Review Chapter 13 and Chapter 14

Chapter 13 Outline

• Expected Returns and Variances of a portfolio• Announcements, Surprises, and Expected

Returns• Risk: Systematic and Unsystematic• Diversification and Portfolio Risk• Systematic Risk and Beta• The Security Market Line (SML)

Portfolios

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

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Portfolio = a group of assets held by an investor

Portfolio weights = Percentage of a portfolio’s total value in a particular asset

Portfolio Expected Returns (1)

• The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio

• You can also find the expected return by finding the portfolio return in each possible state and computing the expected value

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m

jjjP REwRE

1

)()(

Calculate Portfolio Variance

• Portfolio variance can be calculated using the following formula:

• Correlation is a statistical measure of how 2 assets move in relation to each other

• If the correlation between stocks A and B = -1, what is the standard deviation of the portfolio?

ULULULUULLP CORRxxxx ,22222 2

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Portfolio Diversification

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Measuring Systematic Risk

• Beta (β) is a measure of systematic risk

• Interpreting beta:– β = 1 implies the asset has the same systematic

risk as the overall market– β < 1 implies the asset has less systematic risk

than the overall market– β > 1 implies the asset has more systematic risk

than the overall market

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Portfolio Expected Returns and Betas

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Rf

Reward-to-Risk Ratio:

• The reward-to-risk ratio is the slope of the line illustrated in the previous slide– Slope = (E(RA) – Rf) / A

– Reward-to-risk ratio =

• If an asset has a reward-to-risk ratio = 8?

• If an asset has a reward-to-risk ratio = 7?

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The Fundamental Result

• The reward-to-risk ratio must be the same for all assets in the market

• If one asset has twice as much systematic risk as another asset, its risk premium is twice as large

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M

fM

A

fA RRERRE

)()(

Security Market Line (2)

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COST OF CAPITAL AND LONG-TERM FINANCIAL POLICY

Chapter 14

The Dividend Growth Model Approach

• Can be rearranged to solve for RE

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P0 D1

RE g

RE D1P0

g

Example

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Example

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Example: Estimating the Dividend Growth Rate

One method for estimating the growth rate is to use the historical average ◦Year Dividend Percent Change◦2005 1.03◦2006 1.13 9.7% Geom. Av = 7.97%◦2007 1.26 11.5%◦2008 1.33 5.55%◦2009 1.40 5.26% arithmetic av.=8% Analysts’ forecast can be used

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Alternative Approach to Estimating Growth

If the company has a stable ROE, a stable dividend policy and is not planning on raising new external capital, then the following relationship can be used:

A company has a ROE of 17% and payout ratio is 15%. If management is not planning on raising additional external capital, what is its growth rate?

Solution: g=17*(1-.15)=14.45%

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g = Retention ratio x ROE

The SML Approach (CAPM)

• Use the following information to compute our cost of equity– Risk-free rate, Rf

– Market risk premium, E(RM) – Rf

– Systematic risk of asset,

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E(RA) = Rf + A(E(RM) – Rf)

SML example

• Suppose the company has an equity beta of 1.28 and the current risk-free rate is 3.2%. If the expected market risk premium is 9.8%, what is the cost of equity capital?

Solution: 15.744%

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Cost of Equity

• Suppose the company has a beta of 1.45. The market return is expected to be 15.2% and the current risk-free rate is 4%. Dividends will grow at 5% per year and last dividend was $1.2. The stock is currently selling for $7.35. What is our cost of equity?

– Using SML: 20.24%

– Using DGM: 22.14%

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Cost of Debt example

• Suppose you have a bond issue currently outstanding that has 17 years left to maturity. The coupon rate is 8% and coupons are paid annually. The bond is currently selling for $955.874 per $1000 bond. What is the cost of debt?

Solution: 8.5%

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Cost of Preferred StockPreferred stock generally pays a constant

dividend every period

Dividends are expected to be paid every period forever

• Preferred stock is perpetuity

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RP = D / P0

Cost of Preferred Stock example

• A company has preferred stock that has an annual dividend of $2. If the current price is $15, what is the cost of preferred stock?

Solution: 13.33%

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Flotation Costs

• The required return depends on the risk, not how the money is raised

• However, the cost of issuing new securities should not just be ignored either

• Basic Approach– Compute the weighted average flotation cost

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DEA fVDfVEf )/()/(

NPV and Flotation Costs example

• A company is considering a project that will cost $1.2 million. The project will generate after-tax cash flows of $250,000 per year for 9 years. The WACC is 12% and the firm’s target D/E ratio is .5 (1/2). The flotation cost for equity is 4% and the flotation cost for debt is 2%. What is the average flotation cost? What is the NPV for the project after adjusting for flotation costs?

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Solution

• D=400,000fd = 400,000*.02 = 8,000

• E=800,000 fE = 800,000*.04 = 32,000

• Fac = .0267 + .0067 =.0334=3.34%

• PV=(1,240,000)• PVFCF= 1,332,062.448• NPV = 92,062.448

positive