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 $10.00 in perpetuity, beginning exactly one quarter from now. If the market requires an annual return of 14.00 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 $285.71 How much would a share of preferred stock cost today if the dividends begin exactly 4 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 $62.65

Solution

a) annual return , r = 14% = 0.14

quarterly return required , i = r/4 = 0.14/4 = 0.035

constant quarterly dividend , d = $10

cost of 1 preferred share today, p0 = d/i = 10/0.035 = $285.71428 or $285.71 ( rounding off to 2 decimal places)

b)

no. of quarters in 4 years = no. of years *4 = 4*4 = 16

if 1st dividend is receved four years from now , p0 will be the cost after 15 quarters

cost of preferred share today = p0/(1+i)¹⁵ = 285.71428/(1.035)¹⁵ = $170.540176 or $170.54 ( rounding off to 2 decimal places)