To find the discount rate used to value the preferred stock, we can use the formula for the price of preferred stock:
\[ \text{Price} = \frac{\text{Dividend}}{r} \]
Where:
- Price is the market price of the preferred stock ($21.96)
- Dividend is the annual dividend ($2.85)
- \( r \) is the discount rate (or required rate of return)
Rearranging the formula to solve for \( r \):
\[ r = \frac{\text{Dividend}}{\text{Price}} \]
Now, substituting the given values:
\[ r = \frac{2.85}{21.96} \]
Calculating \( r \):
\[ r \approx \frac{2.85}{21.96} \approx 0.1296 \]
So, the discount rate is approximately:
\[ r \approx 0.1296 \text{ or } 12.96% \]
Therefore, the market used a discount rate of approximately 12.96% to value the preferred stock.