Model• Example: Capital Asset Pricing Model

])([)( fMifi RRERRE

%5.13%]7[5.1%3)( iRE

Exp

ecte

d re

turn

%5.13

%3

1.5 b

• Economic value defined as: “The intrinsic worth of a financial asset”• Intrinsic value derived from long-term cash flow generating

ability of a company or project• Intrinsic value measured by discounted cash flow (DCF)

• DCF used to evaluate specific investment opportunities (e.g., capital budgeting projects) or entire company

• DCF used to obtain economic value of any financial asset (including human capital)

What is Value?

• Calculating present value is called discounting• Interest rate used in discounting is called the discount

rate• General formula for the present value of $1 to be

received t periods from now at discount rate R (per period) is:

Discounted Cash Flow (DCF)

tRPV

)1(

1

• A 3-year 10% bond that makes annual payments is selling for $960. If the appropriate discount rate (i.e., YTM) is 12%, would you buy the bond?

• Compute the NPV:

NPV in Bond Valuation

2 3

100 100 100 1,000960 8.04

1.12 1.12 1.12NPV

• A stock just paid a dividend of $4. Its future dividends are expected to grow at 3% indefinitely and the current market price is $80. If the appropriate discount rate (i.e., required rate of return) is 8%, would you purchase the stock?

• Compute the NPV:

NPV in Stock Valuation

4 1.0380 2.40

.08 .03NPV

• Payback period is the time until cash flows recover the initial investment

• The decision rule

• Only accept projects with payback periods less than some pre-specified time horizon

• Does this lead to optimal decisions?

The Payback Rule

• Problem #1: Does not consider time value of money

• Payback period treats all cash flows the same no matter whether they are received at time 0 or sometime in the future

• Problem #2: Ignores all cash flows occurring after the cutoff period

• Payback period considers only cash inflows until they sum to the cash outflow – all other cash flows are ignored

The Payback Rule

• Suppose the company accepts all projects with a 2-year payback period

• Consider the following:

The Payback Rule

Project CF0 CF1 CF2 CF3 Payback NPV @ 10%

A -2,000 500 1,000 10,000 2.05 6,794

B -2,000 1,000 1,000 0 2 -264

C -2,000 0 2,000 0 2 -347

• Unfortunately, many companies use the payback period as an initial screening device• Companies that employ payback period as a screening tool typically

state that any project that has a payback period that exceeds some pre-specified time frame are automatically rejected

• Any project that meets the payback period criteria is then analyzed using some other capital budgeting technique (e.g., NPV or IRR)

• As we can see from the examples on the prior page, such companies would have rejected the only positive NPV project

Payback Period

• IRR is the discount rate that sets NPV equal to 0 (like the YTM does for a bond)

• IRR Decision Rule: Accept only the projects with IRRs exceeding the discount rate (aka hurdle rate)

• Hurdle rate typically used is the project’s risk-adjusted discount rate (i.e., the company’s WACC adjusted for the risk of the project relative to the risk of an average project of the firm)

Internal Rate of Return (IRR)

• IRR is the discount rate that sets NPV equal to 0 (like the YTM does for a bond)

• Without a financial calculator, determining the project’s IRR must be accomplished with trial-and-error (a tedious process)

Internal Rate of Return (IRR)

1 2

0 2 ... 01 1

CF CFNPV CF

IRR IRR

IRR Example

You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e., rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

1 2 3

16,000 16,000 466,0000 350,000

(1 ) (1 ) (1 )IRR IRR IRR

IRR = 12.96%

• Problem #1: Non-normal cash flows• Possible for a project to have multiple IRRs• Manager can’t make a decision because doesn’t know which

one to use• In general, the number of sign changes in cash flows equals the

number of IRRs

• Problem #2: Choosing between mutually exclusive projects• NPV and IRR may tell the manager different things (NPV

profile)• Since we know NPV is optimal, IRR won’t always lead to the

correct decision

IRR Problems

IRR Problems

You have two proposals to choose between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer? What about NPV?

Project C0 C1 C2 C3 IRR NPV@7%

Initial Proposal -350 400 14.29% 24,000$ Revised Proposal -350 16 16 466 12.96% 59,000$

• Reinvestment rate assumption • NPV assumes cash flows from a project can be reinvested at the

project’s cost of capital (i.e., project’s risk-adjusted discount rate)• IRR assumes that cash flow from a project can be reinvested at the

project’s internal rate of return

• What is the correct reinvestment rate assumption? • Company should be able to reinvest at its WACC (or it should be

paying out earning to shareholders rather than reinvesting!) • However, a company may find it extremely difficult to reinvest at a

project’s IRR if the project’s IRR is extremely high!• If a company is unable to reinvest at the project’s IRR, then

the project won’t earn its IRR (i.e., the IRR will be overstated)

Comparing NPV and IRR

• Independent projects means that the acceptance of one project doesn’t impact the decision of another project• For projects with normal cash flows, NPV and IRR criteria always

lead to the same accept/reject decision

• Mutually exclusive projects mean that the manager can only invest in one project from a set of projects• NPV will always lead to the correct accept/reject decision• If IRR decision is different from NPV it is due to one of two potential

problems:• (1) Timing difference in cash flows• (2) Project size or scale differences


• Capital Budgeting Decision Rule: Since NPV always provides the correct accept/reject decision, always use NPV!

• Question: Why, then, do we even cover IRR?

• Answer: Many managers still use IRR in their capital budgeting decision-making!


• (1) Average Accounting Return (ARR)

• (2) Discounted Payback Period

• (3) Modified Internal Rate of Return (MIRR)

• (4) Profitability Index (PI)

Other Capital Budgeting Techniques

• The AAR is a measure of accounting profit relative to book value

ARR = [Average Net Income/Average Book Value]

• The AAR is similar to the accounting return on assets (ROA)

• The AAR rule is to undertake a capital budgeting project if the project’s AAR exceeds a benchmark AAR

• AAR is seriously flawed for a variety of reasons• AAR ignores time value• AAR uses net income and book value rather than cash flows and

market value (therefore not economically meaningful)

Average Accounting Return (AAR)

• The Discounted Payback Period is the length of time until the sum of an investment’s discounted cash flows equals its cost

• The Discounted Payback Period rule is to undertake a capital budgeting project if the project’s discounted payback period is less than some cutoff

• Discounted Payback Period is flawed • This method ignores cash flows that occur after the cutoff period

Discounted Payback Period

• The MIRR is a modification to the IRR where the project’s cash flows are modified by:• (1) Discounting the negative cash flows back to the present• (2) Compounding all cash flows to the end of the project’s life, or• (3) Combining (1) and (2) above

• An IRR is then computed on the modified cash flows

• MIRRs are guaranteed to avoid the multiple rate of return problem, but: • (1) It is unclear how to interpret them• (2) They are not truly “internal” because they depend on

externally supplied discounting or compounding rates• (3) Most importantly, MIRR, like IRR cannot be used to rank

mutually exclusive projects

Modified Internal Rate of Return (MIRR)

• The PI, also called the benefit-cost ratio, is the ratio of present value to cost• Also called the benefit-cost ratio:

PI = Present Value/Initial Cost

• The PI rule is to undertake a capital budgeting project if the index exceeds 1

• PI is similar to NPV, but like IRR it cannot be used to rank mutually exclusive projects

Profitability Index (PI)

Relevant Cash Flows

• Relevant Cash Flows– The incremental cash flows associated with the

decision to invest in a project

• The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of undertaking the project– Difference between cash flows with the project and

cash flows without the project– Based on free cash flows, not accounting income

Aspects of Incremental Cash Flows• Sunk Costs

– Costs that have already occurred– Example: Test market expenses

• Opportunity Costs– Cost of best foregone alternative– Cash flows lost by taking one course of action over

another

• Side Effects or Externalities: Erosion– Erosion (or cannibalization): cash flow transferred to

new project from customers and sales of existing products

Aspects of Incremental Cash Flows• Net Working Capital

– Costs associated with an increase in net working capital due to undertaking a project

• Increase in current assets (e.g., inventory and/or A/R) and/or decrease in current liabilities associated with undertaking a capital budgeting project

• Financing Costs– Costs associated with how the project is financed

• Includes interest and dividend expenses

• Other Issues– All cash flows should be after-tax cash flows

Net Working Capital (NWC)

• NWC is the difference between CA and CL– Investment in inventories and A/R net of increase in

A/P

• Generally, firms invest in NWC at beginning of project (t=0) – This investment in NWC is recovered at the end of the

project

• ∆NWC should be included in incremental CFs

Net Working Capital (NWC)

• GM will increase NWC at the beginning:– Firm will increase inventories of raw material– Dealers will require increased A/R financing

• At the end of model’s life, NWC will decline: – Inventories will be allowed to run down– A/R will be paid down

• ∆NWC – Increases at the beginning are cash outflows – Decreases at the end of the project are cash inflows

Additions to NWC

• Given NWC at the beginning of the project (i.e., t=0), we can calculate future NWC as:

– NWC will grow at a rate of X% per year (e.g., 3%)• i.e., NWCYear2 = NWCYear1 x (1 + 0.03)

– NWC will equal Y% of sales each period (e.g., 15%)• i.e., NWCYear2 = SalesYear2 x (0.15)

• Text assumes initial investment in NWC is made in year 0 – So assume this is the case unless told otherwise

Recovery of NWC

• NWC is recovered at the end of the project:

– Bring NWC account to zero• Inventories are run down• Unpaid bills are paid (both A/R and A/P)

• Text assumes initial investment in NWC made in year 0 is all recovered at the end of the project – So assume this is the case unless told otherwise

Recovery of NWC

Year

NWC

Additions to NWC

0

$500,000

$500,000

1

$600,000

$100,000

2

$800,000

$200,000

Recovery in year 3 0 -$800,000

Year

NWC

Additions to NWC

0

$500,000

$500,000

1

$700,000

$200,000

2

$600,000 -$100,000

Recovery in year 3 0

-$600,000

Treatment of Financing Costs

• Should you subtract interest expense or dividends when calculating cash flows?

• No! – We discount project cash flows with a cost of capital

that is the rate of return required by all investors– Therefore we should discount the total amount of cash

flow available to all investors

• They are part of the cost of capital– If we subtracted them from CFs, we would be double

counting capital costs

Depreciation and Capital Budgeting

• Depreciation is a non-cash charge– However, depreciation has cash flow consequences

since it affects taxes

• Companies often calculate depreciation one way for reporting taxes and another for reporting to investors – Tax depreciation is typically determined by MACRS

• Salvage value and economic life are ignored

– Many firms use straight line method for stockholders• Subtract salvage value from cost and divide by asset’s

economic useful life (in years)

MACRS• Modified Accelerated Cost Recovery System

– Set forth guidelines that govern tax depreciation– Created several classes of assets, each with a more-or-less arbitrarily

prescribed life called a recovery period or class life– MACRS class life bears only rough guideline to expected useful economic

life– Major effect has been to shorten the depreciable lives of assets, giving

business larger tax deductions and thus increasing their cash flows available for investment

• Cash flows increased since higher early (time value of money) depreciation reduces taxes, and therefore increases cash flow to stakeholders

• Companies often calculate depreciation one way for reporting taxes and another for reporting to investors – Tax depreciation is typically determined by MACRS

• Salvage value and economic life are ignored

– Many firms use straight line method for stockholders• Subtract salvage value from cost and divide by asset’s economic useful life (in years)

MACRS: Major Classes/Asset LivesClass Type of Property

3-year Certain specialized short-lived property, race horses over 2 years old

5-year Automobiles, trucks, computers7-year Most industrial equipment, office furniture, books10-year Certain longer-lived equipment, vessels, barges, tugs20-year Farm buildings, sewer pipes, very long-lived equipment

27.5-year* Residential rental property such as apartment buildings31.5-year* Nonresidential property, including commercial and industrial

buildings

• *Note: Real estate must be depreciated using the straight line method. Other classes can use either straight line or the accelerated method. Since higher depreciation expense results in lower taxes and higher cash flows, most elect to use the accelerated method.

Half-Year Convention• Under MACRS, assumption is made that the

asset is placed in service in the middle of the first year– For 3-year class property, the recovery period begins in

the middle of the first year and ends three years later– The effect of the half-year convention is that the

recovery period extends out one more year than the asset class

• i.e., 3-year assets are depreciated over four fiscal years

– This convention is incorporated in to the MACRS recovery allowance percentages

• Half-year convention also applies to straight line

MACRS Depreciation Allowance

Year 3-year 5-year 7-year

1

2

3

33.33%

44.44%

14.82%

7.41%4

20%

32%

19.2%

11.52%

11.52%

5.76%

5

6

14.29%

24.49%

17.49%

12.49%

8.93%

8.93%

8.93%

4.45%

7

8

Depreciable Basis

• The depreciable basis under MACRS is:– Purchase price of the asset– Plus: Shipping costs– Plus: Installation costs

• The depreciable basis is not adjusted for salvage value– i.e., the estimated market value of the asset at the end

of the asset’s useful life

Depreciation Summary: For Tax Purposes

• Depreciation is a non-cash charge– Which has cash flow consequences since it affects

taxes

• To estimate depreciation expense:– Calculate depreciable basis

• Cost of asset plus any shipping and/or installation charges

– Ignore economic life and future market value• i.e., ignore salvage value of asset at end of its useful life

– Use tax accounting rules for deprecation• MACRS and Straight line methods both use half-year

convention

Straight Line versus MACRS

Year

MACRS Percentage

MACRS

Depreciation

Straight-line Depreciation

1

20.00%

$6,000

$3,000

2

32.00%

$9,600

$6,000

3

19.20%

$5,760

$6,000

4

11.52%

$3,456

$6,000

5

11.52%

$3,456

$6,000

6

5.76%

$1,728

$3,000

Net Capital Spending

• When starting a new project, we often must invest money in fixed assets at the start (t=0)

• What happens to those assets at the end of the life of the project?

• We ignored salvage value when calculating depreciation expense for tax purposes– But salvage value must be considered in our cash flows

Salvage Value

• If an asset’s value when sold (i.e., salvage value) exceeds (is lower than) its book value, the difference is treated as a gain (loss) for tax purposes– Taxes = (Market Price – Book Value) x Tax Rate– After-Tax Salvage Value = Market Price – Taxes

• At the end of a project’s life, the book value of a piece of equipment is $0; however, assume you can sell it for $5,000 (and also assume your tax rate is 40%) – What taxes will you pay?– Taxes = ($5,000 – $0) x 0.40 = $2,000– After-Tax Salvage Value = $5,000 – $2,000 = $3,000

Salvage Value

• Assume the asset’s book value was $1,000 at the end of the project’s life: – Taxes = ($5,000 – $1,000) x 0.40 = $1,600– After-Tax Salvage Value = $5,000 – $1,600 = $3,400

• Assume the book value was $6,000 at the end of a project’s life:– Taxes = ($5,000 – $6,000) x 0.40 = -$400– After-Tax Salvage Value = $5,000 –(-$400) = $5,400

Capital Budgeting ProblemCox Casting Company

• Cox Casting Company (CCC) Project– Is considering adding a new line to its product mix– You must complete the capital budgeting analysis– Production to be set up in unused space in CCC’s plant– The machinery’s invoice price would be approximately

$200,000• Shipping and installation costs are $10,000 and $30,000

respectively• Machinery has an economic life of 4 years and CCC has

obtained a special ruling which places equipment in MACRS 3-year asset class

• Machinery is expected to have a salvage value of $25,000 after 4 years of use


• Proposed Project Summary– Depreciable Basis

– Economic life of machinery = 4 years

– Salvage value = $25,000

– MACRS 3-year asset class

onInstallatiShippingtInitialCoseBasisDepreciabl

000,30$000,10$000,200$ eBasisDepreciabl


• CCC’s Capital Budgeting Project continued– New line would generate incremental sales of 1,250

units per year for four years– Each unit can be sold for $200 in the first year– Incremental costs would be $100 per unit in the first

year, excluding depreciation– Sales price and costs expected to increase 3% per year – CCC’s NWC to increase (starting in year 0) by an

amount equal to 12% of next year’s sales revenue– CCC’s tax rate is 40%– Project’s risk-adjusted cost of capital is 10%


• Proposed Project Summary– Annual unit sales = 1,250

– Unit sales price in year 1 = $200

– Unit costs in year 1 = $100

– Growth rate in sales and costs = 3% per year (inflation)

– NWC = 12% of next year’s sales revenue

– Tax rate = 40%

– Project cost of capital = 10%


• Incremental Costs– Suppose the plant space could be leased out for

$25,000 a year

– Should this cost be included in the analysis?

– Yes!

– This is an opportunity cost since accepting the project means you will not receive the $25,000 in lease income

– After-Tax Opportunity Cost:

000,15$)40.01(000,25$ ostportunityCAfterTaxOp


• Side Effects or Externalities– Suppose the new product line would decrease sales of

CCC’s other products by $50,000 per year

– Should this cost be included in the analysis?

– Yes!

– This is erosion or cannibalization• Net CF loss on other lines would be a cost to this project

– However, the annual loss would not be the full $50,000 since CCC would save on cash operating costs if its sales dropped

– You would need to figure out the effect on the other products’ operating cash flows


• Summary: Side Effects or Externalities– Externalities can be negative

• If the new product is a substitute to existing products• Erosion or cannibalization

– Externalities can be positive• If the new product is a complement to existing products• Synergy

– In either case, the incremental impact on CFs must be included in your capital budgeting analysis


• Annual Depreciation Expense

Year MACRS % x Initial Basis = Depreciation

1 0.3333 $240,000 $79,992

2 0.4444 106,656

3 0.1482 35,568

4 0.0741 17,784240,000


• Annual Sales and Costs

Year 1 Year 2 Year 3 Year 4

Units 1,250 1,250 1,250 1,250

Unit Price* $200 $206 $212.18 $218.55

Unit Cost* $100 $103 $106.09 $109.27

Sales $250,000 $257,500 $265,225 $273,188

Costs $125,000 $128,750 $132,613 $136,588

* Price and costs growing at 3% per year after year 1


• Adjusting for Inflation– Is it important to include inflation when estimating

CF?

– Nominal rate R > real rate r

– Cost of capital, R, is based on market determined cost of debt and equity and includes a premium for inflation

– If you discount real CFs with the higher nominal rate, R, then your NPV estimate is too low

– Since the cost of capital is already in nominal form, it is usually easiest to adjust cash flows to reflect inflation


• Operating Cash FlowsYear 1 Year 2 Year 3 Year 4

Sales $250,000 $257,500 $265,225 $273,188

Costs $125,000 $128,750 $132,613 $136,588

Deprecation $79,992 $106,656 $35,568 $17,784

EBIT $45,008 $22,094 $97,044 $118,816

Taxes (40%) $18,003 $8,838 $38,818 $47,526

NOPAT $27,005 $13,256 $58,226 $71,290

+ Depreciation $79,992 $106,656 $35,568 $17,784

Net Op. CF $106,997 $119,912 $93,794 $89,074


• Change in Net Working Capital (∆NWC)

Sales

NWC (12% of next

year’s sales)

CF Due toInvestment

in NWC

Year 0 $30,000 -$30,000

Year 1 $250,000 $30,900 -$900

Year 2 $257,500 $31,827 -$927

Year 3 $265,225 $32,783 -$956

Year 4 $273,182 $0 $32,783


• After-Tax Salvage Value– When the project is terminated at the end of year 4, the

equipment can be sold for $25,000

– But it has been fully depreciated (i.e., its book value is zero)

– Therefore, taxes must be paid on the full salvage value

– For this project, the after-tax salvage cash flow is:

TaxRateBkValueMktValueMktValuelvageCFAfterTaxSa )(

000,15$40.0)0$000,25($000,25$ lvageCFAfterTaxSa


• Total Cash Flows from AssetsYear 0 Year 1 Year 2 Year 3 Year 4

Initial Cost -$240,000 0 0 0 0

Op. CF 0 $106,997 $119,912 $93,794 $89,074

NWC CF -$30,000 -$900 -$927 -$956 $32,783

Salvage CF 0 0 0 0 $15,000

Net CF -$270,000 $106,097 $118,985 $92,838 $136,857

NPV = $88,012 at R = 10%


• NPV Analysis– Now you have undertaken NPV analysis for Cox

Casting Company in terms of its new product line capital budgeting project

• Using the project’s 10% cost of capital NPV is $88,012 • Undertaking this project is expected to increase CCC’s

stockholders’ wealth by $88,012

– What do you suggest?

– Obviously, since the NPV is positive, you should accept the project

– However…


• Limitations of NPV Analysis– Fundamental problem in NPV analysis is dealing with

uncertain future outcomes• NPV is only as good as inputs and assumptions used• Need techniques to identify crucial assumptions and explore

what could go wrong

– Techniques• Sensitivity analysis• Scenario analysis• Decision trees


• Sensitivity (also called what-if) Analysis– Sensitivity analysis examines how sensitive NPV is to

changes in the underlying assumptions• Does changing your assumptions (e.g., discount rate,

estimated expected cash flows, etc.) change your decision to invest?

– Under sensitivity analysis, one input is changed by a fixed percent while all other inputs are held constant

• Any input variable that causes a large change in NPV is considered a key variable

• Key variables must be controlled by managers in order to obtain expected NPV


• Sensitivity Analysis– Pros

• Indicates whether NPV analysis can be “trusted”– i.e., if NPV is very sensitive to certain key variables

• Shows where more information is needed– i.e., which assumptions have the biggest effect on NPV

– Cons• Treats each variable in isolation, when in reality, variables

are often related• Says nothing about likelihood of a change in the variable


• Sensitivity Analysis

% Change WACC % Change UNIT SALES % Change SALVAGE

from NPV from Units NPV from Variable NPV

Base Case WACC 88,012 Base Case Sold $88,012 Base Case Cost $88,012

-30% 7.0% $113,273 -30%

875 $16,651 -30% $17,500 $84,939

-15% 8.5% $100,294 -15%

1,063 $52,331 -15% $21,250 $86,476

0% 10.0% $88,012 0%

1,250 $88,012 0% $25,000 $88,012

15% 11.5% $76,380 15%

1,438 $123,694 15% $28,750 $89,549

30% 13.0% $65,352 30%

1,625 $159,375 30% $32,500 $91,086



Change from Resulting NPV (000s)

Base level WACC (r) Unit sales Salvage -30% $113 $17 $85

-15% $100 $52 $86

0% $88 $88 $88

15% $76 $124 $90

30% $65 $159 $91



-30 -20 -10 Base 10 20 30 (%)

88

NPV(000s)

Unit Sales

Salvage

R

Two Methods• Replacement Chain Method

– Also called Matching Cycles Method• This method replicates multiple cycles of asset lives until the

two pieces of equipment have the same number of years

• Equivalent Annual Cost Method (EAC)– Also called the annuity method

• The present value of a project’s costs calculated on an annual basis

• Assumptions• Initial costs versus maintenance• Perpetuity

Example: Two Methods• Assumptions

– Project requires purchase of machinery

– Two machine alternatives

– Machine A has a 3 year life

– Machine B has a 2 year life

– Project risk-adjusted cost of capital is 8%

Example: Two Methods• Approach 1:Replacement Chain Method

• Approach 2: EAC

• Approach 1: Matching Cycles• Two cycles of project A 6 years• Three cycles of project B 6 years

tRR

EACCostsPV

)1(

11)(

actorPVAnnuityFEACCostsPV )(

Example: Replacement Chain0 1 2 3 NPV

@ 8%A -15 -5 -5 -5 -27.89B -10 -6 -6 - -20.70

NPVA=-27.89 NPVA=-27.89

0 2 3 4 6

NPVB=-20.70 NPVB=-20.70NPVB=-20.70

For A: NPV = -27.89 - 27.89/(1.08)3 = -$50.03For B: NPV = -20.70 - 20.70/(1.08)2 - 20.70/(1.08)4 = -$53.66Choose A

Example: Equivalent Annual Cost0 1 2 3 NPV

@ 8%A -15 -5 -5 -5 -27.89B -10 -6 -6 - -20.70

Approach 2: Equivalent Annual Cost EAC = NPVONE CYCLE/[1/r(1 – (1 + r)-T)] = NPVONE CYCLE /AT

r

For A: EAC = -27.89/A38% = -27.89/2.577 = -$10.82

For B: EAC = - 20.70/A28% =-20.70/1.783 = -$11.61

Choose A

0 1 2 3 4…. A - -10.82 -10.82 -10.82 -10.82 B - -11.61 -11.61 -11.61 -11.61

Evaluating Cost Cutting Proposals

Evaluating Cost Cutting Proposals• Consider a project to automate some part of

an existing process• Necessary equipment costs $80,000 to buy and install• Project will save $22,000 per year (pre-tax) by reducing

labor and material costs• Equipment is 5-year MACRS and is expected to have a

salvage value of $20,000 after 5 years• The tax rate is 34%• The risk-adjusted discount rate is 10%

– Note: There is no working capital consequences

• Should you undertake the project?

Evaluating Cost Cutting Proposals• Step 1: Depreciation:• Depreciation of $80,000 of 5-year equipment

using MACRS

MACRS% Depreciation Book value

1 20.00 16,000 64,000

2 32.00 25,600

3 19.20 15,360

4 11.52 9,216

5 11.52 9,216 4,608

6 5.76 4,608 0

100.00 80,000


Year 1 Year 2 Year 3 Year 4 Year 5

Rev – Exp

22,000 22,000 22,000 22,000 22,000

Deprec. 16,000 25,600 15,360 9,216 9,216

EBIT 6,000 -3,600 6,640 12,784 12,784

Taxes @34%

2,040 -1,224 2,258 4,347 4,347

NI

Evaluating Cost Cutting Proposals Item

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

EBIT

6,000

-3,600

6,640

12,784

12,784

Depreciation

16,000

25,600

15,360

9,216

9,216

4,608

Taxes

2,040

-1,224

2,258

4,347

4,347

Operating Cash Flow

19,960

23,224

19,742

17,653

17,653

Net Capital Spending

-80,000

14,767

Total Cash Flow

-80,000

19,960

23,224

19,742

17,653

32,420

NPV = $4,359


• Should you undertake the project?

• Yes!

• The cost cutting project is expected to produce a positive NPV

What is Value? • Economic Value defined as: “The intrinsic worth

of a financial asset”– Intrinsic value derived from long-term cash flow generating

ability of a company or project– Intrinsic value measured by discounted cash flow (DCF)

• DCF used to evaluate– Specific investment opportunities– Strategy of a business unit– An entire company

• DCF used to obtain economic value of any financial asset (including human capital!)

Discounted Cash Flow (DCF) • Calculating present value is called discounting• Interest rate used in discounting is called discount

rate• General formula for the present value of $1 to be

received n periods from now at discount rate i (per period) is:

tRPV

)1(

1$

How is Value Created?• Value results from set of interrelated activities that

most firms already have in place• The issue is to what extent behaviors that promote value

creation are a part of the corporate culture• Prerequisite for value creation is that firm’s actions be based

on a foundation of value thinking

– Value thinking has two dimensions• (1) Value Metrics based on management’s understanding of

how value is created and how the stock market values firms– Management’s ability to balance short-and long-term results

• (2) Value Mindset refers to how much management cares about shareholder value creation

– Management’s willingness to make unpopular decisions if these are necessary to maximize shareholder value in the long-term

Three Revisions to Porter’s Model

• First, Composite Competitive Rivalry Force– (a) Pressure from substitutes and (b) Threat of new entry

combined with traditional competitors into the single category

• Second, Additional Role of Complementors– Market participant considered a complementor if buyers value

company’s product more highly when they have access to complementor’s product

• Third, Addition of Market Turbulence and Market Growth– Considers impact of changing market conditions on risk and

strategy

Financial Research: New Perspective

• Financial Research should determine value proposition– Answer Question: Does capital budgeting project create or destroy value?

• Value creation should be management’s primary goal!– Discounted Cash Flow (DCF) is primary technique to measure value as

Net Present Value (NPV)– However, DCF technique does not measure value of flexibility (i.e., NPV

does not include value of flexibility)

• New technique needed to incorporate real (growth) options– Growth options include opportunity to expand capacity, make new product

introductions, expand basic research, increase advertising– Value of the option is the present value of expected cash flows plus the

value of any new growth opportunity

New Technique: Real Options• Real options technique overcomes restrictiveness of

NPV– DCF understates project’s value (NPV) due to increased flexibility and

additional growth opportunities

• Real options challenge conventional wisdom about capital budgeting– Accepting negative NPV project justified if it creates growth

opportunities and sum of NPV of these new opportunities is positive

and greater than initial project’s negative NPV

• Real options advantage is that is integrates capital budgeting with long-range planning– Investment decisions today can create basis for future investment

decisions

Feasibility Study

• Feasibility study is first step to successful project• Feasibility studies require management to…

– Conduct up-front due diligence– Understand project’s risk analysis, cost analysis, completion time

frame, stakeholders’ analysis, etc.– Follows the ‘ready, aim, fire’ model rather than ‘ready, fire, aim’

• Benefits of accurate and reasonable feasibility study– Avoids danger of loading up evidence in one direction in order to

support a priori decision– It locks company into a mode of planning first, then executing, which

avoids potential waste

Pro Forma Construction• Pro forma, or projected, financial statements reflect

expected future performance of firm or project• Pro forma financial statements constructed and used

to…– Evaluate expected future financial condition of firm or

project– Project financing requirements– Determine how alternative courses of action are likely to

impact firm’s financial conditions and financial requirement

– Provide a standard against which to evaluate actual results

Free Cash Flows• Primary outcome of pro forma financial statement is

ability to forecast free cash flows• Free cash flows are the amount of cash a firm or

project can pay out to investors– Usually annual cash flows after paying for all investments

necessary for growth

• Pro forma Excel models typically incorporate a spreadsheet designed to calculate free cash flows– Purpose of such spreadsheet models is to be used as a

managerial decision-making tool– Permits managers to test potential outcomes of various

scenarios

Time Value of Money

• Economic value defined as the intrinsic worth of a financial asset– Intrinsic value derived from long-term cash flow generating

ability of a financial asset (e.g., capital project)

• To determine economic value future cash flows must be discounted to the present– Calculating present values is called discounting– Interest rate used in discounting is discount rate

• Most financial assets require investment at beginning of asset’s life and generate multiple flows in the future– Each cash flow is discounted back to the present and

summed to obtain the net present value (NPV)

Net Present Value• NPV is the appropriate value measurement managers

should use to determine viability of capital project– NPV recognizes time value of money (i.e., dollar today worth

more than dollar tomorrow)• Dollar today can be invested to start earning interest immediately

– NPV depends solely on forecasted cash flows from the project and the project’s opportunity cost of capital

• NPV unaffected by manager’s taste, company’s choice of accounting method, profitability of company’s other independent projects. Therefore, it will not lead to inferior decisions based on these extraneous factors

– Because present values are all measured in today’s dollars, they can be added up (additive property)

• Once calculated, can be summed to determine expected value creation

Risk Identification

• Although easy to understand, risk may be difficult to define and quantify– Markowitz defined risk of a security as the standard

deviation of returns around the mean or expected return– Factors causing higher dispersion may be harder to

identify• What factors cause one security to have a higher standard

deviation of returns than another security?

• In order to manage risks, managers must first be able to identify the factors underlying risk

Risk Analysis and Management• Managers often take risks as given

– To some extent managers can choose risk their business or project undertakes

– Certain risk can be hedged or insured against

• View risk as uncertainty– Uncertainty resolved through passage of time, actions, and events– Managers can make appropriate mid-course corrections through

change in decisions and strategies

• Real options incorporate learning model akin to having a strategic road map– Manager can reduce risk by building flexibility into project– Traditional analyses neglect managerial flexibility and therefore

undervalue certain projects and strategies

Cost of Capital

• The cost of capital is the firm’s discount rate applied to the average risky project’s cash flows in order to determine the present value of those cash flows– Often referred to as the Weighted Average Cost of Capital

(WACC)

• The 4-step process to determine the discount rate, or WACC, is to determine firm’s:– (1) Optimal capital structure– (2) Capital requirements– (3) Component costs of capital– (4) WACC

Sensitivity and Scenario Analyses• Prior steps of Project Analysis provide information to

conduct sensitivity and scenario analyses– These analyses determine whether results are robust under

alternative assumptions

• Sensitivity analysis determines key variables of project– Project’s ultimate value depends upon controlling these key

variables

• Scenario analysis enables manager to combine key variables into probable situations or outcomes

• Managers use these two analyses to:– Measure change in value due to changes in decisions– Determine probable range of value that the project creates

Capital Budgeting Process• Capital budgeting process summarizes how firms

identify and commit to capital investment projects• Process entails how companies:

– Develop plans and budgets for capital investments– Authorize specific projects to be undertaken– Check to determine whether projects perform as expected and

promised

• Benefits of properly designed capital budgeting process– Process provides means of obtaining accurate information and

forecasts to decision-makers– Process insures managers are rewarded for adding value to

firm– Process provides performance measurement

Valuation• Companies thrive when they create real economic value

to shareholders– Firms create value by investing capital at rates of return that

exceed their cost of capital– The more capital invested at attractive rates or return, the more

value created

• Value creation principles must be part of important managerial decision-making– Value creation plans must be grounded in realistic assessments

of product market opportunities and the competitive environment

– Managers must be able to create tangible links between their strategies and value creation

Investment Decision• Investment decision is the beginning of learning

– As soon as decision is made, managers should begin learning • About business conditions, competitors’ actions, quality of preparations,

etc.

– Managers must respond flexibly to what they learn

• Investment decisions are made under uncertainty– Requires approach to valuation that assists managers to think

strategically• Approach should capture value of managing actively rather than passively

– Capital budgeting project is a series of options rather than series of static cash flows

• Executing project involves making sequence of decisions, some now and some in the future

– Decision to undertake project sets framework within which future decisions will be made

• But at the same time leaves room for learning and for discretion to act based on what is learned

Rick’s Hardware: A Simple Example • Stage 1: The Early Years

– Rick owns a small chain of hardware stores– To keep it simple, FINA 3320 Consultants tell Rick to focus

on Return On Invested Capital (ROIC)

– Rick’s ROIC is 18%, and we suggest WACC is 10%– Rick has a store that is earning 14% ROIC

• If Rick closes the store with the 14% ROIC, he believes he will increase the firm’s average ROIC

• Should Rick close the store with a 14% ROIC?

pitalInvestedCa

NOPLAT

EPPestedInWCCapitalInv

ofitsatingPtedTaxOperAfterAdjusROIC

&&

r

Rick’s Hardware: A Simple Example • Should Rick close the store with the 14% ROIC?

– NO! – FINA 3320 Consultants now tell Rick that he should care

not about ROIC itself, but the combination of two items:• (1) ROIC relative to WACC (the firm’s cost of capital)• (2) Amount of capital invested

– This information can be expressed as Economic Profit:

• FINA 3320 Consultants show Rick that as long as there is a positive spread of ROIC over WACC, additional Invested Capital will produce a higher Economic Profit!

• Rick’s objective should be to maximize long-term Economic Profit

)(r WACCROICpitalInvestedCaofitEconomicP

Rick’s Hardware: A Simple Example • Stage 2: Growing the Business

– For many years, Rick was happy with the Economic Profit framework (until he developed Rick’s Superhardware idea)

• If Rick undertakes Superhardware concept, the firm’s Economic Profit will drop for the first four years, after which it will be higher

• How was Rick to determine the trade-off between short- and long-term Economic Profit?

– FINA 3320 Consultants now tell Rick that he needs some more sophisticated financial tools, DCF:

• DCF Value of firm without the Superhardware concept is $53M• DCF Value of firm with the Superhardware concept is $62M

nn

WACC

FCF

WACC

FCF

WACC

FCFDCFValue

)1(...

)1()1( 22

11

0

Rick’s Hardware: A Simple Example • Should Rick undertake the new concept?

– Of course!• Rick’s new Superhardware concept is projected to be more

valuable than the present concept

– But now Rick is confused and asks: • “When do I use Economic Value and when do I use DCF?”

– FINA 3320 Consultants tell Rick that Economic Profit and DCF are the same:

nn

WACC

FCF

WACC

FCF

WACC

FCFDCFValue

)1(...

)1()1( 22

11

0

)(r WACCROICpitalInvestedCaofitEconomicP

DCFValueofitEconomicP r

Rick’s Hardware: A Simple Example • Stage 3: Rick Goes Public

– Using DCF framework, Rick makes many important long-term strategic decisions and Superhardware is successful

– Rick now wants to expand but needs access to more capital• Rick decides he should undertake an IPO and returns for advice…

– FINA 3320 Consultants tell Rick that he will have to learn to manage both the financial markets and the real markets

– Real Markets• Until now, Rick has had to manage the real markets by addressing:

– Amount of cash flow earned relative to the amount of capital invested– Maximization of value via Economic Profit and DCF

• Decision Rule for Real Market decisions– Choose strategies or make operational decisions that maximize PV of

future FCFs

Rick’s Hardware: A Simple Example – Financial Markets

• FINA 3320 Consultants explain to Rick that when the firm enters the financial, or capital, markets, the real market decision rule does not change

• However, life becomes more complicated because management must now simultaneously deal with outside investors and analysts

– FINA 3320 Consultants tell Rick that he will have to continue maximizing value, but that he must learn to also manage investors’, or the market’s, expectations

• If the market’s expectations are higher than what is ultimately realized, the stock’s price will fall even though ROIC > WACC

– The loss of credibility in this instance may take years to overcome

• If the market’s expectations are too low, share price will be too low, and the firm may be subject to a hostile takeover

Rick’s Hardware: A Simple Example • Stage 4: Conglomerate Expansion

– Publicly-traded Rick’s Hardware grew quickly and regularly beat expectations and became a top market performer

• So, Rick decided to expand into Rick’s Furniture and Rick’s Garden Supplies

• But Rick was concerned about delegating decision-making to management (as he knew he must if he expanded)

– FINA 3320 Consultants explain to Rick that he needed a planning and control system to tell him about the “health” of the firm

• That is, the ability of the firm to continue to grow and create value• This required a forward-looking metric, not just backward-looking

ones

Rick’s Hardware: A Simple Example – FINA 3320 Consultants explain to Rick that the problem

with financial metrics is that they cannot tell how management is doing in terms of creating future value

– For example:• In the short run, managers could improve short-term financial

results by cutting back on customer service– i.e., decreasing the number of employees available in the store at any time to

help customers, or reducing employee training

• Or, in the short run, management could improve short-term financial results by deferring maintenance on existing fixed assets, deferring purchase of new fixed assets, or reducing spending on brand-building (e.g., advertising, etc.)

– Rick’s hardware must incorporate metrics related to customer satisfaction or brand awareness

• Such metrics provide an idea about the future, not just the present

Rick’s Hardware: A Simple Example • Summarizing Rick’s Hardware Lessons

• (1) In the real market, you create value by earning a ROIC greater than the opportunity cost of capital, or WACC

• (2) The more you can invest above the cost of capital, the more value you create

– Growth creates more value as long as the ROIC exceeds the WACC

• (3) You should select strategies that maximize the PV of expected cash flows, or Economic Profit

– You get the same answer regardless of which you choose

• (4) The value of a firm’s shares in the stock market is based on the market’s expectations of future performance

– Market’s expectations can deviate from intrinsic value if the market is less than fully informed about the firm’s true prospects

• (5) After the initial price is set, shareholders’ returns earned depend more on the changes in expectations about the firm’s future performance than the actual realized performance of the firm

Ingredients of Pro Forma• Sales forecast may be derived using one of two

approaches– Top-down:

• Relies heavily on macroeconomic and industry forecasts• However, senior management usually establishes firm’s

objectives for increased sales– Start with reviews of sales and sales growth over past 5-10 years

– Bottom-up:• Begins by talking to customers to assess demand

• Many firms use a blend of the two approaches

Ingredients of Pro Forma• Perfectly accurate forecasts are not available

because sales depends on uncertain future state of:– (1) Economy– (2) Industry– (3) Company

• Scenario analysis should be used to examine what happens under various assumptions and states:– (1) Most Likely Worst-case– (2) Most Likely, or Base-case– (3) Most Likely Best-case

Ingredients of Pro Forma• Pro Forma Financial Statements

– Analyze historical ratios, forecast balance sheet, income statement, and sources and uses of cash

• Asset requirements– What are the firm’s planned capital expenditures?– What are firm’s net working capital needs?

• Financial requirements– How will the firm finance its growth?

• Internal retained earnings (RE): Net income – Dividends• External: New Debt and/or New Equity

– Capital structure and dividend policies

Ingredients of Pro Forma• Economic assumptions

– Interest rates, industry growth rates, etc.

• Plug– Pro forma will usually assume that sales, costs, and net

income grow at g1

– If pro forma assumes that assets and liabilities grow at g2, a third variable (e.g., equity) may be forced to grow at g3 in order to make the first two growth rates compatible and have the balance sheet identity hold:

EquityDebtAssets

Example: Pro Forma – The Plug

%20000,1$

200$arP

Sales

NetIncomeginrofitM

Income Statement 2008 Balance Sheet 2008

Sales $1,000 Assets $500 Debt $250

Costs 800 Equity 250

Net Income $ 200 Total $500 Total $500

– Assume all variables are directly tied to sales (i.e., grow at same rate) and current relations are optimal

– What happens to balance sheet and income statement if sales are forecast to increase by 20% in 2009?

1250$

250$

Equity

DebtuityDebt-to-Eq

Example: Pro Forma – The PlugIncome Statement 2009 Balance Sheet 2009




– Net income is $240 in 2009– But equity only increased by $50 since we assumed it

grew at the same rate as sales– What does this imply about dividends?

– The firm must have paid $190 in dividends

50$240$ DivDivNIRE

Example: Pro Forma – The Plug

Income Statement 2009 Balance Sheet 2009




– If firm pays no dividends, but assets still grow by 20%, what does the balance sheet look like?

– Since equity increased by $240, firm must have bought back $140 of debt in order for assets to grow by 20%

490$240$250$ NIOldEquityNewEquity

110$490$600$ NewEquityNewAssetsNewDebt

110$140$250$Re tiredDebtOldDebtNewDebt

Percent of Sales Method• Most common technique to forecast balance sheet

and income statement– Begins with sales forecast expressed as an annual

growth rate in sales revenues– Assumes that many items on balance sheet and income

statement increase proportionally with sales• Forecasted value is % of forecasted sales• Cash/Sales next year = Cash/Sales this year

– Or average of Cash/Sales for past x years

– Remaining items that are not directly tied to sales depend on firm’s dividend policy and its use of debt versus equity financing

Percent of Sales Method– (1) Forecast sales

– (2) Analyze historical ratios• Percent of sales approach assumes costs/assets are a

specified percentage of that year’s sales• Calculate ratio of costs and/or assets to sales in past years

and assume ratio remains constant in the future

– (3) Forecast income statement• Note: Interest expense is function of amount of debt and

interest rate, and is not assumed to be fixed percent of sales• Tax rate and depreciation also not generally assumed to be

fixed percent of sales

Percent of Sales Method– (4) Forecast balance sheet

• Note: Firms rarely issue common stock or preferred stock, so their forecasts are usually equal to last year’s amount

• Further, we usually assume that firms will not issue any new long-term debt, which often requires approval of board of directors

• Change in RE is function of net income and dividends paid

– (5) Given above forecasts, are additional funds needed?

• Compare forecasted assets to forecasted liabilities + equity

Percent of Sales Method• Current sales = $20,000,000,

and are expected to grow at 10% over the next year

• Assets and current liabilities vary directly with sales (stay same % of sales)

• Profit margin = 10%• Dividend payout = 50%• Given this information,

forecast the firm’s pro forma balance sheet

Balance Sheet 2008

Current Assets $ 6,000,000

Fixed Assets 24,000,000

Total Assets $30,000,000

Current Liabilities $10,000,000

Long-Term Debt 6,000,000

Common Stock 4,000,000

Retained Earnings 10,000,000

Total Liabs & Equity $30,000,000

Percent of Sales Method

• The firm has $33M in assets, but only $32.1M in liabilities and equity, so it needs to issue $900,000 in external funds

Balance Sheet 2008 % of Sales Balance Sheet 2009

Current Assets $ 6,000,000 6/20 = 30% $ 6,600,000 ($22,000,000 x 0.3)

Fixed Assets 24,000,000 24/20 = 120% 26,400,000 ($22,000,000 x 1.2)

Total Assets $30,000,000 30/20 = 150% $33,000,000 ($22,000,000 x 1.5)

Current Liabilities $10,000,000 10/20 = 50% $11,000,000 ($22,000,000 x 0.5)

Long-Term Debt 6,000,000 Constant 6,000,000

Common Stock 4,000,000 Constant 4,000,000

Retained Earnings 10,000,000 11,100,000*

Total Liabs & Equity $30,000,000 $32,100,000

000,100,11$5.0)1.0000,000,22($000,000,10$* oREAdditionsTOldRENewRE

How to Forecast Interest Expense

• Interest expense is actually based on the daily balance of debt during the year

• There are three ways to approximate interest expense– Base it on:

• (1) Debt at end of year• (2) Debt at beginning of year• (3) Average of beginning and ending debt

Forecasting Interest Expense• (1) Base interest expense on debt at end of year

• Will over-estimate interest expense if debt is added throughout the year instead of all on January 1st

• Causes circularity called financing feedback – more debt causes more interest, which reduces net income, which

reduces retained earnings, which causes more debt, etc.

• (2) Base interest expense on beginning of year debt• Will under-estimate interest expense if debt is added throughout the

year instead of all on December 31st

• But doesn’t cause problem of circularity

• (3) Base interest expense on average debt• Will accurately estimate interest payments if debt is added smoothly

throughout year• But also has problem of circularity

Forecasting Interest Expense - Solution• If calculating with calculator (by hand), base interest

expense on beginning debt, but use a slightly higher interest rate– Easy to implement– Reasonably accurate

• If using Excel, the spreadsheet can solve the circularity problem, so use average debt– Office 2003: Open Excel and go to:

Tools Options Calculation (click on iteration)

– Office 2007: Click on Microsoft Office ButtonExcel options Formulas Calculation options

(click on Enable iteration)

Additional Funds Needed (AFN)• If ratios are expected to remain constant, the following

formula can be used to forecast funds needed:

Where A are the assets tied directly to sales

L are the liabilities tied directly to sales

S0 is this year’s sales

∆S is the change in sales

S1 is next year’s projected sales

p is the profit margin

RR is the retention ratio, or (1 – dividend payout ratio)

RRSpSS

LS

S

AAFN

1

00

Additional Funds Needed (AFN)• Using the information from our previous example:

Where A = $30 million (i.e., total assets)

L = $10 million (i.e., current liabilities)

S0 = $20 million (i.e., given)

S1 = $22 million (i.e., $20 x 1.1)

∆S = $2 million (S1 – S0)

p = 0.10 (i.e., given)

RR = 1 – 0.5 (i.e., dividend payout ratio given)

MMMM

MM

M

MAFN 9.0$)5.01(22$1.02$

20$

10$2$

20$

30$

Problems with AFN and Percent of Sales Methods

• In reality, these models are too simple– Costs are not always proportional to sales– Assets are not always a fixed proportion of sales, etc.

• Economies of scale may result in the ratios changing over time as firm size increase

• Fixed assets may be “lumpy” and need to be added in large, discrete units

• Excess capacity can allow sales to grow with no increase in fixed assets

• Percent of sales is only a starting point– Use common sense and your knowledge of the firm to think

more deeply about what items might deviate from a constant proportion

What Determines Sales Growth?• Firms frequently make sales growth assumptions a part

of the planning process

• We know, however, that the goal of management should be shareholder wealth maximization

• Thus, growth should not be a goal in and of itself, but a consequence of decisions that maximize NPV

• Otherwise, if management accepts negative NPV projects just to grow the firm, shareholders (but not necessarily managers) will be worse off!

Sustainable Growth Assumptions• (1) Assets grow in proportion to sales

• (2) Net income is constant proportion of sales– i.e., Profit margin is constant

• (3) Dividend payout (d) and debt/equity ratio (DE) are fixed

• (4) Number of shares outstanding is fixed– i.e., No new equity is issued

SalessTotalAsset %%

SalesNetIncome %%

Sustainable Growth Assumptions• Under the previous assumptions, the amount by which

a firm can increase sales without increasing leverage (i.e., total debt/total assets) or issuing new equity is fixed and given by:

Where , , ,

• Approximation:

Where ,

)1()1(

)1()1(

DEdpT

DEdp

Sales

Sales

Sales

NetIncomep

NetIncome

Dividendsd

Equity

DebtDE

Sales

sTotalAssetT

)1( dROESales

Sales

1'

t

t

EquityrsShareholde

NetIncomeROE purchasesShareymentsDividendPad Re

Sustainable Growth Assumptions• Assumptions 1 and 2 hold investment policy and ROI

constant• Assumptions 3 and 4 hold dividend and financing

policies constant• The formula says that a firm’s sustainable growth

depends on profit margin, asset turnover, dividend policy, and capital structure

• Firm cannot grow faster than ∆S/S, unless– (1) Issue new equity– (2) Change one of the factors in sustainable growth formula

• Decrease dividend payout, Increase profit margin, or ∆ capital structure

Example: Sustainable Growth

p = profit margin = 10%

T = total assets/sales = 150%

DE = D/E = 100%

D = dividend payout = 50%

• If firm does not want to grow, what would it need to do?– Change dividend payout to 100%!

)1()1(

)1()1(

DEdpT

DEdp

Sales

Sales

%14286.7)11()5.01(1.05.1

)11()5.01(1.0

Sales

Sales

Uses of Sustainable Growth

• Bankers and credit analysts use sustainable growth formula to assess a firm’s creditworthiness

• If actual growth consistently exceeds sustainable growth, borrower runs the risk of “growing broke” unless it can continue to raise external funds

REV Revenues - VC Variable Costs of Operations -FCC Fixed Cash Costs (SG&A, or Selling, General & Administrative) -DEP Non-Cash Charges (e.g., depreciation, amortization, depletion) NOI Net Operating Income -kdD Interest on Debt (interest rate on debt x $ amount of Debt) EBT Earnings Before Taxes - T Taxes (corporate tax rate, tc, x EBT) NI Net Income

Calculating FCFs• After-tax cash flows (ATCFs) from operations is

Net Operating Income (NOI) less Taxes (tc):After-tax cash flows from operations may be calculated as follows: DEPNOItNOIATCF c )(

From the pro forma income statement, we know: DEPFCCVCREVNOI Therefore we can rewrite NOI less taxes as follows: DEPtDEPFCCVCREVATCF c )1)((

• To convert ATCF to FCF requires accounting for expenditures including:

• P&E: plant and equipment• Investments in working capital• R&D expenses• Advertising, etc.

This gives us the after tax free cash flow (FCF) available for payment to creditors and shareholders: IDEPtDEPFCCVCREVFCF c )1)((

Since we are interested in future free cash flows as opposed to historic flows, we must prepare pro forma (or expected) free cash flow statements: IDEPtDEPFCCVCREVEFCFE c )1)([()(

Determining All the Firm’s FCFs• Necessary to determine all future FCFs

• Corporations have infinite life therefore infinite FCFs

If assume free cash flows, after an initial period of non-constant growth (say 3 to 7 years), becomes a zero-growth firm, can use formula for a perpetuity to determine present value of the infinite zero-growth free cash flow stream:

WACC

FCFZeroGrowthEPVperp

)(

If assume free cash flows, after an initial period of non-constant growth, becomes a constant growth firm, can use Gordon Model (or constant growth model) to determine present value of the infinite constant-growth free cash flow stream:

gWACC

FCFNextPeriodEPV tGrowthCons

)(

tan

where g = the constant growth rate

Determining WACC• The 4-step process to determine appropriate

discount rate, or WACC, for discounting FCFs of the project (or the firm)

– (1) Determine firm’s optimal capital structure– (2) Determine firm’s capital requirements (i.e., I)– (3) Determine firm’s component costs of capital– (4) Determine firm’s WACC

• After calculating firm’s WACC (appropriate cost of capital for firm’s average risky project), need to determine project’s WACC based on specific project risk compared to risk of firm’s average project

• M&M show that with taxes optimal capital structure is close to 100% debt– However, M&M failed to consider financial distress

costs and agency costs

• Financial distress, or bankruptcy, costs– As a firm increases its proportion of debt, the interest

increases because of two items• The dollar amount of debt increases• The risk, and therefore the interest rate, increases

– As interest increases, the probability of default increases and so does the costs associated with bankruptcy

• Legal fees, loss of asset value, decreased sales, loss of key employees, loss of trade credit, etc.

• Agency cost of debt– As more debt is used to finance firm, shareholders may

pressure management to undertake more risky projects • Referred to as “bondholders’ wealth expropriation”• Therefore, bondholders must write covenants and contracts to

avoid this problem• Cost of writing and enforcing these covenants and contracts

are part of the agency cost of debt

• M&M’s model must be adjusted to reflect these costs:

PVACPVFDPVGLTVTV UL

where TVU = Total Value of an Unlevered (i.e., no debt) Firms PVGL = Present Value of Gains from Leverage PVFD = Present Value of Financial Distress Costs PVAC = Present Value of Agency Costs

Step 3: Component Costs of CapitalAfter-Tax Cost of Debt

First calculate before-tax cost of debt incorporating fixed and variable floatation costs (i.e., floatation costs are fees charged by the issuing investment bank) such that:

$ Amount of Debt Issued -$ Amount of Fixed Floatation Cost -$ Amount of Variable Floatation Cost $ Amount of Debt Proceeds Received by Firm

Dollar amount of debt proceeds received by firm is present value of new debt (PV). Dollar amount of debt issued is future value of new debt (FV). Payment (PMT) is FV (i.e., book value) of new debt times new rate on funding

divided by number of payment periods per year. Time (n) is number of repayment periods until maturity on the new debt. Enter all this information into a financial calculator and press i to find YTM (yield-to-

maturity), or discount rate, on new debt.

After-tax component cost of debt can be calculated using the following formula:

)1( cD tYTMR

where RD = after-tax cost of bonds YTM = floatation-adjusted yield-to-maturity tc = corporate tax rate

Cost of Preferred Stock The cost of preferred stock can be derived using the following formula:

FP

DR

pf

pfpf

where Rpf = cost of new preferred stock Dpf = annual dividend on preferred stock Ppf = current market price of preferred stock F = floatation, or selling, costs (in $s per share) Or

)1( FP

DR

pf

pfpf

where F = floatation, or selling, costs (as percent per share)

Cost of Common Equity There are two sources of suppliers of common equity funds: Retained Earnings: the internal source – i.e., existing shareholders And Issuance of New Common Equity: the external source – i.e., new shares Each of these two common equity sources needs to be looked at individually.

Cost of Retained Earnings

The component cost of retained earnings can be derived in a number of ways.

Two common techniques include the DCF (discounted cash flow or Gordon) Model and the CAPM (Capital Asset Pricing Model).

DCF (Discounted Cash Flow or Gordon) Model

gP

DRE

0

1

where D1 = the expected future dividend P0 = current market price of common stock g = constant, long-term dividend growth rate

CAPM (Capital Asset Pricing Model)

])([ fmfE RRERR

where Rf = risk-free rate of return = firm’s beta coefficient Rm = return on the market

Cost of New Common Stock (rne)

Must be slightly higher than the Cost of Retained Earnings or existing common stock (re) in order to cover flotation costs (again, the fees charged by an underwriting investment bank) associated with the issuance of new common stock. The formula is: Flotation Cost as a Percent/Share

gFP

DRNE

)1(0

1

Flotation Cost as a Dollar Amount/Share

gFP

DRNE

0

1

Terminal Growth Rate, g

There are at least three ways to estimate long-term growth (g)

(1) Sustainable Growth Model

))(1( ROEEPS

Divg

where Div = dividend per share EPS = earnings per share Div/EPS = dividend payout ratio ROE = return on equity

(2) Growth in EPS (Earning Per Share)

dingesOutsCommonShar

kholdersCommonStocvailableToNetIncomeAEPS

tan

2007

20072008

EPS

EPSEPSGrowthRateEPS

(3) Growth in Dividends

2007

20072008

Div

DivDivGrowthRateDiv

Step 4: WACC

• First, obtain component weights from optimal capital structure (Step 1)– Debt %– Preferred Stock %– Retained Earnings %– New Common Stock %

• Second, obtain component costs (Step 3)• Third, multiply component weights with

respective component costs and sum:

Proportion Cost Weighted Costs Debt % RD (%)(RD) Preferred % Rpf (%)(Rpf) Retained Earnings % RE (%)(RE) New Common Equity % RNE (%)(RNE) WACC

Determine Project’s WACC• Firm’s cost of capital defined as expected return on

portfolio of all company’s projects– Used to discount FCFs on projects of average risk– Not the proper discount rate to use if project not

average risky

• Each project should be evaluated at its own opportunity cost of capital– True cost of capital dependent on project risk

• Why estimate firm’s cost of capital?– Majority of projects can be treated as average risky– Firm’s cost of capital good starting point

Determine Firm’s Valuation

• We have…– (1) Determined firm’s (or project’s) FCFs– (2) Calculated firm’s (or project’s) WACC

• Final step is to calculate the present value of the stream of the firm’s (project’s) FCFs using WACC as the discount rate– This present value is the firm’s (project’s) total

valuation

• Subtracting market value of the firm’s debt provides price of firm’s equity

What if FCFs are Wrong?

• What if project’s FCFs are overestimated?– The project’s valuation will be too high– Realized project returns will probably be lower than

anticipated– Value of firm will probably be less than projected– Project may end up being a negative NPV undertaking

• What if project’s FCFs are underestimated?– The project’s valuation will be too low– The project may fail to meet benchmark or hurdle and

therefore be rejected (not undertaken)– Value of firm will probably not be maximized

What is WACC is Wrong?

• What is the project’s WACC is too low?– The valuation of the project will be too high– Realized project returns will probably be lower than

anticipated– Value of firm will probably be less than projected– Project may end up being a negative NPV undertaking

• What if project’s WACC is too high?– The project’s valuation will be too low– The project will fail to meet benchmark or hurdle and

therefore be rejected (not undertaken)– Value of firm will probably not be maximized

Sensitivity Analysis• FCFs and WACC have a significant impact on a

capital budgeting project’s valuation• Both require sensitivity analysis of the base case:

– Increase FCF by fixed percent (e.g., 10%) and view changes in NPV

• Holding all else constant

– Increase WACC by a fixed percent (e.g., 10%) and view changes in NPV


– Finally, change the terminal growth rate, g, and other variables view changes in NPV (to determine key variables)


Question?

What is the difference between a company’s cost of capital versus a

project’s cost of capital?

Answer

• The company’s cost of capital is defined as the expected return on a portfolio of all the company’s existing securities (or projects)

– This rate is used to discount the free cash flows on average risky projects of the company

– This is not the proper rate to use if the project is more or less risky than the average risky project

• Each project should be evaluated using its own opportunity cost of capital

The Enterprise DCF Model

An General Overview

The Enterprise DCF Model• Enterprise DCF model values the entire firm

– And then subtracts the value of debt and preferred equity to obtain common equity value

• Enterprise DCF model useful in multi-business firm– Value of firm is sum of values of each operating unit

• Enterprise DCF model values components of firm that add up to enterprise value instead of just value of equity– Assists managers identify and understand separate investment and financing

sources of value– Helps managers pinpoint key leverage areas and aids in search for value-

enhancing ideas– Model can be applied consistently at various levels of aggregation

The Enterprise DCF Model

Agile Technologies, Inc.:

An Example

Agile Technologies, Inc. – Free Cash Flow Summary (First 5 Years) Pro Forma Free Cash Flow ($ millions)

2006

2007

2008

2009

2010

Earnings Before Interest, Taxes, and Amortization (EBITA)

(1.860) (654) 5.444 27.375 68.610

Cash Taxes on EBITA 0.874 0.307 (2.559) (12.866) (32.247) Net Operating Profits less Adjusted Taxes (NOPLAT)

(0.986) (0.347) 2.886 14.509 36.363

Depreciation 0.002 0.021 0.072 0.137 0.233 Gross Cash Flow (0.984) (0.326) 2.958 14.646 36.596 Change in Working Capital (0.469) (0.704) (2.155) (5.690) (8.570) Capital Expenditures (0.073) (0.053) (0.051) (0.047) (0.051) Increase in Net Other Assets (0.012) (0.011) (0.010) (0.010) (0.009) Gross Investment (0.553) (0.768) (2.216) (5.747) (8.630) Operating Free Cash Flow (1.537) (1.094) 0.741 8.899 27.966 Cash Flow from Non-Operating Investments

0.0 0.0 0.0 0.0 0.0

After-Tax Interest Income 0.0 0.0 0.0 0.0 0.0 Decrease (Increase) in Marketable Securities

2.795 (1.554) 1.885 8.657 27.687

Cash Flow Available to Investors 1.258 (2.649) 2.626 17.556 55.553 Financing Flow Net Interest Expense After Taxes 0.020 0.024 0.024 0.024 0.024 Decrease (Increase) in Net Debt 0.0 0.0 0.0 0.0 0.0 Common Dividends 0.0 0.0 0.0 0.0 0.0 Share Repurchases 0.0 0.0 0.0 0.0 0.0 Financing Flow 1.238 (2.673) 2.602 17.532 55.529

Agile Technologies, Inc. – WACC Summary For consistency with the cash flow definition, the discount rate applied to the free cash flow should reflect the opportunity cost to all the capital providers weighted by their average cost of capital (WACC). The opportunity cost to a class of investors equals the rate of return the investors could expect to earn on other investments of equivalent risk. The cost to the company equals the investors’ costs less any tax benefits received by the company (for example, the tax shield provided by interest expense). The table below shows the WACC calculation for Agile Technologies, Inc. Source of Capital

Proportion Of Total Capital

Opportunity Cost

Tax Rate

After Tax Cost

Contribution To Weighted Average

Debt 0.03% 15.0% 47% 7.95% 0.2% Equity 99.97% 20.0% 20.00% 19.9% WACC 20.1%

Agile Technologies, Inc. – Continuing Value

An additional issue in valuing a business is its infinite life.

The value after the explicit forecast period is referred to as the continuing value.

Formulas derived from discounted cash flows using several simplifying assumptions can be used to estimate continuing value.

One such formula recommended is as follows:

gWACC

ROIC

gNOPLAT

ValueContinuing I

1

where NOPLAT = Net Operating Profits Less Adjusted Taxes (in the year after the explicit forecast period)

ROIC = Incremental Return On new Invested Capital g = Expected perpetual growth in the company’s NOPLAT WACC = Weighted Average Cost of Capital

The table below shows the continuing value calculation for Agile Technologies, Inc.

NOPLAT2015 10.163 ROICI 154% Continuing Value = NOPLATt+1[1-(g/ROICI)] NOPLAT Growth Rate (g) 3% WACC-g WACC 20% = $58.608 million

Agile Technologies, Inc. – Free Cash Flow Valuation Summary

Year Free Cash Flow (FCF) ($ millions)

Discount Factor (20%)

Present value Of FCF ($ millions1)

2006 1.258 0.833 1.048 2007 (2.649) 0.694 (1.839) 2008 2.626 0.579 1.520 2009 17.556 0.482 8.466 2010 55.553 0.402 22.323 2011 116.915 0.335 39.149 2012 207.173 0.279 57.808 2013 267.866 0.233 62.285 2014 370.336 0.194 71.758 2015 581.825 0.161 93.945 Continuing (Terminal) Value 58.608 0.161 9.463 365.925 Mid-Year Adjustment Factor2 1.09546 Value of Operations 400.856 Value of Non-Operating Investments 0.000 Total Enterprise Value 400.856 Less: Value of Debt (0.300) Equity Value 400.556 Equity Value Per Share $41.36

Value of Debt and Value of Equity• The value of a company’s debt

– Equals the present value of cash flow to debt holders discounted at the risk-adjusted rate

– Discount rate used should be equal to current market rate on similar risk debt with comparable terms

• The value of a company’s equity– Is the value of its operations plus non-operating assets

• e.g., Investments in unrelated, unconsolidated businesses

– Less value of its debt and any non-operating liabilities

• The value of Agile Technologies, Inc. equity– Is $400.556 million

What Drives FCF and Value?• Value is based on discounted FCFs and underlying value drivers also

must be based on FCFs• Two key value drivers of FCFs:

– ROIC: Return on Invested Capital

• Company that earns higher profits for every dollar invested will be worth more than similar company that earns less profit on each dollar invested

– Growth Rate: of company’s revenues, profits, and capital base

• Faster growing company will be worth more than a slower growing company if both are earning the same ROIC

• To increase value, company must• (1) Increase level of profits it earns on existing capital• (2) Ensure return on new capital investment exceeds WACC• (3) Increase its growth rate, but only if ROIC exceeds WACC• (4)Reduce its cost of capital

Art of Valuation

• Valuation is a function of:– Understanding the business (analyzing the firms)– Understanding the industry (comparative analysis)– Understanding the general economic environment– Prudently incorporating this information into the

valuation model– Correct method is the easy part!

Art of Valuation

• Requirements of the valuation model:– Pro forma model must include complete income

statement, balance sheet, and cash flow statement (which ties the first two items together!)

• Supporting ratios should also be included

– Ground pro forma model in historical analysis– Complete a similar, though less detailed, analysis

for competitors

Where is Value?

The Value Creation Pyramid

Sources of Value Creation

Financing

Maximize FreeCash Flow

Capital Efficiency

Develop a Dynamic Perspective

Internal Contracts that create proper incentives

NPV

Real Options

Management Factors

` Balance Sheet

Debt vs. Equity

Brief Mention of the Top • Financing

– Adding debt brings tax savings• Interest is tax deductible to the firm

– But adding debt incurs risk• Debt increases the probability of future financial distress

(bankruptcy)• Cost of debt depends on market risk premia

• Cash is King!– Management’s job

• Manage firm so as to maximize free cash flow

• NPV is only as good as the forecasted cash flows– Incentives to manipulate CFs in many firms explains why

this is in the middle of the pyramid

Method versus Process • The base of the value pyramid is process

– Management factors• Internal contracts creating properly aligned incentives for value

creation

• Historically, most – if not all – of the focus in corporate finance was on method (top three cells)

• But consulting with CFOs makes it clear that bad process can destroy the best method!– With a good process, method is

• (1) Not all that important, and• (2) Usually optimized (i.e., it is secondary to process)

• Process forms the basis for value creation!

Harsh Realities • Wall Street places an increasingly high premium on

“transparency”• The internal budgeting process affords a vehicle to:

– Communicate corporate expectations– Characterize perceived business opportunities– Define managerial ability to execute the business plan

• Does Wall Street’s attention to quarterly earnings targets damage long-run value creation?– Some of the blame should be placed on management’s

unwillingness to expand the scope of the “message space” in communications with the Street!

Real Options • A dynamic focus means that when you, as a

manager, make a decision, you do not act as if you are committing the firm to a locked-in stream of future cash flows

• Rather, you are positioning the firm to make future decisions

• The key is identifying the optimal reaction to future states of nature

Big Picture: Dynamic Optimization

• A problem with most firms is the focus on the short-term or static optimization

• There is no easy way to trade-off the competing needs to induce discipline, discourage shirking, and assess talent on the one hand from inducing creativity and a long-term perspective, on the other hand

Conclusion: Some Additional Sources of Value Creation

• Transparency– Increase in analysts’ coverage

• Attracting new investors– Increasing demand for the firm’s stock

• Improved operating performance– Providing better incentives and focus

• Improved corporate governance– Optimal board makeup, stock option awards, etc.

• Increase strategic flexibility– Real options analysis

Time preferences suggest a positive component to all discount rates Call this the risk-free rate...

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