Kilsheimer Company just paid a dividend of $ 4 per share. Future dividends are expected to grow at a constant rate of 6% per year. What is the value of the stock if the required return is 12 %?
70.67
To calculate the value of the stock, we can use the Gordon Growth Model, also known as the Dividend Discount Model (DDM). The Gordon Growth Model is defined by the formula:
\(P_0 = \frac{D_1}{r - g}\)
Where:
\(P_0\) = Value of the stock
\(D_1\) = Expected dividend payment at the end of the first year
\(r\) = Required rate of return (or discount rate)
\(g\) = Expected growth rate of dividends
First, we need to calculate the expected dividend payment at the end of the first year. Since the dividend just paid was $4 per share, and the expected growth rate of dividends is 6%, the dividend at the end of the first year (D1) can be calculated as:
\(D_1 = D_0 \times (1 + g)\)
\(D_1 = $4 \times (1 + 0.06)\)
\(D_1 = $4.24\)
Next, we can substitute the known values into the Gordon Growth Model:
\(P_0 = \frac{\$4.24}{0.12 - 0.06}\)
\(P_0 = \frac{\$4.24}{0.06}\)
\(P_0 = \$70.67\)
Therefore, the value of the stock is $70.67, assuming a required return of 12% and a constant dividend growth rate of 6% per year.