Ch 12 capital market history
Sponsored Links
This presentation is the property of its rightful owner.
1 / 85

Ch 12 Capital market history PowerPoint PPT Presentation


  • 120 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Ch 12 Capital market history

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

  • 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

  • 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%


Figure 12.4


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


Table 12.3 Average Annual Returns and Risk Premiums


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

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


Figure 12.11


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

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

    • Year 15%

    • Year 2-3%

    • Year 312%

    • 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

  • 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?

  • 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

  • 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

  • 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

  • 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

  • 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 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

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

    • StateProbabilityCT

    • Boom0.31525

    • Normal0.51020

    • Recession???21

  • RC = .3(15) + .5(10) + .2(2) = 9.9%

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


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 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

  • Consider the following information:

    • StateProbabilityABC, Inc. (%)

    • Boom.2515

    • Normal.508

    • Slowdown.154

    • Recession.10-3

  • What is the expected return?

  • What is the variance?

  • What is the standard deviation?


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

  • 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

  • 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

  • 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

  • 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

  • Consider the following information

    • Invest 50% of your money in Asset A

    • StateProbabilityAB

    • Boom.430%-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

  • 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

  • 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

  • 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

  • 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

  • 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


Table 13.7


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


Figure 13.1


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 = 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

  • 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


Table 13.8


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

  • Consider the following information:

    Standard DeviationBeta

    • Security C20%1.25

    • Security K30%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

  • 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!


Example: Portfolio Expected Returns and Betas

E(RA)

Rf

A


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

  • 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

  • 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 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

  • 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

  • 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

  • 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

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


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

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

    • YearDividendPercent Change

    • 20021.23-

    • 20031.30

    • 20041.36

    • 20051.43

    • 20061.50

(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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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)


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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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


Figure 17.3


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

  • 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

  • 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

  • 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?


Case II - Example


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

  • 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

  • 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


Figure 17.4


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

  • 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%


Figure 17.5


  • Login