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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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ch 12 capital market history
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
Percentage Returns
  • 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
example calculating returns
Example – Calculating Returns
  • 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%
risk premiums
Risk Premiums
  • 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
Variance and Standard Deviation
  • 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
example variance and standard deviation
Example – Variance and Standard Deviation

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

arithmetic vs geometric mean
Arithmetic vs. Geometric Mean
  • 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
example computing averages
Example: Computing Averages
  • 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%
efficient capital markets
Efficient Capital Markets
  • 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
what makes markets efficient
What Makes Markets Efficient?
  • 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
strong form efficiency
Strong Form Efficiency
  • 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
semistrong form efficiency
Semistrong Form Efficiency
  • 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
weak form efficiency
Weak Form Efficiency
  • 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
ch 13 risk return and the security market line
Ch 13 Risk, return and the security market line
  • 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
Expected Returns
  • 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
example expected returns
Example: Expected Returns
  • 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 deviation1
Variance and Standard Deviation
  • Variance and standard deviation still measure the volatility of returns
  • Using unequal probabilities for the entire range of possibilities
  • Weighted average of squared deviations
example variance and standard deviation1
Example: Variance and Standard Deviation
  • 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
exercise in class
Exercise in class
  • 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?
portfolios
Portfolios
  • 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
example portfolio weights
Example: Portfolio Weights
  • 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
portfolio expected returns
Portfolio Expected Returns
  • 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
example expected portfolio returns
Example: Expected Portfolio Returns
  • 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%
portfolio variance
Portfolio Variance
  • 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
example portfolio variance
Example: Portfolio Variance
  • 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%

expected versus unexpected returns
Expected versus Unexpected Returns
  • 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
systematic risk
Systematic Risk
  • 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.
unsystematic risk
Unsystematic Risk
  • 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.
returns
Returns
  • 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
diversification
Diversification
  • 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
the principle of diversification
The Principle of Diversification
  • 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
diversifiable risk
Diversifiable Risk
  • 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
Total Risk
  • 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
systematic risk principle
Systematic Risk Principle
  • 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
measuring systematic risk
Measuring Systematic Risk
  • 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
total versus systematic risk
Total versus Systematic Risk
  • 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?
beta and the risk premium
Beta and the Risk Premium
  • 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!
reward to risk ratio definition and example
Reward-to-Risk Ratio: Definition and Example
  • 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)?
market equilibrium
Market Equilibrium
  • 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
security market line
Security Market Line
  • 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 capm
The Capital Asset Pricing Model (CAPM)
  • 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
example capm
Example - CAPM
  • 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?
ch 15 the cost of capital
Ch 15 The cost of capital
  • 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
cost of equity
Cost of Equity
  • The cost of equity is the return required by equity investors given the risk of the cash flows from the firm
    • Business risk
    • Financial risk
  • There are two major methods for determining the cost of equity
    • Dividend growth model
    • SML or CAPM
the dividend growth model approach
The Dividend Growth Model Approach
  • Start with the dividend growth model formula and rearrange to solve for RE
dividend growth model example
Dividend Growth Model Example
  • 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?
example estimating the dividend growth rate
Example: Estimating the Dividend Growth Rate
  • 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%

the sml approach
The SML Approach
  • Use the following information to compute our cost of equity
    • Risk-free rate, Rf
    • Market risk premium, E(RM) – Rf
    • Systematic risk of asset, 
example sml
Example - SML
  • 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
example cost of equity
Example – Cost of Equity
  • 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%
cost of debt
Cost of Debt
  • 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
example cost of debt
Example: Cost of Debt
  • 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%
the weighted average cost of capital
The Weighted Average Cost of Capital
  • 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
capital structure weights
Capital Structure Weights
  • 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
example capital structure weights
Example: Capital Structure Weights
  • 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%
taxes and the wacc
Taxes and the WACC
  • 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)
extended example wacc i
Equity Information

50 million shares

$80 per share

Beta = 1.15

Market risk premium = 9%

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
extended example wacc ii
Extended Example – WACC - II
  • 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%
extended example wacc iii
Extended Example – WACC - III
  • 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%
ch 17 capital structure
Ch 17 Capital structure
  • 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
capital restructuring
Capital Restructuring
  • 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
capital structure theory
Capital Structure Theory
  • 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
capital structure theory under three special cases
Capital Structure Theory Under Three Special Cases
  • 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
case i propositions i and ii
Case I – Propositions I and II
  • 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
case i equations
Case I - Equations
  • 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
case i example
Case I - Example
  • 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%
the capm the sml and proposition ii
The CAPM, the SML and Proposition II
  • 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)
business risk and financial risk
Business Risk and Financial Risk
  • 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)
case ii cash flow
Case II – Cash Flow
  • 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?
interest tax shield
Interest Tax Shield
  • 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
case ii proposition i
Case II – Proposition I
  • 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
example case ii proposition i
Example: Case II – Proposition I
  • 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
case ii proposition ii
Case II – Proposition II
  • 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%
example case ii proposition ii
Example: Case II – Proposition II
  • 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%
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