Question

Mobray Corp. is experiencing rapid growth. Dividends are expected to grow at 30 percent per year during the next three years, 20 percent over the following year, and then 5 percent per year indefinitely. The required return on this stock is 11 percent, and the stock currently sells for $60 per share. What is the projected dividend for the coming year?

Answer 1

Given

P0= price of the share today = $60

Required rate (r)= 11% = 0.11

Perpetual growth rate g = 5% =0.05

Let D0 be the dividend today and D1 be the dividend next year, D2 the dividend after 2 years and so on

D1= D0*1.3 ,

D2 = D1*1.3

D3= D2*1.3 = D1*1.3^2

D4 = D3*1.2 =D1*1.3^2 *1.2

D5 = D4*1.05 =D1*1.3^2 *1.2*1.05

The Horizon value at the end of 4 years (when the constant perpetual growth of 5% starts) H4 is given by

H4  = D5/(r-g) = D1*1.3^2 *1.2 *1.05 / (0.11-0.05) = 35.49*D1

As the share price today is equal to the present value of all future dividends

P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3+ D4/(1+r)^4 + ( D5/(1+r)^5.+ ...

=D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3+ D4/(1+r)^4 + H4/(1+r)^4

=D1/1.11 + 1.3*D1/1.11^2 + 1.69*D1/1.11^3+ 2.028*D1/1.11^4 + 35.49*D1/1.11^4

=> 60 = 27.90599 * D1    

=> D1= $2.15

So, the projected dividend for the coming year is $2.15