Question

Company ABC has 10,000 shares outstanding and the stock price is $100. The company is expected to pay a dividend of $10 per share next year and thereafter the dividend is expected to grow indefinitely by 6% a year. The company now makes an announcement: It will repurchase shares next year instead of issuing cash dividends. But from year 2 on the payout policy stays the same with cash dividends.

1. What is the expected rate of return on the stock?

2. At what price will the company repurchase shares next year? How many shares will be repurchased?

3. After the payout, what is the percentage ownership of an investor who holds 1% of the shares before the payout and does not sell shares during the repurchase?

4. Will this investor prefer cash dividend or stock repurchase? Please show your calculation.

Answer 1

Current stock price - P0	Given	100
Dividend end of Year 1 - D1	Given	10
Growth rate - g	Given	6%
Expected rate of return - Ke	To find'
As per Gordon's model
P0 = D1/(Ke-g)
100 = 10/(Ke-0.06)
Ke-0.06 = 10/100
Ke = 0.10+0.06
Ke = 16%
Expected ROR	16%
Price at end of next year P1 =	P0(1+Ke)
P1	100(1+0.16)
P1	116
No. of shares to be repurchased =	Total amount of dividend payable / P1
	10000 shares * 10$ Dividend per share / 116
	100000/116
	862.07
The company will repurchase 862 shares.
Existing number of shares		10000
No. of shares to be repurchased =		862
Remaining number of shares		9138
No. of shares held by investor	1% of 10000	100
Revised % of holding by investor		1.0943%
In case investor receives dividend
Value of dividend received	100 shares * 10	1000
Value of shares held	P1 = 116-D1
	P1 = 116-10
	P1 = 106
	106*1000 shares	106000
Value of investor's holdings		107000
In case investor does not receive dividend
Value of investor's holdings	116*1000 shares	116000
Therefore the investor would prefer stock repurchase only.