What is wrong with the following example: Assume a Modigliani Miller (without taxes) world. An unlevered firm is worth$1000. Another firm with $500 debt has the same value, $1000. The risk-free rate is 5%. The income of both firms is $100.

According to Modigliani and Miller, capital structure does not matter in this case, hence there should be no arbitrage opportunities under such circumstances.

However, here is one: You own 10% of the all equity firm, and obviously, your investment entitles you to 10% of the profit, i.e. $10. You sell your share in the unlevered company and have $100 to invest. You now buy 20% of the equity of the levered firm ($500 equity, $500 debt). That firm's income is:$100 -0.05 x $500(interest) = $75. Since you own 20% of the firm, you receive -0.2 x $75 =$15. (hint and request -it is a long question, but the answer should be short. You need no more than two sentences).