Option (a) is correct
Here we will use the Gordon model formula of share price. As per Gordon model, share price is given by:
Share price = D1 / k -g
where, D1 is next years' dividend, k is cost of equity or required rate of return and g is the growth rate.
First we will calculate next years' dividend. Dividend will grow at the rate of 6% annually. So we will calculate the D1 by future value formula as per below:
FV = P * (1 + r)10
where, FV = Future value, which is the dividend next year, P is current years' dividend = $2.46, r is the rate of interest = 6% and n is 1 year.
Now, putting these values in the above formula, we get,
FV = $2.46 * (1 + 6%)1
FV = $2.46 * (1 + 0.06)1
FV = $2.46 * (1.06)1
FV = $2.46 * 1.06
FV = $2.6076
So, the value of D1 is $2.6076
Now, we will calculate the cost of equity by putting the values in the below formula:
Share price = D1 / k -g
$30 = $2.6076 / k - 6%
k - 6% = $2.6076 / $30
k - 0.06 = 0.08692
k = 0.08692 + 0.06
k = 0.14692 or 14.69%.
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