Question

XYZ Company announced today that it will begin paying annual dividends next year. The first dividend will be $0.1 a share. The following dividends will be $0.1, $0.2, $0.3, and $0.4 a share annually for the following 4 years, respectively. After that, dividends are projected to increase by 2 percent per year. How much are you willing to pay to buy one share of this stock today if your desired rate of return is 8 percent?

Answer 1

Year 1 dividend = 0.1

Year 2 dividend = 0.1

Year 3 dividend = 0.2

Year 4 dividend = 0.3

Year 5 dividend = 0.4

Year 6 dividend = 0.4 (1 + 2%) = 0.408

Value at year 5 = D6 / required rate - growth rate

Value at year 5 = 0.408 / 0.08 - 0.02

Value at year 5 = 0.408 / 0.06

Value at year 5 = 6.8

Price = Present value of cash flows

Price = 0.1 / (1 + 0.08)^1 + 0.1 / (1 + 0.08)^2 + 0.2 / (1 + 0.08)^3 + 0.3 / (1 + 0.08)^4 + 0.4 / (1 + 0.08)^5 + 6.8 / (1 + 0.08)^5

Price = $5.46

You are willin to pay $5.46