To determine: The projected dividend for the upcoming year
Introduction:
Dividend is a sum of money paid to the shareholders of the company. It is distributed among the investors from the portion of a company’s earnings. This can be issued or paid as shares of stock or cash payment.
Answer to Problem 19QP
The projected dividend for the future year is $2.80.
Explanation of Solution
Given information:
M Company has sold stock for $86 per share. The required
Formula:
The formula to calculate dividends of “n” number of Years:
Where,
Dn refers to the dividend paid in “n” number of years
Do refers to the current year dividend paid n refers to the number of years
g refers to the constant dividend’s growth rate
The formula to calculate current dividends using current stock price formula:
Where,
Po refers to the price of the stock of the 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 constant rate of growth in the second year
g3 refers to the constant rate of growth in the third year
gn refers to the constant rate of growth in n number of year
n refers to the number of years
The formula to calculate projected dividend for the next year:
Where,
Do refers to the current year dividend paid
g1 refers to the expected growth rate of dividend
D1 refers to the dividend payable in the future year
Compute the dividends in Year 3:
Hence, the dividends in Year 3 is (Do× 1.30)3. Consider this as Equation (1).
Compute the dividend in Year 4:
Hence, the dividends in Year 4 is (Do× 1.30)3(1.20). Consider this as Equation (2).
As the stocks starts growing at a constant growth rate in Year 4, determine the stock price for the Year 4. The formula to calculate stock price for the Year 4 is given below: [Consider this formula as Equation (3)]
Where,
Po refers to the present price of stock
Do refers to the recent dividend per share paid on the stock
R refers to the required return on the stock
g refers to the constant dividend’s growth rate
Substitute Equation (2) in Equation (3) and simplify it into the simplest form as shown below:
Hence, the stock price in Year 4 is Do× 69.86.
Compute the current dividends using current stock price formula:
Hence, the current dividend is $1.60.
Compute the projected dividend for the next year:
Hence, the projected dividend for the future year is $2.80.
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Chapter 8 Solutions
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