Final answer:
Using the Gordon Growth Model and the given stock price of $54.20, market rate of return of 11%, and dividend growth rate of 6%, the expected next dividend for Singer Machines' common stock is calculated to be $2.71.
Step-by-step explanation:
The student's question involves calculating the expected amount of the next dividend for a common stock of Singer Machines. Given that the stock pays an annual dividend expected to increase by 6% annually, has a market rate of return of 11%, and currently sells for $54.20 a share, we can use the Gordon Growth Model (also known as the Dividend Discount Model) to find the expected dividend. According to the Gordon Growth Model, the price of a stock is equal to the next year's dividend divided by the difference between the required rate of return (market rate of return) and the growth rate of dividends.
The formula can be rearranged to solve for the expected dividend (D1):
P = D1 / (r - g)
Where:
- P is the current stock price ($54.20)
- D1 is the next year's expected dividend
- r is the required rate of return (11% or 0.11)
- g is the growth rate of the dividend (6% or 0.06)
By rearranging the equation, we get:
D1 = P * (r - g)
Now we calculate the expected dividend (D1):
D1 = $54.20 * (0.11 - 0.06) = $54.20 * 0.05 = $2.71
Therefore, the expected amount of the next dividend is $2.71, which corresponds to option C.