Chapter 9 - Stocks and Their Valuation Flashcards
What is a method to estimate the value of a share of stock by discounting all expected future dividend payments?
The dividend discount model (DDM)
What is DDM equal to?
PV
What calculator buttons do you use when calculating the DDM?
N, I, and PMT
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?
N = 3 I = 8% PMT = $200 PV = $515.42
What type of rate does the DDM use?
A constant rate
List the dividend discount model’s 2 critical assumptions
- Grow forever at a constant growth rate
2. The growth rate < the required rate of return, otherwise we have a negative stock price
What are the 2 formulas to find DDM using a constant growth rate?
- [D(0) (1 + growth rate)] / (req. ror - growth rate)
2. D(1) / (req. ror - growth rate)
What are the 2 formulas to find dividends yield?
- Dividends / Initial price per share
2. D(0) / P(0)
What is the formula to find capital gains yield?
(Stock price after year 1 / initial stock price) - 1
What is the formula to find total stock return?
Dividend yield + capital gains yield
What do we need to calculate with the constant growth model?
Terminal Value
What will the sum total of both PV of Dividends and PV of Terminal Value reflect?
The Fair Value of the Stock
What are the 3 steps to value common stock with a non constant growth rate?
- Calculate dividend value
- Calculate stock price per share
- Calculate PV and price
What is the formula to calculate D(1)?
D(0) x (1 + growth rate for D(1))
What is the formula to calculate D(2)?
D(1) x (1 + growth rate for D(2))
What is the formula to calculate stock price per share: P(2) using D(3) constant?
D(3) / (req. ror - gr D(3))
D(0) = 4.00, Req. RoR = 12%, GR D(1) = 20%, GR2 = 15%, GR3 = 10% Constant
Calculate dividends
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
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)
P(2) = 6.0702 / (0.12 - 0.10) = 303.60
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
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
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.
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.
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.
c. the stock is a good buy.
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.
e. The stock’s price one year from now is expected to be 5% above the current price.
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.
b. Stock X pays a higher dividend per share than Stock Y.
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.
c. One year from now, Stock X’s price is expected to be higher than Stock Y’s price.
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.
b. The stock’s expected dividend yield and growth rate are equal.
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.
b. Stock A must have a higher dividend yield than Stock B.
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.
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.
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.
d. The stock price is expected to be $54 a share one year from now.
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.
e. The company’s expected stock price at the beginning of next year is $9.50.
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.
a. The dividend yield on a constant growth stock must equal its expected total return minus its expected capital gains yield.
What is the formula to calculate req. ror using CAPM?
Risk-free RoR + beta(MRP)
What is the formula to calculate the dividend value in 10 years?
D(0)(1+g)^10
What is the formula to calculate the stock price per share in 10 years?
P(0)(1+g)^10
What is the capital gains yield equal to?
The growth rate
What is total return equal to?
The required rate of return
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?
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
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?
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
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?
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%
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?
D(10) = D(0)(1+g)^ # of years D(10) = 1.50 (1 + 0.04) ^10 D(10) = 2.2204
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?
N = 10 I = 4% PV = 1.5 FV = 2.2204
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?
P(10) = P(0) (1 + g)^ # of years P(10) = 31.20 (1 + 0.04) ^ 10 P(10) = 46.1836
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?
N = 10 I = 4% PV = 31.20 FV = 46.1836
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.
CGY = G CGY = 4%
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.
DY = D(0) / P(0) DY = 1.50 / 31.20 DY = 5%
OR
DY = rs - g DY = 9% - 4% DY = 5%
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.
TR = RS TR = 9%
