Question

Van Buren, Inc., currently pays $2.07 per share in dividends on its common stock. Dividends are expected to grow at 5.00% per year forever. If you require a 13.00% rate of return (i.e., the discount rate) on this investment, what value would you place on a share of Van Buren common stock? Assume that the current dividend was just paid.

Answer 1

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**.