A preferred stock pays a dividend of $3.50 in perpetuity. If the return required by shareholders is 11%, what is the price per share for this preferred stock?

Question

BlackTom AI · Accepted Answer

To value a preferred stock that pays a perpetual dividend, use the formula Price = Dividend / Required return.
Option by option, consider the given annual dividend of $3.50 and a cost of capital (required return) of 11% (0.11).

Option "$35.08": If the price were $35.08, the implied yield would be 3.50 / 35.08 ≈ 0.0999, or about 9.99%. This is far below the given 11% requirement, so this price is inconsistent with the given return.

Option "$31.82": If the price is $31.82, the implied yield is 3.50 / 31.82 ≈ 0.1100, i.e., 11.00%. This matches the stated required return exactly, which aligns with the perpetual dividend model for preferred stock.

Option "$38.50": With a price of $38.50, the yield would be 3.50 / 38.50 ≈ 0.0909, or about 9.09%. This is not equal to the required 11%, so this price does not satisfy the given condition.

Option "$41.21": A price of $41.21 yields 3.50 / 41.21 ≈ 0.0849, i.e., roughly 8.49%. Again, this is not the 11% required return.

Option "none of these": Since a price that yields 11% exists under the perpetual dividend model (specifically $3.50 / 0.11), this option is not consistent with the calculation.

MSB-250-300-002 Topic 7 Quiz

A preferred stock pays a dividend of $3.50 in perpetuity. If the return required by shareholders is 11%, what is the price per share for this preferred stock?

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