paid cash dividend of $0.2 per share, investors require 16% return, the dividend expected to grow at a steady 8% per year, what is the current value of share, what will be the share worth in five years
Question
paid cash dividend of $0.2 per share, investors require 16% return, the dividend expected to grow at a steady 8% per year, what is the current value of share, what will be the share worth in five years
Solution
The current value of the share can be calculated using the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:
P = D1 / (k - g)
where: P = price of the stock D1 = expected dividend per share one year from now k = required rate of return for the investor g = growth rate of dividends
In this case, D1 can be calculated as the current dividend (0.2 * (1 + 0.08) = $0.216.
Substituting the values into the formula:
P = 2.7
So, the current value of the share is $2.7.
To calculate the value of the share in five years, we can use the formula for the future value of a growing perpetuity:
P5 = D6 / (k - g)
where: P5 = price of the stock in five years D6 = expected dividend per share six years from now
D6 can be calculated as the current dividend (0.2 * (1 + 0.08)^6 = $0.297.
Substituting the values into the formula:
P5 = 3.71
So, the share will be worth $3.71 in five years.
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