Question

Johnny Dei inc. has a perpetual expected EBIT of $56,000,000 and is currently unlevered. The current required return on the firm's equity is 25%. The company has 2 million ordinary shares outstanding. The corporate tax rate is 27%. The firm is planning a recapitalization: it will issue $50,000,000 debt which it plans to keep constant perpetually and use the proceeds to buy back shares. The cost of debt is 7.25%.

1. What is the value of the company before the recapitalization is announced. What is the value of equity before the announcement? What is the price per share? 163,520,000 and 81.76
2. What is the value of the company after the recapitalization plan is announced (but not carried out yet)? What is the value of equity? What is the price per share? 88.51
3. How many shares needs to be repurchased? What is the value of shares after the repurchase? What is the price per share? 564,907.92 and 88.51

Answer 1

a) Value of the firm is the sum of value of equity and value of debt. With no debt, value of firm is value of equity

Value of equity can be found using capitalisation of profits. Profits are capitalised at the cost of equity.

Value of Equity = (EBIT- Interest) (1- Tax) / Cost of Equity

Value of Equity = (56000000 - 0) (1- 0.27) / 25% = 40,880,000 / 25% = 163,520,000

Value per share = Value of Equity/ Number of shares = 163,520,000 / 2,000,000 = 81.76 per share

b) As per Modigilani Approach, value of the enterprise does not depend on the capital structure of the firm. This preposition assumes no tax environment. The approach assumes that any reduction on cost of debt, in turn increases the cost of equity such that overall cost of capital is unchanged thereby the value of the firm is unchanged.

Under the Second Preposition, the value of the firm will increase if the tax picture is considered. Hence value of firm will only increase by the tax portion of debt

Hence revised value of firm/ Value of equity = Value of unlevered firm + Debt * Tax Rate

= 163,520,000 + 50,000,0000 * 0.27 = 163,520,000 + 13,500,000 = 177,020,000

Value of share = Value of Equity/ Number of shares = 177,020,000 / 2,000,000 = 88.51 per share

c) Number of shares needed to repurchase = Amount of Debt / 88.51 = 564,907.92

Shares left after repurchase = 2000,000 - 564,907.92 = 1,435,092.08

Value of Firm = Value of Equity + Value of Debt

= 1,435,092.08* 88.51 + 50,000,000

= 177,020,000

Value per share shall remain the same at 88.51 per share