Question

The risk-free rate is 1.31% and the market risk premium is 5.68%. A stock with a β of 1.65 just paid a dividend of $1.29. The dividend is expected to grow at 20.18% for five years and then grow at 3.97% forever. What is the value of the stock?

Answer 1

Solution:
	the value of the stock   $38.47
Working Notes:
	D1 = D0 x (1+g)^1 = $1.29 x (1+.2018)^1 = $1.550322
	D2 = D0 x (1+g)^2 = $1.29 x (1+.2018)^2 = $1.86317698
	D3 = D0 x (1+g)^3 = $1.29 x (1+.2018)^3 = $2.239166094
	D4 = D0 x (1+g)^4 = $1.29 x (1+.2018)^4 = $2.691029812
	D5 = D0 x (1+g)^5 = $1.29 x (1+.2018)^5 = $3.234079628
	D6 = D0 x (1+g)^5 x (1 +g1) = $1.29 x (1 + 0.0397) x(1+.2018)^5 = $ 3.362472589
	Price at the end of 5th year
	r= cost of capital = Ke is calculated using CAPM
	r = rf + (rm-rf) x B
	r = Required return of stock =??
	B= Beta of the stock =1.65
	rf= risk free rate = 1.31 %
	(rm - rf) = market risk premium = 5.68%
	r = rf + (rm-rf) x B
	r= 1.31% + 5.68% x 1.65
	r =10.682%
	As per constant growth model
	P5 = D6/(r -constant growth rate)
	P5= $ 3.362472589 /(0.10682 -0.0397)
	P5=$50.09643309
	Now
	Current price of the stock
		A	B	C=A x B
Details	Year	Cash Flow	PVF @10.682%	Present value
D1	1	1.550322	0.9034893	1.40070
D2	2	1.86317698	0.8162929	1.52090
D3	3	2.239166094	0.7375119	1.65141
D4	4	2.691029812	0.6663341	1.79312
D5	5	3.234079628	0.6020257	1.94700
P5	5	50.09643309	0.6020257	30.15934
		The price of the stock will be $		38.47
	Therefore value of share = $38.47
Working Notes:
	Notes: PVF is calculated @ r% = 1/(1+r%)^n     where n is the period for which PVF is calculated. And r is required rate of calculated above 10.682%
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