EEyescom just issued some new preferred stock The issue will

E-Eyes.com just issued some new preferred stock. The issue will pay a constant quarterly dividend of $8.00 in perpetuity, beginning exactly one quarter from now. If the market requires an annual return of 11.00 percent with quarterly compounding, how much does a share of preferred stock cost today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Stock price $ 290.91

How much would a share of preferred stock cost today if the dividends begin exactly 10 years from now instead of next quarter? Don\'t forget that the PV formula for a perpetuity assumes the first payment is at the end of the first period. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Stock price $ .

Solution

1) Quarterly dividend (D) = $8

Quarterly return (r) = 11% / 4 = 2.75%

Preferred stock price today = D / r = $8 / 2.75% = $290.90909090909 or $290.91

2) The price above calculated is price at quarter just before next dividend quarter.. So, we need to find the its present value today. Present value of an amount can be computed as -

PV = Amount / (1 + r)ⁿ

where, r is the quarterly return, n being no. of quarters

r = 2.75% or 0.0275, n = 10*4 - 1 = 39 [ -1 because payment starts at 10 years and price above computed is one period before that ]

Stock price = $290.90909090909 / (1 + 0.0275)³⁹ = $100.98710019 or $100.99