The present value of the dividend at the end of year T is $50. To calculate the present value of the dividend at the end of year T, we need to use the formula for the present value of a growing perpetuity.
In this case, the dividend is constant for the first 10 years and then stops forever.
The formula for the present value of a growing perpetuity is:
PV = D / (r - g)
Where:
PV = Present value of the dividend
D = Dividend amount
r = Required rate of return
g = Growth rate of the dividend
In this case, the dividend amount is $7 per year, the required rate of return is 14%, and the growth rate of the dividend is 0% (since it remains constant).
Plugging these values into the formula, we get:
PV = $7 / (0.14 - 0)
Simplifying the equation, we have:
PV = $7 / 0.14
Calculating the value, we find:
PV = $50
Therefore, the present value of the dividend at the end of year T is $50.
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