Answer:
$30.2067
Explanation:
From the given question, using the dividend discount model
[tex]V_0 = \dfrac{D_1}{r - g}[/tex]
where:
r is the Expected return on stock and be calculated as:
Expected return on stock = Risk free rate + Beta × (Expected Market Return - Risk free rate)
Expected return on stock = 5% + 1.25 × (14% - 5%) = 16.25%
However, the current price in this process will b used as the dividend price for all future expenses.
Dividend Yield = Current Dividend/The Share Price
Current dividend D0 = 6% × $25.00 = $1.50
D₁ = D₀ × (1 + g)
D₁ = 1.5 × (1 + g)
Thus, we can now employ the use of the growth dividend model (constant) to determine the value of g as follows:
[tex]25 = \dfrac{1.5 \times (1 + g)}{0.1625 - g}[/tex]
By cross multiply, we have:
4.0625 - 25g = 1.5 + 1.5g
collect like terms, we have:
4.0625 - 1.5 = 1.5g + 25g
2.5625 = 26.5g
Divide both sides by 26.5, we have:
2.5625/26.5 = 26.5g/26.5
g = 9.67%
Similarly, suppose the value for the second year-end to be Y₂;
Then the constant growth dividend model can be computed as:
[tex]Y_2 = \dfrac{D_3}{r - g}[/tex]
where;
D₃ = D₂ × (1 + g)
D₂ × (1 + g) = D₁ × (1 + g) × (1 + g)
D₁ × (1 + g) × (1 + g) = D₀ × (1 + g) × (1 + g) × (1 + g)
D₁ × (1 + g) × (1 + g) = D₀ × (1 + g) × (1 + g) × (1 + g) = D₀ × (1 + g) × 3
D₃ = 1.5 × (1 + 9.67%) × 3
D₃ = $1.9876
Finally:
[tex]Y_2 = \dfrac{D_3}{r - g}[/tex]
[tex]Y_2 = \dfrac{1.9876}{0.1625 - 0.0967}[/tex]
Y₂ = $30.2067
