Chapter 9 - Stocks and Their Valuation

Question 1

What is a method to estimate the value of a share of stock by discounting all expected future dividend payments?

Answer 1

The dividend discount model (DDM)

Question 2

What is DDM equal to?

Answer 2

PV

Question 3

What calculator buttons do you use when calculating the DDM?

Answer 3

N, I, and PMT

Question 4

Suppose that a stock will pay three annual dividends of $200 per year; the appropriate risk-adjusted discount rate, 𝑟𝑠, is 8%.

What is the value of the stock today using a calculator?

Answer 4

N = 3
I = 8%
PMT = $200
PV = $515.42

Question 5

What type of rate does the DDM use?

Answer 5

A constant rate

Question 6

List the dividend discount model’s 2 critical assumptions

Answer 6

1. Grow forever at a constant growth rate

2. The growth rate < the required rate of return, otherwise we have a negative stock price

Question 7

What are the 2 formulas to find DDM using a constant growth rate?

Answer 7

1. [D(0) (1 + growth rate)] / (req. ror - growth rate)

2. D(1) / (req. ror - growth rate)

Question 8

What are the 2 formulas to find dividends yield?

Answer 8

1. Dividends / Initial price per share

2. D(0) / P(0)

Question 9

What is the formula to find capital gains yield?

Answer 9

(Stock price after year 1 / initial stock price) - 1

Question 10

What is the formula to find total stock return?

Answer 10

Dividend yield + capital gains yield

Question 11

What do we need to calculate with the constant growth model?

Answer 11

Terminal Value

Question 12

What will the sum total of both PV of Dividends and PV of Terminal Value reflect?

Answer 12

The Fair Value of the Stock

Question 13

What are the 3 steps to value common stock with a non constant growth rate?

Answer 13

1. Calculate dividend value
2. Calculate stock price per share
3. Calculate PV and price

Question 14

What is the formula to calculate D(1)?

Answer 14

D(0) x (1 + growth rate for D(1))

Question 15

What is the formula to calculate D(2)?

Answer 15

D(1) x (1 + growth rate for D(2))

Question 16

What is the formula to calculate stock price per share: P(2) using D(3) constant?

Answer 16

D(3) / (req. ror - gr D(3))

Question 17

D(0) = 4.00, Req. RoR = 12%, GR D(1) = 20%, GR2 = 15%, GR3 = 10% Constant

Calculate dividends

Answer 17

D(1) = 4(1+0.2) = 4.8
D(2) = 4.8(1+0.15) = 5.52
D(3) = 5.52(1+0.1) = 6.0702

Question 18

D(0) = 4.00, Req. RoR = 12%, GR D(1) = 20%, GR2 = 15%, GR3 = 10% Constant

Calculate stock price per share using D(3) constant (6.0702)

Answer 18

P(2) = 6.0702 / (0.12 - 0.10) = 303.60

Question 19

D(0) = 4.00, Req. RoR = 12%, GR D(1) = 20%, GR2 = 15%, GR3 = 10% Constant, D(1) = 4.8, D(2) = 5.52, D(3) = 6.0702

Calculate PV and Price

Answer 19

PV of D(1) = N = 1, I = 12%, FV = 4.80, PV = 4.2857
PV of D(1) = N = 2, I = 12%, FV = 5.52, PV = 4.4005
PV of P(2) = N = 2, I = 12%, FV = 303.60, PV = 242.0281

Price = 4.2857 + 4.4005 + 242.0281 = $250.7143

Question 20

Which of the following statements is CORRECT?

a. The constant growth model is often appropriate for evaluating start-up companies that do not have a stable history of growth but are expected to reach stable growth within the next few years.
b. If a stock has a required rate of return rs = 12% and its dividend is expected to grow at a constant rate of 5%, then the stock’s dividend yield is also 5%.
c. The stock valuation model, P0 = D1/(rs - g), can be used to value firms whose dividends are expected to decline at a constant rate, i.e., to grow at a negative rate.
d. The price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.
e. The constant growth model cannot be used for a zero growth stock, wherein the dividend is expected to remain constant over time.

Answer 20

c. The stock valuation model, P0 = D1/(rs - g), can be used to value firms whose dividends are expected to decline at a constant rate, i.e., to grow at a negative rate.

Question 21

If a given investor believes that a stock’s expected return exceeds its required return, then the investor most likely believes that:

a. the stock is experiencing supernormal growth.
b. the stock should be sold.
c. the stock is a good buy.
d. management is probably not trying to maximize the price per share.
e. dividends are not likely to be declared.

Answer 21

c. the stock is a good buy.

Question 22

If a stock’s dividend is expected to grow at a constant rate of 5% a year, then which of the following statements is CORRECT? The stock is in equilibrium.

a. The expected return on the stock is 5% a year.
b. The stock’s dividend yield is 5%.
c. The price of the stock is expected to decline in the future.
d. The stock’s required return must be equal to or less than 5%.
e. The stock’s price one year from now is expected to be 5% above the current price.

Answer 22

e. The stock’s price one year from now is expected to be 5% above the current price.

Question 23

Stocks X and Y have the following data. Assuming the stock market is efficient and the stocks are in equilibrium, which of the following statements is CORRECT?

Price X = $25 Y = $25
Expected dividend yield X = 5% Y = 3%
Required return X = 12% Y = 10%

a. Stock Y pays a higher dividend per share than Stock X.
b. Stock X pays a higher dividend per share than Stock Y.
c. One year from now, Stock X should have the higher price.
d. Stock Y has a lower expected growth rate than Stock X.
e. Stock Y has the higher expected capital gains yield.

Answer 23

b. Stock X pays a higher dividend per share than Stock Y.

Question 24

Stocks X and Y have the following data. Assuming the stock market is efficient and the stocks are in equilibrium, which of the following statements is CORRECT?

Price X = $30 Y = $30
Expected dividend yield X = 6% Y = 4%
Required return X = 12% Y = 10%

a. Stock X has a higher dividend yield than Stock Y.
b. Stock Y has a higher dividend yield than Stock X.
c. One year from now, Stock X’s price is expected to be higher than Stock Y’s price.
d. Stock X has the higher expected year-end dividend.
e. Stock Y has a higher capital gains yield.

Answer 24

c. One year from now, Stock X’s price is expected to be higher than Stock Y’s price.

Question 25

Stock X has the following data. Assuming the stock market is efficient and the stock is in equilibrium, which of the following statements is CORRECT? Expected dividend, D1 = $3.00 Current Price, P0 = $50 Expected constant growth rate = 6.0% a. The stock’s required return is 10%. b. The stock’s expected dividend yield and growth rate are equal. c. The stock’s expected dividend yield is 5%. d. The stock’s expected capital gains yield is 5%. e. The stock’s expected price 10 years from now is $100.00.

Answer 25

b. The stock’s expected dividend yield and growth rate are equal.

Question 26

Stocks A and B have the following data. The market risk premium is 6.0% and the risk-free rate is 6.4%. Assuming the stock market is efficient and the stocks are in equilibrium, which of the following statements is CORRECT? Beta A = 1.10 B = 0.90 Constant growth rate A = 7.00% B = 7.00% a. Stock A must have a higher stock price than Stock B. b. Stock A must have a higher dividend yield than Stock B. c. Stock B’s dividend yield equals its expected dividend growth rate. d. Stock B must have the higher required return. e. Stock B could have the higher expected return.

Answer 26

b. Stock A must have a higher dividend yield than Stock B.

Question 27

The required returns of Stocks X and Y are rX = 10% and rY = 12%. Which of the following statements is CORRECT? a. If the market is in equilibrium, and if Stock Y has the lower expected dividend yield, then it must have the higher expected growth rate. b. If Stock Y and Stock X have the same dividend yield, then Stock Y must have a lower expected capital gains yield than Stock X. c. If Stock X and Stock Y have the same current dividend and the same expected dividend growth rate, then Stock Y must sell for a higher price. d. The stocks must sell for the same price. e. Stock Y must have a higher dividend yield than Stock X.

Answer 27

a. If the market is in equilibrium, and if Stock Y has the lower expected dividend yield, then it must have the higher expected growth rate.

Question 28

The expected return on Natter Corporation’s stock is 14%. The stock’s dividend is expected to grow at a constant rate of 8%, and it currently sells for $50 a share. Which of the following statements is CORRECT? a. The stock’s dividend yield is 7%. b. The stock’s dividend yield is 8%. c. The current dividend per share is $4.00. d. The stock price is expected to be $54 a share one year from now. e. The stock price is expected to be $57 a share one year from now.

Answer 28

d. The stock price is expected to be $54 a share one year from now.

Question 29

A stock is expected to pay a year-end dividend of $2.00, i.e., D1 = $2.00. The dividend is expected to decline at a rate of 5% a year forever (g = -5%). If the company is in equilibrium and its expected and required rate of return is 15%, then which of the following statements is CORRECT? a. The company’s current stock price is $20. b. The company’s dividend yield 5 years from now is expected to be 10%. c. The constant growth model cannot be used because the growth rate is negative. d. The company’s expected capital gains yield is 5%. e. The company’s expected stock price at the beginning of next year is $9.50.

Answer 29

e. The company’s expected stock price at the beginning of next year is $9.50.

Question 30

Which of the following statements is CORRECT, assuming stocks are in equilibrium? a. The dividend yield on a constant growth stock must equal its expected total return minus its expected capital gains yield. b. Assume that the required return on a given stock is 13%. If the stock’s dividend is growing at a constant rate of 5%, then its expected dividend yield is 5% as well. c. A stock’s dividend yield can never exceed its expected growth rate. d. A required condition for one to use the constant growth model is that the stock’s expected growth rate exceed its required rate of return. e. Other things held constant, the higher a company’s beta coefficient, the lower its required rate of return.

Answer 30

a. The dividend yield on a constant growth stock must equal its expected total return minus its expected capital gains yield.

Question 31

What is the formula to calculate req. ror using CAPM?

Answer 31

Risk-free RoR + beta(MRP)

Question 32

What is the formula to calculate the dividend value in 10 years?

Answer 32

D(0)(1+g)^10

Question 33

What is the formula to calculate the stock price per share in 10 years?

Answer 33

P(0)(1+g)^10

Question 34

What is the capital gains yield equal to?

Answer 34

The growth rate

Question 35

What is total return equal to?

Answer 35

The required rate of return

Question 36

Solve the problem: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, and the constant growth rate is g = 4.0%. What is the current stock price?

Answer 36

``` D(1) = D(0) (1 + g) D(1) = 1.50 (1 + 0.04) D(1) = 1.56 ``` ``` P(1) = D(1) / (rs - g) P(1) = 1.56 / (0.09 - 0.04) P(1) = $31.20 ```

Question 37

Solve the problem: The risk free rate of return (rf) is 6%, market risk premium (MRP=(rm–rf)) is 4%, and JP Morgan Chase’s stock has a beta coefficient of 1.5. If the dividend expected during the coming year is $2.25 (D1), and if the growth rate is constant at 5%, at what price should JP Morgan Chase’s stock sell?

Answer 37

``` RS = rf + b(MRP) RS = 0.06 + 1.5(0.04) RS = 12% ``` ``` P(0) = D(1) / (rs - g) P(0) = 2.25 / (0.12 - 0.05) P(0) = $32.14 ```

Question 38

Solve the problem: Gray Manufacturing is expected to pay a dividend of $1.25 per share at the end of the year (D1 = $1.25). The stock sells for $22.50 per share, and its required rate of return is 10.5%. The dividend is expected to grow at some constant rate, g, forever. What is the equilibrium expected growth rate?

Answer 38

``` P(0) = D(1) / (rs - g) 22.50 = 1.25 / (0.105 - g) 22.50(0.105 - g) = 1.25 2.3625 - 22.50g = 1.25 -22.50g = -1.1125 g = 4.94% ```

Question 39

Solve the problem in equation form: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, and the constant growth rate is g = 4.0%. What is the dividend value in 10 years?

Answer 39

``` D(10) = D(0)(1+g)^ # of years D(10) = 1.50 (1 + 0.04) ^10 D(10) = 2.2204 ```

Question 40

Solve the problem using a calculator: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, and the constant growth rate is g = 4.0%. What is the dividend value in 10 years?

Answer 40

``` N = 10 I = 4% PV = 1.5 FV = 2.2204 ```

Question 41

Solve the problem in equation form: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, the stock price per share is P(0) = 31.20, and the constant growth rate is g = 4.0%. What is the stock price per share in 10 years?

Answer 41

``` P(10) = P(0) (1 + g)^ # of years P(10) = 31.20 (1 + 0.04) ^ 10 P(10) = 46.1836 ```

Question 42

Solve the problem using a calculator: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, the stock price per share is P(0) = 31.20, and the constant growth rate is g = 4.0%. What is the stock price per share in 10 years?

Answer 42

``` N = 10 I = 4% PV = 31.20 FV = 46.1836 ```

Question 43

Solve the problem: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, and the constant growth rate is g = 4.0%. Calculate capital gains yield.

Answer 43

``` CGY = G CGY = 4% ```

Question 44

Solve the problem: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, the stock price per share is $31.20, and the constant growth rate is g = 4.0%. Calculate dividends yield.

Answer 44

``` DY = D(0) / P(0) DY = 1.50 / 31.20 DY = 5% ``` OR ``` DY = rs - g DY = 9% - 4% DY = 5% ```

Question 45

Solve the problem: A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 9.0%, and the constant growth rate is g = 4.0%. Calculate the total return.

Answer 45

``` TR = RS TR = 9% ```