Exercise 1

1. The value of the unlevered firm is V_U = EBIT (1 − T_C)/r_U . Hence, V_U = 1, 200 × (1 − 0.35)/0.12 = 6, 500 (since it is a perpetuity). Value of Debt= 200/0.8 = 2500. Now, from MM theorem with taxes, we have V_L = V_U + T_CB. Therefore, V_L = 6, 500 + 0.35 × 2500 = 7, 375.
2. All should be financed with debt.

• No, there are bankruptcy costs and personal taxes.

Exercise 2

1. a_H should make the shareholder indifferent between accepting and not. Hence,

H = (1 − a_H )(H + x) ⇒ a_H = x/(H + x)                            (1)

Similarly, a_L = x/(L + x). Since H > L, a_L > a_H follows.

• No, given a_H < a < a_L, it will only accept it when the value is L. Accordingly, upon observing the bank accepting the offer, the government should infer that the value of the bank is L.
• The market value of the bank’s equity before the decision to accept or not the offer is V = 0.5(H + L). After a decision to reject, the market infers that the value of the company’s equity must be H > V . As a result, the market valuation has increased. Denoting with N the number of outstanding shares, the initial share price is p₀ = V/N which is lower than the ex-post share price p₁ = H/N . Things are slightly more complicated if the bank accepts. In this case, we need to take into account the cash injection. The ex-post market value is L+x. Let G denote the number of shares issued to the government, so that the total number of shares is N + G. G must be such that the stake acquired by the government

is equal to a. Hence, G/(N + G) = a, which implies G = Na/(1 − a). The total number of shares is thus G + N = N/(1 − a) and the ex-post share price is p₁ = (1 − a)(L + x)/N . Substituting a = a_L yields a share price p₁ = L/N . Compared with p₀ = V/N , the share price has dropped. Reasons: by rejecting

the offer, the bank signals to the market that the offer undervalues its shares. The market reacts by increasing the share price. The opposite occurs when the bank accepts the offer.

Exercise 3

1. No. Substituting debt with equity is not necessarily value decreasimg in the trade off theory. Firms with significant expected bankruptcy costs (i.e. firms to the “right” of the optimal debt-equity ratio) may increase their value by replacing debt with equity.
2. Yes. Issuing equity conveys bad news compared to issuing debt. A company replacing equity with debt sends a strong signal to the market (i.e. executives believe the company’s stocks are undervalued). A company replacing debt with equity signals that the management is not confident about the firm’s prospects.

Exercise 4

1. Determine the maximum price the bidder can offer shareholders without making losses.

This is given by p = v − c

• Assuming that the bidder offers the above price, will the takeover be successful?

No, the minimum price an individual shareholder will accept is p = v. This is because, by holding on his shares, a shareholder obtains v when the takeover succeeds (if the takeover fails the shareholder gets q independently of whether he sells or nor). Notice however that shareholders would benefit from the takeover at all prices p > q. For prices between q and p a successful takeover would increase the welfare of shareholders, but it nevertheless fails because of the free rider problem. See the lecture notes for a discussion.

• Assume now that, when acquiring the company, the bidder obtains, in addition to v, a private benefit h > c. Can the takeover take place in this case? Can you provide an example where the value of the company to the bidder is larger than the value to its shareholders?

Yes. The bidder can now afford to pay up to p = v − c + h > v. Hence, there exist prices p ∈ (v, v − c + h) at which the takeover can succeed. Examples of

private benefit: the takeover bid may be promoted by the company’s executives (a management buyout) who may use it as a way to consolidate their grip over the firm. The takeover may be strategic, in the sense that the buyer sees the acquisition as a way to hedge/diversify its own business. For instance, an oil company may strategically choose to acquire a solar energy firm to hedge against future regulation. A tobacco company may choose to buy a firm producing electronic cigarettes.