Final answer:
Using the constant dividend growth valuation model, the market believes that the stock's price at the end of 3 years will be approximately $88.90 per share.
Step-by-step explanation:
To find the stock's price at the end of 3 years, we can use the constant dividend growth valuation model. The formula for this model is:
Pt = Dt+1 / (r - g)
Where Pt is the stock price at time t, Dt+1 is the dividend expected to be received at time t+1, r is the required rate of return, and g is the constant dividend growth rate.
In this case, we are given that D1 = $1.50, the risk-free rate is 4.8%, the market risk premium is 4%, and the stock price is $80. We need to find the constant dividend growth rate g.
Using the Dividend Discount Model, we can calculate:
$80 = $1.50 / (r - g)
Simplifying this equation, we have:
80(r - g) = 1.50
r - g = 1.50/80
r - g = 0.01875
Since we are given that r = 0.048 (4.8%), we can substitute this value into the equation:
0.048 - g = 0.01875
g = 0.048 - 0.01875
g = 0.02925
Now, we can use this value of g to find the stock's price at the end of 3 years:
P3 = D4 / (r - g)
Since the dividend is expected to grow at a constant rate, D4 = D1 * (1+g)3.
Substituting the given values, we have:
P3 = 1.50 * (1+0.02925)3 / (0.048 - 0.02925)
Calculating this expression, we get:
P3 ≈ 1.50 * (1.02925)3 / 0.01875 ≈ $88.8968
Therefore, the market believes that the stock's price at the end of 3 years will be approximately $88.90 per share.