Question

Explain how a repurchase changes the number of shares but not the stock price.

A firm’s most recent FREE CASH FLOW (FCF) was $2.4 million, and its FCF is expected to grow at a constant rate of 5%. The firm’s WEIGHTED AVERAGE COST OF CAPITAL (WACC) is 14%, and it has 2 million shares outstanding. The firm has $12 million in short-term investments that it plans to liquidate and then distribute in a stock repurchase; the firm has no other financial investments or debt.

1. What is the value of operations?
2. Immediately prior to the repurchase, what are the intrinsic value of equity and the intrinsic stock price?
3. How many shares will be repurchased? How many shares will remain after the repurchase?
4. Immediately after the repurchase, what are the intrinsic value of equity and the intrinsic stock price

Answer 1

	Before the repurchase, the value of the firm includes the cash or cash equivalents
	that would be used for repurchase. The per share price would be total value/number
	of shares repurchased. On repurchase, the value of the firm gets reduced by the cash
	used for research. At the same time, the number of shares also goes down to an extent
	that the share price after repurchase is the same as the price before repurchase.
	This is illustrated in the solution below:
1)	Value of operations = 2.4*1.05/(0.14-0.05) =	$           28.00	million
2)	Intrinsic value of equity = 28+12 =	$           40.00	million
	Intrinsic stock price = 40/2 =	$           20.00
3)	Shares repurchased = 12/20 =	0.60	million
4)	Shares remaining = 2-0.60 =	1.40	million
5)	Intrinsic value of equity after repurchase	$           28.00	million
	Intrinsic stock price = 28/1.4 =	$           20.00