502-4 Common Stock Valuations and Performance Measurements

Question 1

Explain the terms listed in the following table that are associated with the payment of common stock dividends: ex-dividend date

Answer 1

The ex-dividend date is the second business day preceding the date of record that was fixed by the corporation. On that date, the stock trades exclusive of any right to the next dividend payment. An investor who purchases the stock on or after the ex-dividend date will not receive the next dividend payment.

Question 2

Explain the terms listed in the following table that are associated with the payment of common stock dividends: date of record

Answer 2

The date of record is the second business day after the ex- dividend date. On the record date, trades are settled and reflected on the corporation’s books. To have a right to a dividend, an investor must purchase stock before the ex-dividend date. For example, assume that Monday, April 6, is the ex-dividend date. Therefore, the record date is Wednesday, April 8. The investor must have purchased the stock on or before Friday, April 3, in order to receive the next dividend.

Question 3

Does a stock dividend change the firm’s assets or liabilities? Explain your answer?

Answer 3

Stock dividends are a form of recapitalization and do not affect the assets or liabilities of the firm; only the entries in the equity section of the firm’s balance sheet are affected. A stock dividend transfers an amount equal to the market price of the shares from retained earnings to common stock and additional paid-in capital. Although there has been an increase in the number of shares outstanding, there has not been an increase in the firm’s cash.

Question 4

List the primary advantage and the primary disadvantage of a stock dividend.

Answer 4

• The primary disadvantage is the expense. Among the costs are those related to issuing new certificates, paying taxes or listing fees on the new shares, and revising the firm’s stockholder records.
• A primary advantage is that it brings to the current stockholders’ attention the fact that the firm is retaining its cash in order to grow (i.e., a stock dividend is issued instead of a cash dividend). The stockholders eventually may be rewarded through the firm’s retention of assets and its increased earning capacity.

Question 5

If a company decides to raise its dividend payout ratio (and its future return on equity [ROE] is projected to remain constant), how would the decision to raise the dividend payout ratio affect its dividend growth rate?

Answer 5

The dividend growth rate will be lower because the company will retain less of its earnings to finance its future growth. Should the company need additional funds for future expansion, it will have to seek those funds through a stock or debt offering because the shareholders will have already received a portion of the money that could have been used to internally finance growth.

Question 6

How would a company’s stock price be affected if the company raises the payout ratio?

Answer 6

The price could rise or fall; it is not possible to determine the impact on the stock based solely on this decision.

Question 7

Briefly define the following term: expected rate of return

Answer 7

The expected rate of return is the anticipated return on an investment. It is the sum of interest or dividend income and capital gains.

Question 8

Briefly define the following term: required rate of return

Answer 8

The required rate of return is the minimum return the investor wants to receive to compensate for the risk associated with investing in a particular security. It is computed using the formula for the security market line (also known as CAPM)—the sum of a risk-free rate and a risk premium based on the market return and the security’s beta.

Question 9

Briefly define the following term: intrinsic value of a stock

Answer 9

Intrinsic value, which is the underlying or inherent value of a stock, is a function of the stock’s current dividend, the anticipated growth rate in dividends, and the investor’s required rate of return.

Question 10

Briefly define the following term: risk-free return

Answer 10

The risk-free return is the nominal rate of return that an investor could earn on a risk-free security (e.g., a U.S. Treasury bill).

Question 11

Why is present value analysis used to calculate intrinsic value under the dividend growth model?

Answer 11

Present value analysis is used because the value of any security can be determined by discounting the future stream of economic benefits (cash flows—generally dividends) that the investor expects to receive.

Question 12

Under the dividend growth model, what are the three factors on which a stock’s intrinsic value is based?

Answer 12

Intrinsic value is based on (1) the current dividend, (2) the expected future growth in earnings and dividends, and (3) the required rate of return.

Question 13

If a company does not pay a dividend, how can the intrinsic value of its stock be determined?

Answer 13

The intrinsic value can be computed using the P/E ratio, the price-to- sales ratio, the price-to-book ratio, and the PEG ratio. Even if the company pays a cash dividend, it is wise to estimate intrinsic value using all of these techniques to determine if the various approaches validate each other.

Question 14

An investor is considering purchase of a $2.50 series A preferred stock. His required return is 10%. Should he purchase this stock if it is selling for $27 per share?

Answer 14

$2.50/.10 = $25

According to the zero growth model, the maximum price to pay would be $25. Since the stock is currently selling at $27, it would be considered overvalued and should not be purchased.

Question 15

Assume that the risk-free rate of return is 8.5%, that the expected rate of return of the market is 13%, and that the stock has a beta coefficient of 1.2. What is the investor’s required rate of return for the stock?

Answer 15

Ri =Rf +(Rm −Rf)β

8.5+ (13-8.5)1.2
8.5+(4.5)1.2
=13.9%

The investor’s required rate of return is 13.9%

Question 16

What is the DDM model?

Answer 16

Constant growth dividend discount model, which is used to calculate the intrinsic value of dividend paying stock.

Question 17

The current dividend is $2.20 annually, and it is expected to grow at 5% per year. What is the intrinsic value of the stock using the DDM. Return is 13.9%.

Answer 17

D0 (1+G)/ R-G

2.20 (1+.05)/.139-.05= 25.96

Question 18

Stock BLQ pays an annual dividend of $2.45; its dividends are expected to increase at 4% annually. The stock has a beta coefficient of .72; the risk-free rate is 6.9%; and the market rate of return is 14%. The current market price of Stock BLQ is $35 per share.

What should be an investor’s required rate of return for Stock BLQ?

Answer 18

r = 6.9 + (14 – 6.9) .72 =

6. 9 + (7.1) .72 =
7. 9 + 5.1 = 12%

Question 19

Stock BLQ pays an annual dividend of $2.45; its dividends are expected to increase at 4% annually. The stock has a beta coefficient of .72; the risk-free rate is 6.9%; and the market rate of return is 14%. The current market price of Stock BLQ is $35 per share.

What is the intrinsic value of Stock BLQ?

Answer 19

V= D0(1+G)/R−G

2.45(1.04)/.12-.04= $31.85

Question 20

Stock BLQ pays an annual dividend of $2.45; its dividends are expected to increase at 4% annually. The stock has a beta coefficient of .72; the risk-free rate is 6.9%; and the market rate of return is 14%. The current market price of Stock BLQ is $35 per share.

What is the expected rate of return on Stock BLQ?

Answer 20

E(r) = D0 (1 + G)/P +G

=2.45(1.04)/ 35 +.04

=.1128 or 11.28%

Question 21

An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for Stock CMR

Intrinsic value using the DDM.

Answer 21

V= D0(1+G)/R−G
.85(1.07)/.10-.07
=30.32

Question 22

An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for Stock CMR.

expected return

Answer 22

E(r) = D0 (1 + G)/P +G

.1050 = 10.50%

Question 23

An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for Stock CMR.

P/E ratio

Answer 23

26/1.40 =18.57

Question 24

An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for Stock CMR.

PSR

Answer 24

26/29= .90

Question 25

An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for Stock CMR.

P/B Ratio

Answer 25

26/14= 1.86

Question 26

How can an investor use intrinsic value in deciding what action to take concerning a security?

Answer 26

The intrinsic value of a security is compared to the security’s current market price to determine if the security is undervalued (i.e., the market price is less than the intrinsic value) or overvalued (i.e., the market price is greater than the intrinsic value). If an asset is undervalued, the asset may be an attractive investment. If an asset is overvalued, the asset may be less attractive as an investment.

Question 27

Jon Allen is a retired widower who wants extra income. He has $5,000 available to invest in the stock market, but he is not sure which of the following two stocks he should purchase. His required rate of return is 13%.

Stock 1
Current dividend $1.84 
Dividend growth 3% 
Current market $20/share 
Current yield 9.2%

Stock 2
Current dividend $2.36
Dividend growth 6% 
Current market $32/share 
Current yield 7.4%

According to the dividend valuation method, is Stock 1 currently overvalued or undervalued using Jon’s required rate of return?

Answer 27

Stock 1 is overvalued for Jon at the current stock market price of $20 because, using Jon’s required rate of return, its intrinsic value is only $18.95.

Question 28

Jon Allen is a retired widower who wants extra income. He has $5,000 available to invest in the stock market, but he is not sure which of the following two stocks he should purchase. His required rate of return is 13%.

Stock 1
Current dividend $1.84 
Dividend growth 3% 
Current market $20/share 
Current yield 9.2%

Stock 2
Current dividend $2.36
Dividend growth 6% 
Current market $32/share 
Current yield 7.4%

Does Stock 1 meet Jon’s required rate of return?

Answer 28

No. Stock 1 has an expected return of 12.48%, which is less than Jon’s required rate of return of 13%.

Question 29

Jon Allen is a retired widower who wants extra income. He has $5,000 available to invest in the stock market, but he is not sure which of the following two stocks he should purchase. His required rate of return is 13%.

Stock 1
Current dividend $1.84 
Dividend growth 3% 
Current market $20/share 
Current yield 9.2%

Stock 2
Current dividend $2.36
Dividend growth 6% 
Current market $32/share 
Current yield 7.4%

According to the dividend growth method, is Stock 2 currently overvalued or undervalued using Jon’s required rate of return?

Answer 29

Stock 2 is currently undervalued using Jon’s required rate of return because its intrinsic value is more than the current stock market price.

Question 30

A growth company paid a dividend of $0.50 per share in the last fiscal year. They estimate increasing the dividend by 15% per year for the next three years, after which it is expected to grow at a constant rate of 8%. The investor’s required return is 12%. What is the intrinsic value of the stock?

Answer 30

Step 1
Year 1 dividend .50 × 1.15 = .575
Year 2 dividend .575 × 1.15 = .6613
Year 3 dividend .6613 × 1.15 = .7604

Step 2
.7604x1.08/.12-.08= 20.53

Step 3
Calculator keystrokes

12 I
0 CF0
.575 CF1
.6613 CF2
.7604 + CF3 20.53
SHIFT NPV 16.19

Question 31

Two stocks have been presented for your consideration. The beta of Stock A is 1.3, while the beta of Stock B is 0.7. The annual growth rates of dividends are 11% and 6%, respectively. The dividend yields are 5% and 7%, respectively.

Since Stock A offers higher potential growth, should it be purchased? Why?

Answer 31

Just because Stock A offers higher potential growth is not a sufficient reason to buy it. Additional information that would be required before a purchase is made would include the investor’s required return, the stock’s intrinsic value, and the stock’s current market price. In accordance with the efficient market hypothesis, the higher growth expectations may already be reflected in the current market price.

Question 32

Assume that the estimated earnings per share for a stock have been forecast to be $3. The stock’s P/E ratio has ranged from 9 to 12.

From the information given, what is the possible price range for the stock?

Answer 32

The possible price range is $27 to $36.
Low: $3 × 9 = $27
High: $3 × 12 = $36

Question 33

Assume that the estimated earnings per share for a stock have been forecast to be $3. The stock’s P/E ratio has ranged from 9 to 12.

From the information given, what is the possible price range for the stock?

Answer 33

The possible price range is $27 to $36.
Low: $3 × 9 = $27
High: $3 × 12 = $36

Question 34

What is the objective of performance evaluation?

Answer 34

The objective of performance evaluation is to provide an opportunity to alter an investment strategy to improve portfolio performance. Performance evaluation measures are used to judge the managers of portfolios. They also can be used by individual investors to measure the success of their investment approaches.

Question 35

Investment policy statements (IPS) have now become mainstream in financial planning practices.

What are the four basic purposes of an IPS?

Answer 35

• Setting objectives; includes risk tolerance and return objectives
• Defining the asset allocation policy—includes the asset classes to be used and how diversification will be achieved
• Establishing management procedures—guide for selecting and monitoring the investments as well as evaluating the performance
• Determining communication procedures—make sure all parties are aware of the process and objectives, and who is responsible for implementation

Question 36

Investment policy statements (IPS) have now become mainstream in financial planning practices.

What are the major content areas that should be covered in an IPS?

Answer 36

• Return requirement  Risk tolerance
• Liquidity
• Time horizon
• Laws and regulations
• Taxes
• Unique preferences and circumstances
• Permitted and excluded investments

Question 37

The capital asset pricing model is the basis for the Jensen, Treynor, and Sharpe performance indexes. What does the CAPM specify about the required return on an investment?

Answer 37

The CAPM specifies that the required return on an investment depends on (1) the return an investor may earn on a risk-free asset and (2) a risk premium. This is important in performance measurement because all three approaches measure whether the portfolio is achieving the risk premium anticipated.

Question 38

Answer each of the following questions on the Jensen performance index.

What information does the Jensen index provide about a specific investment or portfolio?

Answer 38

The Jensen performance index determines by how much the realized return differs from the return required by the CAPM.

Question 39

The Jensen equation can be expressed as follows:
a=Rp −[Rf +(Rm −Rf)β]

Why is this form of the equation useful in performance evaluation?

Answer 39

This form of the equation is useful because it measures alpha, which is the difference between the realized return and the risk- adjusted required return. A portfolio manager’s performance can be judged relative to the security market line. The numerical value of a in the equation indicates a superior or inferior performance. The absolute numerical values of alpha allow for the ranking of relative performance, with higher scores indicating better performances.

Question 40

What does a positive alpha indicate about a portfolio manager’s performance? What does a negative alpha indicate?

Answer 40

A positive alpha indicates that a portfolio manager consistently does better than the CAPM projections (i.e., the manager outperformed the market on a risk-adjusted basis). If the performance is inferior, the alpha is negative. A zero alpha means that the performance matches the market on a risk-adjusted basis.

Question 41

The Jensen index measures the risk premium in terms of beta. On what assumption is this risk measure based?

Answer 41

Measuring the risk premium in terms of beta is based on an assumption that the portfolio is well diversified. (A well-diversified portfolio’s total risk is primarily its systematic risk.) If a portfolio were not sufficiently diversified, the portfolio’s risk would include both unsystematic and systematic risk, and the standard deviation of the portfolio’s returns would be a more appropriate measure of risk.

Question 42

Answer each of the following questions on the Treynor performance measurement.

What limitations are associated with the Treynor ratio?

Answer 42

The Treynor ratio does not indicate whether a given portfolio manager outperformed or underperformed the market. Also, as with the Jensen index, the Treynor ratio assumes that the portfolio is part of a fully diversified portfolio.

Question 43

Answer each of the following questions on the Treynor performance measurement.

The Treynor ratio does not indicate whether a given portfolio manager outperformed or underperformed the market.

How can these limitations be overcome?

Answer 43

The Treynor ratio can be computed for the market to determine whether the portfolio manager outperformed the market. If the portfolio in question is not a part of a diversified portfolio containing other asset classes, then the Sharpe ratio can be used instead of the Treynor ratio.

Question 44

Answer each of the following questions on the Sharpe performance measurement.

In what one way does the Sharpe ratio formula differ from the Treynor ratio formula?

Answer 44

The Sharpe performance formula uses the standard deviation of the portfolio rather than its beta in the denominator of the equation.

Question 45

Answer each of the following questions on the Sharpe performance measurement.

The Sharpe performance formula uses the standard deviation of the portfolio rather than its beta in the denominator of the equation. Of what significance is this difference?

Answer 45

The significance is that the Sharpe ratio does not assume that the portfolio is well diversified.

Question 46

The Sharpe ratio has a limitation that is the same as a limitation of the Treynor ratio. What is this limitation, and how is it overcome?

Answer 46

Both the Sharpe and Treynor ratios do not indicate whether a given portfolio manager outperformed or underperformed the market. The limitation is overcome by computing the Sharpe ratio for the market and comparing the Sharpe ratio of the portfolio to that of the market.

Question 47

Is one of the three performance measurements (Jensen, Sharpe, or Treynor) better than the others?

Answer 47

Whether a performance measurement is preferred by an investor depends on the investments being evaluated.
-The Sharpe ratio encompasses total risk, and it would seem to be more appropriate if an investor’s total portfolio is not well diversified. If an investor is concerned with evaluating the performance of a mutual fund, for example, and the fund represents the investor’s total risk.

• The Sharpe ratio would be preferred. If the goal is to evaluate how the portfolio performed relative to the market (alpha) and/or to other portfolios.
• The Jensen index would be used. If the investor’s entire portfolio is well diversified, then the Treynor ratio would be appropriate.

Question 48

Your client has found a mutual fund that she likes. Performance and risk characteristics of the fund and the market are as shown in the following table. Compute the Treynor ratio for the fund and for the market, and determine if the fund outperformed the market.

Excess return Fund: 13%
Beta 1.4
R-squared with market 88%
Treynor ratio: 9.29

Excess return Market: 11%
Beta 1.0
R-squared N/A
Treynor ratio: 11

Answer 48

The client’s fund did not outperform the market. The Treynor ratio for the market is greater than that same ratio for the fund.

Question 49

Using both the Sharpe and Treynor ratios, indicate which of the two funds shown in the following table has the best risk-adjusted performance. (The risk-free rate is 6%.)

Assume that the R2 for Fund A is 85% and that it is 89% for Fund B.

A
Return 18%
Beta 1.3
Standard deviation 24

B
Return 16%
Beta 1.1
Standard deviation 30

Answer 49

Fund A has the best risk-adjusted performance as computed by both the Sharpe and Treynor ratios. The Treynor ratio can be used because both funds have a high R2 (greater than 70%).

Ta=9.23
Sa=.50

Tb=9.09
Sb=.33

Question 50

Using both the Sharpe and Treynor ratios, indicate which of the two funds shown in the following table has the best risk-adjusted performance. (The risk-free rate is 6%.)

Assume that the R2 for Fund A is 46% and that it is 89% for Fund B. What impact does Fund A’s lower R2 have on the calculations?

A
Return 18%
Beta 1.3
Standard deviation 24

B
Return 16%
Beta 1.1
Standard deviation 30

Answer 50

The Treynor ratio cannot be used because the Fund A beta may be unreliable due to the low R2. Therefore the only ratio that can be used in this case is the Sharpe ratio. Fund A has the best risk- adjusted performance if the Sharpe ratio is use