Final answer:
To calculate the value of a Gamma Corporation share with a dividend growth from $0.90 to $1.20 over 7 years and a required return of 20%, we use the Gordon Growth Model. The stock value is found by calculating the expected dividend using the growth rate and then applying the formula Stock Value = D1 / (k - g). The calculated share value is approximately $7.81.
Step-by-step explanation:
The question asks for the calculation of the value of a share of Gamma Corporation common stock given a specific dividend growth rate and a required rate of return. To calculate this, we'll need to use the Gordon Growth Model (also known as the Dividend Discount Model), which requires the current dividend amount (D0), the growth rate of the dividends, and the required rate of return.
First, calculate the growth rate of the dividends from $0.90 to $1.20 over 7 years using the formula for compound annual growth rate (CAGR):
Growth Rate = [(D1/D0)^(1/n)] - 1
Where D1 is the latest dividend, D0 is the dividend 7 years ago, and n is the number of years. Plugging in our values gives us a growth rate of approximately 4.1%.
Next, we use the Gordon Growth Model formula:
Stock Value = D1 / (k - g)
Where D1 is the dividend expected at the end of the next period (which is $1.20 growing at 4.1%), k is the required rate of return (20%), and g is the growth rate of the dividends (4.1%). The expected dividend D1 thus is $1.20 * (1 + 4.1%) = $1.2492. Using these values, the stock value is calculated to be approximately $1.2492 / (0.20 - 0.041) = $7.81.
Therefore, a share of Gamma Corporation common stock is worth approximately $7.81 to an investor requiring a 20 percent return on her investment, based on the given growth rate and dividends.