Question

1. Suppose B&E Press paid dividends at the end of each year according to the schedule below. It also reduced its share count by repurchasing 5 million shares at the end of each year at the ex-dividend stock prices shown. (Assume perfect capital markets.)

	2009	2010	2011	2012	2013
Ex-Dividend Stock Price ($/share)	10.00	12.00	8.00	11.00	15.00
Dividend ($/share)		0.50	0.50	0.50	0.50
Shares Outstanding (millions)	100	95	90	85	80

a.   What is total market value of B&E’s equity, and what is the total amount paid out to share­holders, at the end of each year?

b.   If B&E had made the same total payouts using dividends only (and so kept its share count constant), what dividend would it have paid and what would its ex-dividend share price have been each year?

c.   If B&E had made the same total payouts using repurchases only (and so paid no dividends), what share count would it have had and what would its share price have been each year?

d.   Consider a shareholder who owns 10 shares of B&E initially, does not sell any shares, and reinvests all dividends at the ex-dividend share price. Would this shareholder have preferred the payout policy in (b), (c), or the original policy?

Answer 1

	2009	2010	2011	2012	2013	Formula
a. Ending Equity Value	1000	1140	720	935	1200	Equity Value= Stock Price × Shares Outstanding
Total Dividends		50	47.5	45	42.5	Total Dividends= Dividend × Shares
Total Repurchases		60	40	55	75	Total Repurchases= Shares Repurchased × Share Price
Total Payout		110	87.5	100	117.5	Total Payout= Total Dividends + Repurchases
b. Dividends Only Shares	100	100	100	100	100	Shares= Initial Shares
Dividend ($ share)		1.1	0.88	1	1.18	Dividend= Total Payout / Initial Shares
Stock Price (ex-div)	10	11.4	7.2	9.35	12	Stock Price= Equity Value / Initial Shares
c. Repurchases Only Beginning Shares		100	91.2	81.32	73.46	Beginning Shares= Last Period's Ending Shares
Stock Price	10	12.5	8.85	12.73	17.93	Stock Price= (Equity Value + Total Payout) / (Beginning Shares) a*
Shares Repurchased		8.8	9.88	7.86	6.55	Shares Repurchased= Total Payout / Stock Price
Ending Shares	100	91.2	81.32	73.46	66.91	Ending Shares= Beginning Shares –Repurchased Shares
Ending Equity Value	1000	1140	720	935	1200	Ending Shares * Stock Price

a* because stock price is the same before and after repurchase

d. According to Modigliani-Miller Dividend Irrelevance proposition, the shareholder should be indifferent.

As long as the investor keeps the fraction invested the same (in this case, fully invested), the value of his portfolio should be independent of the policy. 1because stock price is the same before and after repurchase