Question

Two identical firms (except for leverage) have perpetual earnings before interest and tax (EBIT) of $100K . One firm is unlevered while the other has $1 million of 4% coupon perpetual debt. cost of unlevered equity is 10 ½ % p.a. cost of levered equity is 15% p.a. Current market yield on the debt is 9% p.a. and there are no taxes. Assuming MM are correct, show how you can make risk free profits for the same return. (hint: calculate the value of the levered and unlevered firms, then state the cashflows of the buy/sell actions in your argument). Explain how your actions help to restore equilibrium and why the risk remains the same. Calculate the MM levered equity return and draw a graph of return vs D/E ratio to illustrate your answer. Having trouble with this textbook question

Answer 1

Earnings for shareholders of unlevered firm = $100,000

Earnings for shareholders of levered firm = $100,000 - interest cost = $100,000 - 4% of $1,000,000 = $60,000

Value of unlevered firm = $100,000/cost of equity = $100,000/0.105 = $952,381

Value of levered firm = Equity value+Debt value

Equity value= $60,000/0.15 = $400,000

Debt value = interest cost/debt yield = $40,000/0.09

= $444,444

Value of levered firm = $400,000+$444,444 = $844,444

Shareholders of unlevered firm will get high dividend as compare to shareholders of levered firm because of no interest cost.

As per MM approach, value of both levered and unlevered firms remain same due to the fact that there are no taxes, perfectly efficient market and no bankruptcy cost.

MM levered return = Return of unlevered firm + (Debt/Equity)*(return of unlevered firm - cost of debt)

= 10.5+(444,444/400,000)*(10.5-9) =12.165%