Question

The risk-free rate is 2.69% and the market risk premium is 8.23%. A stock with a...

The risk-free rate is 2.69% and the market risk premium is 8.23%. A stock with a β of 1.29 just paid a dividend of \$2.04. The dividend is expected to grow at 24.18% for three years and then grow at 4.18% forever. What is the value of the stock?

Calculation of required rate of return (Ke ):

Risk free rate (Rf) = 2.69%

Beta = 1.29

=2.69%+1.29*8.23%

=2.69%+10.62%

=13.31%

D1 = D0*(1+growth rate) = 2.04*1.2418=2.533

D2 = D1*(1+growth rate) = 2.533*1.2418= 3.145

D3 = D2*(1+growth rate) = 3.145*1.2418= 3.906

D4 = D3*(1+growth rate) = 3.906*1.0418 = 4.069 (from 4th year growth rate changes to 4.18%)

P3 = D4/ke-g

= 4.069/13.31%-4.18%

=4.069/9.13%

=44.57

Calculation of Value of the stock:

 Particulars Cash flows (1) Discounting factor @13.31% (2) Discounted Cash flows (3) (1*2) D1 2.533 1/1.1331=0.8825 2.235 D2 3.145 1/1.1331*1/1.1331= 0.7788 2.449 D3 3.906 1/1.1331*1/1.1331*1/1.1331= 0.6873 2.684 P3 44.57 1/1.1331*1/1.1331*1/1.1331=0.6873 30.633 Value of the stock 38.001

Value of the stock = 38.001