The growth in dividends of Music Doctors,Inc.is expected to be 8%/year for the next two years,followed by a growth rate of 4%/year for three years; after this five year period,the growth in dividends is expected to be 3%/year,indefinitely.The required rate of return on Music Doctors,Inc.is 11%.Last year's dividends per share were $2.75.What should the stock sell for today?
A)$8.99
B)$25.21
C)$39.71
D)$110.00
E)none of the above

Question

Quizplus · Accepted Answer

We need to use the dividend discount model to find the stock price today:
P0 = D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D5/(1+r)^5 + D6/(r-g)

D0 = $2.75
g1 = 8%
g2 = 4%
g3-∞ = 3%
r = 11%

D1 = D0*(1+g1) = $2.75*(1+0.08) = $2.97
D2 = D1*(1+g2) = $2.97*(1+0.04) = $3.09
D3 = D2*(1+g2) = $3.09*(1+0.04) = $3.21
D4 = D3*(1+g2) = $3.21*(1+0.04) = $3.34
D5 = D4*(1+g2) = $3.34*(1+0.04) = $3.47
D6 = D5*(1+g3)/(r-g3) = $3.47*(1+0.03)/(0.11-0.03) = $44.71

P0 = $2.97/(1+0.11)^1 + $3.09/(1+0.11)^2 + $3.21/(1+0.11)^3 + $3.34/(1+0.11)^4 + $3.47/(1+0.11)^5 + $44.71/(0.11-0.03)/(1+0.11)^5
P0 = $39.71

Therefore, the stock should sell for $39.71 today, which is option C.

The Growth in Dividends of Music Doctors,Inc