E-Eyes just issued some new preferred stock. The issue will pay an annual dividend of $15 in perpetuity, beginning 20 years from now. If the market requires a return of 4.5 percent on this investment, how much does a share of preferred stock cost today

The price of the stock today is $144.43.

Explanation:

The price of the preferred stock today can be calculated by using the zero growth model of the DDM. The zero growth model values the stock based on its constant dividend and required rate of return. As the stock will pay its first dividend 20 years from now, we will calculate the stock price at t = 19 and discount it back to today's value.

The price formula under zero growth model is,

P = D / r

P19 = 15 / 0.045

P 19 = $333.3333333

The price of the stock today is,

P0 = 333.3333333 / (1+0.045) ^19

P0 = $144.43