A share is expected to pay its first dividend of $0.20 in five years' time. The dividend is then anticipated to increase at a constant 3% p.a. indefinitely. If the required return is 7%, what is a fair value of this share today? Group of answer choices $5.00 $4.44 $4.67 $3.81 $4.37
Question
A share is expected to pay its first dividend of $0.20 in five years' time. The dividend is then anticipated to increase at a constant 3% p.a. indefinitely. If the required return is 7%, what is a fair value of this share today?
Group of answer choices
$5.00
$4.44
$4.67
$3.81
$4.37
Solution
To calculate the fair value of the share today, we need to use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:
P = D / (r - g)
where: P = price of the stock today D = dividend expected in one year r = required rate of return g = growth rate of dividends
However, in this case, the first dividend is not expected in one year, but in five years. Therefore, we need to adjust the formula to account for this. The adjusted formula is:
P = D / ((1 + r)^n * (r - g))
where: n = number of years until the first dividend
Substituting the given values into the formula:
P = 0.20 / ((1 + 0.07)^5 * (0.07 - 0.03))
Calculating the above expression gives a price of approximately 4.37.
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