Question

Fifth National Bank just issued some new preferred stock. The issue will pay an annual dividend of $22 in perpetuity, beginning 11 years from now. If the market requires a return of 3.6 percent on this investment, 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.)

Please provide as many details as possible on formulas and calculations (Excel preferred).Thank you.

Answer 1

The value of the preferred stock as of today would be the present value of all future cash flows.

The discounting rate to be used is 3.6%.

Firstly, we will calculate the discounted value of all cash flows 10 years from today. ()

Then, we will discount this value by 10 years to find the present value of all cash flows today.

Here is a step by step calculation of the value of stock 10 years from today (value being denoted as X)

X = (22/1.036) + (22/1.036^2) + (22/1.036^3) +... + (22/1.036^n)

Taking 1/1.036 common out of the equation

X = (1/1.036)( 22 + (22/1.036) + (22/1.036^2) + (22/1.036^3) +... + (22/1.036^n))

Now note that the underlined part is nothing but X itself

X = (1/1.036)(22 + X)

1.036X = 22 + X

X = 22/0.036 (also written as , denoting value 10 years from today)

$ 611.1111

Value of preferred stock will be $611.11, ten years from today.

To find the present value today

Value = 611.11/(1.036)^10 = $429.06 (also written as , denoting value as of today)

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