Question

The risk-free rate is 2.89% and the market risk premium is 7.59%. A stock with a β of 1.59 just paid a dividend of $2.55. The dividend is expected to grow at 23.34% for five years and then grow at 3.79% forever. What is the value of the stock?

Answer 1

Given about a stock,

stock's beta = 1.59

Risk free rate Rf = 2.89%

Market risk premium MRP = 7.59%

=> required return on stock using CAPM is

rs = Rf + beta*MRP = 2.89 + 1.59*7.59 = 14.96%

Last dividend paid D0 = $2.55

The dividend is expected to grow at 23.34% for five years

=> D1 = D0*1.2334 = 2.55*1.2334 = $3.1452

D2 = D1*1.2334 = 3.1452*1.2334 = $3.8793

D3 = D2*1.2334 = 3.8793*1.2334 = $4.7847

D4 = D3*1.2334 = 4.7847*1.2334 = $5.9014

D5 = D4*1.2334 = 5.9014*1.2334 = $7.2788

thereafter growth rate g = 3.79%

So, stock price at year 5 using constant dividend growth rate is

P5 = D5*(1+g)/(rs-g) = 7.2788*1.0379/(0.1496-0.0379) = $67.6451

So, stock price today is sum of PV of future dividends and P5 discounted at rs

=> P0 = D1/(1+rs) + D2/(1+rs)^2 + D3/(1+rs)^3 + D4/(1+rs)^4 + D5/(1+rs)^5 + P5/(1+rs)^5

=> P0 = 3.1452/1.1496 + 3.8793/1.1496^2 + 4.7847/1.1496^3 + 5.9014/1.1496^4 + 7.2788/1.1496^5 + 67.6451/1.1496^5

=> P0 = $49.52

value of the stock is $49.52