A rapidly growing company just paid a dividend of $1.50 a share. For the next three years, the earnings growth rate is projected to be 15% each year, and then 4% each year thereafter. If the required rate of return is 9%, what is the value of the stock

$41.66

Explanation:

Let us assume the dividend in year n be denoted by Dn and the Stock price by Pn

Given that,

D0 = $1.50

Now

Growth rate for next 3 years

g1 = 15%

D1 = D0 × (1 + g1)

    = 1.50 × (1 + 0.15)

   = 1.725

D2 = D1 × (1 + g1)

= 1.725 × (1 + 0.15)

= 1.984

D3 = D2 × (1 + g1)

= 1.984 × (1 + 0.15)

= 2.282

Subsequent Growth rate = g2 = 4%

Now  

D4 = D3 × (1 + g2)

     = 2.282 × (1 + 0.04)

     = 2.373

So, According to Gordon's Growth Rate,

P3 = D4 ÷(r - g2)

P3 = 2.373 ÷ (0.09 - 0.04)

    = $47.46

Now  

Value of Stock now  is

= P0

= D1 ÷ (1 + r) + D2 ÷ (1 + r)^2 + D3 ÷ (1 + r)^3 + P3 ÷ (1 + r )^3

= 1.725 ÷ (1 + 0.09) + 1.984 ÷ (1 + 0.09)^2 + 2.282 ÷ (1 + 0.09)^3 + 47.46 ÷ (1 + 0.09)^3

= $41.66

d. low interest rates