El n´ umero de Nagami - Funciones cardinales y el n´ umero de Nagami 39

4. Funciones cardinales y el n´ umero de Nagami 39

4.2. El n´ umero de Nagami

(5.6) Capital gains yield

. Given the following information, calculate the expected capital gains yield for Chicago Bears

Inc.: beta = 0.6; rM = 15%; rRF = 8%; D1 = $2.00; P0 = $25.00. Assume the stock is in equilibrium and exhibits constant growth.

a. 3.8% b. 0% c. 8.0% d. 4.2% e. 2.5% (5.6) Capital gains yield and dividend yield

ii_. _{Conner Corporation has a stock price of $32.35 per share. The last dividend was $3.42 (i.e., D0 =} $3.42). The long-run growth rate for the company is a constant 7 percent. What is the company’s capital gains yield and dividend yield?

a. Capital gains yield = 7.00%; Dividend yield = 10.57%. b. Capital gains yield = 10.57%; Dividend yield = 7.00%. c. Capital gains yield = 7.00%; Dividend yield = 4.31%. d. Capital gains yield = 11.31%; Dividend yield = 7.00%. e. Capital gains yield = 7.00%; Dividend yield = 11.31%. (5.5) Risk and stock value

(5.5) Stock growth rate

iii_. _{Grant Corporation's stock is selling for $40 in the market. The company's beta is 0.8, the market} risk premium is 6 percent, and the risk-free rate is 9 percent. The previous dividend was $2 (i.e., D0 = $2) and dividends are expected to grow at a constant rate. What is the growth rate for this stock?

a. 5.52% b. 5.00% c. 13.80% d. 8.80% e. 8.38% (5.11) Required return

iv_. _{An increase in a firm's expected growth rate would normally cause the firm's required rate of} return to

a. Increase. b. Decrease. c. Fluctuate. d. Remain constant. e. Possibly increase, possibly decrease, or possibly remain unchanged.

v_{. The probability distribution for rM for the coming year is as follows:} Probability rM 0.05 7% 0.30 8 0.30 9 0.30 10 0.05 12

If rRF = 6.05% and Stock X has a beta of 2.0, an expected constant growth rate of 7 percent, and D0 = $2, what market price gives the investor a return consistent with the stock's risk?

a. $25.00 b. $37.50 c. $21.72 d. $42.38 e. $56.94

(5.11) Required return

vi_. _{If the expected rate of return on a stock exceeds the required rate,}

a. The stock is experiencing supernormal growth. b. The stock should be sold.

c. The company is probably not trying to maximize price per share. d. The stock is a good buy.

(5.12) Efficient markets hypothesis Answer: e Diff: E vii_. _{Which of the following statements is most correct?}

a. If a market is strong-form efficient this implies that the returns on bonds and stocks should be identical.

b. If a market is weak-form efficient this implies that all public information is rapidly incorporated into market prices.

c. If your uncle earns a return higher than the overall stock market, this means the stock market is inefficient.

d. Both answers a and b are correct. e. None of the above answers is correct. (5.12) Market efficiency

viii_. _{Which of the following statements is most correct?}

a. Semistrong-form market efficiency implies that all private and public information is rapidly incorporated into stock prices.

b. Market efficiency implies that all stocks should have the same expected return.

c. Weak-form market efficiency implies that recent trends in stock prices would be of no use in selecting stocks.

d. All of the answers above are correct. (5.11) Required return

ix_. _{If the expected rate of return on a stock exceeds the required rate,}

a. The stock is experiencing supernormal growth. b. The stock should be sold.

c. The company is probably not trying to maximize price per share. d. The stock is a good buy.

i_. _{(5.6) Capital gains yield} _{Answer: d Diff: M}

Required rate of return, rs = 8% + (15% - 8%)0.6 = 12.2%.

Calculate dividend yield and use to calculate capital gains yield: Dividend yield = P D 0 1 = $25.00 $2.00 = 0.08 = 8%.

Capital gains yield = Total yield - Dividend yield = 12.2% - 8% = 4.2%.

Alternative method: P0 = g - r D s 1 ; $25 = g - 0.122 42

$3.05 - $25g = $2 (Multiply both sides by (0.122 - g))

$25g = $1.05 g = 0.042 = 4.2%.

Since the stock is growing at a constant rate, g = Capital gains yield.

. (5.6) Capital gains yield and dividend yield Answer: e Diff: M

Calculate D1 as $3.42  1.07 = $3.66. The dividend yield is $3.66/$32.35 = 11.31%. The capital gains yield is equal to the long-run growth rate for this stock (since constant growth) or 7%.

iii

. (5.5) Stock growth rate Answer: e Diff: M

The required rate of return on the stock is 9% + (6%)0.8 = 13.8%. Using the constant growth model, we can solve for the growth rate as $40 = [$2(1 + g)]/(13.8% - g) or g = 8.38%.

v_. _{(5.5) Risk and stock value Answer: d Diff: M} Numerical solution:

Required return on market and stock

rM = 0.05(7%) + 0.30(8%) + 0.30(9%) + 0.30(10%) + 0.05(12%) = 9.05%. rs = 6.05% + (9.05% - 6.05%)2.0 = 12.05%.

Expected equilibrium stock price

. 38 . 42 $ 07 . 0 1205 . 0 ) 07 . 1 ( 2 $ P ö 0    vi

. (5.11) Required return Answer: d Diff: E

vii_. _{(5.12) Efficient markets hypothesis} _{Answer: e Diff: E}

Statements a through d are incorrect; therefore, statement e is correct. Statement a is incorrect. Strong-form efficiency states that current market prices reflect all pertinent information, whether publicly available or privately held. If it holds, even insiders would find it impossible to earn abnormal returns in the stock market. Statement b is incorrect; this describes semi-strong form efficiency.

viii

. (5.12) Market efficiency Answer: c Diff: E

Statement c is correct; the other statements are false. Semistrong-form market efficiency implies that only public information, not private, is rapidly incorporated into stock prices. Markets can be efficient yet still price securities differently depending on their risks.

CHAPTER 5 Review Questions

Basic Stock Valuation

(5.6) Capital gains yield Answer: d Diff: M

. Given the following information, calculate the expected capital gains yield for Chicago Bears

Inc.: beta = 0.6; rM = 15%; rRF = 8%; D1 = $2.00; P0 = $25.00. Assume the stock is in equilibrium and exhibits constant growth.

a. 3.8% b. 0% c. 8.0% d. 4.2% e. 2.5%

(5.6) Capital gains yield and dividend yield Answer: e Diff: M

(5.5) Stock growth rate Answer: e Diff: M

a. 5.52% b. 5.00% c. 13.80% d. 8.80% e. 8.38%

(5.11) Required return Answer: e Diff: E

iv_. _{An increase in a firm's expected growth rate would normally cause the firm's required rate of} return to

a. Increase. b. Decrease. c. Fluctuate. d. Remain constant. e. Possibly increase, possibly decrease, or possibly remain unchanged.

v_{. The probability distribution for rM for the coming year is as follows:} Probability rM 0.05 7% 0.30 8 0.30 9 0.30 10 0.05 12

If rRF = 6.05% and Stock X has a beta of 2.0, an expected constant growth rate of 7 percent, and D0 = $2, what market price gives the investor a return consistent with the stock's risk?

a. $25.00 b. $37.50 c. $21.72 d. $42.38 e. $56.94

(5.11) Required return Answer: d Diff: E

vi_. _{If the expected rate of return on a stock exceeds the required rate,}

a. The stock is experiencing supernormal growth. b. The stock should be sold.

c. The company is probably not trying to maximize price per share. d. The stock is a good buy.

(5.12) Efficient markets hypothesis Answer: e Diff: E vii_. _{Which of the following statements is most correct?}

a. If a market is strong-form efficient this implies that the returns on bonds and stocks should be identical.

b. If a market is weak-form efficient this implies that all public information is rapidly incorporated into market prices.

c. If your uncle earns a return higher than the overall stock market, this means the stock market is inefficient.

d. Both answers a and b are correct. e. None of the above answers is correct.

(5.12) Market efficiency Answer: c Diff: E

viii_. _{Which of the following statements is most correct?}

a. Semistrong-form market efficiency implies that all private and public information is rapidly incorporated into stock prices.

b. Market efficiency implies that all stocks should have the same expected return.

c. Weak-form market efficiency implies that recent trends in stock prices would be of no use in selecting stocks.

d. All of the answers above are correct.

(5.11) Required return Answer: d Diff: E

ix_. _{If the expected rate of return on a stock exceeds the required rate,}

a. The stock is experiencing supernormal growth. b. The stock should be sold.

c. The company is probably not trying to maximize price per share. d. The stock is a good buy.

i_. _{(5.6) Capital gains yield} _{Answer: d Diff: M}

Required rate of return, rs = 8% + (15% - 8%)0.6 = 12.2%.

Calculate dividend yield and use to calculate capital gains yield: Dividend yield = P D 0 1 = $25.00 $2.00 = 0.08 = 8%.

Capital gains yield = Total yield - Dividend yield = 12.2% - 8% = 4.2%.

Alternative method: P0 = g - r D s 1 ; $25 = g - 0.122 42

$3.05 - $25g = $2 (Multiply both sides by (0.122 - g))

$25g = $1.05 g = 0.042 = 4.2%.

Since the stock is growing at a constant rate, g = Capital gains yield.

ii_. _{(5.6) Capital gains yield and dividend yield} _{Answer: e Diff: M}

Calculate D1 as $3.42  1.07 = $3.66. The dividend yield is

$3.66/$32.35 = 11.31%. The capital gains yield is equal to the long- run growth rate for this stock (since constant growth) or 7%.

iii_. _{(5.5) Stock growth rate Answer: e Diff: M}

The required rate of return on the stock is 9% + (6%)0.8 = 13.8%. Using the constant growth model, we can solve for the growth rate as $40 = [$2(1 + g)]/(13.8% - g) or g = 8.38%.

iv_. _{(5.11) Required return Answer: e Diff: E}

v_. _{(5.5) Risk and stock value} _{Answer: d Diff: M}

Numerical solution:

Required return on market and stock

rM = 0.05(7%) + 0.30(8%) + 0.30(9%) + 0.30(10%) + 0.05(12%) = 9.05%. rs = 6.05% + (9.05% - 6.05%)2.0 = 12.05%.

Expected equilibrium stock price

. 38 . 42 $ 07 . 0 1205 . 0 ) 07 . 1 ( 2 $ P ö 0   

vi_. _{(5.11) Required return Answer: d Diff: E}

vii_. _{(5.12) Efficient markets hypothesis} _{Answer: e Diff: E}

viii_{. (5.12) Market efficiency} _{Answer: c Diff: E}

Statement c is correct; the other statements are false. Semistrong- form market efficiency implies that only public information, not private, is rapidly incorporated into stock prices. Markets can be efficient yet still price securities differently depending on their risks.

CHAPTER 7 Review Questions

In document T E S I S UNA BREVE INTRODUCCIÓN A LOS GRUPOS TOPOLÓGICOS Y EL NÚMERO DE NAGAMI MATEMÁTICO UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO (página 45-50)