This year, Hope Corporation just paid a dividend of $0.50 per share. The company expect dividends to increase dividends at an annual rate of 3.5% forever. If investors require a return of 12%, what is the value of a Hope Corporation share today? Group of answer choices $6.09 $5.88 $4.17 $0.50 $6.59
Question
This year, Hope Corporation just paid a dividend of $0.50 per share. The company expect dividends to increase dividends at an annual rate of 3.5% forever. If investors require a return of 12%, what is the value of a Hope Corporation share today?
Group of answer choices
$6.09
$5.88
$4.17
$0.50
$6.59
Solution
To calculate the value of a Hope Corporation share today, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model is used to determine the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate. Given a dividend per share that is expected to increase at a constant rate (g) and a required return (k), the formula for the price of a stock (P) is:
P = D1 / (k - g)
Where: D1 = D0 * (1 + g) is the dividend expected next year. D0 is the dividend just paid, and g is the rate of growth.
In this case, D0 = $0.50, g = 3.5% or 0.035, and k = 12% or 0.12.
First, calculate D1: D1 = D0 * (1 + g) = 0.5175
Then, substitute D1, k, and g into the formula to find P: P = D1 / (k - g) = 6.09
So, the value of a Hope Corporation share today is $6.09.
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