The First Bank of Ellicott City has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock. What is the current price of this preferred stock given a required rate of return of 13.0 percent?

The Gordon Growth Model (also known as Gordon-Shapiro Model) can be used to calculate the current stock price. It states:

P0 = D1 / (r – g)

where P0 is the current stock price. D1 represents the next dividend that will be paid. r = Return rate required. g = Continuous Growth Rate for Dividends

The preferred stock would receive a quarterly dividend from the bank of $1.65. This is $1.65 x 4, which equals $6.60 annually.

Divide the dividend by current stock prices to get g. This is $6.60/ $100 = 0.0666

By substituting the values into the formula we have: P0 = $6.60 / (0.13 – 0.066) P0 = $6.60 / 0.064 P0 = $103.125

The current price for the preferred stock at a 13.0 percent return rate is therefore $103.125

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