ACF ppt slide

Implementing Basic Valuation

Part I: Discounted Cashflows

Jiro E. Kondo

McGill University - Desautels Faculty of Managementand

Northwestern University - Kellogg School of [email protected]

FINE-443: Applied Corporate FinanceMcGill University - Desautels

Winter 2012

Do Not Distribute or Copy in Any Part Without the Prior Consent of the Author

Jiro E. Kondo (McGill) Implementing Basic Valuation Winter 2012

Lecture Note 1 Part I

Outline for Topic 1 (Part I)

Review of NPV w/ WACC

� Obtaining After-Tax Cashflows From Earnings Forecasts

� Obtaining the Weighted-Average Cost of Capital (WACC)

Estimating the Cost of Capital in Practice

� Practical Strategies for Estimating Discount Rates: Equity and Debt

� Other Considerations: (i) Multiple Divisions, (ii) Private Companies, (iii) Lack of Diversification

� Mini Case Study (Part 1): Discounting Public Pension Liabilities

Forecasting Cashflows: Key Drivers

� Strategies for Forecasting Cashflows: (i) Top-Down vs. Bottom-Up, (ii) Decompositions

� Forecasting Terminal Values

� Mini Case Study (Part 2): Forecasting Public Pension Liabilities

DCF is Not A Number: Sensitivity Analysis

� Determining a Plausible Range of Values


Lecture Note 1 Part Ia

Topic 1 (Part Ia): NPV w/ WACC



NPV w/ WACC: Outline of Technique

Theorem

A common approach to valuing projects/companies is discounted cashflow analysis (DCF). Themost common version of this is NPV w/ WACC. This procedure involves the following steps:

Step 1: (a) Forecast the components of expected future earnings and (b) use these to obtainafter-tax cashflows using:

CFt = (1 − Tax) × EBITDt + Tax × DEPRt − CAPXt − ΔWCt (1)

Step 2: (a) Get the after-tax discount rates (for valuing the cashflows estimated above)using the weighted-average cost of capital (WACC) formula:

E[r] = (D/V ) × (E[rD] × (1 − Tax)) + (E/V ) × E[rE] (2)

where (b) the values of E[rD] and E[rE ] are obtained from market prices (e.g., yields ondebt of similar risk) or using an asset pricing model (e.g., the CAPM).

Step 3: Take the output from Steps 1 and 2 and combine into the NPV formula.

Review of NPV w/ WACC: Our first goal in the course is to re-gain comfort with this

procedure using examples.



NPV w/ WACC (Step 1): Obtaining After-Tax Cashflows

Components of the Cashflow Formula From (1):

CFt = (1 − Tax) × EBITDt| {z }Accounting

+ Tax × DEPRt − CAPXt| {z }Capital Expenditures

−ΔWCt| {z }Other

Accounting: Only operations and ignores depreciation.

Capital Expenditures: Capital purchases are straightforward, but make sure you factor intaxes in the case of capital sales...

CAPXt = Sales Pricet − ˆTax × (Sales Pricet − Book Valuet| {z }Capital Gain on Salet

) (3)

Other: In this course, we focus on account receivable, accounts payable, and inventory.

ΔWCt = ΔARt + ΔINVt − ΔAPt (4)

In your accounting courses, you will see that working capital is more generally defined ascurrent assets minus current liabilities. The cashflow formula at the top of this page is validin this more general case as well.



NPV w/ WACC: Additional Notes



NPV w/ WACC: Obtaining After-Tax Cashflows

Exercise 1: The Jamie Blanchard Goalie School is considering the purchase of 5 brand new puck shootingmachine systems to help train its students to become good goaltenders. These systems, known as “TheBoni Showdown 1 on 1”, cost $9,000 each and are expected to last 10 years. For accounting purposes,they would be depreciated on a straight-line basis over 10 years down to a salvage value of zero. However,after 10 years, they would be sold for $1,000 each.

Currently, the school does not have any puck shooting systems and instead hires local hockey players toshoot pucks at their goalies. The incremental costs due to this labor are $3,000 per year and purchasingthe puck shooting system would eliminate this source of cost. All other labor and operations costs totalto $25,000 per year regardless of whether the puck shooting system is purchased or not.

By moving to high-tech shooting systems, the school expects to increase enrollment in its school from95 to 100 students per year and the cost of enrollment (tuition) from $800 to $820 per year. Every year,80% of students pay their tuition at the end of that year while the other 20% pay their tuition at the endof the following year.

Assume that the goalie school pays 28% of its accounting profits as taxes every year. The after-taxdiscount rate to use for valuing the school’s cashflows is 8% (expressed as an EAR).

Should the goalie school purchase these puck shooting machine systems?

What is the payback period and IRR on this project? Why is NPV w/ WACC favorable to these metrics?



Practical Tip: Getting Organized w/ Cashflows



Depreciation in The Real World (USA): MACRS Schedule

Source: Internal Revenue Service (2007)



NPV w/ WACC: Obtaining After-Tax Cashflows

Exercise 2: Redo Exercise 1 with the 10-year MACRS depreciation schedule from the previous slide.



NPV w/ WACC (Step 2): Obtaining After-Tax Discount Rates

Components of the WACC Formula (2): “Portfolio” weighted-average of required rates ofreturn on debt and equity...

E[r] = (D/V ) × (E[rD] × (1 − Tax))| {z }The Tax-Benefit of Debt

+(E/V ) × E[rE]

Portfolio Weights: Fraction of (total) firm value that is represented by debt (D/V ) andequity (E/V ).

Capital Asset Pricing Model (CAPM): A model of expected returns...

E[ri] = rf + βi × (E[rm] − rf )| {z }Risk Premium ∝ Beta

(5)

where (E[rm] − rf ) is the market risk premium, rf is the riskless rate, and βi is thebeta of investment i. βi attempts to capture nondiversifiable risk by measuring how muchinvestment i’s returns and the market portfolio’s returns:

βi =Cov[ri − rf , rm − rf ]

V [rm](6)

Of course, there are other approaches and details to getting E[rD] and E[rE] in practice.We will discuss these later on in this Topic.



NPV w/ WACC: Obtaining After-Tax Discount Rates

Exercise 3: Your firm operates in the fast food industry. This industry only has one type of project:the production of nasty food. Your firm’s debt has a market value of D = 240M and a current marketcapitalization of E = 960M . You have estimates for the beta of your firm’s debt and equity: βE = 0.7and βD = 0. The risk free rate is 4% and the market risk premium is 5%. Your firm has a tax rate of30%.

Using the CAPM and WACC, what is the appropriate discount rate for nasty food production projects?

Solution: To compute the discount rate for your firm, we need to compute E[rD ] and E[rE ] for thefirm. We will do so using the CAPM:

E[rD] = rf + βD × (E[rm] − rf )

= 0.04 + 0 × 0.05

= 4%

E[rE ] = rf + βE × (E[rm] − rf )

= 0.04 + 0.7 × 0.05

= 7.5%

Now, we can use the WACC formula to get the discount rate:

E[r] = (240/1200) × (0.04 × (1 − 0.3)) + (960/1200) × (0.075) = 6.56%




Key Assumption in Previous Exercise: The project in question was a typical firm project.In other words, the discount rate for the project would equal the discount rate for the firmas a whole.

Alternative Scenarios: What if the discount rate for the firm as a whole cannot be estimated

(e.g., because the firm is private) or the project in question is not a typical firm project (e.g.,

because the firm has many different divisions)? If you want a fine-tuned discount rate, you

must use an alternative approach. One popular approach is to estimate discount rates using

comparables.

� Direct Comparables: Find other companies whose risk resembles that of the project

in question and whose discount rate for the firm as a whole can be estimated. These

are generally focused companies (“pure plays”) in the project’s industry.

� Synthetic Comparables: This approach will be highlighted with step-by-step instruc-

tions in Homework 1.




Exercise 4: You are considering a proposal to start a new airline. To evaluate the proposal, you willneed an estimate of the cost of capital in the airline industry. You have run CAPM regressions on thestock returns of 5 existing airlines that are comparable to the operations of the new business you areconsidering. You have also obtained estimates of the betas of the debt for these 5 firms. The risk freeinterest rate is 4% and the market risk premium is 5%. All firms have a tax rate of 30%.

Company Equity Beta Debt Beta Debt-Equity Ratio

Southwest Airlines Co. 1.13 0.00 0.15SkyWest, Inc. 1.69 0.15 1.05Alaska Air Group, Inc. 1.80 0.15 1.06Mesa Air Group, Inc. 3.27 0.30 3.52Continental Airlines, Inc. 3.76 0.40 5.59

Why are the equity betas (and debt betas) so different across firms? Does this imply that the variousairline company’s have very different levels of risk?

Use this information to estimate the beta and the cost of capital for a typical project in the airline industry?



NPV w/ WACC: Two Approaches w/ Comparables

Approach #1: Average the comparables’ discount rates...

E[r] =1

N×

“E[r1] + ... + E[rN ]

”(7)

where E[rn] is the estimated discount rate for comparable n.

Approach #2: Average the comparables’ unlevered betas and lever up using your firm’scapital structure...

βA =1

N×

“β1

A + ... + βNA

”and E[r] = E[rA] − (D/V ) × E[rD] × Tax (8)

where βnA is the unlevered (asset) beta of comparable n. I’ve assumed a constant D/V in

the second equation.

Is There A Best Choice Between The Two Options?

� Not necessarily. The best option depends on your view of what’s most comparable

across firms: business risk (i.e., E[rA]) or discount rates (i.e., E[r]).



NPV w/ WACC: Fully-Fledged Exercise

Exercise 5: Bart and Mogul Inc. (BM) is planning to enter the online book-selling business. Doing so isexpected to require $50M in upfront investments which are to be split equally between now (at t = 0)and next year (at t = 1). These investment costs entirely fall under capital expenditures and will bedepreciated over 5 years (from t = 2 till t = 6). These capital assets will never be sold.

Following this setup period, the company is expected to have yearly operational expenses that will startat $20M (at t = 2) and will rise by 10% per year for the next 8 years (until t = 10). Meanwhile, itsoperational revenues will start at $17.5M (at t = 2) and will rise by 30% per year for the next 8 years(until t = 10). After this period, everyone will be reading e-books and BM’s book-selling business willcease to generate any cashflows (i.e., let’s assume that they won’t enter the online e-book market).

BM believes that the risk involved in this project lies exactly between those of Amazon.com (AMZN)and Barnes and Noble (BN). AMZN and BN’s stocks both have (equity) betas of 1.5. However, 30%of AMZN’s firm value comes from debt while this number equals 45% for BN. Both AMZN’s and BN’sdebt have (debt) betas of zero. The riskless rate is 5% while the expected return on the market portfolioequals 15% (both rates are expressed as EARs).

All three firms (BM, AMZN, and BN) have a corporate tax rate of 35%.

BMs other lines of business are primarily center around Hoola-hoop production and sales. Historically, ithas applied a discount rate of 10% on those projects.

BM should not use the 10% discount rate for the current project under consideration. Why? Morespecifically, determine the discount rate it should be using (given the statements above).

Should BM undertake this project?


Lecture Note 1 Part Ib

Topic 1 (Part Ib): Estimating the Cost of Capital in Practice



Cost of Capital: Two Practical Approaches to Estimation


E[r] = (D/V )| {z }D-Weight (3)

× (E[rD] × (1 − Tax))| {z }After-Tax Cost of Debt (2)

+ (E/V )| {z }E-Weight (3)

× E[rE]| {z }Cost of Equity (1)

To get the cost of capital for a firm/project, we must estimate each component of thisformula.

Estimate w/ Market Data of Traded Assets: Uses market data (e.g., returns or promisedyields) on your own company or comparable companies along with other aggregate marketdata to generate an estimate of your project’s cost of capital. The key is that you useinformation about risk reflected in market valuation dynamics to gauge risk. In other words,you are exploiting the collective “brain” of participants in asset markets.

Estimate w/ Accounting Data: Uses accounting data (e.g., earnings or cashflows) on yourown company or comparable companies along with other aggregate accounting data togenerate an estimate of your project’s cost of capital. In most of these approaches, you arenot exploiting the collective knowledge of markets and the validity of the approaches hingeson making additional assumptions.

Remark: It is common to use different approaches for estimating the different components ofa project’s cost of capital (e.g., estimating E[rD] and E[rE ]). In practice, some approachesare more geared for estimating the cost of equity while other are targeted towards assessingthe cost debt. As a result, we will discuss estimating the cost of equity and the cost ofdebt separately.



Cost of Equity: The Capital Asset Pricing Model (CAPM)

Components of the CAPM Formula (5): The most commonly used model for obtaining thecost of equity is the CAPM...

E[ri] = rf|{z}Riskless Rate

+ βi|{z}i’s Equity Beta

× (E[rm] − rf )| {z }Mkt Risk Premium

where stock i’s beta is given by formula (6) earlier in the slides.

Implementation: In order to use the CAPM in practice, we must estimate each component

of the CAPM formula. For each component, we will consider a few approaches to estimation.

� Equity Beta: (i) Own Returns, (ii) Comparable Returns, (iii) Accounting Approach.

� Market Risk Premium: (i) Historical Data, (ii) Survey-Based, (iii) Model-Implied (Variety of Op-

tions Here).

� Riskless Rate: (i) Yields on Riskless Government Debt, (ii) Yields on Riskless Government Debt

Plus An Illiquidity Premium.



Cost of Equity w/ Market Data: Estimating Equity Betas (i)

Estimating a Traded Firm’s Equity Beta: The simplest and most common approach is to run an ordinaryleast-squares regression with time-series data on stock i’s return:

rit − rft = ai + bi × (rmt − rft)| {z }Systematic

+ εit|{z}Idiosyncratic

(9)

With enough data, the coefficient bi equals Cov[ri − rf , rm − rf ]/V [rm] which is exactly the formulafor stock i’s beta (βi) from (6).

We call rit − rft and rmt − rft the (realized) excess returns of stock i and the market, respectively.

As discussed earlier, the coefficient ai is called the alpha of an investment i.

� The CAPM predicts that no investment has a positive or negative alpha (market efficiency).

Some useful facts:

� The systematic (non-diversifiable) component of excess returns is bi × (rmt − rft) which has a

variance σ2sys,i = β2

i · σ2M (Systematic Variance)

� The idiosyncratic (i.e., diversifiable) component of excess returns is εit which has a variance

denoted by σ2idio,i = σ2

iε = σ2i − σ2

sys,i (Idiosyncratic Variance)

� An asset’s total variance always equals its systematic variance plus its idiosyncratic variance.

� The R-square of the regression can be interpreted as the fraction of total variance that is system-

atic: R2 = σ2sys,i/σ2

i How can we interpret 1-R2?



Visualization: Estimating Amazon’s Equity Beta

Here’s a scatter plot displaying the excess returns of Amazon and the market from May 2000to April 2005. Let’s do a CAPM-based characterization and decomposition of Amazon’s risk.

Amazon Excess Return

Mkt Excess Return

rAt − rF t = −0.0014 + 1.3053∗∗∗ · (rMt − rF t) + εAt

R2 = 0.326

σM = 0.0451 and σA = 0.1032

Amazon’s beta (βA)

Systematic StDev: 1.30532 · 0.04512 = 0.0589 Idiosyncratic StDev: Solves 0.10322 = 0.05892 + σ2idio,A ⇒ σidio,A = 0.0847

Notice: Systematic Variance/Total Variance = 0.05892/0.10322 = 0.326 = R2!



Excel Tip: Using the Analysis ToolPak to Run Regressions



Cost of Equity w/ Market Data: More on Equity Betas (i)

Question: How many years of data should you use? What frequency of returns?

� Betas are not constant over time so you don’t necessarily want to use the longest possible horizon

of returns when estimating betas.

� It’s common to use five years of monthly data or a couple of years of weekly data.

Question: What is the market portfolio and the riskless rate in CAPM regressions?

� For the market portfolio, it’s common to use the S&P500 index. Using other indexes like the

Wilshire 5000, the NYSE Composite Index, or even the full index of all NYSE, NASDAQ and

AMEX firms will give fairly similar beta estimates.

� Could also use (or construct) a world stock index or include other asset classes when computing

returns. Unfortunately, data on these are tougher to come by.

� For the riskless rate, it’s common to use the promised yields on 30-day Treasury bills or another

longer-term US gov’t bond.

Remark: You can also buy more sophisticated beta estimates from certain data vendors(e.g., from Value Line, Barra, etc).



Visualization: How AT&T’s Equity Beta Changed Over Time

Figure: AT&T’s Beta



Cost of Equity w/ Market Data: Estimating Equity Betas (ii)

An Alternative Method w/ Mkt Data: Perform the same analysis but using the returnsof comparables.

Important Caveat: Take into account leverage differentials across comparables...

„E

V

«× βE =

1

N×

»„E1

V 1

«× β1

E + ... +

„EN

V N

«× βN

E

–(10)

where xn denotes the value of x for comparable n. I’ve assumed βD = β1D = ... = βN

D = 0and a constant D/V in this formula.

The comparables approach can be especially useful if:

� There is an identifiable and appropriate set of comparables for the firm/project (obvious!).

� The company in question is private or the project is atypical for the firm. In this case, it is

impossible to estimate an equity beta for the firm/project using own returns since there is no data

on these returns (either at the firm or the division-level).

� The estimate of the equity beta for the company is very uncertain (large standard errors on slope

coefficient of the CAPM regression). This can happen if the firm only recently had an IPO or if it

has a large amount of idiosyncratic risk.



Cost of Equity w/ Market Data: Comparables Example (Time?)

Exercise 6: It is January 2010 and the Desautels Hospitality Group is the target of a possible acquisitionand its board is entertaining a few offers from private equity firms and large publicly traded companies.In order to estimate a fair value of the company, it must determine the cost of capital for the company.To do so, it will first estimate its beta of equity using the following comparables:

Name Industry D/V βD βE

Intercontinental Hotels Lodging 0.14 0.10 1.85Starwood Hotels & Resorts Lodging 0.26 0.10 2.20Windham Hotels Lodging 0.43 0.15 3.00McCormick & Schmick’s Restaurant 0.16 0.20 2.50Ruth’s Hospitality Restaurant 0.38 0.20 3.15

Throughout this exercise, assume that 70% of DHG’s value is due to its lodging line of business and 30%is due to its restaurant line of business. Also assume that the debt of all the comparables has a beta ofzero and that DHG has no existing debt.

Get D/V for each comparable using its most recent balance sheet and market capitalization data. (Dis-regard the fact that it is not January 2010...)

Calculate a bottom-up (equity) beta for DHG using equity return data for the comparables from January2005 till December 2009. A bottom-up beta involves decomposing a company into its lines of business(e.g., Lodging and Restaurants in DHG’s case) and estimating the betas for each lines of business usingcomparables. Then you combine the “line of business betas” into a firm-wide beta (using the formula forthe beta of a portfolio).



Cost of Equity w/ Accounting Data: Estimating Equity Betas (iii)

Estimating a Nontraded Firm’s Beta: Aside from using comparables, another approach that is (some-what) used is to run an ordinary least-squares regression with time-series data on one of firm i’s ac-counting numbers. For example, we could use percentage changes in net income (NI):

„ΔNIit

NIi,t−1

«= ai + bi ×

„ΔNImt

NIm,t−1

«| {z }

“Systematic”

+ εit|{z}“Idiosyncratic”

(11)

where bi is often used as the estimate of asset i’s beta (βi) from (6). It is often called an accountingbeta. Here’s an example of accounting beta estimation for the private company InfoSoft (as of 1998:Q2):

Period InfoSoft Mkt Period InfoSoft Mkt Period InfoSoft Mkt

1992:Q1 7.5% -1.3% 1994:Q2 12.3% 4.7% 1996:Q3 22.5% 7.2%1992:Q2 8.3% 2.2% 1994:Q3 13.0% 4.5% 1996:Q4 20.0% 6.0%1992:Q3 8.8% 2.5% 1994:Q4 11.1% 4.2% 1997:Q1 17.1% 5.8%1992:Q4 7.9% 3.0% 1995:Q1 18.6% 7.1% 1997:Q2 22.2% 8.0%1993:Q1 14.3% 3.6% 1995:Q2 24.1% 8.5% 1997:Q3 17.8% 6.1%1993:Q2 16.5% 5.1% 1995:Q3 17.5% 6.0% 1997:Q4 14.5% 4.5%1993:Q3 17.1% 5.5% 1995:Q4 16.0% 5.0% 1998:Q1 8.5% 1.3%1993:Q4 13.5% 6.2% 1996:Q1 27.0% 8.1% 1998:Q2 3.5% -0.5%1994:Q1 11.5% 4.3% 1996:Q2 21.3% 7.0%

Running the above OLS regression yields a beta of 2.15.



Cost of Equity w/ Accounting Data: Caveat Regarding (iii)

When is this approach likely to be most valid? Should it be used in a broad set ofcircumstances?



Cost of Equity: Estimating the Market Risk Premium (i) and (ii)

Using Historical Data: If we assume that “the past is reflective of the future”, we can use historicaldata on returns to get the market risk premium...

1926-2010 1970-2010E[ri] σi E[ri] σi

Asset Class i Geo Ari Risk Geo Ari Risk

Small Stocks 12.1% 16.7% 32.6% 12.5% 15.1% 23.4%Large Stocks 9.9% 11.9% 20.4% 10.0% 11.6% 17.9%Mkt Portfolio (S&P500) 10.8% 14.1% 27.2% 11.1% 13.8% 20.7%LT Gov’t Bonds 5.5% 5.9% 9.5% 8.7% 9.3% 11.7%MT Gov’t Bonds 5.4% 5.5% 5.7% 8.0% 8.2% 6.6%Treasury Bills 3.6% 3.7% 3.1% 5.6% 5.6% 3.1%

To get the market risk premium, take the historical return on the market portfolio minus a horizon-matched riskless rate (i.e., T-Bill for short-term project, LT Gov’t Bond for long-term project).

Using a Survey of Forecasters: The following are surveyed estimates from 2005 (published in the WSJ)for expectations forecasts through 2050...

Mkt RiskForecaster Organization Stocks Gov’t Bonds Corp Bonds Premium

William Dudley Goldman Sachs 5.0% 2.0% 2.5% 3.0%Jim Glassman JP Morgan 4.0% 2.5% 3.5% 1.5%David Rosenberg Merrill Lynch 4.0% 3.0% 4.0% 1.0%Jeremy Siegel Wharton 6.0% 1.8% 2.3% 4.2%Robert Shiller Yale 4.6% 2.2% 2.7% 2.4%



Cost of Equity: Estimating the Market Risk Premium (iii)

(Forward) Dividend Strips: A dividend strip (a.k.a. an index dividend future) is a standardized contract

where, at maturity, the buyer pays the futures price, which is determined today, and the seller pays the

dollar amount of dividends during a calendar year.

� Relevant Market: Over the past decade, these contracts have been traded over-the-counter for

various indices (e.g., S&P500, Nikkei 225, DJ Eurostoxx 50, etc.).

� Remark: Like other forward and futures contracts you’ve seen (e.g., forwards lending contracts),

no cash changes hands initially and “all” cashflows are exchanged at maturity.

Using Dividend Strips to Get Model-Implied Market Risk Premia: Let’s introduce some notation...

� Fm,T : The forward dividend strip price on a contract for index m that matures in T years.

� Dm,T : The expected total dividend payments on index m in year T . This has to be estimated

using a forecasting model ⇒ E.g., Forecast growth rates: Dm,T = Dm,0 × (1 + gm,T )T

� rf,T : The T -year riskless rate of return (e.g., from the US Treasury yield curve).

� rm,T : The T -year expected return on index m for it’s dividends at year T .

These variables are related to each other according to the following formula:

Fm,T =

»Dm,T

(1 + rm,T )T

–| {z }PV of Future Dividend

× (1 + rf,T )T| {z }Pay Later ⇒ FV

and Δm,T| {z }Mkt Risk Prem

= rm,T − rf,T (12)



Cost of Equity: Additional Notes on Mkt Premium (iii)



Visualization: Market Risk-Premium w/ Dividend Strips (USA)



Visualization: Market Risk-Premium w/ Dividend Strips (JPN)



Cost of Equity: Estimating the Riskless Rate (i) and (ii)

Approach (i): Use US Gov’t Treasuries.

� Implementation (i.a): Use the 30-day T-Bill. It is the closest thing to a riskless security out there.

� Implementation (i.b): Use another US Gov’t Treasury whose maturity roughly matches the horizon

of your project.

� Implementation (i.c): Use time-appropriate riskless rate according to the US Treasury yield curve

(e.g., the yield on a 2-yr T-Bond to get the riskless rate used for a 2-yr cashflow). (Best comple-

ments the use of time-varying market premia obtained from Dividend Strips).

Approach (ii): Adjust (i) To Account For An Illiquidity Premium.

� How can we obtain a reasonable illiquidity premium for this adjustment?

� Krishnamurthy and Vissing-Jorgensen (2011) suggest looking at the historical spread between safe

assets that are illiquid (e.g., FDIC insured CDs) and safe assets that are liquid (e.g., T-Bills). From

1926-2008, this spread has averaged 0.46%. Are FDIC insured CDs the right benchmark?

� To perform the adjustment to (i), we simply add the illiquidity premium:

rf|{z}

Riskless for Illiquid

= rTreasuryf

| {z }

From (i)

+ ΔIlliq|{z}

Illiquidity Adj.

(13)



Cost of Debt w/ Market Data: Credit Ratings and Beyond

Approach (i): Use Your Firm’s Cost of Debt or That of “Ratings-Matched” Firms.

� Remark: The latter requires your firm to have a credit rating.� Table I in the next slide gives historical data on credit spreads (i.e., avg. yield minus the T-Bill

rate) from the 1995-1999 period across different credit ratings and maturities. From this table, wecan (roughly) compute the cost of debt, E[rD ], as follows:

1 + E[rD ] = [1 − (1 − Pbkrpt) · (1 − Rbkrpt)]| {z }Adjustment Due to Possibility of Default

×

0BB@1 + rf|{z}

Treasury

+ ΔCredit| {z }Own Credit Class

1CCA

| {z }“Promised” Return

(14)

where Pbkrpt is the probability of bankruptcy/default and Rbkrpt is the average recovery rate to

creditors conditional on default.

Approach (ii): Use Some-Type of Econometric Analysis.

� We can also try to predict credit spreads using a regression model which predicts credit spreads

as a function of firm-specific variables, macroeconomic variables. See Table II in a few slides.

� Similarly, you can get a predicted rating using firm-specific variables and more advanced econo-

metric techniques (e.g., ordered multinomial model).

� Most useful for firms that don’t have a credit rating (e.g., because all their debt is private).



Cost of Debt w/ Mkt Data: Credit Ratings and Yield Spreads



Visualization: Beware... Credit Spreads Change Over Time!



Cost of Debt w/ Market Data: Evidence From Campbell-Taksler



Cost of Debt w/ Market Data: Evidence (Cont’d)



Mini Case (Part 1): Discounting Public Pension Liabilities



Mini Case (Part 1): Key Issues



Mini Case (Part 1): Analysis



WACC Weights: How Do We Get the Market Value of Debt?

Market Value of Equity: Easy for publicly traded firms...

E = Shares Outstanding × Price Per Share (15)

Market Value of Debt: Far more complicated because a lot of a company’s debt is notpublicly traded (e.g., syndicated loans, lines of credit). How can we deal with this? Two(imperfect) approaches.

Approach (i): Just use the book value of the company’s debt (e.g., found in balancesheet).

Approach (ii): A more sophisticated approach tries to incorporate average maturity and

coupon payments using back-of-the-envelope PV calculations.� Let DBV be the book value of the company’s debt (from (i)). Furthermore, let T be the average

maturity of a company’s debt and C be the company’s most recent interest expenses (e.g., foundin the income statement). A reasonable estimate of the market value of debt is:

D =C

E[rD]×

»1 − 1

(1 + E[rD])T

–| {z }

PV of Coupons ⇒ Annuity

+DBV

(1 + E[rD])T| {z }PV of Principal

(16)

What assumptions are made in this calculation?



Additional Notes: Overview of Implementing WACC...


E[r] = (D/V )| {z }D-Weight (3)

× (E[rD] × (1 − Tax))| {z }After-Tax Cost of Debt (2)

+ (E/V )| {z }E-Weight (3)

× E[rE]| {z }Cost of Equity (1)



Caveat: Is WACC Appropriate for Private Companies?

Two Cases:

� Case #1: Company owners are well-diversified.

� Case #2: Company owners are not well-diversified.


Lecture Note 1 Part Ic

Topic 1 (Part Ic): Forecasting Cashflows: Key Drivers



Fundamental Approaches to Forcasting Cashflows

Common Across Approaches: Forecasting the income statement for EBITDt and the

balance sheet for CAPXt and ΔWCt. To do this, you must:

� Determine Key Drivers: Usually involves focusing on one or two important line items and pro-

jecting the others based on a forecast ratio relative to these.

� Question: Can you think of qualitative and quantitative ways to do this?

Bottom-Up: Focus on the operations of the company/project and, for example, forecastthe key drivers of demand to determine future revenues and required capital expenditures.(Micro-Approach)

Top-Down: Focus on the markets the company/project is involved in and, for example,forecast the key drivers of market size and share to determine future revenues and requiredcapital expenditures. (Macro-Approach)



Forecasting Cashflows: Items to Forecast

Line Item Reported In Comments

Revenues Income Statement Often a focus of the forecaster.COGS Income Statement Often based on a forecast ratio of revenues.

↪→ Sometimes also a focus of the forecaster.SG&A Income Statement Often based on a forecast ratio of revenues.Depreciation Income Statement Often based on CAPX forecasts.EBITD Income Statement Mechanically based on previous line items.Capital Expenditures Balance Sheet Often a focus of the forecaster.Accounts Payable Balance Sheet Often based on a forecast ratio of revenues.Inventory Balance Sheet Often based on a forecast ratio of revenues.Accounts Receivable Balance Sheet Often based on a forecast ratio of revenues.

Remark: The science and art of forecasting is truly multidisciplinary...

� Example #1: Revenue forecasting often involves marketing and strategy knowledge.

� Example #2: COGS often involves operations knowledge.

� So pay attention in your other classes... and this one. ;-)



Forecasting Cashflows: Bottom-Up Approach For NetFlix



Additional Notes: NetFlix Cashflows



Forecasting Cashflows: Top-Down Approach For Ford



Additional Notes: Ford Cashflows



Practical Tip: Decompose Forecasting By Major Lines-of-Business



Comparables Approaches to Forcasting Cashflows

Forecasting w/ Comparables: Jeremy Stein (2001) describes a strategy for obtaining forecasted cashflow

estimates using a panel regression technique. We slightly adapt his process here. The steps are:

� Step #1: Identify a set of N comparables for your firm/project.� Step #2: Estimate a forecasting model of expected cashflows using these comparables and historical

data. The model Stein uses is:

0@ CFnt

An,t−1

1A = aq +b1 ·

0@ CFn,t−1

An,t−2

1A+b2 ·

0@ CFn,t−2

An,t−3

1A+b3 ·

0@ CFn,t−3

An,t−4

1A+b4 ·

0@ CFn,t−4

An,t−5

1A+εnt (17)

where n indexes comparables and t is measured in quarters. There are N × T observations in

this regression where T is the number of quarters of data included. (Stein uses 5 years of data so

T = 20 in his case)

� Step #3: Use the estimated forecasting model to forecast future cashflows for your firm/project

(additional details on next slide).

Question #1: How do we identify comparables?

� Stein splits his sample of firms into terciles of size, then terciles of profitability, then terciles of

industry risk, then terciles of equity volatility. This creates 34 = 81 buckets of comparables.

� Sometimes referred to as “34-Comparables”.

� Alternatives suggestions? There are many reasonable options.



Comparables Approaches to Forcasting Cashflows (Cont’d)

Question #2: How do we forecast future cashflows using the panel regression results?

� Show approach via example.� Suppose the estimates of the forecasting model (17) are:

0@ CFnt

An,t−1

1A = aq +0.5·

0@ CFn,t−1

An,t−2

1A+0.2·

0@ CFn,t−2

An,t−3

1A+0.1·

0@ CFn,t−3

An,t−4

1A+0.3·

0@ CFn,t−4

An,t−5

1A+εnt (18)

Why is the fact that b4 > b3 not surprising?� Get CFn,t+1: Suppose aq for that quarter is -0.001. Let the three previous “normalized” cashflows

be 0.05, 0.03, 0.02, 0.06. Ant = 250m. Then:

CFn,t+1 = 250m × (−0.001 + 0.5 · 0.05 + 0.2 · 0.03 + 0.1 · 0.02 + 0.2 · 0.06)| {z }Equals 0.05

= 12.5m (19)

� Get CFn,t+2: Suppose aq for that quarter is -0.004. Let the three previous “normalized” cashflowsbe 0.05, 0.03, 0.02, 0.06. An,t+1 = 250m. Then:

CFn,t+2 = 250m × (−0.004 + 0.5 · 0.05 + 0.2 · 0.05 + 0.1 · 0.03 + 0.2 · 0.02)| {z }Equals 0.04

= 10m (20)

Note that we have assumed zero asset growth in this step. If you want to incorporate asset growth,

you need to build a predictive model of assets along with cashflow.

This Techique is Useful Beyond Cashflow Forecasting: See Stein paper...



Forecasting Cashflows: Stein’s “34-Comparables” for Dell (2001)



Forecasting Cashflows: 1-Yr CF Dists Using “34-Comparables”



Mini Case (Part 2): Forecasting Public Pension Liabilities



Mini Case (Part 2): Key Issues



Mini Case (Part 2): Analysis



Visualization: Value of An Existing Worker’s Liability



Visualization: Forecasted (Aggregate) Liabilities Over Time



Summary of Novy-Marx and Rauh’s Main Findings (Table IV)



Terminal Value: A Way to Avoid Forecasting All Cashflows

Terminal Value and NPV: Rather than forecasting all cashflows for a company/project, it can be useful tostop the detailed cashflow forecasts after an “early period” and estimate the “continuation” or “terminal”value of the company/project after the last forecasted cashflow. Given these, NPV is given by:

NPV =

»CF0 +

CF1

(1 + E[r])1+ ... +

CFT

(1 + E[r])T

–+

TVT

(1 + E[r])T(21)

In essence, terminal value is given by:

TVT =CFT+1

(1 + E[r])1+

CFT+2

(1 + E[r])2+ ... (22)

Estimating Terminal Value: A “Gordon Growth” Approach... We can use a growing perpetuity formulato estimate terminal values...

TVT =CFT × (1 + gstable)

(E[r] − gstable)(23)

where gstable is often estimated from “stable” (i.e., mature) comparables in the company’s industry. Thisgrowth rate can be estimated from historical data or from comparables’ profitability and investment policy.One way that the latter can be quantified is using the following formula adapted from the Gordon growthmodel:

gstable = ˆPBRstable × ˆROAstable (24)

where ˆPBR is the fraction of cashflow that is reinvested in the firm and ˆROA is calculated as the ratioof cashflow to book value of assets.



Terminal Value: Additional Notes



HQ: “Should We Completely Rely on the Forecasts of Others?”

Dilbert: “Probably Not...”

Many practitioners and academics agree with Dilbert.

� Poterba-Summers (1995) survery and find that CEOs use excessively high discount rates partially

as “fudge factors” to account for optimistic forecasts by division managers.

� Proper way to account for this? Two points of view... See syllabus for detailed references.

� Fischer Black (1998) argues that we should adjust division managers CF forecasts downwards.

� Richard Ruback (2011) argues that we should occasionally adjust both division managers CF fore-

casts downwards and discount rates upwards.


Lecture Note 1 Part Id

Topic 1 (Part Id): DCF Is Not A Number: Sensitivity Analysis



Sensitivity Analysis: Two Main Applications

Sensitivity Analysis: How Does Value Vary w/ Alternative Baseline Assumptions?

� What Baseline Assumptions?

� Cashflow Drivers: Prices (revenue and/or cost), quantities, capacity, tax-rates, etc.

� Discount Rate Drivers: Betas, risk-premia, tax-rates, etc.

Main Applications: Three often used applications are...

� Identify “Key Drivers” of Value: What parameters most influence company/project

value? Should influence which variables you focus most on in the cashflow forecasting

and discount rate estimation stage. (I won’t go over an example of this though...)

� Get “Trigger Points” For Decision-Making: E.g., At what cost of carbon emissions

credits should a power plant switch to emissions-minimizing energy production facili-

ties? Should influence your capital budgeting decisions and let you know which market

variables to focus on in the short-term.

� Assess a Range of Plausible Values: E.g., What’s a plausible range of “fair values”

for an acquisition? Would the loss implied by the lower range be acceptable?

� Plan of Attack: We’ll gain comfort w/ this topic via examples.



“Trigger Points” in Consumer Choice: Mazda3 vs. Toyota Prius

Exercise 7: You have decided to purchase either a Mazda3 or a Toyota Prius and will baseyour decision on minimizing the NPV of car-related payments. You consider two types ofcosts (car payments and fuel costs) and one type of revenue (car sale after 4 years). Thedetails of these costs are included in the table below. Assume that gas costs $4.20 per gallonand that the discount rate is 5% expressed as a monthly-APR.

Category Subcategory Mazda3 Prius

Car Costs Downpayment: $3,000 $4,300Monthly Loan Pay.: $333.33 $396.10# of Months: 36 48

Fuel Use City Mileage: 21 48Monthly City: 400 400Hwy Mileage: 29 45Monthly Hwy: 200 200

Car Sale Revenue: $10,000 $16,750At Month: 48 48

Which car should you buy? At what (“trigger”) gas price do you switch from purchasing aMazda3 to buying a Toyota Prius?

Side Question: Where can we get a forecast for the revenue of the future car sale?



Breaking Down The Problem Into Simple Steps



Excel Tip: Using Solver To Do Algebra



This Can Be Relevant...

Chart: Chicago Area Gas Prices



Typical Sensitivity Analysis: InBev Buys Some BUD

Exercise 8: On July 13, 2008, Anheuser-Busch (BUD) agreed to be purchased by InBev in a transactionthat would form the world’s leading global brewer. BUD shareholders would receive $70 per share in cash(for an aggregate equity value of $52bn). Citigroup Global Markets acted as a financial advisor to BUD inthis transaction and, among other things, performed a valuation analysis to assess the fairness of InBev’soffer. The DEFM14A table below provides cashflow estimates for the firm from the end of 2008 till theend of 2012.

Citi estimates a WACC of 7.5% for BUD and a stable growth rate of 2.0% starting at the end of 2012. IfBUD’s debt has a market value of $10.1bn (at the end of 2008), what’s Citi’s estimate of BUD’s equityvalue (at the end of 2008)? (Assume the transaction takes place at the end of 2008)

Of course, Citi isn’t certain of its WACC and stable growth rate estimates. Perform a sensitivity analysiswith a WACC range of +/- 1.5% (increments of 0.5%) and a stable growth range of +/- 0.5% (incrementsof 0.25%).



Excel Tip: Using Data Tables To Perform Sensitivity Analysis



Determine a Sensible Range for Vars in Sensitivity Analysis?

Comparables-Based Approaches: Some Examples...

� WACC: E.g., Range for firm’s WACC implied by the range of WACC’s estimated for comparable

firms (both pure comparables and synthetic ones constructed from a bottom-up analysis).

� High Growth Period for a Start-Up: E.g., Range for terminal date implies by 10th and 90th

percentiles of high growth period for a sample of past IPOs. (Must define: (i) growth of what

(e.g., sales)? (ii) when the phase ends (e.g., two consecutive years of sales growth below 5%)?)

Statistics-Based Approaches: Some Examples...

� Beta: E.g., Range for firm’s beta implied by a confidence interval around beta estimate from a

regression. Usually use [β̂ − σβ , β̂ + σβ ]. (This is a 68% confidence interval. Generally avoid the

95% interval since this often produces a very wide range)

� Mkt Premium: E.g., Range for mkt premium implied by a confidence interval around the historical

average of realized market returns. Again, often use +/- 1 standard deviation of this return.

Qualitative Approaches: An Example...

� Survey-Based: E.g., Range for market premium implied by WSJ’s survey of forecasters in Topic 1

(Part 1B). The range was 1.0%-4.2%.



Getting a Range for WACC: One Approach

Exercise 9: Let’s estimate a range for the WACC of BUD ourselves. In performing thecalculation, you will use the CAPM to estimate BUD’s cost of equity (with the S&P500 asthe market portfolio and 5-years worth of returns using price data from June 1, 2003 till July1, 2008). Assume that BUD has a cost of debt of 5.7% and that the WACC-weights areequal to those implied by the transaction terms (i.e., D = 10.1bn and E = 52bn).

Considering only a range implied by variation in beta, is the WACC range consistent withCiti’s estimate of beta? (BTW, another of BUD’s advisors on the transaction, GoldmanSachs, estimated a WACC of 8%)

How would your range change if you included variation in the market premium?



Getting a Range for WACC: Additional Notes



Overview of Topic 1 (Part I)

Review of NPV w/ WACC:

Estimating the Cost of Capital in Practice:



Overview of Topic 1 (Part I): Continued

Forecasting Cashflows: Key Drivers

DCF is Not A Number: Sensitivity Analysis



Overview of Topic 1 (Part I): Additional Notes


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