Company ABC has 10,000 shares outstanding and the stock price is $100. The company is expected to pay a dividend of $10 per share next year and thereafter the dividend is expected to grow indefinitely by 6% a year. The company now makes an announcement: It will repurchase shares next year instead of issuing cash dividends. But from year 2 on the payout policy stays the same with cash dividends.
1. What is the expected rate of return on the stock?
2. At what price will the company repurchase shares next year? How many shares will be repurchased?
3. After the payout, what is the percentage ownership of an investor who holds 1% of the shares before the payout and does not sell shares during the repurchase?
4. Will this investor prefer cash dividend or stock repurchase? Please show your calculation.
Current stock price - P0 | Given | 100 |
Dividend end of Year 1 - D1 | Given | 10 |
Growth rate - g | Given | 6% |
Expected rate of return - Ke | To find' | |
As per Gordon's model | ||
P0 = D1/(Ke-g) | ||
100 = 10/(Ke-0.06) | ||
Ke-0.06 = 10/100 | ||
Ke = 0.10+0.06 | ||
Ke = 16% | ||
Expected ROR | 16% | |
Price at end of next year P1 = | P0(1+Ke) | |
P1 | 100(1+0.16) | |
P1 | 116 | |
No. of shares to be repurchased = | Total amount of dividend payable / P1 | |
10000 shares * 10$ 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. |
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