Question

CX Enterprises has the following expected​ dividends:

$ 1.01$1.01

in one​ year,

$ 1.25$1.25

in two​ years, and

$ 1.34$1.34

in three years. After​ that, its dividends are expected to grow at

3.9 %3.9%

per year forever​ (so that year​ 4's dividend will be

3.9 %3.9%

more than

$ 1.34$1.34

and so​ on). If​ CX's equity cost of capital is

12.2 %12.2%​,

what is the current price of its​ stock?

Answer 1

g = growth rate = 3.9%

r = cost of capital = 12.2%

D1 = Dividend in 1 year = $1.01

D2 = Dividend in 2 years = $1.25

D3 = Dividend in 3 years = $1.34

D4 = Dividend in 4 years = D3 * (1+g) = $1.34 * (1+3.9%) = $1.39226

Horizon Value in Year 3 = D4 / (r-g)

= $1.39226 / (12.2%-3.9%)

= $1.39226 / 8.3%

= $16.7742169

Current Price of stock = Present Value of Future dividends

= [D1 / (1+r)^1] + [D2 / (1+r)^2] + [D3 / (1+r)^3] + [Horizon Value / (1+r)^3]

= [$1.01 / (1+12.2%)^1] + [$1.25 / (1+12.2%)^2] + [$1.34 / (1+12.2%)^3] + [$16.7742169 / (1+12.2%)^3]

= [$1.01 / 1.122] + [$1.25 / 1.258884] + [$1.34 / 1.41246785] + [$16.7742169 / 1.41246785]

= $0.900178253 + $0.992942956 + $0.94869416 + $11.8758221

= $14.7176375

Therefore, Current price of stock is $14.72