Question

The brown company just announced that it will be increasing its annual dividend to $1.68 next year and that future dividends will be increased by 2.5% annually. how much would you be willing to pay for one share of the brown company stock if you require a 12% rate of return?

a. $14.35
b. $14.63
c. $17.68
d. $18.13
e. $19.81

Answer 1

Using the Gordon Growth Model, the price one would be willing to pay for a share of The Brown Company, considering the projected growth rate of dividends and required 12% rate of return, is $17.68.

Step-by-step explanation:

The question asks us to determine the price one would be willing to pay for a share of The Brown Company stock based on a required rate of return and the future dividends announced by the company. To find this price, we can use the Gordon Growth Model which assumes that dividends will increase at a constant rate infinitely. The model formula is P = D1 / (k - g), where P is price, D1 is the dividend next year, k is the required rate of return, and g is the growth rate.

In this case, the dividend next year (D1) is $1.68, the required rate of return (k) is 12% or 0.12, and the growth rate of dividends (g) is 2.5% or 0.025. Plugging the numbers into the formula gives us: P = $1.68 / (0.12 - 0.025) = $1.68 / 0.095 = $17.68. Therefore, the price one would be willing to pay per share if they require a 12% rate of return is $17.68.