Question

The Market Place recently announced that it will pay its first annual dividend three years from today. The first dividend will be $0.05 a share with that amount quadrupling each year for the following four years. After that, the dividend is expected to increase by 1 percent annually. What is the value of this stock today if the required return is 20 percent?

Group of answer choices

$24.08

$80.84

$7.22

$68.08

$17.01

Answer 1

Year 3 dividend = 0.05

Year 4 dividend = 0.05 * 4 = 0.2

Year 5 dividend = 0.2 * 4 = 0.8

Year 6 dividend = 0.8 * 4 = 3.2

Year 7 dividend = 3.2 * 4 = 12.8

Year 8 dividend = 12.8 (1 + 1%) = 12.928

Value in year 7 = Year 8 dividend / required rate - growth rate

Value in year 7 = 12.928 / 0.2 - 0.01

Value in year 7 = 12.928 / 0.19

Value in year 7 = 68.04211

Value of stock today = Present value of cash inflows

Present value = Future value / (1 + rate)^time

Present value = 0.05 / (1 + 0.2)^3 + 0.2 / (1 + 0.2)^4 + 0.8 / (1 + 0.2)^5 + 3.2 / (1 + 0.2)^6 + 12.8 / (1 + 0.2)^7 + 68.04211 / (1 + 0.2)^7

Present value = 0.02894 + 0.09645 + 0.3215 + 1.07167 + 3.57225 + 18.9893

Present value = $24.08