Amihud and Mendelson Model: Stock Price Calculation with Perpetual Dividend and Low Trading Volume

The Amihud and Mendelson (1986) model is used to calculate the effective spread, which is a measure of the cost of trading a stock. The formula for the model is:

Effective spread = (|R − Rm| / Rm) * sqrt(V)

where:

• R is the required rate of return
• Rm is the market rate of return
• V is the trading volume (as a fraction of total shares outstanding)

To find the price of the stock, we need to use the following formula:

Price = Dividend / (R - Effective spread)

In this case, the stock pays a perpetual dividend of $2, has a required rate of return of 9%, a relative bid-ask spread of 0.5%, and a relative trading frequency of 0.1 (u = 0.1). Let's assume the market rate of return is 0.

First, we need to calculate the effective spread:

Effective spread = (|0.09 - 0| / 0) * sqrt(0.1) = infinity

Since the effective spread is infinite, we cannot use the Amihud and Mendelson (1986) model to calculate the price of the stock. This is likely due to the low trading volume (0.1) relative to the total shares outstanding.

Therefore, we cannot determine the price of the stock using the given information.