Question

​Rally, Inc., is an​ all-equity firm with assets worth $ 21 billion and 66 billion shares outstanding. Rally plans to borrow

$ 8 billion and use funds to repurchase shares.​ Rally's corporate tax rate is 35 %​, and Rally plans to keep its outstanding debt equal to$ 8 billion permanently.

a. Without the increase in​ leverage, what would be​ Rally's share​ price?

b. Suppose Rally offers $ 3.84$ per share to repurchase its shares. Would shareholders sell for this​ price?

c. Suppose Rally offers $ 4.20 per​ share, and shareholders tender their shares at this price. What will be​ Rally's share price after the​ repurchase?

d. What is the lowest price Rally can offer and have shareholders tender their​ shares? What will be its stock price after the share repurchase in that​ case?

a. Without the increase in​ leverage, what would be​ Rally's share​ price?

Without the increase in​ leverage, Rally's share price is ​$( )​ (Round to the nearest​ cent.)

b. Suppose Rally offers$ 3.84$ per share to repurchase its shares. Would shareholders sell for this​ price?

The minimum share price they would sell for is​$ ( )​ (Round to the nearest​ cent.)

c. Suppose Rally offers $ 4.20per​ share and shareholders tender their shares at this price. What will be​ Rally's share price after the​ repurchase?

If Rally offers $ 4.20 per​ share, and shareholders tender their shares at this​ price, the share price after the repurchase will be​$( ) ​(Round to the nearest​ cent.)

d. What is the lowest price Rally can offer and have shareholders tender their​ shares? What will be its stock price after the share repurchase in that​ case?

The lowest offer per share is​$ ( )(Round to the nearest​ cent.)

The stock price after repurchase is ​$( )​ (Round to the nearest​ cent.)

Answer 1

Value of the unlevered firm Vu = 21 billion

Number of shares outstanding (n) = 6 billion

a). Share price = Vu/n = 21/6 = $3.5

b). Before the repurchase, total assets will be

21 + cash from debt + tax shield = 21 + 8 + 35%*8 = 31.8 billion

Equity = 31.8 - 8 = 23.8 billion

Share price = 23.8/6 = $3.97

If Rally offers $3.84 per share then shareholders will not sell for this price.

c). After the repurchase:

Assets = 21 + tax shield = 21 + 35%*8 = 23.8 billion

Equity = 23.8 - 8 = 15.8 billion

Number of shares bought back at $4.20 is 8 billion/4.20 = 1.90 billion

Shares outstanding = 6 - 1.90 = 4.10 billion

Share price (after repurchase) = 15.8 billion/4.10 billion = $3.86

d). As calculated in (b), fair share price is $3.97 per share. This is the lowest for which shareholders can tender their share.

Number of shares bought back = 8 billion/3.97 = 2.02 billion

Shares outstanding = 6 billion - 2.02 billion = 3.98 billion

Equity value = 15.8 billion

Share price = 15.8 billion/3.98 billion = $3.97

Note: There appears to be a typo in the question (number of shares 66 billion) which was not making sense with the calculations. So, number of shares has been taken as 6 billion. In case, this number changes, the subsequent answers will change as well.