Question

ABC Company just paid out a dividend of $2 and expects this dividend to grow indefinitely at a rate of g% per year. ABC has 100,000 shares outstanding with a current market price of $26 per share. ABC’s beta is 1.5, the return on the market is 9%, and the risk-free rate is 3%. Calculate the growth rate “g” so that the market is in equilibrium  (i.e., the CAPM-based return on ABC shares equals the Dividend-Growth-Model based return).

Answer 1

Solution-

Beta = 1.5

Market return (Rm)= 9%

Risk free rate (Rf) = 3%

Required rate of return (ke)= Rf+beta*(Rm - Rf)

Ke = 3 + 1.5*(9-3)= 12%

Required rate of return (ke) = 12%

Current market price (P0) = $26

Dividend paid (D0) =$2

Growth rate (g) =?

Ke = [D0(1+g)/P0]+g

0.12 = [2(1+g)/26]+g

0.12*26 = 2 + 2g + 26g

3.12 - 2= 28g

1.12=28g

g= 1.12/28= 0.04

Growth rate (g) = 4%