Concept explainers
Two-Stage Dividend Growth [LO1] Regarding the two-stage dividend growth model in the chapter, show that the price of a share of stock today can be written as follows;
Can you provide an intuitive interpretation of this expression?
To prove: The current price of a share under the two-stage dividend growth model expressed as:
Where,
Po refers to the price of the stock of current year
Do refers to the current year dividend paid
R refers to the required rate of return on its stock
g1 refers to the expected growth rate of dividend
g2 refers to the growth rate of one period
t refers to the number of times
Introduction:
Stock price is a price of a particular stock of the company. It is a financial asset of the company.
Two-stage dividend growth model is used to determine the value of a stock. This model is used to express the two stages of growth. The first stage of growth has a high growth rate and second stage has a constant growth rate.
Answer to Problem 37QP
As per the two-stage dividend growth model, the current stock price can be denoted as:
Where,
Po refers to the price of the stock of current year
Do refers to the current year dividend paid
R refers to the required rate of return on its stock
g1 refers to the expected growth rate of dividend
g2 refers to the growth rate of one period
t refers to the number of times
Explanation of Solution
In the two-stage dividend growth model, the current stock price can be determined by considering the present value (PV) of first time’s (t) dividends which is the PV of a rising annuity. Then, add PV of stock price at the number of times (t) which can be expressed as shown below:
Where,
Po refers to the price of the stock of the current year
PV refers to thepresent value
Pt refers to the stock price at time t
t refers to the number of times
Substitute the equation for PV of a rising annuity by using the expected growth rate of dividend (g1) which can be expressed as:
Where,
Po refers to the price of the stock of current year
PV refers to thepresent value
Pt refers to the stock price at time t
t refers to the number of times
D1 refers to thenext period dividend per share
R refers to the required rate of return on its stock
g1 refers to the expected growth rate of dividend
Later, the dividend in one year can be increased at an expected growth rate of dividend (g1) so the equation of current stock price can be expressed as:
Then, rearrange the equation as follows: [Consider the equation as Equation (1)]
The constant dividend growth model equation can be used to determine the price of the stock at time (t). The equation of constant dividend growth model is given below: [Consider the equation as Equation (2)]
Where,
Pt refers to the price of the stock at time t
t refers to the number of times
Dt refers to thedividend per share at time t
R refers to the required rate of return on its stock
g2 refers to the growth rate of one period
Now, consider the dividend at
Substitute, the equation of
Rearrange, the equation to determine the present value of future stock price which can be expressed as follows:
Where,
PV (Pt) refers to the present value of the future stock price
Do refers to the current year dividend paid
R refers to the required rate of return on its stock
t refers to the number of times
g1 refers to the expected growth rate of dividend
g2 refers to the growth rate of one period
Simplify the current equation into the simplest form: [Consider the equation as Equation (3)]
After that, substitute Equation (3) into Equation (1). The present equation will be expressed as:
The interpretation of equation emphasizes that the right-hand side of equation denotes the PV of the first “t” dividends. On the other hand, the left-hand side denotes the PV of stock price at the time after the dividend growth continues to be constant.
Hence, the current stock price can be denoted as:
Want to see more full solutions like this?
Chapter 8 Solutions
Fundamentals of Corporate Finance
- The dividend-Growth model may be used to value a stock: V= D0 (1+g) / k-g What is the value of a stock if : D0 = $2 k = 10% g = 6% What is the value of this stock if the dividend is increased to $3and the other variables remain constant? What is the value of this stock if the required return declines to 7.5 percent and the other variable remains constant? What is the value of this stock if the growth rate declines to 4 percent and the other variables remain constant? What is the value of this stock if the dividend is increased to $2.30, the growth rate declines to 4 percent, and the required return remains 10 percent?arrow_forwardthe dividend growth model may be use to value a stock v=Do(1+g) k-g a. what is the value of a stock if: Do=$2 k==10% g=6% b. what is the value of this stock if the dividend is increased to $3 and the other variables remain constant? c. what is the value os this stock if the required return decline to 7.5 percent and the other variables remain constant? d. what is the value of this stock if the growth rate declines to 4 percent and the other variables remin constant? e. what is the value of this stock if the dividend is increased to $2.30, the growth rate declines to 4 percent, and the required return remains 10 percent?arrow_forwardTrue or False, pls explain why 13) A stable peso dividend policy tries to maintain a relatively stable percentage dividend over time True Falsearrow_forward
- The dividend discount model constant growth It is a method of evaluating dividends that assumes a fix ed dividend in the future Select one: O True O Falsearrow_forwardThe dividend-growth model may be used to value a stock: Do(1+9) V = k - g Round your answers to the nearest cent. a. What is the value of a stock if: Do = $3.10 k = 12% 9 = 8% b. What is the value of this stock if the dividend is increased to $4.30 and the other variables remain constant? $ c. What is the value of this stock if the required return declines to 9 percent and the other variables remain constant? d. What is the value of this stock if the growth rate declines to 5 percent and the other variables remain constant? e. What is the value of this stock if the dividend is increased to $3.70, the growth rate declines to 5 percent, and the required return remains 12 percent? $arrow_forwardcan someone explain with example and formulas and steps about how to solve for 3 stage supernormal growth in stock and how to find the pv and and all the p1 p2arrow_forward
- Investors are more concerned with future dividends than historical dividends, so go to ESTIMATES and scroll down to the Consensus Estimates on the screen. Click on the Available Measures menu to toggle between earnings per share and dividends per share. How do analysts expect Apple's payout policy to behave in the future?arrow_forwardThe dividend growth model I. assumes that dividends increase at a constant rate forever. II. can be used to compute a stock price at any point in time. III. can be used to value zero-growth stocks. IV. requires the growth rate to be less than the required return.arrow_forward13 The value of the stock: Group of answer choices Increases as the required rate of return increases Increases as the dividend growth rate increases and increases as the required rate of return decreases Increases as the dividend growth rate increases Increases as the required rate of return decreasesarrow_forward
- Question Help ▼ According to the Generalized Dividend Model, the final sales price of a stock depends on the following except the O A. price of the stock in the last period. OB. number of periods. OC. required retum on investments in equity. O D. dividend payments. If a company called Advanced Technologies has yet to pay a dividend on its stock, the generalized dividend model predicts that the company's stock may still have value because O A. people expect Advanced Technologies to pay dividends in the future. B. all companies that have any physical assets have value. OC. the required return on investment for high technology companies is zero. O D. all companies are legally required to pay dividends within ten years of the initial public offering of stock. Click to select your answer.arrow_forwardACTIVITY 4 Given the following data, what should the price of the stock be? Required return: 10% Present dividend: P100 Dividend growth rate: 5%arrow_forwardThe dividend-growth model may be used to value a stock: Round your answers to the nearest cent. a. What is the value of a stock if: Do = $2.30 k = 8% 9 = 5% V = Do(1+g) k-9 $ b. What is the value of this stock if the dividend is increased to $4.30 and the other variables remain constant? $ c. What is the value of this stock if the required return declines to 6 percent and the other variables remain constant? $ d. What is the value of this stock if the growth rate declines to 3 percent and the other variables remain constant? $ e. What is the value of this stock if the dividend is increased to $2.90, the growth rate declines to 3 percent, and the required return remains 8 percent? $arrow_forward
- Fundamentals Of Financial Management, Concise Edi...FinanceISBN:9781337902571Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage LearningFundamentals of Financial Management, Concise Edi...FinanceISBN:9781285065137Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage Learning