Consider a firm that has an EBIT of $3,000,000 per year for ever. There are 1,00

Question

Consider a firm that has an EBIT of $3,000,000 per year for ever. There are 1,000,000 shares outstanding. The firm also has $10 million of perpetual debt with an interest rate of 8 percent (also its coupon rate) in its capital structure. At the existing capital structure, the firm’s cost of equity is 12 percent and the cost of debt is 8 percent. The firm faces a tax rate of 30 percent. The firm announces that it wishes to raise the debt level to $14 million. The old debt will be retired and the firm will issue another $14 million of new debt and use the proceeds to buy back shares. At the higher debt level, the cost of debt is expected to be 9 percent and the cost of equity 13 percent. (i) What is the value of the firm before the capital structure change and what is the stock price? (ii) What will be the value of the firm and the stock price after the capital structure change? (iii) How many shares will be outstanding after the capital structure change and what will be the firm’s debt to asset ratio?

Consider a same firm as above. The firm announces that it wishes to raise the debt level to $14 million. However, the old debt will be not be retired and the firm will issue another $4 million of new debt and use the proceeds to buy back shares. At the higher debt level, the cost of debt is expected to be 9 percent and the cost of equity 13 percent. (iv) What will be the value of the firm and the stock price after the capital structure change? (v) How many shares will be outstanding after the capital structure change and what will be the firm’s debt to asset ratio?

I am only stuck on (vi) and (v) if you could please answer and explain

Explanation / Answer

Exisiting capital structure of the firm

Debt

$ 10 Million

Equity

Value of equity = FCFE/ke

FCFE= PAT

EBIT = 3 M

Interest = 10 M * 8% = 800,000

PBT = 2.2 M

Taxes =0.3*2.2 = 0.66

Net Income= PAT = 1.54 M

Value of Equity = 1.54/0.12 = 12.83 Million

Price per share = 12.83 M/ 1 M= $ 12.83

Case II ( New capital Structure)

New Debt after raise = $ 14 Million

Additional debt = $ 4 M

Total Debt = $ 18 Million

Total oustanding Equity = 12.83 M - 4 M( As $4 M of debt is used to buy back shares)= $ 8.83 M

iv) Total Value of firm = Debt + Equity = 18+ 8.83 = 26.83 Million

For finding stock price , we must find the number of stocks oustanding

$ 4 M will be used to repurchase = 4M/ 12.83 = 311,769 shares from the market

So outstanding shares = 1M -311,769 = 688,231 shares O/S in the market

So Price per share = 8.83 M/688,231 = $ 12.83

ie it will remain the same irrespective of the stock buyback.

v)

Shares O/s = 688,231 shares O/S in the market

Debt to Asset Ratio = 18/26.83 = 0.67

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