Estimating beta: Continental Airlines. Estimating bet

1
(more practice with capital budgeting)

• SG Company currently uses a packaging machine
  that was purchased 3 years ago. This machine is
  being depreciated on a straight line basis toward
  a 400 salvage value, and it has 5 years of
  remaining life. Its current book value is 2500
  and it can be sold for 3500 at this time.
• SG is offered a replacement machine which has a
  cost of 10,000, an estimated useful life of 5
  years, and an estimated salvage value of 1000.
  This machine would also be depreciated on a
  straight line basis toward its salvage value.
  The replacement machine would permit an output
  expansion, so sales would rise by 1500 per year
  even so, the new machines much greater
  efficiency would still cause before tax operating
  expenses to decline by 1800 per year. The
  machine would require that inventories be
  increased by 2000, but accounts payable would
  simultaneously increase by 750. No further
  change in working capital would be necessary over
  th4 e5 years. SGs marginal tax rate is 40, and
  its discount rate for this project is 12.
  Should the company replace the old machine?
  (Assume that at the end of year 5 SG would
  recover all of its net working capital
  investment, and the new machines could be sold at
  book value at the end of its useful life).

2
Risk Return

• Chapter 9 3,12,13,17
• Chapter 10 3,5,13,17,22,27,34,38
• Note - In chapter 10, skip the following
  sections
• Efficient set (section 10.4)
• Efficient set for many securities skip the
  first part of section 10.5, page 270 to middle of
  271
• The optimal portfolio, p. 278-280.

3
Measuring historical returns

• Total return dividend income capital gains
• total return Rt1 (Divt1 Pt1- Pt)/Pt
• Geometric mean returns
• (1 R)T (1R1)(1R2)(1Rt)(1RT)
• RA (1.15)(1.00)(1.05)(1.20)(1/4)-1 ? .0972
  9.72
• RB (1.30)(0.80)(1.20)(1.50)(1/4)-1 ? .1697
  16.97
• Arithmetic mean returns
• R (R1 R2 RT)/T
• RA .15 .00 .05 .20/4 .10 10
• RB .30 -.20 .20 .50/4 .20 20

4
Measuring total risk

• Return volatility the usual measure of
  volatility is the standard deviation, which is
  the square root of the variance.

5
Calculating historical risk return example

• The variance, ?² or Var(R) .0954/(T-1)
  .0954/3 .0318
• The standard deviation, ? or SD(R) ?.0318
  .1783 or 17.83

6
Historical Perspective
7
Capital Market History Risk Return Tradeoff
(Ibbotson, 1926-2003)
Risk premium difference between risky
investment's return and riskless return.
8
EXPECTED (vs. Historical) RETURNS VARIANCES
Calculating the Expected Return
Expected return (-1.25 7.50 8.75) 15
9
EXPECTED (vs. Historical) RETURNS VARIANCES
Calculating the variance
10
PORTFOLIO EXPECTED RETURNS VARIANCES

• Portfolio weights 50 in Asset A and 50 in
  Asset B
• E(RP) 0.40 x (.125) 0.60 x (.075) .095
  9.5
• Var(RP) 0.40 x (.125-.095)² 0.60 x
  (.075-.095)² .0006
• SD(RP) ?.0006 .0245 2.45
• Note E(RP) .50 x E(RA) .50 x E(RB) 9.5
• BUT Var(RP) ? .50 x Var(RA) .50 x Var(RB)
  !!!!

11
PORTFOLIO EXPECTED RETURNS VARIANCES
New Portfolio weights put 3/7 in A and 4/7 in
B
E(RP) 10 SD(RP) 0 !!!!
12
Covariance and correlation measuring how two
variables are related

• Covariance is defined
• ?AB Cov(RA,RB)
• Expected value of (RA-RA) x (RB-RB)
• Correlation is defined (-1lt ?ABlt1)
• ?AB Corr(RA,RB) Cov(RA,RB) / (?A x ?B)
  ?AB / (?A x ?B)

13
Portfolio risk return

• If XA and XB the portfolio weights,
• The expected return on a portfolio is a weighted
  average of the expected returns on the individual
  securities
• Portfolio variance is measured

14
Portfolio Risk Return Example
RA (-0.20 0.10 0.30 0.50)/4 0.175
Var(RA) ?²A .2675/4 .066875 SD(RA) ?A
?.066875 .2586 RB (0.05 0.20 - 0.12
0.09)/4 0.055 Var(RB) ?²B .0529/4
.013225 SD(RB) ?B ?.013225 .1150 ?AB
Cov(RA,RB) -0.0195/4 -0.004875 ?AB
Corr(RA,RB) ?AB / ?A?B -0.004875/(.2586x.1150)
-.1369
15
Benefits of diversification

• Consider two companies A B, and portfolio
  weights XA .5, XB .5
• Stock A Stock B
• E(RA)10 E(RB)15
• ?A10 ?B30
• Case 1 ?AB 1 (?AB ?AB/?A?B)

16
Benefits of diversification

• Stock A Stock B
• E(RA)10 E(RB)15
• ?A10 ?B30
• Case 2 ?AB 0.2 (?AB ?AB/?A?B)

17
Benefits of diversification

• Stock A Stock B
• E(RA)10 E(RB)15
• ?A10 ?B30
• Case 3 ?AB 0 (?AB ?AB/?A?B)

18
Intuition of CAPM

• Components of returns
• ? Total return Expected return Unexpected
  return
• R E(R) U
• The unanticipated part of the return is the true
  risk of any investment.
• ? The risk of any individual stock can be
  separated into two components.
• 1. Systematic or market risks (nondiversifiable).
  
• 2. Unsystematic, unique, or asset-specific
  (diversifiable risks).
• R E(R) U
• E(R) systematic portion unsystematic
  portion

19
(No Transcript)
20
Measuring systematic risk beta

• Rm proxy for the "market" return
• Portfolio beta weighted ave of individual
  assets betas

21
Portfolio risk (beta) vs. return

• Consider portfolios of
• Risky asset A, ßA 1.2, E(RA) 18
• Risk free asset, Rf 7

22

23
Market equilibrium

• Reward/risk ratio E(Ri) - Rf constant!
• ßi
• The line that describes the relationship between
  systematic risk and expected return is called the
  security market line.

24
Market equilibrium

• The market as a whole has a beta of 1. It also
  plots on the SML, so

25
Using the CAPM risk free rate and risk premium
26
Historic Returns and Equity Premia
27
Using the CAPM estimating beta

• Regression output
• Data providers
• Bloomberg, Datastream, Value Line

28
Estimating beta Continental Airlines

29
Estimating beta Continental Airlines

30
Estimating beta Continental Airlines

31
Estimating beta

• How much historical data should we use?
• What return interval should we use?
• What data source should we use?

32
DETERMINANTS OF BETA Operating vs. financial
leverage

• Sales
• - costs
• - depr
• EBIT
• - interest
• - taxes
• Net income

33
Determinants of beta financial leverage

• With no taxes, beta of a portfolio of debt
  equity beta of assets, or
• If Debt is not too risky, assume ?D 0 , so
• or
• In most cases, it is more useful to include
  corporate taxes

34
Example equity betas vs. leverage

• McDonnell Douglas (pre merger)
• equity (levered) beta 0.59 D/E .875
• Tax rate 34 risk premium 8.5
• T-Bill 5.24
• Unlevered beta current beta/(1 (1-tax
  rate)(D/E)
• .59/(1(1-.34)(.875) .374

35
Estimating betas using betas of comparable
companies

• Continental Airlines, 1992 restructuring

36
Example estimating beta

• Novell, which had a market value of equity of 2
  billion and a beta of 1.50, announced that it was
  acquiring WordPerfect, which had a market value
  of equity of 1 billion, and a beta of 1.30.
  Neither firm had any debt in its financial
  structure at the time of the acquisition, and the
  corporate tax rate was 40.
• Estimate the beta for Novell after the
  acquisition, assuming that the entire acquisition
  was financed with equity.
• Assume that Novell had to borrow the 1 billion
  to acquire WordPerfect. Estimate the beta after
  the acquisition.

37
(No Transcript)
38
(No Transcript)
39
Example estimating beta

• Southwestern Bell, a phone company, is
  considering expanding its operations into the
  media business. The beta for the company at the
  end of 1995 was 0.90, and the debt/equity ratio
  was 1. The media business is expected to be 30
  of the overall firm value in 1999, and the
  average beta of comparable media firms is 1.20
  the average debt/equity ratio for these firms is
  50. The marginal corporate tax rate is 36.
• a. Estimate the beta for Southwestern Bell in
  1999, assuming that it maintains its current
  debt/equity ratio.
• b. Estimate the beta for Southwestern Bell in
  1999, assuming that it decides to finance its
  media operations with a debt/equity ratio of 50.

40
Boeing commercial aircraft division
41
Boeing commercial aircraft division
42
WACC

• The key is that the rate will depend on the risk
  of the cash flows
• The cost of capital is an opportunity cost - it
  depends on where the money goes, not where it
  comes from.

WACC (E/V) x Re (D/V) x RD x (1 - T)
43
Cost of Equity Dividend Growth Model
44
Northwestern Corporation 8/04 - WACC

• WACC (E/V) x Re (D/V) x RD x (1 - T)
• Historical beta?
• Sources for beta?

45
Northwestern Corporation - peers
Sources?
46
Northwestern Corporation - peers
47
Northwestern Corporation - Beta
48
Northwestern Corporation Cost of equity

• re rf ße(rm rf)
• Levered beta .41(1(1-.385)1.381) 0.75
• Ibbotson 03, (rm rf) 7
• 20 year bond 4/02 5.9
• Re 5.9 0.75(7) 9.85
• Adding a 1.48 size risk premia (Ibbottson), and
  2 company specific risk premia, cost of equity
  13.33
• Arithmetic mean, large stocks long term
  treasury bonds, time period not specified

49
Northwestern Corporation - WACC

• WACC (E/V) x re (D/V) x rD x (1 - T)