To determine the value of a share of Van Buren common stock, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is as follows:
\[ P_0 = \frac{D_0 \times (1 + g)}{r - g} \]
Where:
- \( P_0 \) = price of the stock today
- \( D_0 \) = current dividend (which was just paid)
- \( g \) = growth rate of dividends
- \( r \) = required rate of return
In this scenario:
- \( D_0 = 2.07 \)
- \( g = 0.05 \) (5%)
- \( r = 0.13 \) (13%)
Plugging in the values:
\[ P_0 = \frac{2.07 \times (1 + 0.05)}{0.13 - 0.05} \]
Calculating \( D_1 \):
\[ D_1 = D_0 \times (1 + g) = 2.07 \times 1.05 = 2.1735 \]
Now plug \( D_1 \) back into the formula for \( P_0 \):
\[ P_0 = \frac{2.1735}{0.13 - 0.05} = \frac{2.1735}{0.08} \]
Calculating \( P_0 \):
\[ P_0 = 27.16875 \]
Therefore, the value you would place on a share of Van Buren common stock is approximately $27.17.