Question

Stock ABC is trading at $50 per share. The stock has an expected year-end dividend of $5 (i.e., D1=$5), which is expected to grow at a constant rate throughout time (g). The stock’s return has a covariance with the market portfolio return of 0.06. The standard deviation of the market portfolio is 0.2. The risk free rate is 6%, and the market risk premium is 8%. If you believe that the stock is efficiently priced, what would be your forecast of the growth rate in dividends (g)?

please show all the fraction number and be easy to follow the steps

Answer 1

first we need to calculate required return on the stock.

required return = risk-free rate + beta*market risk premium

beta = covariance with the market portfolio return/variance of the market portfolio

variance of the market portfolio = standard deviation of the market portfolio² = 0.2² = 0.04

beta = 0.06/0.04 = 1.5

required return = 6% + 1.5*8% = 6% + 12% = 18%

current price per share = expected dividend/(required return - dividend growth rate)

$50 = $5/(0.18 - dividend growth rate)

$50*(0.18 - dividend growth rate) = $5

(0.18 - dividend growth rate) = $5/$50

(0.18 - dividend growth rate) = 0.10

0.18 = 0.10 + dividend growth rate

dividend growth rate = 0.18 - 0.10 = 0.08 or 8%

your forecast of the growth rate in dividends (g) would be 8%.