Purcell Corporation has preference shares with an annual dividend of $2.91. If the required return on Purcell's preference shares is 7.7%, what is its price? (Hint: For a preference share, the dividend growth rate is zero.)
Question
Purcell Corporation has preference shares with an annual dividend of $2.91. If the required return on Purcell's preference shares is 7.7%, what is its price? (Hint: For a preference share, the dividend growth rate is zero.)
Solution
To calculate the price of the preference shares, we can use the formula for the price of a perpetuity, since preference shares have a fixed dividend and no growth rate. The formula is:
Price = Dividend / Required Return
Given in the problem, the Dividend (D) is $2.91 and the Required Return (r) is 7.7% or 0.077 in decimal form.
Substituting these values into the formula, we get:
Price = $2.91 / 0.077
Now, perform the division to find the price:
Price = $37.79
So, the price of Purcell Corporation's preference shares is approximately $37.79.
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