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 $ 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 machine’s 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. SG’s 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

3. Measuring historical returns
Total return = dividend income + capital gains
% total return = Rt+1 = (Divt+1+ Pt+1- Pt)/Pt
Geometric mean returns
(1+ R)T = (1+R1)(1+R2)…(1+Rt)…(1+RT)
RA = [(1.15)(1.00)(1.05)(1.20)](1/4)-1  = 9.72%
RB = [(1.30)(0.80)(1.20)(1.50)](1/4)-1  = 16.97%
Arithmetic mean returns:
R = (R1 + R2 + …+ RT)/T
RA = [ ]/4 = .10 = 10%
RB = [ ]/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 = 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 = ( ) = 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) x (.075) = .095 = 9.5%
Var(RP) = 0.40 x ( )² x ( )² = .0006
SD(RP) =.0006 = = 2.45%
Note: E(RP) = .50 x E(RA) x E(RB) = 9.5%
BUT: Var(RP) ≠ .50 x Var(RA) 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 (-1< AB<1):
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 = ( )/4 = 0.175
Var(RA) = ²A = .2675/4 =
SD(RA) = A =  = .2586
RB = ( )/4 = 0.055
Var(RB) = ²B = .0529/4 =
SD(RB) = B =  = .1150
AB = Cov(RA,RB) = /4 =
AB = Corr(RA,RB) = AB / AB = /(.2586x.1150) =

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%
A=10% B=30%
Case 1: AB = 1 (AB = AB/AB)

16. Benefits of diversification
Stock A Stock B
E(RA)=10% E(RB)=15%
A=10% B=30%
Case 2: AB = 0.2 (AB = AB/AB)

17. Benefits of diversification
Stock A Stock B
E(RA)=10% E(RB)=15%
A=10% B=30%
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

20. Measuring systematic risk: beta
Rm = proxy for the "market" return
Portfolio beta =weighted ave of individual asset’s betas

21. Portfolio risk (beta) vs. return
Consider portfolios of:
Risky asset A, ßA = 1.2, E(RA) = 18%
Risk free asset, Rf = 7%

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
Arithmetic
T Bill 1% ; 12.2 – 3.8 = 8.4%
Geometric
T Bond 5%
10.2 – 5.5 = 4.7%
If Beta = 1, 9.4% vs. 9.7%

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 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 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.

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?
Selection of Comparable Companies used factor including:

46. Northwestern Corporation - peers

47. Northwestern Corporation - Beta

48. Northwestern Corporation – Cost of equity
re = rf + βe(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% *(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)