Firms X and Y are identical in all respects except for capital structure. These firms operate in a perfect$-$world tax$-$exempt haven where firms and individuals pay no taxes at all. Current data on the financial structure of the two firms is as follows:

Firm X: $1,000$ shares outstanding, current market price of $$10$ per share

$100$ bonds outstanding with a current bond price of $$100$ per bond

Firm Y: $2,000$ shares outstanding, current market price of $$9$ per share

$50$ bonds outstanding with a current bond price of $$100$ per bond

The bonds in both firms are risk free and the risk$-$free interest rate is $10\%.$ An individual investor can also borrow or lend from a bank at the $10\%$ risk$-$free rate.

Identify a portfolio that includes a long position in exactly $100$ shares of stock in firm X and is guaranteed to make you a risk$-$free immediate profit. How large are these profits? $[$Hint: consider the value of unlevered versions of firm X and firm Y and identify a percent of the unlevered versions of these firms in which you go long one and short the other in the same percentages so as to generate a sure profit.$]$