(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 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).

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.

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  .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%

Measuring total risk Return volatility: the usual measure of volatility is the standard deviation, which is the square root of the variance.

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%

Historical Perspective

Capital Market History: Risk Return Tradeoff (Ibbotson, 1926-2003) Risk premium = difference between risky investment's return and riskless return.

EXPECTED (vs. Historical) RETURNS & VARIANCES Calculating the Expected Return: Expected return = (-1.25 + 7.50 + 8.75) = 15%

EXPECTED (vs. Historical) RETURNS & VARIANCES Calculating the variance:

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) !!!!

PORTFOLIO EXPECTED RETURNS & VARIANCES New Portfolio weights: put 3/7 in A and 4/7 in B: E(RP) = 10% SD(RP) = 0 !!!!

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)

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:

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

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)

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)

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)

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

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

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

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.

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

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%

Historic Returns and Equity Premia

Using the CAPM: estimating beta Regression output Data providers Bloomberg, Datastream, Value Line

Estimating beta: Continental Airlines

Estimating beta: Continental Airlines

Estimating beta: Continental Airlines

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

DETERMINANTS OF BETA: Operating vs. financial leverage Sales - costs - depr EBIT - interest - taxes Net income

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:

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

Estimating betas using betas of comparable companies Continental Airlines, 1992 restructuring

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.

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%.

Boeing – commercial aircraft division

Boeing – commercial aircraft division

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)

Cost of Equity: Dividend Growth Model

Northwestern Corporation 8/04 - WACC WACC = (E/V) x Re + (D/V) x RD x (1 - T) Historical beta? Sources for beta?

Northwestern Corporation - peers Sources? Selection of Comparable Companies used factor including:

Northwestern Corporation - peers

Northwestern Corporation - Beta

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% + 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

Northwestern Corporation - WACC WACC = (E/V) x re + (D/V) x rD x (1 - T)