Chapter 1 – The Equity Valuation Process
Solutions
1. A. A satisfactory answer includes any four of the following uses of valuation
models: (1) stock selection, (2) inferring market expectations (about
variables such as future growth), (3) evaluating corporate events, (4)
fairness opinions, (5) evaluating business strategies and models, (6)
communication with analysts and shareholders, or (7) appraisal of private
businesses.
B. A portfolio manager’s most important use of valuation models is stock
selection.
C. A corporate officer would be most directly concerned with using valuation
concepts and models to evaluate corporate events, evaluate business
strategies and models, and communicate with analysts and shareholders.
To the extent that the corporate officer’s company had a program of
acquisitions, the use of valuation models in fairness opinions would also
be relevant.
2. A. If Cornell had used a higher discount rate, the revenue growth rate
consistent with a price of $61.50 would have been higher than 20 percent a
year.
B. In any present value model, present value is inversely related to the
discount rate applied to expected future cash flows. The higher the
discount rate applied, the greater the future cash flows needed to equal a
given value such as $61.50. To obtain the higher future revenue estimates
needed to obtain a present value of $61.50 assuming a higher discount
rate, a higher revenue growth rate assumption must be made. Therefore, if
Cornell had assumed a higher discount rate, he would have concluded that
the market expected Intel’s revenue growth rate to be even higher than 20
percent.
3. A. As part of the planning step (after specification of investment objectives),
the investor will generally elaborate on his approach to investment
analysis and security selection. An active investor may specify in
substantial detail the valuation models and/or criteria that he plans to use.
B. In the execution step, investment strategies are integrated with
expectations to select a portfolio. In selecting a portfolio, the investor is
continually put to the test to make accurate valuations of securities.
Therefore, skill in valuation plays a key role in this step of the portfolio
management process.
1
,4. An investor trying to replicate a stock index does not need to make valuation
judgments about securities. For example, the manager of an account indexed to
the S&P 500, a type of passive investment strategy, seeks only to replicate the
returns on the S&P 500, whether or not the index is fairly valued. In contrast,
active investors attempt to identify mispriced securities—in particular, securities
expected to earn a positive excess risk-adjusted return.
5. A. The ex ante alpha is the expected return minus the required return for a
stock. Because the analysts feel their stocks are undervalued, the expected
returns should exceed the required rates of return and the ex ante alphas
should be positive (greater than zero).
B. The ex post alpha is the actual return minus the contemporaneous required
return.
For KMG, the ex post alphas are as follows:
1998: –34.0% – 26.6% = –60.6%
1999: 65.4% – 19.6% = 45.8%
2000: 20.9% – (–8.5%) = 29.4%
2001: –12.9% – (–11.0%) = –1.9%
For NUE, the ex post alphas are as follows:
1998: –8.5% – 29.2% = –37.7%
1999: 29.4% – 21.5% = 7.9%
2000: –25.3% – (–9.3%) = –16.0%
2001: 37.3% – (–12.1%) = 49.4%
6. A. Wal-Mart’s expected return consists of the following:
Price correction = 56.00 – 53.12 = $2.88
Additional price appreciation 4.87
Cash dividends 0.28
Total return $8.03
The expected rate of return is the expected dollar return divided by the
price, or 8.03/53.12 = 15.1 percent.
B. Ex ante alpha = Expected holding-period return – Required return
Ex ante alpha = 15.1 – 9.2 = 5.9 percent
C. Ex post alpha = Actual holding-period return – Contemporaneous required
return
Ex post alpha = 8.9 – (–10.4) = 19.3 percent
7. A. Ex ante alpha is the expected holding-period return on a security minus the
security’s required return. An asset with a positive (negative) expected
alpha is undervalued (overvalued).
B. Alpha of Security 1 = 0.20 − 0.21 = −0.01 or −1 percent
Alpha of Security 2 = 0.18 − 0.08 = 0.10 or 10 percent
Alpha of Security 3 = 0.11 − 0.10 = 0.01 or 1 percent
The ranking is
Security 2, alpha =10% (most attractive)
Security 3, alpha = 1%
2
, Security 1, alpha = −1% (least attractive)
C. According to Part B, Security 2 and Security 3 offer positive expected
alphas. We might thus decide to invest in Security 2 and Security 3. The
risks in such a decision include the following:
• We may have made an incorrect or incomplete adjustment for risk.
We may not have accounted for all sources of risk reflected in the
prices of the securities.
• Our own expectations may be biased or otherwise flawed.
• Even if our expectations are more accurate than the expectations
reflected in the prices of the securities, there is no assurance that the
mispricing will be corrected during our investment horizon, if at all.
It is also possible to enumerate other risks. For example, Chapter 2
will discuss the uncertainty associated with estimating beta, the measure
of risk in the CAPM.
8. A. The analyst collects, organizes, analyzes, and communicates corporate
information to investors and then recommends appropriate investment
actions based on his analysis. When an analyst does his work well, clients
are helped in reaching their investment objectives.
B. When well executed, the work of analysts promotes informed buy and sell
decisions. Such informed decisions make asset prices better reflections of
underlying value, with the result that capital flows to its highest-valued
uses. By monitoring managers’ actions, investment analysts can also help
prevent managers from exploiting corporate resources for their own
benefit.
9. We need to know (1) the time horizon for the price target and (2) the required rate
of return on MBFG.MI. The price target of €9.20 represents a rate of return to
investing in the stock calculated as (€9.20 + 0.05)/€7.73 − 1.0 = 0.197, or 20
percent. Without a time frame, we cannot evaluate how attractive that rate is.
Suppose that the time horizon is one year. To further interpret a 20 percent
expected one-year rate of return, we need to adjust it for risk. Subtracting the
required rate of return from 20 percent would give the share’s expected alpha.
This number would allow us to conclude whether the stock was fairly valued.
Another acceptable answer is that we would need to know the analyst’s
current estimate of intrinsic value for MBFG.MI. This may or may not be the
target price of €9.20.
10. A. XMI’s expensing policies with respect to acquisitions inflate its earnings
per share growth rate. By pushing down pre-acquisition EPS to an
artificially low number, XMI can show unusual post-acquisition earnings
growth rates.
B. Based on both expensing and revenue recognition policies, earnings
clearly do not accurately reflect underlying economics. As noted in Part
A, XMI attempts to manipulate the expensing policy of acquisitions to
3
, benefit its own earnings growth rate. In speeding up the recognition of
revenue in its telecommunications subsidiary, XMI’s revenue recognition
policy is aggressive. In summary, the quality of XMI earnings is poor.
(Note that the quality of XMI’s disclosures is also poor, but disclosure was
treated under the rubric of accounting risk factors in the text.)
C. The statement is a comparison of value, based on XMI’s P/E relative to
the P/Es of similar stocks. The underlying model is a relative valuation
model (or the method of comparables).
D. Risk factors might include:
• Possible negative regulatory and legal developments. When and if
XMI’s accounting and business practices become known, XMI may be
subject to legal and regulatory action.
• Risks in the forecasts. Because of the poor quality of XMI’s earnings
and the poor quality of its accounting disclosures, there is great
uncertainty in any forecasts in a valuation of XMI.
• Other risks. A downward revision to the market price of XMI could
occur if the extent of its quality of earnings issues and management’s
policies were to become known.
4
Solutions
1. A. A satisfactory answer includes any four of the following uses of valuation
models: (1) stock selection, (2) inferring market expectations (about
variables such as future growth), (3) evaluating corporate events, (4)
fairness opinions, (5) evaluating business strategies and models, (6)
communication with analysts and shareholders, or (7) appraisal of private
businesses.
B. A portfolio manager’s most important use of valuation models is stock
selection.
C. A corporate officer would be most directly concerned with using valuation
concepts and models to evaluate corporate events, evaluate business
strategies and models, and communicate with analysts and shareholders.
To the extent that the corporate officer’s company had a program of
acquisitions, the use of valuation models in fairness opinions would also
be relevant.
2. A. If Cornell had used a higher discount rate, the revenue growth rate
consistent with a price of $61.50 would have been higher than 20 percent a
year.
B. In any present value model, present value is inversely related to the
discount rate applied to expected future cash flows. The higher the
discount rate applied, the greater the future cash flows needed to equal a
given value such as $61.50. To obtain the higher future revenue estimates
needed to obtain a present value of $61.50 assuming a higher discount
rate, a higher revenue growth rate assumption must be made. Therefore, if
Cornell had assumed a higher discount rate, he would have concluded that
the market expected Intel’s revenue growth rate to be even higher than 20
percent.
3. A. As part of the planning step (after specification of investment objectives),
the investor will generally elaborate on his approach to investment
analysis and security selection. An active investor may specify in
substantial detail the valuation models and/or criteria that he plans to use.
B. In the execution step, investment strategies are integrated with
expectations to select a portfolio. In selecting a portfolio, the investor is
continually put to the test to make accurate valuations of securities.
Therefore, skill in valuation plays a key role in this step of the portfolio
management process.
1
,4. An investor trying to replicate a stock index does not need to make valuation
judgments about securities. For example, the manager of an account indexed to
the S&P 500, a type of passive investment strategy, seeks only to replicate the
returns on the S&P 500, whether or not the index is fairly valued. In contrast,
active investors attempt to identify mispriced securities—in particular, securities
expected to earn a positive excess risk-adjusted return.
5. A. The ex ante alpha is the expected return minus the required return for a
stock. Because the analysts feel their stocks are undervalued, the expected
returns should exceed the required rates of return and the ex ante alphas
should be positive (greater than zero).
B. The ex post alpha is the actual return minus the contemporaneous required
return.
For KMG, the ex post alphas are as follows:
1998: –34.0% – 26.6% = –60.6%
1999: 65.4% – 19.6% = 45.8%
2000: 20.9% – (–8.5%) = 29.4%
2001: –12.9% – (–11.0%) = –1.9%
For NUE, the ex post alphas are as follows:
1998: –8.5% – 29.2% = –37.7%
1999: 29.4% – 21.5% = 7.9%
2000: –25.3% – (–9.3%) = –16.0%
2001: 37.3% – (–12.1%) = 49.4%
6. A. Wal-Mart’s expected return consists of the following:
Price correction = 56.00 – 53.12 = $2.88
Additional price appreciation 4.87
Cash dividends 0.28
Total return $8.03
The expected rate of return is the expected dollar return divided by the
price, or 8.03/53.12 = 15.1 percent.
B. Ex ante alpha = Expected holding-period return – Required return
Ex ante alpha = 15.1 – 9.2 = 5.9 percent
C. Ex post alpha = Actual holding-period return – Contemporaneous required
return
Ex post alpha = 8.9 – (–10.4) = 19.3 percent
7. A. Ex ante alpha is the expected holding-period return on a security minus the
security’s required return. An asset with a positive (negative) expected
alpha is undervalued (overvalued).
B. Alpha of Security 1 = 0.20 − 0.21 = −0.01 or −1 percent
Alpha of Security 2 = 0.18 − 0.08 = 0.10 or 10 percent
Alpha of Security 3 = 0.11 − 0.10 = 0.01 or 1 percent
The ranking is
Security 2, alpha =10% (most attractive)
Security 3, alpha = 1%
2
, Security 1, alpha = −1% (least attractive)
C. According to Part B, Security 2 and Security 3 offer positive expected
alphas. We might thus decide to invest in Security 2 and Security 3. The
risks in such a decision include the following:
• We may have made an incorrect or incomplete adjustment for risk.
We may not have accounted for all sources of risk reflected in the
prices of the securities.
• Our own expectations may be biased or otherwise flawed.
• Even if our expectations are more accurate than the expectations
reflected in the prices of the securities, there is no assurance that the
mispricing will be corrected during our investment horizon, if at all.
It is also possible to enumerate other risks. For example, Chapter 2
will discuss the uncertainty associated with estimating beta, the measure
of risk in the CAPM.
8. A. The analyst collects, organizes, analyzes, and communicates corporate
information to investors and then recommends appropriate investment
actions based on his analysis. When an analyst does his work well, clients
are helped in reaching their investment objectives.
B. When well executed, the work of analysts promotes informed buy and sell
decisions. Such informed decisions make asset prices better reflections of
underlying value, with the result that capital flows to its highest-valued
uses. By monitoring managers’ actions, investment analysts can also help
prevent managers from exploiting corporate resources for their own
benefit.
9. We need to know (1) the time horizon for the price target and (2) the required rate
of return on MBFG.MI. The price target of €9.20 represents a rate of return to
investing in the stock calculated as (€9.20 + 0.05)/€7.73 − 1.0 = 0.197, or 20
percent. Without a time frame, we cannot evaluate how attractive that rate is.
Suppose that the time horizon is one year. To further interpret a 20 percent
expected one-year rate of return, we need to adjust it for risk. Subtracting the
required rate of return from 20 percent would give the share’s expected alpha.
This number would allow us to conclude whether the stock was fairly valued.
Another acceptable answer is that we would need to know the analyst’s
current estimate of intrinsic value for MBFG.MI. This may or may not be the
target price of €9.20.
10. A. XMI’s expensing policies with respect to acquisitions inflate its earnings
per share growth rate. By pushing down pre-acquisition EPS to an
artificially low number, XMI can show unusual post-acquisition earnings
growth rates.
B. Based on both expensing and revenue recognition policies, earnings
clearly do not accurately reflect underlying economics. As noted in Part
A, XMI attempts to manipulate the expensing policy of acquisitions to
3
, benefit its own earnings growth rate. In speeding up the recognition of
revenue in its telecommunications subsidiary, XMI’s revenue recognition
policy is aggressive. In summary, the quality of XMI earnings is poor.
(Note that the quality of XMI’s disclosures is also poor, but disclosure was
treated under the rubric of accounting risk factors in the text.)
C. The statement is a comparison of value, based on XMI’s P/E relative to
the P/Es of similar stocks. The underlying model is a relative valuation
model (or the method of comparables).
D. Risk factors might include:
• Possible negative regulatory and legal developments. When and if
XMI’s accounting and business practices become known, XMI may be
subject to legal and regulatory action.
• Risks in the forecasts. Because of the poor quality of XMI’s earnings
and the poor quality of its accounting disclosures, there is great
uncertainty in any forecasts in a valuation of XMI.
• Other risks. A downward revision to the market price of XMI could
occur if the extent of its quality of earnings issues and management’s
policies were to become known.
4
