Question

XYZ company announced today that it will begin paying annual dividends next year. The first dividend will be $0.12 a share. The following dividends will be $0.15, $0.20, $0.50, and $0.60 a share annually for the following 4 years, respectively. After that, dividends are projected to increase by 5 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

Answer-

XYZ Company

Dividend next year = D1 = $ 0.12
D2 = $ 0.15
D3 = $ 0.20
D4 = $ 0.50
D5 = $ 0.60

The dividends are expected to grow at 5 % / year
g = 5 % = 0.05

Required rate of return = r = 8 % = 0.08
1+r = 1+ 0.08 = 1.08
1+g = 1 + 0.05 = 1.05  

Value of stock today = V0

V0 = D1 / (1+r) + D2 / (1+r)2 + D3 / (1+r)3 + D4 / (1+r)4 + D5 x ( 1+g) / [ (1+r)5 x (r-g) ]

V0 = $ 0.12 / (1.08) + $ 0.15 / (1.08)2 + $ 0.20 / (1.08)3 + $ 0.50 / (1.08)4 + $ 0.60 x 1.05  / [ (1.08)5  x ( 0.08 - 0.05) ]

V0 = $ 0.111 + $ 0.15 / 1.1664 + $ 0.20 / 1.2597 + $ 0.50 / 1.36 + $ 0.63 / 1.469 x 0.03

V0 = $ 0.111 + $ 0.1286 + $ 0.1588 + $ 0.3676 + $ 14.286

V0 = $ 15.052

Therefore the price that one will be willing to pay to buy one share of this stock today = $ 15.052