Question

Google has paid $2 in dividends one year ago and this year has just paid $4 yesterday. In the next three years the dividends are expected to be $1, $5, and $4 at the end of year three. From there on, the dividend will grow with a yearly growth rate g. What is this implied growth rate that shareholders expect if the stock price today is $40? (The required rate of return for this stock is 10%.)

Answer 1

Required Rate of Return (ke) = 10%

Expected Dividend at the end of Year 1 (D1) = $ 1

Expected Dividend at the end of Year 2 (D2) = $ 5

Expected Dividend at the end of Year 3 (D3) = $ 4

Dividends will grow at a Constant Rate 'g' from Year 4

Price of Stock (Po) = $ 40

Price of Stock (Po) = Present Value of (D1,D2,D3, P3)

where P3 is the Price of the Stock immediately after receiving D3

Price of Stock (Po) = ($ 1 * 0.9091) + ($5 * 0.8264) + ($ 4* 0.7513) + (P3 * 0.751)

$ 40 = $ 8.0466 + (P3 * 0.751)

(P3 * 0.751) = $ 31.9534

P3 = $ 42.53

Price of a Share if dividends are growing at Constant Rate,

Pn = Dn (1+g) / (Ke - g)

P3 = D3 (1+g) / (Ke - g)

$ 42.53 = $4 (1+g) / (0.10 - g)

$ 10.63 (0.10 -g) = 1 + g

1.063 - 10.63 g = 1 + g

11.63 g = 0.063

Therefore, Implied growth Rate (g) = 5.4 % (approx)

Year	PVF @ 10%	Computation
1	0.909091	(1.1)^(-1)
2	0.826446	(1.1)^(-2)
3	0.751315	(1.1)^(-3)