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:
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