Question

BVPS_Current = $95.

ROE_Early = 16% for next 5 yrs

ROELate = 4% after 5 yrs (in perpetuity)

Expected ROE (discount rate) = 5.1 %

Above numbers are independent from plow backs/ policy below.  

Dividend Policy:
Plow back = 90% of earnings in early period.  
Plow back = 20% of earnings in late period

Question: What is the price of your stock today?

Answer 1

			g=Growth Rate =ROE*Plow back
			Growth Rate Early=0.9*16%=	14.4%
			g1=Growth Rate early	14.4%
			g2=growth rate in late period=0.2*4%	0.80%
		D0	Current Dividend =(1-0.9)*16%*95	$1.52
		D1=D0*(1+g1)	Dividend in year1	$1.74	(1.52*1.144)
		D2=D1*(1+g1)	Dividend in year2	$1.99	(1.74*1.144)
		D3=D2*(1+g1)	Dividend in year3	$2.28	(1.99*1.144)
		D4=D3*(1+g1)	Dividend in year4	$2.60	(2.28*1.144)
		D5=D4*(1+g1)	Dividend in year5	$2.98	(2.60*1.144)
		D6=D5*(1+g2)	Dividend in year6	$3.04	(2.98*1.08)
			Price in year 5=P5=D6/(R-g2)
			R=Discount Rate=5.1%=0.051
			P5=3.04/(0.051-0.008)=	$70.65
			Present Value (PV) of Cash Flow:
			(Cash Flow)/((1+i)^N)
			i=Discount Rate=5.1%=0.051
			N=Year of Cash Flow
			N	A	B=A/(1.051^N)
			Year	Cash flow	PV of cash flow
		D1	1	$1.74	1.654500476
		D2	2	$1.99	1.800902516
		D3	3	$2.28	1.960259256
		D4	4	$2.60	2.133717021
		D5	5	$2.98	2.32252357
		P5	5	$70.65	55.09241957
				SUM	$64.96
			PRICE OF THE STOCK =Present Value of Future Cash Flows
			PRICE OF THE STOCK TODAY	$64.96