Finance Lecture7

MBAM 614 Finance Diversification and the Capital Asset Pricing Model • MBAM614 Class 7 - 1 Summary of Last Class 1. The greater the potential reward, the greater the risk 2. The mean and variance of past returns may be reasonable estimates for the expected value and variance of future returns 3. If returns are random and normally distributed then returns will be within one S.D. of the mean roughly 66% of the time, within 2 S.D.s roughly 95% of the time, and within 3 S.D.s more than 99% 4. E(R) = Σ Σ N S (pi * Ri) 5. Var(R) = i=1 (xi * Ri) 7. Var(R) ≠ Σ Σ N S (pi * [ Ri - E(R) ]2) i=1 (xi * [ Ri - E(R) ]2) Class 7 - 2 6. E(Rp) = i=1 i=1 • MBAM614 1 Summary of Last Class 1. E(Rp) = Σ [xi * E(Ri)] i=1 N 2. A portfolio’s variance is, in general, less than the weighted average of its security variances and depends on the correlation between portfolio securities. 3. Total Return = Expected Return + Unexpected Return 4. R = E(R) + Systematic Portion + Unsystematic Portion 5. Diversification reduces or eliminates the Unsystematic Portion • MBAM614 Class 7 - 3 Agenda 1. 2. 3. 4. 5. Portfolio Risk and the Principle of Diversification Measuring Systematic Risk The Security Market Line Expected Returns and Systematic Risk The Cost of Capital • MBAM614 Class 7 - 4 2 Portfolio Risk The greater the number of different assets in a portfolio, the more Diversified a portfolio is As we have seen, portfolio variability (risk) can be quite different from the variability of individual stocks Principle of Diversification - when several assets are held, the collection can have less variability (risk) than the typical individual asset – this is a function of the asset correlations • MBAM614 Class 7 - 5 Effects of Diversification Average annual standard deviation (%) 49.2 Due to Unique or Unsystematic Risk Diversifiable risk 23.9 19.2 Nondiversifiable risk 1 10 20 30 40 1000 Due to Market or Systematic Risk Number of stocks in portfolio Class 7 - 6 • MBAM614 3 The Principle of Diversification The portion of variability present in a single security that is NOT present in a portfolio of securities is called Diversifiable Risk The level of variance that remains in a portfolio is called Undiversifiable Risk When securities are combined in portfolios, their unique risk (0) tends to cancel out unique or unsystematic risk is diversifiable risk large portfolios have little or no unsystematic risk • MBAM614 Class 7 - 7 Diversification and Systematic Risk Systematic risk (m), the variability due to influences that affect all assets (more or less), cannot be eliminated by diversification Systematic risk is undiversifiable risk Total Risk Systematic Risk Unsystematic Risk = + Total Risk = Undiversifiable Risk + Diversifiable Risk • MBAM614 Class 7 - 8 4 Systematic Risk and Reward There is a reward for bearing risk {E(R) depends on risk} Since unsystematic risk can be diversified away, the reward for bearing risk depends on systematic or undiversifiable risk only This is the Systematic Risk Principle An asset’s E(R) depends only on its systematic risk Regardless of an asset’s total risk, its expected return depends only on its systematic or undiversifiable risk • MBAM614 Class 7 - 9 Measuring Systematic Risk The Beta Coefficient, β, of an asset measures how much systematic risk that asset has relative to an asset of “average” systematic risk β = 1 means “average” risk Highest Total Risk Barrick BCE General Motors Imasco Seagram Total Risk • MBAM614 Highest Systematic Risk β 1.195 0.522 1.014 0.926 0.985 Avg. M. Return 2.22% 0.83% 1.46% 1.22% 1.37% σR 8.56% 3.10% 9.02% 5.72% 5.53% Systematic Risk Class 7 - 10 5 Portfolio Betas While portfolio variance is not the weighted average of the asset variances, a portfolio’s beta, βP, is the weighted average of the individual security betas. Eg. Suppose you have the following portfolio. What is its beta? Amount Invested $6,000 $4,000 $2,000 Portfolio Weight 50% 33% 17% Beta Coef. 0.522 1.014 0.985 Stock BCE GM Seagram Product 0.261 0.335 0.167 0.763 βP = 0.763 • MBAM614 Class 7 - 11 Beta and the Risk Premium How are portfolio expected returns related to systematic risk? Consider a portfolio with an investment in Stock A which has βA = 1.2 and E(RA) = 18% and a T-bill with a return of 7%. Given different portfolio weights, what is the E(RP)? Since the risk-free asset (T-bill) has no systematic risk, βf = 0 E(RP) = xf * Rf + xA * E(RA) β P = xf * β f + xA * βA = xf * 0 + xA * β A = xA * βA • MBAM614 Class 7 - 12 6 Possible Portfolios Proportion Invested in stock A 0% 25% 50% 75% 100% 125% Proportion invested in Rf 100% 75% 50% 25% 0% -25% Portfolio expected return 7.00% 9.75% 12.50% 15.25% 18.00% 20.75% Portfolio beta 0.00 0.30 0.60 0.90 1.20 1.50 More that 100% invested in risky assets and negative weight on Tbills represents money borrowed at the risk-less rate to see how E(RP) and βP are related, we can plot them • MBAM614 Class 7 - 13 E(RP) and βP E(RP) E(RA)=18% E(RP) 7.00% 9.75% 12.50% 15.25% 18.00% 20.75% βP 0.00 0.30 0.60 0.90 1.20 1.50 Rf = 7% Slope = Rise Run = E(RA) - Rf βA = (18% - 7%)/1.2 = 9.2% 0 0 1.2 = βA βP Class 7 - 14 • MBAM614 7 Reward-to-Risk Ratio the ratio E(RA) - Rf βA is called the Reward-to-Risk Ratio Measures the reward per unit of risk borne Eg. For Stock A in previous example, the Reward-to-risk ratio was Risk Premium or reward for bearing risk Units of risk borne (0.18 - 0.07)/1.2 = 0.092 or 9.2% • MBAM614 Class 7 - 15 Risk and Reward Consider two stocks A & B. Stock A has a reward-to-risk ratio of 12% and stock B has a reward-to-risk ratio of 9%. Which do you prefer? Why? Since A is offering a greater reward per unit of risk, we prefer A and will ignore B In an active, competitive market in which only systematic risk affects expected returns, the reward-to-risk ratio must be the same for all assets and portfolios in the market Thus, the expected returns and betas of all assets and portfolios must plot on the same straight line. This line is called the Security Market Line or SML • MBAM614 Class 7 - 16 8 Example: Finding the Risk-free Rate Investors expect CitiGroup’s return to be 12% based on its low historical systematic risk. The low systematic risk is also reflected in C’s beta, βC = 0.800. Consolidated Moose Pastures is somewhat more risky with a beta of βCMP = 2.000. Of course, CMP’s expected return of 20% is also higher. What is the current riskfree rate? Since all securities plot on the SML, all have the same reward-torisk ratio: E(RC) - Rf βC = E(RCMP) - Rf βCMP or 12%- Rf 0.800 = 20%- Rf 2.000 Solving for Rf gives 8% = 1.2 Rf or Rf = 6.7% • MBAM614 Class 7 - 17 The SML The portfolio that contains all of the assets in the market is called the Market Portfolio, M By definition, M has average systematic risk so βM = 1 Since all assets and portfolios lie on the SML when appropriately priced, so must the market portfolio If the expected return on M is E(RM), then the slope of the SML is Market Risk Premium E(RM) - Rf E(RM) - Rf SML Slope = = = E(RM) - Rf βM 1 • MBAM614 Class 7 - 18 9 The Capital Asset Pricing Model Since all assets plot on the SML, the expected return to any asset i, E(Ri), must satisfy the same reward-to-risk ratio as the market portfolio E(Ri) - Rf βi = E(RM) - Rf E(Ri) = Rf + βi* [ E(RM) - Rf ] This is the Capital Asset Pricing Model or CAPM • MBAM614 Class 7 - 19 The CAPM E(Ri) = Rf + βi* [ E(RM) - Rf ] the CAPM states that the expected return on an asset depends on: – The time value of money as measured by Rf – The reward per unit of systematic risk, E(RM) - Rf – The asset’s systematic risk as measured by β • MBAM614 Class 7 - 20 10 Example: AT&T’s E(R) AT&T Corp. has a beta of 0.522. If the current risk-free (T-bill) rate is 6.5% per year and the expected market premium is 9.2% (this is actually the historical market risk premium), what is E(RT)? Using CAPM: E(RT) = Rf + βT* [ E(RM) - Rf ] = 6.5% + 0.522 * [9.2%] E(RT) = 11.3% If E(RIMS) = 15.7%, the risk-free rate is 9%, and the expected market premium is 6%, what is Imasco’s beta? E(RIMS) = Rf + βIMS* [ E(RM) - Rf ] = 9% + βIMS * [6%] = 15.7% βIMS = 1.12 • MBAM614 Class 7 - 21 The Cost of Capital How do we determine the appropriate discount rate to use when evaluating projects? Two step process: – Determine the riskiness of the project. That is, find the systematic risk or β – Determine the expected return on alternative investments of similar risk. That is, find the expected return in financial markets for that β • MBAM614 Class 7 - 22 11 The Cost of Capital The Cost of Capital is the minimum expected return an investment must offer to be attractive – The cost of capital is also called the Required Rate of Return The cost of capital, when taken as the market rate on a financial asset of equal systematic risk, is an Opportunity Cost because other profitable opportunities have been forgone. • MBAM614 Class 7 - 23 Example: Purchasing Harris Bank When the Bank of Montreal was considering the purchase of Harris Bank, a cost was determined and projections of cash inflows and out-flows were made. The intent was to check the NPV of purchasing HB. Assuming that Harris Bank and California Federal had the same amount of systematic risk (a BIG assumption), that CF had a beta of 0.700, that the risk-free rate was 7.2%, and that the expected market premium was 9.2%, what discount rate should BOM have used in their analysis? Since βHB = βCF = 0.700, applying the CAPM E(RHB) = 7.2% + 0.700 * [9.2%] = 13.6% The required rate of return for the HB investment should have been 13.6% • MBAM614 Class 7 - 24 12 Key Points 1. Total Return = Expected Return + Unexpected Return 2. R = E(R) + Systematic Portion + Unsystematic Portion 3. Diversification reduces or eliminates the Unsystematic Portion • MBAM614 Class 7 - 25 Key Points 4. Total Risk = Systematic Risk + Unsystematic Risk 5. Because Unsystematic Risk can be diversified away, only Systematic Risk is rewarded 6. An asset’s beta measures its Systematic Risk - the market portfolio of all assets has average risk, βM = 1 - the risk-free asset has no systematic risk, βf = 0 7. All properly priced assets plot on the SML which has the slope E(RM) - Rf 8. The CAPM: E(Ri) = Rf + βi* [ E(RM) - Rf ] • MBAM614 Class 7 - 26 13 MBAM 614 Finance The Cost of Capital • MBAM614 Class 7 - 27 Agenda 1. Required Returns and the Cost of Capital 2. The Cost of Equity 3. The Cost of Debt 4. Capital Structure 5. The Weighted Average Cost of Capital • MBAM614 Class 7 - 28 14 Required Return & Cost of Capital All investments with the same systematic risk have the same expected return. Can be viewed in many ways: – Required Return is from the investor’s point of view – Cost of Capital is from the firm’s point of view – Opportunity Cost is the return available in financial markets on investments with same systematic risk These are all the same thing! A firm’s Cost of Capital is the return investors expect to earn by investing in the firm • MBAM614 Class 7 - 29 Example: Cost of Capital The Cost of Capital is an Opportunity Cost: it depends on what the money is invested in, not where it comes from Ford Motor Company is considering the introduction of a new line of automobiles at a cost of $2B. The entire $2B can be borrowed at a cost of 9.25% in interest. Bonds, available from your broker for up to $3B, with identical systematic risk are currently yielding 12.5%. If Ford borrowed the money and invested in the new car line, what would the cost of capital for the new car line be? Since Ford could have invested in the bonds yielding 12.5%, the new car line MUST earn at least 12.5% otherwise it is a poor investment. The cost of capital is 12.5% not 9.25%. • MBAM614 Class 7 - 30 15 Sources of Capital Firms usually use more than one type of security to raise capital. Common types are: – Bonds or Debt (less risky) – Preferred Stock (moderate risk) – Common Stock (more risky) A firm’s Capital Structure is the particular combination of these securities used by the firm. For now, this is taken as given. A firm’s overall cost of capital will reflect the average riskiness of all its securities – just like the expected return on a portfolio of securities Means we need to find the cost of each type of capital • MBAM614 Class 7 - 31 Cost of Equity Cost of Equity, Re, is the return expected by investors for investing in the firm’s stock Can be estimated using – Dividend Growth Model – SML or CAPM • MBAM614 Class 7 - 32 16 Dividend Growth Model Recall that when dividends are expected to grow at a constant rate P0 = D0* (1 + g)/(Re - g) = D1/(Re - g) Dividend Yield Re = D1/P0 + g Growth or Capital Gains To implement, find most recent dividend (D0 or D1) and price (P0). Financial press or company, for example. Must estimate g • MBAM614 Class 7 - 33 Estimating Growth Analysts’ forecasts – – – – – Value Line Financial Post Dun & Bradstreet Your Broker Often, these are forecasts of earnings growth but if payout doesn’t change, it’s also dividend growth Historical growth rates – Might use average annual change in dividends over last 4 or 5 years • MBAM614 Class 7 - 34 17 Example: Historical Dividends Given the following dividend history for CMP, what would you estimate CMP’s growth rate to be? If the current share price is $45, what is Re for CMP? Year 1998 1999 2000 2001 2002 Dividend $4.00 4.40 4.75 5.25 5.65 ∆ Dividend $0.40 0.35 0.50 0.40 % Change 10.00 7.95 10.53 7.62 g = average = (10.00% + 7.95% + 10.53% + 7.62%)/4 = 9.025% Re = D1/P0 + g Re = ($5.65 * 1.09025)/$45 + 0.09025 = 22.714% • MBAM614 Class 7 - 35 Pros & Cons of CGM Advantages – Easy to use – Widely recognized Disadvantages – Only works if firm pays dividends – Re is VERY sensitive to estimate of g – History may not be a reliable predictor of future – Risk is only indirectly accounted for by use of price • MBAM614 Class 7 - 36 18 Using CAPM CAPM (SML) says Re depends on: – Risk-free rate, Rf – Expected market risk premium, E(RM) - Rf – amount of systematic risk, measured by β Re = Rf + βe* [E(RM) - Rf] To implement: – βs are widely available (Broker, PFSI, Web, etc.) – T-Bill rate often used for Rf – Must estimate Market Risk Premium, E(RM) - Rf , using either historical averages or analysts’ forecasts • MBAM614 Class 7 - 37 Pros & Cons of CAPM Advantages – Consistent with capital market history, method specifically adjusts for risk – Applicable to virtually all publicly traded stocks, not just those paying dividends Disadvantages – History may not be a reliable predictor of future for market risk premiums and βs – Not as widely understood thus less frequently used Best to use both CGM and CAPM and compare – use average if reasonably close – use most reliable if different • MBAM614 Class 7 - 38 19 Example: Cost of Equity for Exxon Mobil Exxon Mobil Corp. (XOM) has a beta of 1.05. If the risk-free rate is 6.5% and the market risk premium is the 7%, what is XOM’s cost of equity? Using CAPM: Re = Rf + βe* [E(RM) - Rf] Re = 6.5% + 1.05(7%) = 13.85% Irving Oil, which does not currently have publicly traded shares, is considering selling some. What is Irving’s cost of equity? If Irving plans to pay a $2.00 dividend after one year and have it grow at 7% thereafter, what will their share price probably be? Assuming Irving Oil and Exxon Mobil have similar systematic risk, Irving’s cost of equity would be 13.85% P0 = D1/(Re - g) = $2.00/(13.85% - 7%) = $29.20 • MBAM614 Class 7 - 39 Cost of Debt Although CAPM applies to bonds, seldom need to use it The Cost of Debt, Rd, can easily be estimated from current market conditions: – Yield-to-maturity on current debt – Yield-to-maturity on debt with same rating (risk) Eg. If Pohl Corp. issued a 10-year bond 5 years ago with a coupon rate of 13% that is currently selling for $1,075, what is Pohl’s cost of debt? Assuming annual interest, the YTM that makes a 5 year annuity of $130 + the PV of $1,000 in 5 years have a present value of $1,075 is 10.97% or approximately 11% • MBAM614 Class 7 - 40 20 Example: Cost of Debt for BBD On March 1/97, Bombardier had a 34-year AA bond outstanding yielding 7.632%. If BBD wanted to issue 8-year bonds (also rated AA), what would the cost of that debt have been? Other AA 8year issues outstanding on March 1/97 were: Issuer Bell Canada CIBC Canadian Utilities PanCanadian Petroleum Thompson Corp Yield 6.577% 6.727% 6.488% 6.578% 6.805% Since there is such a great difference in term-to-maturity, the new bonds would not have had similar risk to the 34-year bonds. An average of the 8-year AA bonds would be a better estimate. Rd = 6.635% (actually had a 9 yr yielding 6.746%) • MBAM614 Class 7 - 41 Cost of Preferred CAPM also applies to preferreds but seldom need to use it The Cost of Preferred, Rp, can easily be estimated from current market conditions, too: – Since a preferred share is a perpetuity, simply the dividend yield on current preferreds Rp = Dp / P0 – Dividend yield on preferreds with same rating (risk) • MBAM614 Class 7 - 42 21 Example: Cost of Preferred Equity for CMB Prior to its merger with J.P. Morgan, Chase Manhattan had the following preferred issues outstanding. What was CMB’s cost of preferred equity? Share CMB.PR.C CMB.PR.G Dividend $2.71 $2.74 Price $28.625 $27.625 Rp 9.47% 9.92% Average cost of preferred was Rp = 9.70% • MBAM614 Class 7 - 43 Average Cost of Capital What is the average cost of capital for the firm? Must be the same as the average return required by all investors. What is that? If you purchased all the securities of a firm, you have purchased a portfolio. Your expected (required) return on the portfolio will be the average cost of capital for the firm. Weighted average of the security required returns: Re, Rd, Rp Portfolio weights are simply market value invested in each security as a percentage of total portfolio market value Cost of Capital for firm is the weighted average cost of the different types of capital the firm has issued - called WACC • MBAM614 Class 7 - 44 22 Portfolio Weights for Cost of Capital Determine market value of each type of security outstanding – E - market value of firm’s equity (# shares × share price) – D - market value of firm’s debt (# bonds × bond price) – P - market value of preferreds (# preferred shares × preferred share price) – V - total market value of the firm’s securities (total market value to security holders) V=E+D+P The weights E/V, D/V, and P/V are called the Capital Structure Weights and reflect the Capital Structure of the firm (how it has raised capital) • MBAM614 Class 7 - 45 Unadjusted WACC Unadjusted Weighted Average Cost of Capital is simply the weighted average of the various costs WACC(unadjusted) = (E/V) × Re + (D/V) × Rd + (P/V) × Rp Eg. HRM Corp’s common equity has a market value of $5MM, their debt has a market value of $15MM, and (since HRM is not preferred by anyone) no preferred. If HRM’s cost of equity is 14% and their cost of debt is 8%, what is their WACC(unadjusted)? V = E + D = $5MM + $15MM = $20MM E/V = $5MM/$20MM = 25% D/V = $15MM/$20MM = 75% WACC(unadjusted) = (0.25)(14%) + (0.75)(8%) = 9.5% • MBAM614 Class 7 - 46 23 Taxes and WACC When discounting after-tax cash flows, we require an after-tax discount rate Although a firm pays full interest on debt, interest is tax deductible so on an after-tax basis, only a portion, (1 - TC), of the cost of debt is actually paid The after-tax Weighted Average Cost of Capital is: WACC = (E/V) × Re + (D/V) × Rd × (1 - TC) + (P/V) × Rp WACC is the overall return the firm must earn on its assets to maintain the value of its stock • MBAM614 Class 7 - 47 Example: PFS Inc. Passport Financial Services Inc. has 1 million shares outstanding with a market price of $12 per share. The firm’s outstanding bonds have ten years to maturity, a face value of $5MM, a coupon rate of 10%, and are selling for $985 per bond. The risk-free rate is 7%, and analysts’ expected return for the market is 14%. PFSI is in the 40% marginal tax bracket and their stock has a beta of 1.2. What is PFSI’s WACC? Capital Structure Weights: E = 1,000,000 * $12 = $12,000,000 D = $5,000,000 * 0.985 = $4,925,000 V = E + D = $12,000,000 + $4,925,000 = $16,925,000 E/V = $12,000,000/$16,925,000 = 0.709 or 70.9% D/V = $4,925,000/$16,925,000 = 0.291 or 29.1% • MBAM614 Class 7 - 48 24 Example: PFS Inc. Cost of Equity: Re = Rf + βe* [E(RM) - Rf] Re = 7% + 1.2(14% - 7%) = 7% + 8.4% = 15.4% Cost of Debt: YTM on the bonds (a ten year annuity of $100/yr plus $1,000 in year 10 has a PV of $985) is 10.25% before taxes. WACC: WACC = (E/V) × Re + (D/V) × Rd × (1 - TC) WACC = (0.709)(15.4%) + (0.291)(10.25%)(1.0-0.40) = 12.7% • MBAM614 Class 7 - 49 WACC and Project Risk The WACC is the average cost of capital for the firm and reflects the firm’s average systematic risk Thus, the WACC is an appropriate discount rate for any project that has the same systematic risk as the firm’s average systematic risk - that is, that is similar to the firm’s “average project” Conversely, if a project has significantly different systematic risk, then the WACC is NOT an appropriate discount rate • MBAM614 Class 7 - 50 25 Key Points 1. Required return and cost of capital are the same thing from different perspectives 2. Cost of Equity is estimated - with the CGM: - with the CAPM: Re = D1/P0 + g Re = Rf + βe* [E(RM) - Rf] 3. Cost of Debt can be observed in the market as can the cost of preferred 4. Weights and values are ALWAYS based on market value 5. WACC is after-tax: WACC = (E/V) × Re + (D/V) × Rd × (1 - TC) + (P/V) × Rp • MBAM614 Class 7 - 51 26