Question

​Rally, Inc., is an​ all-equity firm with assets worth

$59

billion and

16

billion shares outstanding. Rally plans to borrow

$32

billion and use funds to repurchase shares.​ Rally's corporate tax rate is

35%​,

and Rally plans to keep its outstanding debt equal to

$32

billion permanently.

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

b. Suppose Rally offers

$4.25

per share to repurchase its shares. Would shareholders sell for this​ price?

c. Suppose Rally offers

$4.52

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?

Answer 1

a). Share Price = Total Equity / Shares Outstanding = 59/16 = $3.69

b). Assets = Value of unlevered firm + Value of Debt + Tax Shield

= 59 + 32 + [0.35 * 32] = 91 + 11.2 = $102.2 billion

Equity = Assets - Debt = 102.2 - 32 = $70.2 billion

Share Price = Total Equity / Shares Outstanding = 70.2/16 = $4.39

Therefore, shareholders will not sell for $4.25 per share.

c). Assets = Value of unlevered firm + Tax Shield

= 59 + [0.35 * 32] = 59 + 11.2 = $70.2 billion

Equity = Assets - Debt = 70.2 - 32 = $38.2 billion

New shares outstanding = Old share outstanding - Shares Repurchased

= 16 - [32/4.52] = 16 - 7.08 = 8.92 billion shares

Share Price = Total Equity / Shares Outstanding = 38.2/8.92 = $4.28

d). From (b), fair value of the shares prior to repurchase is $4.39.

At this price, new shares outstanding

= 16 - [32/4.39]

= 16 - 7.29 = 8.71 billion shares

Share Price after repurchase = 38.2/8.71 = $4.39

Therefore, shares will be willing to sell at this price.