Question

1. Consider an all-equity firm. The face value of the shares is 15€ and the book value of equity is 225 million euros. The company does not have own shares in treasury. The annual EBIT is 36 million euros and the firm has a pay-out ratio of 100%.

a) If there are no taxes and the required return on equity is 12%, compute the price per share and the market value of the firm

b) Management is considering a change in the financing structure of the firm by issuing100M€ in perpetual debt paying interests at 7%. If the firm uses the proceedings from the debt issue to distribute an extraordinary dividend at t=0, compute again the value of the firm and the share value after the dividend is paid (assume the M&M world).

c) Prove that the price per share obtained in the previous question is the same as the price per share we would obtain if instead of paying an extraordinary dividend the firm repurchased own shares with the proceedings from the debt issue.

d) Given the new debt ratio (D/E) and the interest on debt given, determine again the expected return on equity. Is it different from before? Explain.

Answer 1

1.

a) As there is no debt and no taxes, EBIT = PAT = 36 million Euros

As all amount is paid as dividend, there is no growth and

Constant Dividend = 36 million Euros

No. of shares = Book value of equity/Face Value of shares

= 225 million Euros / 15 Euro per share = 15 million Shares

From Gordon's Zero Growth model

Value of Equity = Dividend / Return on Equity = 36 million/0.12 = 300 million Euros which is the Market value of firm.

Price per share = 300 million Euros/15 million = 20 Euros per share

b) As per MM hypothesis, Value of the firm will not change if Debt replaces Equity

Once Cash is paid, the equity would reduce by 100 million Euro to become 200 million Euros

the New Cost of equity = 12%+ (12%-7%)* 100/200 = 14.50%

So, Now, EBIT = 36 million

Less : Interest = 7 million

EBT = PAT = 29 million

Value of Equity = 29 million/0.145 = 200 million Euros

and Value of Debt = 100 million Euros

So, value of firm = 200 million+ 100 million = 300 million Euros

Value of a share = 200 million Euros/ 15 million = 13.33 Euros per share

(Plus a value of 100 million /15 million = 6.67 Euro per share paid as Extraordinary dividend). So total value per share = 20 Euros per share

c) If shares are repurchased

No of shares repurchased = 100 million/20 = 5 million shares (In Treasury)

Shares outstanding = 15 million - 5 million = 10 million shares , and value = 20 million Euros

Now, PAT = 29 million Euros (as above)

New Cost of equity = 12%+ (12%-7%)* 100/200 = 14.50%

alue of Equity = 29 million/0.145 = 200 million Euros

and Value of Debt = 100 million Euros

So, value of firm = 200 million+ 100 million = 300 million Euros

Value of a share = 200 million Euros/ 10 million = 20 Euros per share

So, price will remain the same

d) The Expected Return on Equity (cost of equity) has been calculated as above as per the new D/E ratio and it is the same in the two cases where One time dividend is paid and Share repurchase has happened