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# Ch 12 Capital market history - PowerPoint PPT Presentation

Ch 12 Capital market history. Returns The Historical Record Average Returns: The First Lesson The Variability of Returns: The Second Lesson More on Average Returns Capital Market Efficiency. Percentage Returns.

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• Returns

• The Historical Record

• Average Returns: The First Lesson

• The Variability of Returns: The Second Lesson

• More on Average Returns

• Capital Market Efficiency

• It is generally more intuitive to think in terms of percentages than in dollar returns

• Dividend yield = income / beginning price

• Capital gains yield = (ending price – beginning price) / beginning price

• Total percentage return = dividend yield + capital gains yield

• You bought a stock for \$35 and you received dividends of \$1.25. The stock is now selling for \$40.

• What is your dollar return?

• Dollar return = 1.25 + (40 – 35) = \$6.25

• What is your percentage return?

• Dividend yield = 1.25 / 35 = 3.57%

• Capital gains yield = (40 – 35) / 35 = 14.29%

• Total percentage return = 3.57 + 14.29 = 17.86%

• The “extra” return earned for taking on risk

• Treasury bills are considered to be risk-free

• The risk premium is the return over and above the risk-free rate

• Variance and standard deviation measure the volatility of asset returns

• The greater the volatility, the greater the uncertainty

• Historical variance = sum of squared deviations from the mean / (number of observations – 1)

• Standard deviation = square root of the variance

Variance = .0045 / (4-1) = .0015 Standard Deviation = .03873

• Arithmetic average – return earned in an average period over multiple periods

• Geometric average – average compound return per period over multiple periods

• The geometric average will be less than the arithmetic average unless all the returns are equal

• Which is better?

• The arithmetic average is overly optimistic for long horizons

• The geometric average is overly pessimistic for short horizons

• So the answer depends on the planning period under consideration

• 15 – 20 years or less: use arithmetic

• 20 – 40 years or so: split the difference between them

• 40 + years: use the geometric

• What is the arithmetic and geometric average for the following returns?

• Year 1 5%

• Year 2 -3%

• Year 3 12%

• Arithmetic average = (5 + (–3) + 12)/3 = 4.67%

• Geometric average = [(1+.05)*(1-.03)*(1+.12)]1/3 – 1 = .0449 = 4.49%

• Stock prices are in equilibrium or are “fairly” priced

• If this is true, then you should not be able to earn “abnormal” or “excess” returns

• Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market

• There are many investors out there doing research

• As new information comes to market, this information is analyzed and trades are made based on this information

• Therefore, prices should reflect all available public information

• If investors stop researching stocks, then the market will not be efficient

• Prices reflect all information, including public and private

• If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed

• Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns

• Prices reflect all publicly available information including trading information, annual reports, press releases, etc.

• If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information

• Implies that fundamental analysis will not lead to abnormal returns

• Prices reflect all past market information such as price and volume

• If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information

• Implies that technical analysis will not lead to abnormal returns

• Empirical evidence indicates that markets are generally weak form efficient

• Expected Returns and Variances

• Portfolios

• Announcements, Surprises, and Expected Returns

• Risk: Systematic and Unsystematic

• Diversification and Portfolio Risk

• Systematic Risk and Beta

• The Security Market Line

• The SML and the Cost of Capital: A Preview

• Expected returns are based on the probabilities of possible outcomes

• In this context, “expected” means average if the process is repeated many times

• The “expected” return does not even have to be a possible return

• Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?

• State Probability C T

• Boom 0.3 15 25

• Normal 0.5 10 20

• Recession ??? 2 1

• RC = .3(15) + .5(10) + .2(2) = 9.9%

• RT = .3(25) + .5(20) + .2(1) = 17.7%

• Variance and standard deviation still measure the volatility of returns

• Using unequal probabilities for the entire range of possibilities

• Weighted average of squared deviations

• Consider the previous example. What are the variance and standard deviation for each stock?

• Stock C

• 2 = .3(15-9.9)2 + .5(10-9.9)2 + .2(2-9.9)2 = 20.29

•  = 4.5

• Stock T

• 2 = .3(25-17.7)2 + .5(20-17.7)2 + .2(1-17.7)2 = 74.41

•  = 8.63

• Consider the following information:

• State Probability ABC, Inc. (%)

• Boom .25 15

• Normal .50 8

• Slowdown .15 4

• Recession .10 -3

• What is the expected return?

• What is the variance?

• What is the standard deviation?

• A portfolio is a collection of assets

• An asset’s risk and return are important in how they affect the risk and return of the portfolio

• The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets

• Suppose you have \$15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?

• \$2000 of DCLK

• \$3000 of KO

• \$4000 of INTC

• \$6000 of KEI

• DCLK: 2/15 = .133

• KO: 3/15 = .2

• INTC: 4/15 = .267

• KEI: 6/15 = .4

• The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio

• You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities

• Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?

• DCLK: 19.69%

• KO: 5.25%

• INTC: 16.65%

• KEI: 18.24%

• E(RP) = .133(19.69) + .2(5.25) + .267(16.65) + .4(18.24) = 15.41%

• Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm

• Compute the expected portfolio return using the same formula as for an individual asset

• Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

• Consider the following information

• Invest 50% of your money in Asset A

• State Probability A B

• Boom .4 30% -5%

• Bust .6 -10% 25%

• What are the expected return and standard deviation for each asset?

• What are the expected return and standard deviation for the portfolio?

Portfolio

12.5%

7.5%

• Realized returns are generally not equal to expected returns

• There is the expected component and the unexpected component

• At any point in time, the unexpected return can be either positive or negative

• Over time, the average of the unexpected component is zero

• Risk factors that affect a large number of assets

• Also known as non-diversifiable risk or market risk

• Includes such things as changes in GDP, inflation, interest rates, etc.

• Risk factors that affect a limited number of assets

• Also known as unique risk and asset-specific risk

• Includes such things as labor strikes, part shortages, etc.

• Total Return = expected return + unexpected return

• Unexpected return = systematic portion + unsystematic portion

• Therefore, total return can be expressed as follows:

• Total Return = expected return + systematic portion + unsystematic portion

• Portfolio diversification is the investment in several different asset classes or sectors

• Diversification is not just holding a lot of assets

• For example, if you own 50 Internet stocks, you are not diversified

• However, if you own 50 stocks that span 20 different industries, then you are diversified

• Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns

• This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another

• However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

• The risk that can be eliminated by combining assets into a portfolio

• Often considered the same as unsystematic, unique or asset-specific risk

• If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

• Total risk = systematic risk + unsystematic risk

• The standard deviation of returns is a measure of total risk

• For well-diversified portfolios, unsystematic risk is very small

• Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

• There is a reward for bearing risk

• There is not a reward for bearing risk unnecessarily

• The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away

• How do we measure systematic risk?

• We use the beta coefficient to measure systematic risk

• What does beta tell us?

• A beta of 1 implies the asset has the same systematic risk as the overall market

• A beta < 1 implies the asset has less systematic risk than the overall market

• A beta > 1 implies the asset has more systematic risk than the overall market

• Consider the following information:

Standard Deviation Beta

• Security C 20% 1.25

• Security K 30% 0.95

• Which security has more total risk?

• Which security has more systematic risk?

• Which security should have the higher expected return?

• Remember that the risk premium = expected return – risk-free rate

• The higher the beta, the greater the risk premium should be

• Can we define the relationship between the risk premium and beta so that we can estimate the expected return?

• YES!

• The reward-to-risk ratio is the slope of the line illustrated in the previous example

• Slope = (E(RA) – Rf) / (A – 0)

• Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5

• What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)?

• What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)?

• In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market

• The security market line (SML) is the representation of market equilibrium

• The slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / M

• But since the beta for the market is ALWAYS equal to one, the slope can be rewritten

• Slope = E(RM) – Rf = market risk premium

• The capital asset pricing model defines the relationship between risk and return

• E(RA) = Rf + A(E(RM) – Rf)

• If we know an asset’s systematic risk, we can use the CAPM to determine its expected return

• This is true whether we are talking about financial assets or physical assets

• Consider the betas for each of the assets given earlier. If the risk-free rate is 2.13% and the market risk premium is 8.6%, what is the expected return for each?

• The Cost of Capital: Some Preliminaries

• The Cost of Equity

• The Costs of Debt and Preferred Stock

• The Weighted Average Cost of Capital

• Divisional and Project Costs of Capital

• Flotation Costs and the Weighted Average Cost of Capital

• The cost of equity is the return required by equity investors given the risk of the cash flows from the firm

• Financial risk

• There are two major methods for determining the cost of equity

• Dividend growth model

• SML or CAPM

• Start with the dividend growth model formula and rearrange to solve for RE

• Suppose that your company is expected to pay a dividend of \$1.50 per share next year. There has been a steady growth in dividends of 5.1% per year and the market expects that to continue. The current price is \$25. What is the cost of equity?

• One method for estimating the growth rate is to use the historical average

• Year Dividend Percent Change

• 2002 1.23 -

• 2003 1.30

• 2004 1.36

• 2005 1.43

• 2006 1.50

(1.30 – 1.23) / 1.23 = 5.7%

(1.36 – 1.30) / 1.30 = 4.6%

(1.43 – 1.36) / 1.36 = 5.1%

(1.50 – 1.43) / 1.43 = 4.9%

Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%

• Use the following information to compute our cost of equity

• Risk-free rate, Rf

• Market risk premium, E(RM) – Rf

• Systematic risk of asset, 

• Suppose your company has an equity beta of .58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is your cost of equity capital?

• RE = 6.1 + .58(8.6) = 11.1%

• Since we came up with similar numbers using both the dividend growth model and the SML approach, we should feel pretty good about our estimate

• Suppose our company has a beta of 1.5. The market risk premium is expected to be 9% and the current risk-free rate is 6%. We have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and our last dividend was \$2. Our stock is currently selling for \$15.65. What is our cost of equity?

• Using SML: RE = 6% + 1.5(9%) = 19.5%

• Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55%

• The cost of debt is the required return on our company’s debt

• We usually focus on the cost of long-term debt or bonds

• The required return is best estimated by computing the yield-to-maturity on the existing debt

• We may also use estimates of current rates based on the bond rating we expect when we issue new debt

• The cost of debt is NOT the coupon rate

• Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid semiannually. The bond is currently selling for \$908.72 per \$1,000 bond. What is the cost of debt?

• N = 50; PMT = 45; FV = 1000; PV = -908.72; CPT I/Y = 5%; YTM = 5(2) = 10%

• We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm.

• This “average” is the required return on the firm’s assets, based on the market’s perception of the risk of those assets

• The weights are determined by how much of each type of financing is used

• Notation

• E = market value of equity = # of outstanding shares times price per share

• D = market value of debt = # of outstanding bonds times bond price

• V = market value of the firm = D + E

• Weights

• wE = E/V = percent financed with equity

• wD = D/V = percent financed with debt

• Suppose you have a market value of equity equal to \$500 million and a market value of debt = \$475 million.

• What are the capital structure weights?

• V = 500 million + 475 million = 975 million

• wE = E/V = 500 / 975 = .5128 = 51.28%

• wD = D/V = 475 / 975 = .4872 = 48.72%

• We are concerned with after-tax cash flows, so we also need to consider the effect of taxes on the various costs of capital

• Interest expense reduces our tax liability

• This reduction in taxes reduces our cost of debt

• After-tax cost of debt = RD(1-TC)

• Dividends are not tax deductible, so there is no tax impact on the cost of equity

• WACC = wERE + wDRD(1-TC)

50 million shares

\$80 per share

Beta = 1.15

Risk-free rate = 5%

Debt Information

\$1 billion in outstanding debt (face value)

Current quote = 110

Coupon rate = 9%, semiannual coupons

15 years to maturity

Tax rate = 40%

Extended Example – WACC - I

• What is the cost of equity?

• RE = 5 + 1.15(9) = 15.35%

• What is the cost of debt?

• N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = 3.9268

• RD = 3.927(2) = 7.854%

• What is the after-tax cost of debt?

• RD(1-TC) = 7.854(1-.4) = 4.712%

• What are the capital structure weights?

• E = 50 million (80) = 4 billion

• D = 1 billion (1.10) = 1.1 billion

• V = 4 + 1.1 = 5.1 billion

• wE = E/V = 4 / 5.1 = .7843

• wD = D/V = 1.1 / 5.1 = .2157

• What is the WACC?

• WACC = .7843(15.35%) + .2157(4.712%) = 13.06%

• The Capital Structure Question

• The Effect of Financial Leverage

• Capital Structure and the Cost of Equity Capital

• M&M Propositions I and II with Corporate Taxes

• Bankruptcy Costs

• Optimal Capital Structure

• The Pie Again

• Observed Capital Structures

• A Quick Look at the Bankruptcy Process

• We are going to look at how changes in capital structure affect the value of the firm, all else equal

• Capital restructuring involves changing the amount of leverage a firm has without changing the firm’s assets

• The firm can increase leverage by issuing debt and repurchasing outstanding shares

• The firm can decrease leverage by issuing new shares and retiring outstanding debt

• Modigliani and Miller Theory of Capital Structure

• Proposition I – firm value

• Proposition II – WACC

• The value of the firm is determined by the cash flows to the firm and the risk of the assets

• Changing firm value

• Change the risk of the cash flows

• Change the cash flows

• Case I – Assumptions

• No corporate or personal taxes

• No bankruptcy costs

• Case II – Assumptions

• Corporate taxes, but no personal taxes

• No bankruptcy costs

• Case III – Assumptions

• Corporate taxes, but no personal taxes

• Bankruptcy costs

• Proposition I

• The value of the firm is NOT affected by changes in the capital structure

• The cash flows of the firm do not change; therefore, value doesn’t change

• Proposition II

• The WACC of the firm is NOT affected by capital structure

• WACC = RA = (E/V)RE + (D/V)RD

• RE = RA + (RA – RD)(D/E)

• RA is the “cost” of the firm’s business risk, i.e., the risk of the firm’s assets

• (RA – RD)(D/E) is the “cost” of the firm’s financial risk, i.e., the additional return required by stockholders to compensate for the risk of leverage

• Data

• Required return on assets = 16%, cost of debt = 10%; percent of debt = 45%

• What is the cost of equity?

• RE = 16 + (16 - 10)(.45/.55) = 20.91%

• Suppose instead that the cost of equity is 25%, what is the debt-to-equity ratio?

• 25 = 16 + (16 - 10)(D/E)

• D/E = (25 - 16) / (16 - 10) = 1.5

• Based on this information, what is the percent of equity in the firm?

• E/V = 1 / 2.5 = 40%

• How does financial leverage affect systematic risk?

• CAPM: RA = Rf + A(RM – Rf)

• Where A is the firm’s asset beta and measures the systematic risk of the firm’s assets

• Proposition II

• Replace RA with the CAPM and assume that the debt is riskless (RD = Rf)

• RE = Rf + A(1+D/E)(RM – Rf)

• RE = Rf + A(1+D/E)(RM – Rf)

• CAPM: RE = Rf + E(RM – Rf)

• E = A(1 + D/E)

• Therefore, the systematic risk of the stock depends on:

• Systematic risk of the assets, A, (Business risk)

• Level of leverage, D/E, (Financial risk)

• Interest is tax deductible

• Therefore, when a firm adds debt, it reduces taxes, all else equal

• The reduction in taxes increases the cash flow of the firm

• How should an increase in cash flows affect the value of the firm?

• Annual interest tax shield

• Tax rate times interest payment

• 6,250 in 8% debt = 500 in interest expense

• Annual tax shield = .34(500) = 170

• Present value of annual interest tax shield

• Assume perpetual debt for simplicity

• PV = 170 / .08 = 2,125

• PV = D(RD)(TC) / RD = DTC = 6,250(.34) = 2,125

• The value of the firm increases by the present value of the annual interest tax shield

• Value of a levered firm = value of an unlevered firm + PV of interest tax shield

• Value of equity = Value of the firm – Value of debt

• Assuming perpetual cash flows

• VU = EBIT(1-T) / RU

• VL = VU + DTC

• Data

• EBIT = 25 million; Tax rate = 35%; Debt = \$75 million; Cost of debt = 9%; Unlevered cost of capital = 12%

• VU = 25(1-.35) / .12 = \$135.42 million

• VL = 135.42 + 75(.35) = \$161.67 million

• E = 161.67 – 75 = \$86.67 million

• The WACC decreases as D/E increases because of the government subsidy on interest payments

• RA = (E/V)RE + (D/V)(RD)(1-TC)

• RE = RU + (RU – RD)(D/E)(1-TC)

• Example

• RE = 12 + (12-9)(75/86.67)(1-.35) = 13.69%

• RA = (86.67/161.67)(13.69) + (75/161.67)(9)(1-.35)RA = 10.05%

• Suppose that the firm changes its capital structure so that the debt-to-equity ratio becomes 1.

• What will happen to the cost of equity under the new capital structure?

• RE = 12 + (12 - 9)(1)(1-.35) = 13.95%

• What will happen to the weighted average cost of capital?

• RA = .5(13.95) + .5(9)(1-.35) = 9.9%