Answer:
P3 = $96.9425 rounded off to $96.94
Explanation:
To calculate the market price of the stock three years from today (P3), we will use the constant growth model of DDM. The constant growth model calculates the values of the stock based on the present value of the expected future dividends from the stock. The formula for price today under this model is,
P0 = D1) / (r - g)
Where,
- D1 is the dividend expected for the next period
- g is the constant growth rate
- r is the required rate of return on the stock
To calculate the price of the stock today (P0), we use the dividend expected for the next period (D1). So, to calculate the price at the end of 3 years (P3) we will use D4.
We first need to calculate r using the CAPM equation. The equation is,
r = rRF + Beta * rpM
Where,
- rRF is the risk free rate
- rpM is the market risk premium
r = 0.058 + 0.6 * 0.05
r = 0.088 or 8.8%
Using the price formula for DDM above and the values for P0, D1 and r, we can calculate the g to be,
80 = 1.75 / (0.088 - g)
80 * (0.088 - g) = 1.75
7.04 - 80g = 1.75
7.04 - 1.75 = 80g
5.29/80 = g
g = 0.066125 or 6.6125%
We first need to calculate D4.
D4 = D1 * (1+g)^3
D4 = 1.75 * (1+0.066125)^3
D4 = 2.12061793907
Using the formula from DDM for P3, we can calculate P3 to be,
P3 = 2.12061793907 / (0.088 - 0.066125)
P3 = $96.9425 rounded off to $96.94
