PIN Ltd is a firm that has been underperforming for many years and has just had a change in management. The new management team have just made an announcement that they expect to start paying an annual dividend 4 years from today, and they expect that after the initial dividend of $4 it will grow at a constant rate of 6% per annum. The required rate of return for PIN Ltd shares is 14% per annum. Which of the following is closest to the value of PIN Ltd shares? (a) $18.41 (b) $21.36 (c) $29.60 (d) $33.75
Question
PIN Ltd is a firm that has been underperforming for many years and has just had a change in management. The new management team have just made an announcement that they expect to start paying an annual dividend 4 years from today, and they expect that after the initial dividend of 18.41 (b) 29.60 (d) $33.75
Solution
To calculate the value of PIN Ltd shares, we need to use the Gordon Growth Model (a version of the Dividend Discount Model) which is used to determine the intrinsic value of a stock that's expected to pay dividends that will grow at a constant rate. However, in this case, the dividends are not starting immediately, but 4 years from now.
The formula for the Gordon Growth Model is:
Value = D1 / (r - g)
Where: D1 = Dividend expected next year r = Required rate of return g = Dividend growth rate
In this case: D1 = $4 (the dividend expected 4 years from now) r = 14% or 0.14 g = 6% or 0.06
So, first we calculate the value of the stock as if the dividends were starting next year:
Value = 40
However, this value is 4 years from now, and we need the present value. So, we need to discount this value back to the present using the required rate of return:
Present Value = 21.36
Therefore, the closest option to the value of PIN Ltd shares is (b) $21.36.
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