Question

You are a security analyst in ABC Investment Company Limited and are asked to analyse BBA Company, an IT employment agency that supplies computer programmers to financial institutions. BBA’s beta coefficient is 1.2. The risk-free rate is 7% and the expected rate of return on the market is 12%. BBA just paid a dividend of $2.00 each share.

(c) Now, assume that BBA’s dividends are expected to grow at 30% per year for the next 3 years, and then maintain a long-run constant growth rate of 6% per year in the foreseeable future.

(i) What is BBA’s stock price today?

(ii) What are the expected dividend yield and capital gain yield today?

(iii) What are the expected dividend yield and capital gain yield in Year 3?

Answer 1

	Required rate of return for BBA per CAPM = risk free rate+beta*(expected market return-risk free rate)
	= 7%+1.2*(12%-7%) =	13.00%
i]	Stock price today is the PV of the expected dividends
	when discounted at 13%.
	Year	Dividend	PVIF at 13%	PV at 13%
	0	$          2.000
	1	$          2.600	0.88496	$              2.30
	2	$          3.380	0.78315	$              2.65
	3	$          4.394	0.69305	$              3.05
	Sum of PV of dividends of years 1 to 3			$              7.99
	Continuing value of dividends at t3 = 4.394*1.06/(0.13-0.06) =	$       66.538
	PV of continuing value = 66.538*0.69305 =			$            46.11
	Price of the stock today = 7.99+46.11 =			$            54.11
ii]	Stock price 1 year from today is the PV of the expected dividends
	when discounted at 13%.
	Year	Dividend	PVIF at 13%	PV at 13%
	0	$          2.000
	1	$          2.600
	2	$          3.380	0.88496	$              2.99
	3	$          4.394	0.78315	$              3.44
	Sum of PV of dividends of years 2 to 3			$              6.43
	Continuing value of dividends at t3 = 4.394*1.06/(0.13-0.06) =	$       66.538
	PV of continuing value = 66.538*0.78315 =			$            52.11
	Price of the stock 1 year from today = 6.43+52.11 =			$            58.54
	Dividend yield today = 2.600/54.11 =	4.81%
	Capital gain yield today = 58.54/54.11-1 =	8.19%
	Total yield	13.00%
iii]	Stock price 2 years from today is the PV of the expected dividends
	when discounted at 13%.
	Year	Dividend	PVIF at 13%	PV at 13%
	0	$          2.000
	1	$          2.600
	2	$          3.380
	3	$          4.394	0.88496	$              3.89
	PV of dividends of year 3			$              3.89
	Continuing value of dividends at t3 = 4.394*1.06/(0.13-0.06) =	$       66.538
	PV of continuing value = 66.538*0.88496 =			$            58.88
	Price of the stock 2 years from today = 3.89+58.88 =			$         62.771
	Stock price 3 year's from today is the PV of the expected dividends
	when discounted at 13%.
	Price at the end of t3 = Continuing value of dividends at t3 = 4.394*1.06/(0.13-0.06) =	$       66.538
	Dividend yield in the 3rd year = 4.394/62.77 =	7.00%
	Capital gains yield in the 3rd year = 66.54/62.771-1 =	6.00%
	Total yield	13.00%