Question

Your firm has a beta of 1.3, a current stock price of $55, and you just paid a dividend of $1.25. You are considering a new project that would raise your beta to 1.6. If the risk-free rate is 2% and the expected market return is 6%, what growth rate must the new project have to make it feasible?

Answer 1

Given about a stock,

Stock price P0 = $55

Last Dividend paid D0 = $1.25

New beta of the firm = 1.6

Risk free rate Rf = 2%

Expected market return Rm = 6%

So, based on new beta, required return on stock using CAPM is Rf + Beta*(Rm - Rf)

=> rs = 2 + 1.6*(6 - 2) = 8.4%

Using constant dividend growth rate model, stock price is calculated as

P0 = D0*(1+g)/(rs - g)

=> 55 = 1.25*(1+g)/(0.084 - g)

=> 44*(0.084 - g) = 1.25*(1+g)

=> 3.696 - 44g = 1.25 + 1.25g

=> g = (3.696-1.25)/(44+1.25) = 5.41%

So, a growth rate of 5.41% will make new project feasible.