Chapter 11 – Chapter 11 – Risk, Return Risk, Return and Capital Budgetingand Capital Budgeting

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Measuring Market RiskMeasuring Market Risk

Market PortfolioMarket Portfolio - Portfolio of all - Portfolio of all assets in the economy. In practice a assets in the economy. In practice a broad stock market index, such as broad stock market index, such as the S&P Composite, is used to the S&P Composite, is used to represent the market.represent the market.

BetaBeta - Sensitivity of a stock’s return to - Sensitivity of a stock’s return to the return on the market portfolio.the return on the market portfolio.

Measuring Market RiskMeasuring Market RiskExampleExample - Turbo - Turbo

Charged Seafood Charged Seafood has the following % has the following % returns on its returns on its stock, relative to stock, relative to the listed changes the listed changes in the % return on in the % return on the market the market portfolio. The beta portfolio. The beta of Turbo Charged of Turbo Charged Seafood can be Seafood can be derived from this derived from this information.information.

Month Market Return % Turbo Return %

1 + 1 + 0.8

2 + 1 + 1.8

3 + 1 - 0.2

4 - 1 - 1.8

5 - 1 + 0.2

6 - 1 - 0.8

When the market was up 1%, When the market was up 1%, Turbo average % change was Turbo average % change was +0.8%+0.8%

Month Market Return % Turbo Return %

1 + 1 + 0.8

2 + 1 + 1.8

3 + 1 - 0.2

4 - 1 - 1.8

5 - 1 + 0.2

6 - 1 - 0.8

(.08 + 1.8 -.02)/3 = .08

When the market was When the market was downdown 1%, 1%, Turbo average % change was -Turbo average % change was -0.8%0.8%

Month Market Return % Turbo Return %

1 + 1 + 0.8

2 + 1 + 1.8

3 + 1 - 0.2

4 - 1 - 1.8

5 - 1 + 0.2

6 - 1 - 0.8

(.08 + 1.8 -.02)/3 = .08

(-1.8 + 0.2 – 0.8)/3 = -.08

The average change of 1.6 % (-0.8 to 0.8) The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8.market produces a beta of 0.8.

B = = 0.81.62

Month Market Return % Turbo Return %

1 + 1 + 0.8

2 + 1 + 1.8

3 + 1 - 0.2

4 - 1 - 1.8

5 - 1 + 0.2

6 - 1 - 0.8

(.08 + 1.8 -.02)/3 = .08

(-1.8 + 0.2 – 0.8)/3 = -.08

Measuring Market RiskMeasuring Market Risk

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Market Return %

Turbo return %

Actual returnsSmooth

regression returns

Portfolio BetasPortfolio Betas

Diversification decreases variability Diversification decreases variability from from unique riskunique risk, but not from , but not from market market riskrisk..

The beta of your portfolio will be an The beta of your portfolio will be an average of the betas of the securities average of the betas of the securities in the portfolio.in the portfolio.

If you owned all of the S&P If you owned all of the S&P Composite Index stocks, you would Composite Index stocks, you would have an average beta of 1.0 have an average beta of 1.0

Stock BetasStock Betas

.31Heinz.H.J

.41ExxonMobil

.57Pfizer

.66sMcDonald'

.67PepsiCo

1.00Airlines Delta

1.05Ford

1.18GE

2.14erDellComput

3.30Amazon

BetaStock

B

HP Beta =

2.00

Mutual Funds – Actively-Mutual Funds – Actively-ManagedManaged

Vanguard Windsor IIVanguard Windsor II

Beta of this conservative fund was .66

+1

Mutual Funds – Actively-Mutual Funds – Actively-ManagedManaged

Beta of this conservative fund was .66But investors still had some unique risk

Index Mutual FundIndex Mutual FundVanguard 500Vanguard 500

Beta = 1.0

Investors had no unique risk – only market risk

Security Market Security Market LineLine shows the shows the greater the systematic greater the systematic (non-diversifiable) (non-diversifiable) risk, the greater the risk, the greater the market risk premium market risk premium demanded by demanded by investorsinvestors

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Beta

Exp

ecte

d R

etu

rn (

%)

.

Security Market Line

+ 1

Security Market Security Market LineLine shows the shows the greater the greater the systematic (non-systematic (non-diversifiable) risk, the diversifiable) risk, the greater the market greater the market risk premium risk premium demanded by demanded by investorsinvestors

Market Risk Market Risk PremiumPremium Difference between Difference between market return and market return and return on risk-free return on risk-free Treasury bills.Treasury bills.

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Beta

Exp

ecte

d R

etu

rn (

%)

.

Security Market LineRisk-Free (T-bill) Rate

Capital Asset Pricing Capital Asset Pricing modelmodel

CAPMCAPM - Theory of the relationship between risk and - Theory of the relationship between risk and return which states that the expected risk return which states that the expected risk premium on any security equals its beta times the premium on any security equals its beta times the market risk premium.market risk premium.

Market risk premium = r - r

Risk premium on any asset = r - r

Expected Return = r + B(r - r )

m f

f

f m f

Capital Asset Pricing Capital Asset Pricing modelmodel

CAPMCAPM - Theory of the relationship between risk and - Theory of the relationship between risk and return which states that the expected risk return which states that the expected risk premium on any security equals its beta times the premium on any security equals its beta times the market risk premium.market risk premium.

Market risk premium = r - r

Risk premium on any asset = r - r

Expected Return = r + B(r - r )

m f

f

f m f

Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?

Market risk premium = r - r

Risk premium on any asset = r - r

Expected Return = r + B(r - r )

m f

f

f m f

Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?

Expected Return = 3% + 1.2(10% - 3%) = 3% + 8.4%

= 11.4%

Market risk premium = r - r

Risk premium on any asset = r - r

Expected Return = r + B(r - r )

m f

f

f m f

Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?

Expected Return = 3% + 1.2(10% - 3%) = 3% + 8.4%

= 11.4%

Risk Premium = 11.4% - 3% = 8.4%

Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?

Expected Return

rf = 3%

Beta1.0

rm = 10%

Security Market Line

+2

Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?

Expected Return

rf = 3%

Beta1.0

rm = 10%

1.2

r = 11.4%

Security Market Line

+1

Example: If the Treasury bill rate is 3%, the expected market return is 10% and a stock has a Beta of 1.2, what is its expected return and risk premium?

Expected Return

rf = 3%

Beta1.0

rm = 10%

1.2

r = 11.4%

Security Market Line

Added risk

Added return

Capital Budgeting & Project Capital Budgeting & Project RiskRisk

The project cost of capital depends The project cost of capital depends on the use to which the capital is on the use to which the capital is being put. Therefore, it depends on being put. Therefore, it depends on the risk of the the risk of the projectproject and not the and not the risk of the risk of the companycompany. .

Example Example - - Based on the CAPM, ABC Company Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(14-4)). has a cost of capital of 17%. (4 + 1.3(14-4)). A breakdown of the company’s investment A breakdown of the company’s investment projects is illustrated below. What is the projects is illustrated below. What is the company’s cost of capital for a new dog food company’s cost of capital for a new dog food plant?plant?

1/3 Nuclear Parts Mfr.. 1/3 Nuclear Parts Mfr.. ββ=2.0 =2.0

1/3 Computer Hard Drive Mfr.. 1/3 Computer Hard Drive Mfr.. ββ=1.3=1.3

1/3 Dog Food Production 1/3 Dog Food Production ββ=0.6=0.6

AVG. AVG. ββ of assets = 1.3 of assets = 1.3

Example Example - Based on the CAPM, ABC - Based on the CAPM, ABC Company has a cost of capital of 17%. Company has a cost of capital of 17%. (4 + 1.3(14-4)). A breakdown of the (4 + 1.3(14-4)). A breakdown of the company’s investment projects is company’s investment projects is listed below. When evaluating a new listed below. When evaluating a new dog food production investment, dog food production investment, which cost of capital should be used?which cost of capital should be used?

Go with theGo with the which has a Beta which has a Beta of .6of .6

r = 4 + 0.6 (14 - 4 ) = 10%r = 4 + 0.6 (14 - 4 ) = 10%

10% reflects the opportunity cost of capital on 10% reflects the opportunity cost of capital on an investment given the unique risk of the an investment given the unique risk of the project.project.

6.6. You are considering acquiring a You are considering acquiring a firm that you believe can generate firm that you believe can generate expected cash flows of $10,000 a expected cash flows of $10,000 a year forever. However, you year forever. However, you recognize that those cash flows recognize that those cash flows are uncertainare uncertain

a) Suppose you believe that a) Suppose you believe that the beta of the firm is .4. the beta of the firm is .4. How How much is the firm worthmuch is the firm worth if the risk- if the risk-free rate is 4% and the expected free rate is 4% and the expected rate of return on the market rate of return on the market portfolio is 12%portfolio is 12%

6.6. You are considering acquiring a firm that you You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those a year forever. However, you recognize that those cash flows are uncertaincash flows are uncertain

a) Suppose you believe that the beta of a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected the risk-free rate is 4% and the expected rate of return on the market portfolio is 12%rate of return on the market portfolio is 12%

The expected cash flows from the firm are in the form of a perpetuity. The discount rate is:rf + (rm – rf ) = 4% + 0.4 (12% – 4%) = 7.2%

Therefore, the value of the firm would be: 89.888,138$

072.0

000,10$

r

flowCash P0

6.6. You are considering acquiring a firm that you You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those a year forever. However, you recognize that those cash flows are uncertaincash flows are uncertain

a) Suppose you believe that the beta of the a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on free rate is 4% and the expected rate of return on the market portfolio is 12%the market portfolio is 12%

b) By how much will you overvalue the b) By how much will you overvalue the firm if the beta is actually .6?firm if the beta is actually .6?If the true beta is actually 0.6, the

discount rate should be: rf + (rm – rf ) = 4% + 0.6 (12% – 4%) = 8.8%

Therefore, the value of the firm is:

6.6. You are considering acquiring a firm that you You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those a year forever. However, you recognize that those cash flows are uncertaincash flows are uncertain

a) Suppose you believe that the beta of the a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on free rate is 4% and the expected rate of return on the market portfolio is 12%the market portfolio is 12%

b) By how much will you overvalue the b) By how much will you overvalue the firm if the beta is actually .6?firm if the beta is actually .6?If the true beta is actually 0.6, the

discount rate should be: rf + (rm – rf ) = 4% + 0.6 (12% – 4%) = 8.8%

Therefore, the value of the firm is: 36.636,113$

088.0

000,10$

r

flowCash P0

6.6. You are considering acquiring a firm that you You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those a year forever. However, you recognize that those cash flows are uncertaincash flows are uncertain

a) Suppose you believe that the beta of the a) Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk-firm is .4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on free rate is 4% and the expected rate of return on the market portfolio is 12%the market portfolio is 12%

b) By how much will you overvalue the b) By how much will you overvalue the firm if the beta is actually .6?firm if the beta is actually .6?If the true beta is actually 0.6, the

discount rate should be: rf + (rm – rf ) = 4% + 0.6 (12% – 4%) = 8.8%

Therefore, the value of the firm is: 36.636,113$

088.0

000,10$

r

flowCash P0

By underestimating beta, you would overvalue the firm by:

$138,888.89 – $113,636.36 = $25,252.53

8. Investors expect the market rate of return this year to be 14%. A stock with a beta of .8 has an expected rate of return of 12%. If the market return this year turns out to be 10%, what is your best guess as to the rate of return on the stock?

Beta tells us how sensitive the stock return is to changes in market performance. The market return was 4 percent less than your prior expectation (10% versus 14%). Therefore, the stock would be expected to fall short of your original expectation by:

0.8 4% = 3.2%The ‘updated’ expectation for the stock return is: 12% – 3.2% = 8.8%

8. Investors expect the market rate of return this year to be 14%. A stock with a beta of .8 has an expected rate of return of 12%. If the market return this year turns out to be 10%, what is your best guess as to the rate of return on the stock?

13.You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are:

Years Cash Flow

0 -100

1-10 +15

Based on the behavior of the firm’s stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4 percent and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project?

The appropriate discount rate for the project is:

r = rf + (rm – rf ) = 4% + 1.4 (12% – 4%) = 15.2%

The initial investment = 100 and the annual cash flow for 10 years = 15

13.You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are:

Years Cash Flow

0 -100

1-10 +15

Based on the behavior of the firm’s stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4 percent and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project?

The appropriate discount rate for the project is:

r = rf + (rm – rf ) = 4% + 1.4 (12% – 4%) = 15.2%

The initial investment = 100 and the annual cash flow for 10 years = 15

1.Calculate PV of the cash flow =PV(15.2%,10,-15) = 74.71

2. Subtract investment to get NPV = 74.71 – 100 = -25.289

REJECT

15. A share of stock with a Beta of .75 now sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 8%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year?

From the CAPM, the appropriate discount rate is: r = rf + (rm – rf ) = 4% + (0.75 8%) = 10%

50

)50P(2

price

gain capital DIV10.0r 1

P1 = $53

15. A share of stock with a Beta of .75 now sells for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 8%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year?

5 = 2 + P1 – 50

P1 = 5 – 2 + 50

Chapter 11 – Chapter 11 – Risk, Return Risk, Return and Capital Budgetingand Capital Budgeting

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