Question

I am confused about this problem. Thank you!

LevBuyout Corp is an all equity firm. It has 20 million shares. EBIT is expected to be $75 million in one year, and to grow by 5% per year in perpetuity. LevBuyout's (equity) beta is 0.8, the risk-free rate is 3%, and the market risk premium is 10%. The corporate tax rate is 20%. LevBuyout is considering doing a leveraged recapitalization, i.e., issuing debt to buy back some shares. (a) What is the value and share price of LevBuyout if it remains an all equity firm? (b) Suppose LevBuyout announces that it will henceforth switch to 30% debt financ- ing, by issuing debt and buying back the appropriate amount of stock. LevBuyout can issue debt at an interest rate of 5% per year. What is the value of Lev Buyout after this announcement? (c) What is the value of the debt that LevBuyout needs to issue? (d) At what price does LevBuyout buy back its shares? (e) Who gains from the leveraged recapitalization and by how much?

Answer 1

(a) Number of Shares Outstanding = N = 20 million, EBIT = $ 75 million, Tax Rate = 20%, Beta = 0.8, Risk-Free Rate = Rf = 3 % and Market Risk Premium = MRP = 10%, Perpetual Growth Rate = g = 5 % 0

NOPAT (Net Operating Profit After-Tax) = EBIT x (1-Tax Rate) = 75 x (1-0.2) = $ 60 million

Using CAPM(Capital Asset Pricing Model), Cost of Equity = ke = Rf + Beta x MRP = 3 + 0.8 x 10 = 11 %

Firm Value = NOPAT / (ke-g) = 60 / (0.11-0.05) = $ 1000 million or $ 1 billion

Price per Share = 1000 / 20 = $ 50

(b) Proposed Debt Financing = 30 % of Value and Interest Rate = kd = 5 %

Although the debt raised is used to repurchase shares, thereby increasing debt and reducing shareholder's equity on the balance sheet, the firm value will see some rise owing to the benefits of the present value of the interest tax shield on the newly raised debt.

Let the amount of debt raised be $ D million

Interest Expense = kd x D = 0.05 x D and Tax Shield on Interest Expense = Tax Rate x kd x D = 0.2 x 0.05 x D = $ 0.01 D million

Present Value of Interest Tax Shield = PV(ITS) = (0.01 / 0.05) x D = $ 0.2 D million

Firm Value post Debt Issuance = 1000 + 0.2D

Debt Value post Debt Issuance = 30% of Firm Value = 0.3 x (1000 + 0.2D)

Therefore, D = 0.3 x (1000 + 0.2D)

D = 300 + 0.06 D

D = 300 / 0.94 = $ 319.149 million

Firm Value = 1000 + 0.2 x 319.149 = $ 1063.83 million

(c) Debt Raised = D = $ 319.149 million ~ $ 319.15 million

(d) The increment in the firm value happens immediately after the announcement of recapitalization, owing to the assumption of markets being perfect.

Firm Value post Announcement = $ 1063.83 million and Number of Shares Outstanding = 20 million

Repurchase Price = 1063.83 / 20 = $ 53.1915 ~ $ 53.19

(e) As is observable, the recapitalization exercise increases the firm's share price immediately after the recapitalization is announced and much before the actual process is carried out. This implies that shares are repurchased at a higher price than originally planned. Hence, recapitalization benefits stockholder's.