Answer:
P0 = $57.6722 rounded off to $57.67
Explanation:
To calculate the market price of the stock today, we will use the two stage growth model of DDM. The two stage growth model calculates the values of the stock today based on the present value of the expected future dividends from the stock. The formula for price today under this model is,
P0 = D0 * (1+g1) / (1+r) + D0 * (1+g1)^2 / (1+r)^2 + ... + D0 * (1+g1)^n / (1+r)^n + [(D0 * (1+g1)^n * (1+g2)) / (r - g2)] / (1+r)^n
Where,
- g1 is the short term growth rate
- g2 is the long term or constant growth
- r is the required rate of return on the stock
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 = 0.08 + 1.4 * 0.035
r = 0.129 or 12.9%
Using the price formula for DDM above, we can calculate the price today to be,
P0 = 2.2 * (1+0.18) / (1+0.129) + 2.2 * (1+0.18)^2 / (1+0.129)^2 +
[(2.2 * (1+0.18)^2 * (1+0.08)) / (0.129 - 0.08)] / (1+0.129)^2
P0 = $57.6722 rounded off to $57.67
