Question

The Oxford Heating Company has been very successful in the past four years. Over these years, it paid common stock dividends of $4.2 in the first year, $4.20 in the second year, $4.41 in the third year, and its most recent dividend was $4.9. The company wishes to continue this dividend growth indefinitely. What is the value of the company's stock if the required rate of return is 10 percent?

a. $61.32
b. $67.45
c. $78.63
d. $84.47

Answer 1

Using the Gordon Growth Model and the historical dividend growth, the calculated stock value of Oxford Heating Company is approximately $109.25, which does not match any of the provided options. This suggests an error in the calculation or the provided answer choices.

Step-by-step explanation:

To find the value of the Oxford Heating Company's stock with a dividend growth pattern and a required rate of return, we can use the Gordon Growth Model. This model assumes that dividends will continue to grow at a consistent rate indefinitely. Using the formula Stock Value = D1 / (r - g), where D1 is the expected dividend next year, r is the required rate of return, and g is the growth rate of dividends.

The growth rate can be calculated based on the historical dividend growth: from $4.2 to $4.20 is a 0% increase, from $4.20 to $4.41 is about 5% increase, and from $4.41 to $4.9 is about an 11.11% increase. Averaging these gives a growth rate (g) of approximately (0% + 5% + 11.11%) / 3 = 5.37% (Note: This is a simplified approximation).

The next expected dividend D1 is $4.9 * (1 + 5.37%) = $5.16 approximately.

The required rate of return (r) is 10% or 0.10.

Using the Gordon Growth Model, Stock Value = $5.16 / (0.10 - 0.0537) = $109.25 approximately.

The closest answer to $109.25, from the provided options, is not listed, indicating a possible error in the calculation or in the options provided.