Alpha Corporation has outstanding an issue of preferred stock with a par value of $100. It pays an annual dividend equal to 8 percent of par value. If the required return on Alpha’s preferred stock is 6 percent, and if Alpha pays its next dividend in one year, what is the market price of the preferred stock today? Explain why the price would change, if the required rate increased to 10 percent.

Par value of preferred stock = $100

Annual dividend DP = 8% of $100 = $8
Required rate of return KP = 6%
Market price of preferred stock= DP / KP
= $8 / 0.06
= $133.33
Required rate of return KP = 10%
Market price of preferred stock= $8 / 0.10
= $80
There is inverse relationship between required rate of return and price, so when the required rate increased from 6% to 10%, price of the preferred stock decreased from $133 to $80.

To calculate the market price of the preferred stock, we need to use the formula for the present value of a perpetuity. The formula is as follows:

Market Price = Dividend / Required Return

First, let's calculate the dividend. The dividend is equal to 8 percent of the par value of $100. Thus, the dividend is 0.08 * $100 = $8.

Next, let's calculate the market price using the required return of 6 percent:

Market Price = $8 / 0.06 = $133.33

Therefore, the market price of the preferred stock is $133.33 when the required return is 6 percent.

Now, let's calculate the market price if the required rate increases to 10 percent. Using the same formula as before:

Market Price = $8 / 0.10 = $80

Therefore, if the required rate increases to 10 percent, the market price of the preferred stock would decrease to $80.

The reason for this change in price is because the required return is the rate of return that investors expect to earn on a particular investment. When the required return increases, it means that investors are demanding a higher return on their investment. As a result, the market price of the preferred stock decreases because the dividend payment remains the same, but the higher required return reduces the value of the investment to investors.