Answer:
a. Year 1 dividend - $5.40; Year 2 dividend = $5.83; Year 3 dividend = $6.30; and Year 4 dividend = $6.80
b. Price of stock today = $76.26
c. When the the expected return is increased from 12% to 16%, the price of stock today will fall from $76.26 to $66.27. This indicates a 13% decrease in price. Therefore, there is a negative relationship between the price of stock today and the expected return. That is, as the expected return increases, the price of stock today decreases.
d. The price of stock at the end of fourth year is $141.62.
e. When the the expected return is decreased from 12% to 8%, the price of stock the end of fourth year falls from $141.62 to $122.44. This indicates a 14% decrease in price. Therefore, there is a positive relationship between the price of stock today and the expected return. That is, as the expected return decreases, the future price of stock also decreases.
Step-by-step explanation:
a. Find out the dividend of each of the next four years. [2 marks]
Growth rate = 8%, or 0.08
Year 1 dividend = Last year dividend * (1 + Growth rate) = $5 * (1 + 0.08) = $5 * 1.08 = $5.40
Year 2 dividend = Year 1 dividend * (1 + Growth rate) = $5.40 * (1 + 0.08) = $5.40 * 1.08 = $5.832, or $5.83
Year 3 dividend = Year 2 dividend * (1 + Growth rate) = $5.832 * (1 + 0.08) = $5.832 * 1.08 = $6.29856, or $6.30
Year 4 dividend = Year 3 dividend * (1 + Growth rate) = $6.29856 * (1 + 0.08) = $6.29856 * 1.08 = $6.8024448, or $6.80
b. If the stocks are selling at $120 at the end of fourth year, find out the price of stock today, assuming expected return as 12%.[2 marks]
To calculate this, we use the present value (PV) formula as follows:
PV = FV / (1 + r)^n ..................... (1)
Where,
PV = Price of stock today = ?
FV = Stock selling price at the end of fourth year = $120
r = expected return = 12%, or 0.12
n = number of years = 4
Substitute the values into equation (1), we have:
PV = $120 / (1 + 0.12)^4 = $120 / (1.12)^4 = $120 / 1.57351936 = $76.26
Therefore, the price of stock today is $76.26
c. Write a detailed comment on what will happen to the today’s selling price of the stock if the expected return is increased from 12% to 16%.[3 marks]
To calculate the price of stock today, we use equation (1) in part b above and change r to 16%, or 0.16; while other values remain the same. Substituting the values into equation (1), we have:
PV = $120 / (1 + 0.16)^4 = $120 / (1.16)^4 = $120 / 1.81063936 = $66.27
Percentage change in price = ($66.27 - $76.26) / $76.26 = -0.13, or -13%
Comment:
When the the expected return is increased from 12% to 16%, the price of stock today will fall from $76.26 to $66.27. This indicates a 13% decrease in price. Therefore, there is a negative relationship between the price of stock today and the expected return. That is, as the expected return increases, the price of stock today decreases.
d. If the stocks are selling at $90 today, find out the price of stock at the end of fourth year, assuming expected return as 12%. [2 marks]
To calculate this, we use the future value (FV) formula as follows:
FV = PV * (1 + r)^n ..................... (2)
Where,
FV = Stock selling price at the end of fourth year = ?
PV = Price of stock today = $90
r = expected return = 12%, or 0.12
n = number of years
Substitute the values into equation (2), we have:
FV = $90 * (1 + 0.12)^4 = $90 * (1.12)^4 = $90 * 1.57351936 = $141.62
Therefore, the price of stock at the end of fourth year is $141.62.
e. Write a detailed comment on what will happen to the selling price of the stock at the end of fourth year if the expected return is decreased from 12% to 8%.
To calculate the price of stock at the end of fourth year, we use equation (2) in part c above and change r to 8%, or 0.08; while other values remain the same. Substituting the values into equation (2), we have:
FV = $90 * (1 + 0.08)^4 = $90 * (1.08)^4 = $90 * 1.36048896 = $122.44
Percentage change in price = ($141.62 - $122.44) / $141.62 = -0.14, or -14%
Comment:
When the the expected return is decreased from 12% to 8%, the price of stock the end of fourth year falls from $141.62 to $122.44. This indicates a 14% decrease in price. Therefore, there is a positive relationship between the price of stock today and the expected return. That is, as the expected return decreases, the future price of stock also decreases.