Question

6. A firm paid a dividend of $2 per share yesterday. You expect that dividends will grow by 8% next year, 6% the second year, and the grow at a constant rate of 2%. The return on the market portfolio is 8%, the risk-free rate is 2%, and the firm has a Beta of .8. What is the value of the stock today?

Answer 1

=> First we have to find the required rate of return or discount rate

* According to CAPM model:

, where r is the discount rate, is the risk free rate(2%) , is the Beta(0.8) and is the market portfolio return(8%)

* Plug these values into the formula to find the discount rate

* Therefore the discount rate = 6.8%

=> Now we can find the value of the stock

* It is given that D0 = $2 per share (D0 is dividend in this year) and growth rate in next year is 8% and growth rate in 2nd year is 6%. we can use this to find the D1 and D2

* D1 = D0(1+g1) = 2(1+0.08) = 2.16

* D2 = D1(1+g2) = 2.16(1+0.06)=2.2896

=> It is given that from year 3 onwards dividend grows at constant rate of 2%, we can use Gordon's dividend growth model to find the value of stock in year 2 (P2)

* Gordon's dividend growth model:

, where D2 is dividend in the 2nd year(2.2896), g is the growth rate(2%) and r is the discount rate(6.8%)

* Plug the values into the formula

=> Now we have to find the sum of the present values of D1,D2 and P2 to find the value of stock today

=> Therefore the value of the stock today is $ 46.6854