E-Eyes just issued some new preferred stock. The issue will pay an annual dividend of $10 in perpetuity, beginning 8 years from now. If the market requires a 9 percent return on this investment, how much does a share of preferred stock cost today

A share of preferred stock cost $55.76 today

Explanation:

The price of a perpetuity can be calculated using the zero growth model in dividend discount model. The formula for the price of such a stock is,

P0 = Dividend / r

Where r is the required rate of return.

However, in this case the stock will start paying dividend after 7 years from now. So we will adjust this formula as this will provide us the future Price after 7 yearsvor in the eighth year of such a stock.

The adjusted formula will be,

P0 = (Dividend / r) / (1+r) ^8

So,

P0 = (10 / 0.09) / (1+0.09) ^8

P0 = $55.762