Fifth National Bank just issued some new preferred stock. The issue will pay an annual dividend of $11 in perpetuity, beginning 16 years from now. If the market requires a return of 4.1 percent on this investment, how much does a share of preferred stock cost today?

The cost of the share is the present value of future cash flows which is $146.84

Explanation:

The formula for the total dividends payable in perpetuity is given as

dividends / (return rate - growth rate)

since dividends growth rate is zero the dividends in perpetuity can be written as $11 / (0.041-0) = $268.29 in today's terms

The dividends in perpetuity needs to be discounted to show that the present value today by a way of discounting.

the formula for discounting is given as pv=fv / (1+r) ^n

where fv future value of dividends is $268.29

rate is 4.1%

n is 15 years since dividend payment begins at the commencement of sixteenth year

PV=268.29 / (1+0.041) ^15

PV=$146.84