To determine whether the preference share is overvalued or undervalued, we need to compare its intrinsic value (based on the required rate of return) with its market price.

Step 1: Calculate the dividend.

The preference share pays a fixed dividend of 7% on the $20 face value. The dividend can be calculated as:

$\text{Dividend} = 0.07 \times 20 = 1.40$

Step 2: Calculate the intrinsic value.

The intrinsic value of a preference share is the present value of its dividends in perpetuity. The formula is:

$\text{Intrinsic Value} = \frac{\text{Dividend}}{\text{Required Rate of Return}}$

Substitute the values:

$\text{Intrinsic Value} = \frac{1.40}{0.11} = 12.73$

Step 3: Compare intrinsic value to market price.

The market price per share is $15, but the intrinsic value is $12.73. Since the market price is higher than the intrinsic value, the preference share is overvalued.

Conclusion:

The preference share is overvalued because the market price ($15) is greater than the intrinsic value ($12.73).

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Would you like more details or have any other questions?
Here are five questions related to this problem:

1. How is the dividend rate determined for preference shares?
2. What factors affect the required rate of return for a preference share?
3. What happens to the valuation if the required rate of return increases?
4. How do changes in market price affect the classification of a share as overvalued or undervalued?
5. What is the difference between preference shares and common shares in terms of dividends?

Tip: The required rate of return reflects the risk associated with an investment. The higher the risk, the higher the required return.