Final answer:
The Net Present Value (NPV) of purchasing a stock, we calculate the Present Discounted Value (PDV) of all future dividend payments using the growth rate and required return, and then subtract the stock's current price.
Step-by-step explanation:
The student's question is about calculating the Net Present Value (NPV) of purchasing one share of stock today, given a series of future dividends that will grow at a constant rate and having a known required rate of return. To calculate the NPV, we apply the concept of Present Discounted Value (PDV) to discount future dividends back to their present value and then subtract the cost of the investment.
To start, we calculate the PDV for the first dividend payment using the formula PDV = D / (1+r)^t, where D is the dividend payment, r is the required rate of return, and t is the time in years. We then use the Gordon Growth Model, which assumes a constant growth rate for dividends, to find the PDV of all future dividends. The Gordon Growth Model formula we use is P = D1 / (r - g), where D1 is the expected dividend one year from now, r is the required rate of return and g is the growth rate of the dividends.
Once we have the PDV of all future dividends, we can find the NPV by subtracting the current price of the stock from the PDV figure. Since the student provided a specific example where the growth rate (g) is 2.1%, the required rate of return is 10.4%, and the first dividend payment is $1.2, the NPV would be calculated specifically for these values.