The dividend-growth model may be used to value a stock: V = D 0 (1+g) / k-g a.Wh

Question

The dividend-growth model may be used to value a stock:

V = D0(1+g) / k-g
a.What is the value of a stock if:
D0 = $2
k = 10%
g = 6%

b. What is the value of this stock if the dividend is increased to$3 and the other variables
remain constant?
c. What is the value of this stock if the required return declinesto 7.5 percent and the
other variables remain constant?
d. What is the value of this stock if the growth rate declines to 4percent and the other
variables remain constant?
e. What is the value of this stock if the dividend is increased to$2.30, the growth rate
declines to 4 percent, and the required return remains 10 percent?

Explanation / Answer

(a) Calculating theStock value (V): Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2(1+0.06) / (0.10 -0.06) Stock Value (V) = $2.12 / 0.04 Stock Value (V) =$53 (b) Calculating the Value ofthe Stock, if the dividend is increased to$3: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $3(1+0.06) / (0.10 -0.06) Stock Value (V) = $3.18 / 0.04 Stock Value (V) =$79.50 (c ) Calculating Value of theStock, if the Required Rturn declines to7.5%: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2(1+0.06) / (0.075 -0.06) Stock Value (V) = $2.12) /0.015) Stock Value (V) =$141.33 (d) Calculating Value of theStock, if the growth rate declines to 4%: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2(1+0.04) / (0.10 -0.04) Stock Value (V) = $2.08/ 0.06 Stock Value (V) =$34.67 (e) Calculating Stock Value, ifthe dividend is increase to $2.30, growth rate declines to 4% andthe required return remains 10%: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2.30 (1+0.04) / (0.10 -0.04) Stock Value (V) = $2.39 / 0.06 Stock Value (V) =$39.87 (a) Calculating theStock value (V): Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2(1+0.06) / (0.10 -0.06) Stock Value (V) = $2.12 / 0.04 Stock Value (V) =$53 (b) Calculating the Value ofthe Stock, if the dividend is increased to$3: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $3(1+0.06) / (0.10 -0.06) Stock Value (V) = $3.18 / 0.04 Stock Value (V) =$79.50 (c ) Calculating Value of theStock, if the Required Rturn declines to7.5%: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2(1+0.06) / (0.075 -0.06) Stock Value (V) = $2.12) /0.015) Stock Value (V) =$141.33 (d) Calculating Value of theStock, if the growth rate declines to 4%: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2(1+0.04) / (0.10 -0.04) Stock Value (V) = $2.08/ 0.06 Stock Value (V) =$34.67 (e) Calculating Stock Value, ifthe dividend is increase to $2.30, growth rate declines to 4% andthe required return remains 10%: Stock Value (V)   =  D0 (1+g) / (k-g) Stock Value (V) = $2.30 (1+0.04) / (0.10 -0.04) Stock Value (V) = $2.39 / 0.06 Stock Value (V) =$39.87

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