Question

What would be the price of a stock? Next year's dividend will be $5.00, and then dividend will grow for two years at 20% annual rate. After these first three dividends, the dividend will grow at 6% annual rate forever. The required return (discount rate) is 15%.

Answer 1

Using the dividend discount model (DDM) and a required return of 15%, the stock price would be $92.59.

Step-by-step explanation:

To determine the price of a stock, we can use the dividend discount model (DDM). The DDM calculates the present value of all future dividends. In this case, we have three periods with different dividend growth rates. After year 2, the dividend will grow at a constant rate of 6%. Using a required return of 15%, we can calculate the present value of all future dividends and the stock price.

First, let's calculate the present value of the next three dividends:

1. Year 1 dividend = $5.00 / (1 + 0.15) = $4.35
2. Year 2 dividend = $5.00 * (1 + 0.20) / (1 + 0.15)^2 = $4.14
3. Year 3 dividend = $5.00 * (1 + 0.20)^2 / (1 + 0.15)^3 = $4.49

Next, let's calculate the present value of all future dividends after year 3:

Using the constant growth formula, the present value of all future dividends can be calculated as:

PV = Year 3 dividend * (1 + growth rate) / (required return - growth rate) = $4.49 * (1 + 0.06) / (0.15 - 0.06) = $79.61

Finally, let's sum up the present value of all dividends to calculate the stock price:

Stock price = Present value of Year 1 dividend + Present value of Year 2 dividend + Present value of Year 3 dividend + Present value of all future dividends = $4.35 + $4.14 + $4.49 + $79.61 = $92.59