11-1
in whole or in part.
CHAPTER 11
RISK-ADJUSTED EXPECTED RATES OF RETURN AND
THE DIVIDENDS VALUATION APPROACH
11.1 The Dividends-Based Valuation Approach. The theory behind the dividends
valuation approach is straightforward. Dividends are value-relevant to common
equity shareholders because the dividends are cash flows directly to the equity
shareholders.
11.2 Valuation Approach Equivalence. Conceptually, students should understand
that the dividends valuation approach yields equivalent value estimates as the
two sides to the same equation. The dividends approach is based on when cash is
paid out to shareholders, whereas the free cash flows approach is based on when
11.3 The Risk-Return Trade-Off. Analysts and investors use risk-adjusted expected
adjusted discount rate, the value estimate reflects the price the analyst should be
averse.
11.4 The Components of the CAPM. The CAPM computes expected rates of return
using the following model (described in the chapter):
The first component (E[RF]) represents the return an investor can expect on a risk-
free investment. This component represents the return to capital for forgoing
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Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach
11-2
in whole or in part.
systematic risk in an investment in Firm j relative to the average level of
systematic risk in the market.
11.5 Nondiversifiable and Diversifiable Risk Factors. Firm-specific factors that
increase the firm’s nondiversifiable risk (systematic risk) include the firm’s
exposure to economy-wide risk factors such as interest rate changes, inflation,
management competence, and operating control. Models of risk-adjusted
expected returns include no expected return premia for diversifiable risk because,
in theory, a risk-averse investor can avoid the positive and negative consequences
11.6 Debt and the Weighted-Average Cost of Capital. Investors typically accept a
lower risk-adjusted rate of return on debt capital than on equity capital because
debt is typically less risky because fixed claims bear less residual risk than equity
claims. Also, in the United States and most other countries, debt capital costs such
capital than equity.
11.7 Firms That Do Not Pay Periodic Dividends. The dividends valuation approach
is applicable to firms that do not pay periodic (quarterly or annual) dividends
because the capital reinvested in the firm is ultimately returned to the common
holder reinvests all of the interest.
11.8 Dividend Policy Irrelevance. The chapter relies on the seminal work of
Modigliani and Miller (1961), with which most students will be familiar, to assert
that dividends are relevant even though the firm’s dividend policy is irrelevant.
Chapter 11
Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach
11-3
in whole or in part.
hold, including when dividend payments signal information to shareholders or
when a nondividend-paying firm becomes increasingly vulnerable to agency
problems because managers are underinvesting the firm’s resources.
shareholders through stock repurchases minus capital raised from equity
shareholders through stock issues.
11.10 Calculating Required Rates of Return on Equity Capital across Different
Industries.
Both industries are engaged in the production of energy. The typical utility
(such as worldwide movements in energy prices) because utilities are
firms.
Food Products (Grocery Stores) versus Apparel (Retailers) 0.68 versus 1.09
Both industries are engaged in retail sales of consumer goods. The typical
as a greater degree of seasonality, leading to a higher-than-average exposure
can be characterized as a type of nonsystematic risk that can be diversified
Chapter 11
Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach
11-4
in whole or in part.
Banking (Depository Institutions) versus Financial Trading (Security
and Commodity Brokers) 0.76 versus 1.09
Both industries provide financial services. The typical depository institution
mitigate systematic risk. A typical security broker-dealer, on the other hand,
experiences a greater degree of systematic risk because its business model is
more dependent on stock portfolio performance, fees from clients’ trading,
and fees from arranging deals and placements of capital.
Industry Median Beta
Expected Return
per CAPM
Perpetuity Value
per $1 of
Dividends
Utilities 0.77 7.85% $20.62
Petroleum and
Natural Gas 1.09 10.55% $13.25
Food Products
Chapter 11
Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach
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in whole or in part.
11.11 Calculating the Cost of Capital. (dollar amounts in millions)
b. Whirlpool IBM Target Stores
Weighted-Average Cost of Capital:
Note that Whirlpool has the highest weighted-average costs of capital because
regardless of its capital structure.
c. As shown in the chapter, the formula to compute unlevered equity (asset) beta
from a levered equity beta is as follows:
Whirlpool:
IBM:
Target Stores:
Note that a large part of the high levered equity beta for Whirlpool comes from
its financial leverage. Its unlevered equity beta is the smallest of the three
because of their already high unlevered equity betas.
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Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach
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in whole or in part.
d. The revised equity beta for each company is as follows:
Whirlpool:
IBM:
Target Stores
The projected costs of equity capital are as follows:
The projected weighted-average costs of capital are as follows:
Chapter 11
Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach
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in whole or in part.
11.12 Calculation of Dividends-Based Value.
This problem is a straightforward and comprehensive application of the techniques
of Chapter 11 to Royal Dutch Shell Corporation (ticker: RDSA.AS).
Required
b. The sum of the present value of total dividends for Years +1 through +5 is as
follows (dollar amounts in millions):
Year +1 Year +2 Year +3 Year +4 Year +5
Total Dividends to
Common Equity
(0.0705 – 0.03)
d. Sum of Present Value Dividends, Years +1 through +5 $ 61,780
e. Total Present Value of Equity …………………………………………… $376,815
shares appear underpriced by about 59%.
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in whole or in part.
11.13 Valuing the Equity of a Privately Held Firm.
a. Clean surplus accounting applied to MSC each year in each of the three
scenarios reveals that MSC is not paying any dividends.
Year 8 Year 9 Year 10 Year 11 Year 12
Best-Case Scenario:
Most Likely Scenario:
Net Income $135,343 $74,437 $72,899 $109,357 $149,977
Worst-Case Scenario:
Net Income $128,263 $18,796 $–39,902 $–58,316 $–77,156
Scenario
Year 12
Common Equity:
Present Value
Factor
Present
Value
Chapter 11
11-9
in whole or in part.
expected value of adding gas stoves is likely to exceed the value of not adding
gas stoves, suggesting that MSC should make this strategic change to its
business model.
(not students) from the book’s website for instructors: Go to instructor’s resources
This problem estimates cost of equity capital for Walmart and uses the
dividends valuation model to estimate Walmart’s share value. The problem also
2012.
Required
a. Following the CAPM, Walmart faces a required rate of return on equity
capital of 9.0% at the end of 2012. This rate is computed as follows:
amounts and proportions:
Amount Weight