Question

Carnes Cosmetics Co.'s stock price is $64.34, and it recently paid a $1.25 dividend. This dividend is expected to grow by 19% for the next 3 years, then grow forever at a constant rate, g; and rs = 15%. At what constant rate is the stock expected to grow after Year 3? Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

	g1	Growth Rate in next three years=19%	0.19
	D0	Recently paid dividend in Year0	$1.25
	D1=D0*(1+g1)	Expected Dividend in Year1	$1.49
	D2=D1*(1+g1)	Expected Dividend in Year2	$1.77
	D3=D2*(1+g1)	Expected Dividend in Year3	$2.11
		Current Stock price=Present Value of future cash flows=$64.34
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+R)^N)
		R=Discount Rate=Required Return=15%=0.15
		N=Year of Cash Flow
	g	Constant growth rate fromyear 4 onwards
	D4	Expected dividend in year 4=2.11*(1+g)
	P3=D4/(R-g)	Price at end of Year 3
	N	Year	1	2	3	3
			D1	D2	D3	P3
	A	Cash flow	$1.49	$1.77	$2.11	2.11*(1+g)/(0.15-g)
	PV=A/(1.15^N)	Present Value of Cash flow	1.293478	1.338469	1.385024	(2.11*(1+g)/((0.15-g)*(1.15^3))
		Present Value of Cash flow=$64.34=4.017+	(2.11*(1+g)/((0.15-g)*(1.15^3))
		(2.11*(1+g)/((0.15-g)*(1.15^3))=	60.323
		(2.11*(1+g)/((0.15-g)*1.520875)=
		(1+g)/(0.15-g)=	43.48045
		1+g=6.522-43.4805*g
		44.4805*g=5.522
		g=5.522/44.4805=	0.124144
		Expected Constant growth rate after Year 3	12.41%
	D4=D3*(1+g)	Expected dividend in year4	$2.37
	P3=D4/(R-g)	Expected Price in year3	$91.58	(2.37/(0.15-0.124144)