Question

The stock price of Jenkins Co. is $60. Investors require a 11.50 percent rate of return on similar stocks. Required: If the company plans to pay a dividend of $3.50 next year, what growth rate is expected for the company’s stock price? (Select rounded answers as directed, but do not use the rounded numbers in intermediate calculations.)

multiple choice
a) 6.24%
b) 5.10%
c) 17.33%
d) 5.67%
e) 5.83%

Answer 1

To find the growth rate expected for the company's stock price, we can use the Gordon Growth Model. The expected growth rate is approximately 5.83%.

Step-by-step explanation:

To find the growth rate expected for the company's stock price, we can use the Gordon Growth Model. This model states that the expected stock price growth rate is equal to the dividend per share divided by the required rate of return minus the growth rate. In this case, the dividend per share is $3.50 and the required rate of return is 11.50 percent. Let's solve the equation:

Growth rate = Dividend / (Required rate of return - Growth rate)

Substituting the given values, we get:

Growth rate = $3.50 / (11.50% - Growth rate)

Multiplying both sides of the equation by (11.50% - Growth rate), we get:

Growth rate * (11.50% - Growth rate) = $3.50

Expanding the equation, we have:

Growth rate * 11.50% - Growth rate^2 = $3.50

1. Rearrange the equation to a quadratic equation:
2. Growth rate^2 - 11.50% * Growth rate + $3.50 = 0
3. Use the quadratic formula to solve for Growth rate:
4. Growth rate = (-(-11.50%) ± √((-11.50%)^2 - 4 * 1 * $3.50)) / (2 * 1)
5. Growth rate ≈ 5.83% or Growth rate ≈ -6.24%
6. Since negative growth rate does not make sense in this context, we can conclude that the expected growth rate for the company's stock price is approximately 5.83%