Suppose D0 is $5.70, R is 10%, and g is 5%. What is the price per share today?
Question
Suppose D0 is $5.70, R is 10%, and g is 5%. What is the price per share today?
Solution
To calculate the price per share today, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:
P0 = D0 * (1 + g) / (R - g)
where: P0 = price per share today D0 = most recent dividend = $5.70 R = required rate of return = 10% = 0.10 g = growth rate of dividends = 5% = 0.05
Substituting the given values into the formula, we get:
P0 = $5.70 * (1 + 0.05) / (0.10 - 0.05)
Now, let's calculate it step by step:
- Calculate (1 + g): 1 + 0.05 = 1.05
- Multiply D0 by (1 + g): 5.985
- Subtract g from R: 0.10 - 0.05 = 0.05
- Finally, divide the result from step 2 by the result from step 3: 119.70
So, the price per share today is $119.70.
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