Pasqually Mineral Water, Inc., will pay a quarterly dividend per share of $1.40 at the end of each of the next 12 quarters. Thereafter, the dividend will grow at a quarterly rate of 1.2 percent, forever. The appropriate rate of return on the stock is 10 percent, compounded quarterly.
What is the current stock price?
16.1
To determine the current stock price, we can use the dividend discount model (DDM) which calculates the present value of all future dividends.
First, we need to find the present value of the 12 quarterly dividends. Since each dividend is $1.40 and the rate of return is 10% compounded quarterly, we can use the formula for the present value of an ordinary annuity:
PV = D * (1 - (1+r)^(-n)) / r
Where:
PV = Present Value
D = Dividend
r = Rate of return (in decimal form)
n = Number of periods
Using the formula, and plugging in the values, we get:
PV1 = $1.40 * (1 - (1+0.10)^(-12)) / 0.10
Next, we need to find the present value of the perpetuity, which represents the infinite stream of dividends that will grow at a rate of 1.2% quarterly. The formula for the present value of a perpetuity is:
PV = D / (r - g)
Where:
PV = Present Value
D = Dividend
r = Rate of return (in decimal form)
g = Growth rate (in decimal form)
Using the formula, and plugging in the values, we get:
PV2 = $1.40 * (1.012) / (0.10 - 0.012)
Finally, to find the current stock price, we add the present values of the dividends:
Current Stock Price = PV1 + PV2
Calculating this sum will give you the current stock price.