Question

Company X has a beta of 1.08, the risk-free rate of interest is currently 2.5%, and the expected return on the market portfolio is 7.5%. The company plans to pay a dividend of $2.73 per share in the coming year and anticipates that its future dividends will increase at a constant annual rate consistent with that experienced over the 2017-2019 period shown below.

Year	Dividend
2017	2.35
2018	2.45
2019	2.60

a.  Determine the required return for this stock using the Capital Asset Pricing Model (CAPM).

b.  Calculate the compounding growth rate of the dividends from 2017 to 2019 (N=2 years) for Company X using the recent dividends, shown in the table above.

c.  Estimate the value of Company X's stock using the answers provided in parts a. and b., and the dividend constant growth model.

Answer 1

Solution:

a)Calculation of required rate of return(Ke) using CAPM

Ke=Risk free rate+Beta(Market rate of return-Risk free rate)

=2.5%+1.08*(7.5%-2.5%)

=2.5%+5.4%=7.90%

Thus,required return for stock using the Capital Asset Pricing Model (CAPM) is 7.90%

b)Calculation of growth rate

Growth rate=[(Present value/Past value)^1/no. of years]-1

=[(2.60/2.35)^1/2]-1

=0.0518 or 5.18%

Thus,compounding growth rate of the dividends from 2017 to 2019 is 5.18%

c)Calculation of value of Company X's stock(P0) using constant growth model.

P0=Expected dividend/Required rate of return-Growth rate

=$2.73/(7.90%-5.18%)

=$100.37

Thus,value of Company X's stock(P0) using constant growth model is $100.37.