Final answer:
The cost of a share of the e-eyes's new 20/20 preferred stock today, which pays an annual dividend of $19 starting from 8 years from now and with a market return rate of 3.3%, is approximately $457.91.
Step-by-step explanation:
The cost of a share of preferred stock issued by e-eyes can be calculated using present value concepts. The stock pays an annual dividend of $19 in perpetuity, but the payments only begin 8 years from now. The required market return on this investment is 3.3%. To find the present value of these future dividends, we use the formula for the present value of a perpetuity:
PV = D / r
Where PV is the present value, D is the dividend, and r is the required rate of return.
The present value calculation must also take into account the fact that dividends start in 8 years, which means we discount the perpetuity value back 7 years (since dividends are paid at the end of each year, we discount from year 8 to year 1).
So, the full calculation to find the present value of this preferred stock today is:
PV = D / r * (1 / (1 + r)^7)
Therefore, substituting the values we get:
PV = $19 / 0.033 * (1 / (1 + 0.033)^7)
= $575.76 * (1 / 1.257)
= $457.91
The cost of a share of e-eyes's new 20/20 preferred stock today is therefore approximately $457.91.