Question

DMB Corporation will issue a dividend in one year for $4.10 per share. Dividends are expected to grow 5.00% per year into the foreseeable future. DMB shares are currently trading at $38.04 per share. What is the implied equity cost of capital for DMB?

Answer 1

To find the implied equity cost of capital for DMB Corporation, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model is represented by the formula:

\[
P_0 = \frac{D_1}{r - g}
\]

Where:
- \(P_0\) = Current price of the stock
- \(D_1\) = Dividend expected in one year
- \(r\) = Implied equity cost of capital
- \(g\) = Growth rate of dividends

From the problem:
- \(P_0 = 38.04\)
- \(D_1 = 4.10\)
- \(g = 0.05\) (or 5%)

We need to rearrange the formula to solve for \(r\):

\[
r = \frac{D_1}{P_0} + g
\]

Substituting the values into the formula:

\[
r = \frac{4.10}{38.04} + 0.05
\]

Calculating the dividend yield:

\[
\frac{4.10}{38.04} \approx 0.1075
\]

Now, adding the growth rate:

\[
r \approx 0.1075 + 0.05 \approx 0.1575
\]

Thus, the implied equity cost of capital \(r\) is approximately:

\[
r \approx 0.1575 \text{ or } 15.75\%
\]

Therefore, the implied equity cost of capital for DMB Corporation is **15.75%**.