A share just paid a dividend of $0.60. The dividend is expected to increase at an annual rate of 4% forever. If the required return is 10%, what is a fair value of this share today? Group of answer choices $11.00 $6.24 $0.62 $10.00 $10.40
Question
A share just paid a dividend of $0.60. The dividend is expected to increase at an annual rate of 4% forever. If the required return is 10%, what is a fair value of this share today?
Group of answer choices
$11.00
$6.24
$0.62
$10.00
$10.40
Solution
The fair value of the share can be calculated using the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:
P = D1 / (r - g)
where: P = price of the stock D1 = expected dividend in the next year r = required rate of return g = growth rate of dividends
Given in the problem: D0 (the dividend just paid) = $0.60 g = 4% = 0.04 r = 10% = 0.10
First, we need to calculate D1, the expected dividend in the next year. Since the dividends are growing at a rate of 4%, D1 = D0 * (1 + g) = 0.624.
Now we can substitute D1, r, and g into the formula to find the price of the stock:
P = 10.40
So, the fair value of the share today is $10.40.
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