A firm pays a dividend of $1.20 per share in perpetuity with a zero growth rate. The required return is 10%. We need to find the value of the preferred stock.

Applied MathematicsFinancial MathematicsValuationPerpetuityStock Valuation
2025/7/8

1. Problem Description

A firm pays a dividend of $1.20 per share in perpetuity with a zero growth rate. The required return is 10%. We need to find the value of the preferred stock.

2. Solution Steps

Since the dividend is paid in perpetuity with a zero growth rate, we can use the following formula to calculate the value of the preferred stock:
Value=DividendRequiredReturnValue = \frac{Dividend}{Required Return}
The dividend is $1.20 per share, and the required return is 10%, or 0.
1

0. Plugging these values into the formula, we get:

Value=1.200.10=12Value = \frac{1.20}{0.10} = 12

3. Final Answer

The value of the firm's preferred stock is $
1

2. So the answer is a. $12.

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