Question

1. A $50 par value preferred stock pays a quarterly dividend of $.50 and you require a return of 6% on this investment based on the risk you are taking.
   1. If the stock is perpetual, what is the value of this stock?
   2. If the stock is required to be retired after 10 more years, what is the value of this stock?
   3. Why is the perpetual stock that pays dividends forever worth less than the stock that gets retired in 10 years?

Answer 1

a) The value of Perpetual stock = D1/(Required rate/4) = 0.5/(6%/4) = 33.33

b) if stock is retired after 10 years
Rate = 6%/4 = 1.5%,
Number of periods = 4*10 = 40
Price of Stock = D1*(1-(1+r)^-n)/r +Par Value/(1+r)ⁿ  = 0.5*(1-(1+1.5%)^-40)/40 + 0.5/(1+1.5%)⁴⁰ = 42.52

c) The price of perpetual stock is less because the par value of 50 is never realized where as finite life stock pays par value of 50.

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