Question

Sunday Inc. just paid dividends of $2 per share. Assume that dividends will grow as follows, 5% next year, 8% in year two, and 10% in year 3. After that growth is expected to level off to a constant growth rate of 11% per year thereafter. The required rate of return is 15%. 

a. Calculate the present value of the stock. (Po) 

b. What is the value of the stock in Year 2 (P₃) ? 

Answer 1

Assume that current year dividend as D0, next year D1, then D2, D3, and so on.

Similarly, growth rate on dividend be g1=5%, g2=8%, g3=10% and g=11% be the growth rate constant for indefinite period.

Expected rate of return 'r'=15%= 0.15

So,

D0=$2;

D1= D0(1+g1) = 2*(1+0.05) = $2.1

D2= D1(1+g2) = 2.1(1+ 0.08) = $ 2.268

D3= D2(1+g3) = 2.268(1+ 0.10) = $ 2.4948

D4= D3(1+g) = 2.4948(1+0.11) = $ 2.7692

Now valuation of share can be calculated by discoung all the dividends and applying constant dividen growth model-

P0 = (D1/(1+r))+(D2/(1+r)²)+(D3(1+r)³)+(D4/(r-g))

= (2.1/(1+0.15))+(2.268/(1+0.15)²)+(2.4948/(1+0.15)³)+(2.7692/(0.15-0.11))

= $73.0217

Hence, present value of the stock is $73.0217