Question

1. Your company just paid a dividend of $4.0 per share. The company will increase its dividend by 5% next year and will then increase its dividend growth rate by 2% points per year ( from 5% to 7% to 9% to 11%) until it reaches the industry average of 11% dividend growth, after which the company will keep a constant growth rate forever. The required return on your company’s stock is 13.08%. What will a share of stock sell for today? ____(44)_____. What will a share of stock sell for in one year?_____(45)____.

Answer 1

Answer-

D0 = $ 4 /share
D1= $ 4 X 1.05 = $ 4.2 / share [ Growt of 5 % = ( 1+5% ) = (1+0.05) = 1.05 ]
D2 = $ 4.2 x 1.07 = $ 4.494 / share
D3 = $ 4.494 x 1.09 = $ 4.8985 / share
D4 = $ 4.8985 x 1.11 = $ 5.437 / share

Constant growth of 11 % in perpetuity. = g = 11 % = 0.11

Given

required return on stock = r = 13.08 % = 0.1308

Value of stock today (V0) = D1 / ( 1+r) + D2 / (1+r)2  + D3 / (1+r)3 + D4 x (1+ g) / [ (1+r)4 x (r - g) ]

1+r = 1 +0.1308 = 1.1308

V0 = $ 4.2 / ( 1.1308) + $ 4.494 / ( 1.1308)2 + $ 4.8985 / ( 1.1308)3 + $ 5.437 x ( 1.11) / [ ( 1.1308)4 x ( 0.1308 - 0.11)

V0 =  $ 4.2 / ( 1.1308) + $ 4.494 / ( 1.2787) + $ 4.8985 / (1.446) + $ 6.035 / [ ( 1.635) x ( 0.0208) ]

V0 = $ 3.714 + $ 3.5145 + $ 3.388 + $ 177.5

V0 = $ 188.12

Therefore share or stock price today = $ 188.12

Share of stock one year later =

V1 = (D1 + V0) x ( 1+r)

V1= ($ 4.2 + $ 188.12) x ( 1.1308 )

V1= $ 192.32 x 1.1308
V1 = $ 217.47

Therefore price of share or stock in one year = $ 217.47