Assuming Google\'s common stock just paid its annual dividend of $1.8 par value.

Question

Assuming Google's common stock just paid its annual dividend of $1.8 par value. The required return on the common stock is 12%. Estimate the value of common stock under each of the following assumptions about the dividend:

A. Dividends are expected to grow at an annual rate of 0% to infinity.

B. Dividends are expected to grow at a constant rate of 5% to infinity.

C. Dividends are supposed to grow at a contant annual rate of 5% for each of the next 3 years, followed by a constant growth rate of 4% in years 4 to maturity.

D. Dividends are supposed to grow at an annual rate of 15%, 12%, 10%, 8% for each of the next 4 years respectively, then grow at a constant rate of 5% in years 5 to maturity.

Explanation / Answer

From DDM

P = D(0)*(1+g)/(r-g)

A) g = 0%

P = 1.8/(0.12) = $15

B) g = 5%

P = 1.8*1.05/(0.12-0.05) = $27

C) P = 1.8/1.12 + 1.8*1.05/1.12^2 + 1.8*1.05^2/1.12^3 +P(3)

= 1.8/1.12 + 1.8*1.05/1.12^2 + 1.8*1.05^2/1.12^3 + 1.8*1.05^2*1.04/[ (0.12-0.04)*1.12^3 ] = $22.89

D)P = (1.8*1.15)/1.12 + (1.8*1.15*1.12)/1.12^2 + (1.8*1.15*1.12*1.1)/1.12^3 + (1.8*1.15*1.12*1.1*1.08)/1.12^4 + (1.8*1.15*1.12*1.1*1.08)*1.05/( (0.12-0.05)*1.12^4)

P = $35.71

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