Question

The current price of a preferred stock is $100. The preferred stock just paid a dividend of $1,2. The preferred stock pays dividends every quarter and the growth rate of dividends is 3% per quarter.

a) What is the quarterly discount rate to price this preferred stock?

b) What is the annual percentage rate to price this preferred stock?

c) What is the real annual percentage discount rate if the expected rate of inflation is 2,3%?

d) What is the effective annual rate?

e) What is the real effective annual rate?

Answer 1

a). r = [D1/P0] + g

= [($1.2 x 1.03) / $100] + 0.03 = 0.01236 + 0.03 = 0.04236, or 4.236%

b) Annual Rate = Quarterly Rate x 4 = 4.236% x 4 = 16.944%

c) Real Rate = [(1 + nominal rate) / (1 + inflation)] - 1

= [1.16944 / 1.023] - 1 = 1.14315 - 1 = 0.14315, or 14.315%

d). EAR = [1 + (APR/m)]^m - 1

= [1 + 0.04236]⁴ - 1 = 1.18051 - 1 = 0.18051, or 18.051%

e). Real EAR = [1 + (APR/m)]^m - 1

= [1 + (0.14315/4)]⁴ - 1 = 1.15102 - 1 = 0.15102, or 15.102%