Question

You expect that Bean Enterprises will have earnings per share of $2 for the coming year. Bean
plans to retain all of its earnings for the next three years. For the subsequent two years, the firm
plans on retaining 50% of its earnings. It will then retain only 25% of its earnings from that point
forward. Retained earnings will be invested in projects with an expected return of 20% per year.
If Bean?s equity cost of capital is 10%, then the price of a share of Bean?s stock is closest to
________.
A) $16.54 B) $66.18 C) $24.82 D) $41.36

Please show work!

I will be receiving this question on a test, if you can show me the quickest way to answer this that would be great.

Answer 1

Solution:-
	calculation of price of a share of Bean?s stock
	Years	Earning per share	Dividend per share	Growth
	1	S2.00	$0.00	20%
	2	$2.40	$0.00	20%
	3	$2.88	$0.00	20%
	4	$3.46	$1.73	10%
	5	$3.80	$1.90	10%
	6	$4.18	$3.14	5%
	Note:-	Growth is calculated using this formula	=Retenton ratio*ROI
	where, ROI=20% given
	P0= 1.73/(1.10)^4+ 1.90/(1.10)^5+ (3.14/(.10 - .05))/1.10^5
		=1.73/1.4641+1.90/1.61051+62.8/1.61051
		=1.1816+1.1797+38.9938
		=$41.35
Hence the share price of Bean's stock is closest to $41.36.