Firms X and Y are identical in all respects except for capital structure. These

Question

Firms X and Y are identical in all respects except for capital structure. These firms operate in a 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 they are zero-coupon bonds that will pay the holder principal and interest one year from today. The risk-free interest rate is 10%. An individual investor can also borrow or lend from a bank at the 10% risk-free rate.

Construct an arbitrage portfolio that includes exactly 100 shares of stock in firm X. How large are the arbitrage profits from this portfolio?

Explanation / Answer

The arbitrage profit from this portfolio will be 10% that is risk free rate. In order to earn arbitrage profit, now short sell stock of firm X, deposit the proceeds at risk free rate for one year and after one year take back the deposit plus interest buy the stock of firm X. The interest earned on deposit is the profit from the arbitrage. Here, it is assumed that the price of stock will remain same after one year.

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