To determine the discount rate used by the market to value the preferred stock, you can use the formula for the value of preferred stock, which is calculated as the dividend divided by the discount rate (or required rate of return):
\[ P = \frac{D}{r} \]
where:
- \(P\) = price of the preferred stock
- \(D\) = annual dividend
- \(r\) = discount rate (or required return)
Rearranging this formula to solve for \(r\), we get:
\[ r = \frac{D}{P} \]
Now, substitute the given values:
- \(D = 2.82\)
- \(P = 23.16\)
Calculate the discount rate:
\[ r = \frac{2.82}{23.16} \approx 0.1213 \text{ or } 12.13% \]
Therefore, the discount rate the market used to value the stock is approximately 12.13%.