Citibank: basic of corporate finance
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6-48 CORPORATE VALUATION – RISK
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CORPORATE VALUATION – RISK 6-49
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4 PRACTICE EXERCISE 6.5
Directions: Mark the correct answer to each question. Compare your solutions to the
correct answers in the Answer Key that follow on the next page.
8. Onyx Corporation has a beta of 1.50. The risk-free rate of return is 10% and the
expected return on the market portfolio is 12%. What rate of return would investors in
Onyx Corporation expect to earn?
_____a) 10%
_____b) 11%
_____c) 12%
_____d) 13%
_____e) 15%
9. Mega Company is a stock that you are considering adding to your portfolio. Mega has a
beta of 1.20. The risk-free rate is 13% and the market premium is 2%. What is the
expected rate of return you should earn on Mega Company stock?
_____a) 13.2%
_____b) 15.4%
_____c) 16.9%
_____d) 18.4%
_____e) 19.5%
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6-50 CORPORATE VALUATION – RISK
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ANSWER KEY
8. Onyx Corporation has a beta of 1.50. The risk-free rate of return is 10% and the
expected return on the market portfolio is 12%. What rate of return would investors in
Onyx Corporation expect to earn?
d) 13%
Use CAPM with b
i
= 1.50, E (k
M
) = 12%, and k
RF
= 10%
k
i
= k
RF
+ (k
M
- k
RF
) b
i
k
i
= 10% + (12% - 10%) 1.50
k
i
= 13%
9. Mega Company is a stock that you are considering adding to your portfolio. Mega has a
beta of 1.20. The risk-free rate is 13% and the market premium is 2%. What is the
expected rate of return you should earn on Mega Company stock?
b) 15.4%
Use CAPM with b
i
= 1.20, R
PM
= 2%, and k
RF
= 13%
k
i
= k
RF
+ (R
PM
) b
i
k
i
= 13% + (2%) 1.20
k
i
= 15.4%
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CORPORATE VALUATION – RISK 6-51
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PRACTICE EXERCISE
(Continued)
10. Suppose that U.S. Treasury securities are earning 8% and the expected rate of return
on the market is 14%. If a stock has a beta of 0.60, what is the expected rate of return
for the stock?
_____ a) 8.0%
_____ b) 8.4%
_____ c) 10.6%
_____ d) 11.0%
_____ e) 11.6%
11. With the market conditions the same as above, another stock has an expected return of
20%. What is the beta for this stock?
_____ a) 0.9
_____ b) 1.0
_____ c) 1.5
_____ d) 2.0
_____ e) 2.5
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6-52 CORPORATE VALUATION – RISK
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ANSWER KEY
10. Suppose that U.S. Treasury securities are earning 8% and the expected rate of return
on the market is 14%. If a stock has a beta of 0.60, what is the expected rate of return
for the stock?
e) 11.6%
Use CAPM with: b
i
= 0.60 E (k
M
) = 14% and k
RF
= 8%
k
i
= k
RF
+ (k
M
– k
RF
) b
i
k
i
= 8% + (14% – 8%) 0.60
k
i
= 11.6%
11. With the market conditions the same as above, another stock has an expected return of
20%. What is the beta for this stock?
d) 2.0
Use CAPM with: k
i
= 20% E (k
M
) = 14% and k
RF
= 8%
Solve for b
i
k
i
= k
RF
+ (k
M
- k
RF
) b
i
20% = 8% + (14% - 8%) b
i
12% = (6%) b
i
2.0 = b
i
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CORPORATE VALUATION – RISK 6-53
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UNIT SUMMARY
We began this unit with a discussion of the process for calculating the
expected return on a security and the expected total cash flow from an
investment or project. We then developed the methodology for
quantifying the risk associated with expected cash flows. We used the
two measurements of variation and standard deviation to determine the
amount of volatility among possible cash flows or returns. Standard
deviation represents the total risk for a security or portfolio. A lower
standard deviation indicates less volatility and, therefore, a lower
amount of risk.
Our discussion of portfolio risk indicated that by investing with
different companies and different industries, the riskiness of a
portfolio may be reduced. This process of diversifying the portfolio
only affects the unsystematic or company-specific risk associated
with the securities in a portfolio. Systematic (market) risk cannot be
eliminated by diversification because the unexpected events that
create systematic risk affect all companies in the market.
The relevant risk of holding a security is the individual security's
contribution to the systematic risk of the portfolio. The beta
coefficient reflects the relative movement of a stock as compared
with the market portfolio. An average-risk stock has a beta coefficient
of 1.0, which means that if the market moves up by 10%, the stock
will, on average, move up by 10%. A lower beta indicates that a stock
is less volatile than the market portfolio and, therefore, has less
systematic risk. Portfolio beta is the weighted average of the beta
coefficients of the individual securities in the portfolio.
The beta coefficient is used in the capital asset pricing model (CAPM)
to calculate the required rate of return for an individual security. The
rate of return that investors require to invest in a security includes the
risk-free rate plus a market (systematic) risk premium. The size of the
market risk premium depends on the amount of compensation required
by investors for assuming risk. The CAPM is the most widely-
accepted method for setting market prices because it is sensitive to
systematic risk.
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6-54 CORPORATE VALUATION – RISK
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You have demonstrated your understanding of each of these key concepts in the five
practice exercises; therefore, this unit has no Progress Check. Please continue your
study of corporate value and expected cash flow analysis with Unit Seven: Corporate
Valuation – Cost of Capital, which follows.
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Unit 7
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UNIT 7: CORPORATE VALUATION – COST OF CAPITAL
INTRODUCTION
In Unit Five, we discussed the discounting of a company's expected cash flows or the cash
flows of a potential project a company is considering. We showed how the discount rate is
used to discount the cash flows and arrive at their present value. This discount rate is often
called the required rate of return for the project or the opportunity cost for the funds that
may be used to invest in the company or project. In Unit Six, you also learned how to adjust
rates of return according to the risk involved in the investment. The cost of capital
represents the required rate of return. In this unit, you will learn how to calculate the cost
of each source of capital and the overall cost of capital for a company.
UNIT OBJECTIVES
After you successfully complete this unit, you will be able to:
• Calculate the cost of debt, preferred stock, and common stock (equity)
• Calculate the weighted average cost of capital
SOURCES OF CAPITAL AND THEIR COSTS
Three major
sources
There are three major sources of capital available for financing a
project or investment:
• Debt
• Preferred stock
• Common stock
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