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(more practice with capital budgeting) SG Company currently uses a packaging machine that was purchased 3 years ago. This machine is being depreciated.

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Presentation on theme: "(more practice with capital budgeting) SG Company currently uses a packaging machine that was purchased 3 years ago. This machine is being depreciated."— Presentation transcript:

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 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 = R t+1 = (Div t+1 + P t+1 - P t )/P t Geometric mean returns (1+ R) T = (1+R 1 )(1+R 2 )…(1+R t )…(1+R T ) R A = [(1.15)(1.00)(1.05)(1.20)](1/4)-1 .0972 = 9.72% R B = [(1.30)(0.80)(1.20)(1.50)](1/4)-1 .1697 = 16.97% Arithmetic mean returns: R = (R 1 + R 2 + …+ R T )/T R A = [ ]/4 =.10 = 10% R B = [ ]/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, ) 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(R P ) = 0.40 x (.125) x (.075) =.095 = 9.5% Var(R P ) = 0.40 x ( )² x ( )² =.0006 SD(R P ) = .0006 =.0245 = 2.45% Note:E(R P ) =.50 x E(R A ) +.50 x E(R B ) = 9.5% BUT: Var(R P ) ≠.50 x Var(R A ) +.50 x Var(R B ) !!!!

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

12 Covariance and correlation: measuring how two variables are related Covariance is defined:  AB = Cov(R A,R B ) = Expected value of [(R A -R A ) x (R B -R B )] Correlation is defined (-1<  AB <1):  AB = Corr(R A,R B ) = Cov(R A,R B ) / (  A x  B ) =  AB / (  A x  B )

13 Portfolio risk & return If X A and X B 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 R A = ( )/4 = Var(R A ) =  ² A =.2675/4 = SD(R A ) =  A =  =.2586 R B = ( )/4 = Var(R B ) =  ² B =.0529/4 = SD(R B ) =  B =  =.1150  AB = Cov(R A,R B ) = /4 =  AB = Corr(R A,R B ) =  AB /  A  B = /(.2586x.1150) =

15 Benefits of diversification Consider two companies A & B, and portfolio weights X A =.5, X B =.5 Stock AStock B E(R A )=10%E(R B )=15%  A =10%  B =30% Case 1:  AB = 1(  AB =  AB /  A  B )

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

17 Benefits of diversification Stock AStock B E(R A )=10%E(R B )=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

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20 Measuring systematic risk: beta R m = 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, ß A = 1.2, E(R A ) = 18% Risk free asset, R f = 7%

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23 Market equilibrium Reward/risk ratio =E(R i ) - R f = constant! ß i 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

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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 0.59D/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.

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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

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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 R e + (D/V) x R D x (1 - T)

43 Cost of Equity: Dividend Growth Model

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

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

46 Northwestern Corporation - peers

47 Northwestern Corporation - Beta

48 Northwestern Corporation – Cost of equity r e = r f + β e (rm – r f ) Levered beta =.41*(1+(1-.385)*1.381) = 0.75 Ibbotson ’03*, (r m – r f ) = 7% 20 year bond 4/02 = 5.9% R e = 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 r e + (D/V) x r D x (1 - T)


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