Question

Hors d’Age Cheeseworks has been paying a regular cash dividend of $4 per share each year for over a decade. The company is paying out all its earnings as dividends and is not expected to grow. There are 100,000 shares outstanding selling for $80 per share. The company has sufficient cash on hand to pay the next annual dividend. Suppose that, starting in year 1, Hors d’Age decides to cut its cash dividend to zero and announces that it will repurchase shares instead.

1. How many shares will Hors d’Age purchase?
2. Project and compare future stock prices for the old and new policies. Do this for years 1, 2 and 3.

Answer 1

a.Value of the firm without dividend payment = $80 *100,000 + $4 *(100,000)= $8,400,000

Price per share = $8,400,000/ 100,000 = $84

The firm can repurchase = $400,000 / $84 = 4762 shares

b.

Old policy:
	Year 1	Year 2	Year 3
Total assets at the beginning	8,000,000	8,000,000	8,000,000
Total assets at the end	8,400,000	8,400,000	8,400,000
Dividends(Earnings)	400,000	400,000	400,000
No of shares	100,000	100,000	100,000
Price per share (ex dividend)	$80	$80	$80

New policy
	Year 1	Year 2	Year 3
Total assets at the beginning	8,000,000	8,000,000	8,000,000
Total assets at the end	8,400,000	8,400,000	8,400,000
Dividends(Earnings)	400,000	400,000	400,000
No of shares at the beginning	100,000	95,238	90,703
Price per share at the beginning of the year	80	84	88.20
No of shares repurchased	4,762	4535	4319
No of shares at the end	95,238	90,703	86,384
Price per share (ex dividend) at the end of the year	84	88.20	92.61

Workings:

Year 1 no of shares repurchased = 400,000/ (8,400,000/100,000) = 4762 shares

Year 2 no of shares repurchased = 400,000/ (8,400,000/95238) = 4535 shares

Year 3 no of shares repurchased = 400,000/ (8,400,000/90703) = 4319 shares

Price per share (ex dividend) Year 1 = (8,400,000/100,000) = 84

Price per share (ex dividend) Year 2 = (8,400,000/95238)= 88.20

Price per share (ex dividend) Year 3 = (8,400,000/90703)= 92.61