Valuation Slides Week1 2 - Cost of Capital MPA

Valuation

MPA FIN 286 Alessandro Previtero

Slide Pack Week 1 Part 2 Company Valuation – Cost of Capital

Today’s Content I.  Announcements:

•  HW1 Due this Monday. •  TA Review Sessions: Every Thursday from 5 to 6pm (room TBD) •  Classroom Policy Survey Results:

o  Attendance: not required (76%). o  Using Laptops: anytime (47%). o  Arriving on time: students can walk in and out at any time (71%). o  Displaying name tags: not required (65%). o  Turning your assignments in late: 30% penalty (88%).

II.  Discount Rate

a.  Why we discount FCF b.  Risk-Return Tradeoff c.  CAPM d.  Compute Betas

§  Regressions §  Comparables

III.  Homework Assignment #2

2

•  Introduction •  Discounted Cash Flow (DCF) Models

–  Discount Rate –  No Friction Model –  WACC (Weighted Average Cost of Capital) –  APV (Adjusted Present Value)

•  Multiples •  Other topics: LBO’s, M&A, etc.

I. Company Valuation

Recap: How to Value a Firm

[ ]( )∑

∞

= +=

0 1E

ttt

A rFFCFV

Company Valua-on – DCF Models – Discount Rate 4

MVDNOAVMVE A −+=

NMVEP =

FFCF = EBIT ⋅ (1− tC )+DA−ΔNWC −Capex + AS −CGT

Why discounting Cash Flow? •  One dollar received today is more valuable than one dollar received

in the future (Time Value of Money). ‒ Which would you choose?

I.  $50 for sure TODAY or $50 for sure 1 YEAR FROM NOW II.  $40 for sure TODAY or $50 for sure 1 YEAR FROM NOW

•  Individuals are usually risk-averse: ‒ Which would you choose?

I.  $50 for sure or $0 / $100 at 50% each II.  $40 for sure or $0 / $100 at 50% each

•  The higher the risk, the higher the return (i.e. the discount rate)

riskfor Premium+= frr


Why discounting Cash Flow? •  Risk-Return: Empirical Evidence

Total Risk = Systematic (Common) Risk + Idiosyncratic (Unique) Risk σ β

Common Unique

)(),(

m

mxx rVar

rrCov=β

Ret

urn

( r )

Standard Deviation (σ)


Why discounting Cash Flow? •  Risk-Return: Empirical Evidence

Ret

urn

( r )

Standard Deviation (σ)

Common Unique

β

)( fmf rrrSlopeInterceptr −⋅+=⋅+= ββCapital Asset Pricing Model (CAPM)

)( fmxfx rrrr −⋅+= β

)( fmefe rrrr −⋅+= β)( fmdfd rrrr −⋅+= β)( fmOAfOA rrrr −⋅+= β

Risk-free Rate

Market Risk Premium


Security Market Line (SML)

Valuation in the real world (2/2)

0 10 20 30 40 50 60 70 80

Regulatory decisions

Investor expectations

Dividend discount model

Multibeta CAPM

Arithmetic average hist.return

CAPM

Legend: % of CFOs who always or almost always uses a certain technique Source: Graham and Harvey, Journal of Financial Economics 2001

•  Estimation of cost of capital


Risk-free rate (1/2)

Source: h?p://www.treasury.gov/resource-‐center/data-‐chart-‐center/interest-‐rates/Pages/Historic-‐Yield-‐Data-‐Visualiza-on.aspx


)( fmf rrrr −⋅+= β

Risk-free rate (2/2)

•  The CAPM is an opportunity cost model, where the risk-free rate represents the rate you would earn on an equivalent maturity investment with no risk

•  I use the return on the 20-year or 30-year Treasury (Matches the long-term maturity of equity, is risk-free). However, if I need to value a short term project, I will use a risk free rate that matches the duration of the project.


Market risk premium

•  There is some disagreement (or controversy) regarding the magnitude of the risk premium, since the estimate – Depends on the sample period – Varies with the fixed income instrument used – Depends on whether arithmetic or geometric means are used

•  Which type of average should we use? o  Arithmetic Average = ∑𝑖=1↑𝑁▒𝑟↓𝑖  /𝑁 

o  Geometric Average =√𝑁&∏𝑖=1↑𝑁▒(1+ 𝑟↓𝑖 )   - 1

•  http://faculty.london.edu/icooper/assets/documents/ArithmeticVersusGeometric.pdf


)( fmf rrrr −⋅+= βMarket risk premium

• There is some disagreement (or controversy) regarding the magnitude of the risk premium, since the estimate– Depends on the sample period– Varies with the fixed income instrument used– Depends on whether arithmetic or geometric means are used

• Which type of average should we use?

o Arithmetic Average = ∑

o Geometric Average = ∏ 1 + 𝑟 - 1

• http://faculty.london.edu/icooper/assets/documents/ArithmeticVersusGeometric.pdf

Company Valuation – DCF Models – Discount Rate 11

)( fmf rrrr �� E

Market risk premium

• Annual market risk premium:


Source: Aswath Damodaran’s Website. http://pages.stern.nyu.edu/~adamodar/

-‐80.00%

-‐60.00%

-‐40.00%

-‐20.00%

0.00%

20.00%

40.00%

60.00%

Year

1929

1931

1933

1935

1937

1939

1941

1943

1945

1947

1949

1951

1953

1955

1957

1959

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2011

Stock -‐ bond -‐ Annual

Market risk premium

• Average market risk premium with 5-year rolling periods:



-‐0.15

-‐0.1

-‐0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Year

1929

1931

1933

1935

1937

1939

1941

1943

1945

1947

1949

1951

1953

1955

1957

1959

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2011

5-‐yr moving average

Market risk premium

• Average market risk premium with 10-year rolling periods:



-‐0.1

-‐0.05

0

0.05

0.1

0.15

0.2

0.25

Year

1929

1931

1933

1935

1937

1939

1941

1943

1945

1947

1949

1951

1953

1955

1957

1959

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2011

10-‐yr moving average

Market risk premium

Period Stocks-T.Bills (US) Stocks-T.Bonds (US)

Arithm. Mean Geom. Mean Arithm. Mean Geom. Mean

1928-2012 7.65% 5.74% 5.88% 4.20%

1962-2012 5.93% 4.60% 3.91% 2.93%

2002-2012 7.06% 5.38% 3.08% 1.71%




Market risk premium

• Volatility of Dow Jones Industrial Index returns over time: Is the whole time series from 1897-2013 relatively uniform?

Annualized 1-yr Moving Average Daily Return Volatility


Market risk premium

• VIX index for the last 25 years


Market risk premium - Conclusion •  Some economists (especially before the 2009 financial

crisis) believe that the earlier sample does not look representative of today’s market –  The vol stats show that the market was more volatile

pre-1950 –  We know that important mechanics of the market such

as liquidity and information are much better today

•  The 20 and 30 year periods starting after about 1950 show MRP of around 5%-6%

•  The academic community is in virtual agreement that 6%-7% is too high, and a reasonable number is 4-6%

•  What happen if you use a low MRP? Company Valua-on – DCF Models – Discount Rate 18

Estimating beta

•  Two approaches are used to estimate the beta of the equity of a company: 1.  Regression Approach: compute how the stock

returns co-vary with the stock market returns 2.  Comparables Approach: Choose comparable

companies, unlever and relever betas.



Estimating beta using regressions

•  Firm’s historical or predicted βe –  Estimated by regressing the firm’s excess stock returns

on the excess returns of a market portfolio

•  Many practitioners simply regress returns, not excess

returns, because monthly Treasury returns are not as easy to find as equity returns, and there’s not much difference in the calculated beta

•  Time Period: As a default, we aim for 3-5 years of monthly data (trade-off: more data is better, but use recent data)

( ) ( ) ttfmetfe rrrr εβα +−+=−

Firm’s excess returns Market’s excess returns

USE SAME rf


Estimating beta using regressions

•  Market Portfolio: There are plenty of choices for the

market portfolio (S&P 500, NYSE, NYSE/NASDAQ)   Thankfully, market proxies are so highly correlated it

doesn’t matter much what you use.   I almost always use the S&P 500, and so does almost

everyone else in practice (is easy to get)   in academic papers we use the bigger index

measures like NYSE/AMEX/NASDAQ


HOG Beta Calculation (I)


Estimating beta using regressions •  βe is an estimate subject to random error

–  Individual stock beta estimates have HIGH sd.’s •  Sometime stock returns are not available:   New/IPO companies   Private companies   Unique projects/assets   Subsidiary

•  Use COMPARABLES approach


•  Take two identical companies (same size, industry, products,…), but one with high leverage, and the other with low leverage

•  Which one has higher betas? •  The higher the leverage, the higher the βe and βd •  βe s are not directly comparables between companies •  βA s are not affected by leverage à comparable •  NB: The textbook calls

  βA =Unlevered Equity Betas   βE =Levered Equity Betas

Estimating beta using comparables (1/4)

E1

D1

βe1

βd1

E2

D2

βe2

βd2


A1 A2


Ec3

Dc3

βe_c3

βd_c3

E

D

Βe??

βd

Ec2

Dc2

βe_c2

βd_c2

Ec1

Dc1

βe_c1

Comparables

βd_c1

βA_c1

Unl

ever

ing

βA_c2 βA_c3

βA_c βA

Leve

ring

edA EDE

EDD

βββ+

++

=

Levering/Unlevering Formula


•  To find the βe of a company using the Comparables approach: 1.  Find a set of comparable public firms matching in size, industry,

product, life-cycle, … (but not in Leverage!) 2.  “Unlever” the comp βe to find the βA (unlevered βe ) 3.  Compute weighted-average of the comp βA 4.  “Re-lever” the average βA to the target firm’s capital structure


E

D

Βe??

βd

Ec3

Dc3

βe_c3

βd_c3

Ec2

Dc2

βe_c2

βd_c2

Ec1

Dc1

βe_c1

Comparables

βd_c1

βA_c1

Unl

ever

ing

βA_c1 βA_c1

βA_c βA

Leve

ring


Company Name βe Market

Leverage βA

Abbott Laboratories 0.36 30.05% 0.31 Johnson & Johnson 0.35 3.30% 0.35 Merck 0.81 10.00% 0.75 Pfizer 0.71 17.65% 0.62

Average 0.51

• Compute Genentech’s βe using the comparable companies below, assuming that   Genentech’s and the comparable’s βd =0.20   Genentech’s Market Leverage = 15%

•  NB:


Leverage βA

Abbott Laboratories 0.36 30.05% 0.31 Johnson & Johnson 0.35 3.30% 0.35 Merck 0.81 10.00% 0.75 Pfizer 0.71 17.65% 0.62


Leverage Abbott Laboratories 0.36 30.05% Johnson & Johnson 0.35 3.30% Merck 0.81 10.00% Pfizer 0.71 17.65%

Levering and un-levering beta: Example

Genentech βe = 0.56

edA EDE

EDD

βββ+

++

=

Leverage :Where

)1(

=+

=

−+=+

++

=

EDDL

LLED

EED

DededA βββββ

Leverage :Where

11 )1(

=+

=

−

⋅−

−=→−+=

++

+=

EDDL

LL

LLL

EDE

EDD dA

eededAββ

ββββββ


HOG Beta Calculation (II)


A few caveats on comparables (4/4) •  If you assume βd=0 if the company is not in financial distress

  If βd=0 then the levering/unlevering formula is:

  Be consistent! If βd=0 then rd= rf

  Several indicators can be used to measure the financial health of the company (Leverage, Interest coverage ratio, etc…)

•  Never rely only on one comparable. Choose at least 3 or 4, and then take a weighted average   Compute weights using a score card approach (similarity in Products,

Size, life-cycle statges) •  Some textbooks (including ours!) use a different levering/unlevering

formula where D is replaced by D(1-T):   We’ll see later on why different levering formulas exist


βA =E

D+Eβe = (1− L)βe

Homework Assignment #2


•  Individual Assignment posted on the course website

•  Objective: Find the cost of equity capital for your company.

•  Three Approaches   Regression analysis   Comparables approach

•  Due Wednesday Jan 27th at the beginning of class   Paper format only. Do not email me or the TA with

the assignment.

Problem #1


You are the manager of the hockey helmet division of your Firm. There are three firms that compete with you in the hockey helmet business. Firm 1 is a large, diversified plas-cs business which derives 10% of its revenues from hockey helmet sales. Firm 2 is a single-‐division hockey helmet manufacturer that has been in business for 30 years (prior to that hockey players didn’t wear helmets). Firm 3 is a recent entrant into the hockey helmet business a[er many years in the football helmet business.

Firm 1 Firm 2 Firm 3

Total Assets 20000 1000 500

Debt 500 200 200

Equity 15000 800 300

Total Liab + Equity 20000 1000 500

Earnings 1500 100 -‐5

Bond Ra-ng AA AA BBB

Shares Outstanding 1000 100 100

Share Price 20 15 2

Equity Beta 1.3 1.5 2.2

The table shows some financial informa-on on the comparable firms (all units are in millions except the share price). The risk-‐free rate is 5%, the market risk premium is 6%, and the marginal corporate tax rate is 35%. The target debt-‐to-‐value for the division is 1/3. Compute the cost of equity capital for the hockey helmet division.

Problem #2


Comparison βE D/E

GM 1.20 0.4

Lockheed 0.90 0.9

Northrop 0.85 0.7

In 1989, General Motors (GM) was evalua-ng the acquisi-on of Hughes Aircra[ Corpora-on. Recognizing that the appropriate discount rate for the projected cash flows of Hughes was different than its own cost of capital, GM assumed that Hughes had approximately the same risk as Lockheed and Northrop, which had low-‐risk defense contracts and products that were similar to Hughes. Specifically, assume the following inputs: Also assume that GM’s target debt/equity ra-o, in market value terms, for the Hughes’ acquisi-on is 1. Hughes’ expected nominal cash flow next year will be $300 million and will grow therea[er at the rate of 5 percent per year, the risk-‐free rate is 8%, and the market risk premium is 6%. Compute the equity cost of capital for the Hughes acquisi-on, assuming no taxes.

Your so[ware firm is considering a diversifying investment in the donut business. The logic at headquarters is that your programmers eat so many donuts that you might as well get a piece of the ac-on. There are two other publicly-‐traded firms compe-ng in the donut business: one is a mature firm with significant interests in other businesses and a young, upstart firm which is a pure-‐play in the business you are considering. Summary financial data (in $ millions) for the two comparables are given below: To get a be?er understanding of the mature comparable, you es-mate that half of its revenue is generated in the donut business and the remaining half of its revenue is generated in a variety of businesses which have average market risk. (a) Ignoring taxes, give an es-mate of the cost of capital of asset using the CAPM (assume risk-‐free rate is 5% and whatever market risk premium you deem appropriate). Jus-fy all other assump-ons. (b) What three other pieces of informa-on would you like to have to improve your es-mate?

Problem #3


Mature comp Upstart comp Total assets 1000 200 Short-‐term debt 25 5 Long-‐term debt 475 20 Equity 500 175 Total liab+equity 1000 200 Earnings 100 1 EPS ($) 1 0.05 Share price ($) 10 40 Dividend yield 5% 0 Equity beta 0.8 1.5

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Valuation Slides Week1 2 - Cost of Capital MPA