Question

Jane Wu is employed as a senior investment adviser for a large stock-broking house. One of her major responsibilities is to advise clients on the composition of their portfolios. A client has expressed interest in shares of Oran Chemical Ltd. Jane determines that Oran's ordinary shares are currently trading at $2.50; she also discovers that the company, which has a policy of paying dividends once a year, has just paid a dividend of 30 cents per share. Based on her analysis of the information available to her concerning the company's operations and markets, Jane forms the opinion that dividends will grow 9 percent per annum for the following 3 years and then grow at a constant compound rate of 5 percent into the foreseeable future. She also feels that a required annual rate of return of 15 percent is commensurate with Oran's risk.

(a) Calculate the value of the stock today.

(b) Calculate the value of the stock in one year's time. ( please explain this in detail)

(c) Calculate the dividend yield and capital gains yield in the first year, and show how this relates to required rate of return?

Answer 1

	D0	Just paid Dividend (Year 0)	$0.30
	g1	Dividend growth rate during first 3 years	0.09
	D1=D0*(1+g1)	Expected dividend in year1	$0.33
	D2=D1*(1+g1)	Expected dividend in year2	$0.36
	D3=D2*(1+g1)	Expected dividend in year3	$0.39
	g2	Dividend growth rate from year 4 on wards	0.05
	D4*=D3*(1+g2)	Expected dividend in year4	$0.41
	R	Required annual rate of return	0.15
	P3=D4/(R-g2)	Expected Price in year 3	$4.08	(0.41/(0.15-0.05)
	(a)	Value of stock   today=Present value of future cash flow
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=Required return=15%=0.15
		N=Year of Cash Flow
	N	Year	1	2	3	3
			DividendD1	DividendD2	DividendD3	Price
	CF	Cash Flow	$0.33	$0.36	$0.39	$4.08	SUM
	PV=CF/(1.15^N)	Present Value (PV) of Cash Flow:	$0.28	$0.27	$0.26	$2.68	$3.49
		Value of stock   today=Present value of future cash flows	$3.49
	(b)	value of stock one year from today
	N	Year From one year from today	1	2	2
			DividendD2	DividendD3	Price
			$0.36	$0.39	$4.08	SUM
		Present value of cash flow in Year1	$0.31	$0.29	$3.08	$3.69
		Value of stock in one years time	$3.69
	(.c)	Dividend Yield in year1
		Dividend in year1	$0.33
		Price in year 1	$3.69
		Dividend Yield in year1=Dividend/Price	0.088659317
		Dividend Yield in year1	8.87%
		Total Return =Required Return=	15%
		Capital Gain yield=Required return -Dividend Yield	6.13%	(15-8.87)