What is the value of one share (to the nearest cent) if the last dividend you received was $0.38 and investors require 9.0% return on these shares? The dividends are expected to continue to grow at 1.4% forever. (Please round your answer to the nearest cent but exclude the $ sign when typing your answer.)
Question
What is the value of one share (to the nearest cent) if the last dividend you received was sign when typing your answer.)
Solution
The value of a share of stock can be calculated using the Gordon Growth Model, which is a version of the dividend discount model that assumes dividends grow at a constant rate. The formula is:
Stock Value = D1 / (r - g)
where: D1 is the dividend expected next year, r is the required rate of return, and g is the growth rate of dividends.
Here's how to calculate it:
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First, calculate D1, the dividend expected next year. This is the last dividend received grown by the growth rate. In this case, it's 0.38532.
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Next, subtract the growth rate from the required rate of return. In this case, it's 0.09 - 0.014 = 0.076.
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Finally, divide D1 by this difference to get the stock value. In this case, it's 5.07.
So, the value of one share is $5.07.
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