The growth in dividends of Music Doctors, Inc.is expected to be 8% per year for the next two years, followed by a growth rate of 4% per year for three years.After this five-year period, the growth in dividends is expected to be 3% per 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?

Question

Quizplus · Accepted Answer

Step 1: Calculate the dividends for the next 5 years.

D1 = D0(1+g1) = $2.75(1+0.08) = $2.97
D2 = D1(1+g1) = $2.97(1+0.08) = $3.21
D3 = D2(1+g2) = $3.21(1+0.04) = $3.33
D4 = D3(1+g2) = $3.33(1+0.04) = $3.46
D5 = D4(1+g2) = $3.46(1+0.04) = $3.60

Step 2: Calculate the terminal value of the stock price.

P6 = D6 / (r-g) = $3.60 / (0.11-0.03) = $45.00

Step 3: Discount the future dividends and the terminal value back to the present.

P0 = D1 / (1+r) + D2 / (1+r)^2 + D3 / (1+r)^3 + D4 / (1+r)^4 + D5 / (1+r)^5 + P6 / (1+r)^5
   = $2.97 / (1+0.11) + $3.21 / (1+0.11)^2 + $3.33 / (1+0.11)^3 + $3.46 / (1+0.11)^4 + $3.60 / (1+0.11)^5 + $45.00 / (1+0.11)^5
   = $1.99 + $2.00 + $1.86 + $1.73 + $1.61 + $23.51
   = $32.70

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

The Growth in Dividends of Music Doctors, Inc