Answer:
Stock price is $142.13
Explanation:
Given that:
Dividends (D) = $1.74
Dividend grow rate (g) = 25% = 0.25
Required return (R) = 12% = 0.12
Growth rate period (T) = 11 years
Perpetuity (p) = 6% = 0.06
Stock price = [D(1 + g) / (R-g)] {1 -[(1 + g) / (1 + R)]^T}+ [(1 + g)/(1 + R)]^T[D(1 + p)/(R-p)]
Substituting values:
Stock price = [1.74(1 + 0.25) / (0.12-0.25)] {1 -[(1 + 0.25) / (1 + 0.12)]¹¹}+ [(1 + 0.25)/(1 + 0.12)]¹¹[1.74(1 + 0.06)/(0.12 - 0.06)]
Stock price = [(-16.73) × (-2.34)] + [(3.35) ×(30.74)] = 39.1482 + 102.979 = $142.13
Stock price is $142.13
The price of stock is $142.13 when the growth rate if dividend is 25% while having the rate of perpetuity as 6%.
Computation:
Given.
[tex]D[/tex] =Dividends of $1.74
[tex]g[/tex] =Dividend grow rate is 25% or 0.25
[tex]R[/tex] =Required return is 12% or 0.12
[tex]T[/tex] =Growth rate period is 11 years
[tex]p[/tex] =Perpetuity is 6% or 0.06
The computation of the stock price is as follows:
Formula used is:
[tex]\begin{aligned}\text{Stock price} = [\dfrac{D(1 + g) }{ R-g}] \times[{1 -[\dfrac{(1 + g)} { (1 + R)}^T}]+ [\dfrac{(1 + g)}{(1 + R)}^T]\times[\dfrac{D(1 + p)}{(R-p)}]\end{aligned}[/tex]
Substituting the values in the above formula:
[tex]\begin{aligned}\text{Stock price}& = [\dfrac{\$1.74(1 + 0.25) }{ 0.12-0.25}] \times[{1 -[\dfrac{(1 + 0.25)} { (1 + 0.12)}^{11}}]+ [\dfrac{(1 + 0.25)}{(1 + 0.12)}^{11}]\times[\dfrac{\$1.74(1 + 0.06)}{(0.12-0.06)}]\\&=\$142.13\end{aligned}[/tex]
Therefore, the stock price as per the given data is $142.13.
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