ABC Corporation is financed entirely by equity, has 1 million shares outstanding trading at $100 per...

ABC Corporation is financed entirely by equity, has 1 million shares outstanding trading at $100 per share. Depending on the state of the economy its EBIT will be

recession	expected	expansion
8 million	12 million	16 million

XYZ Corporation has exactly the same EBIT in each economy state, but has $40 million of debt outstanding with an 8% interest rate. It also has 600,000 shares of common stock outstanding priced at $95 per share. Neither firm pays taxes. There are no bankruptcy costs. Assume you can borrow and invest at 8%. Are there any arbitrage opportunities? If yes, propose a detailed arbitrage strategy and prove that it works.

Expert Solution

Calculation of Return of ABC Corporation
Particular	Recession	Expected	Expansion
EBIT	$ 8,000,000	$ 12,000,000	$ 16,000,000
Shares o/s	1000000	1000000	1000000
EPS	$ 8	$ 12	$ 16
Share Price	$ 100	$ 100	$ 100
Return	8%	12%	16%

Calculation of Return of XYZ Corporation
Particular	Recession	Expected	Expansion
EBIT	$ 8,000,000	$ 12,000,000	$ 16,000,000
Cost of Debt	$ 3,200,000	$ 3,200,000	$ 3,200,000
EBT	$ 4,800,000	$ 8,800,000	$ 12,800,000
Shares o/s	600000	600000	600000
EPS	$ 8	$ 15	$ 21
Share Price	$ 95	$ 95	$ 95
Return	8.42%	15.44%	22.46%

If investor borrow money @ 8% then invest in ABC Corporation then minimum return will be 8%, which is equal to borrowing cost 8%, so if economy's Recession condition then no arbitrage opportunity.

Calculation of Arbitrage gain of ABC Corporation
Particular	Recession	Expected	Expansion
Return	8%	12%	16%
Share Price	$ 100	$ 100	$ 100
Inflow	$ 8	$ 12	$ 16
Borrow	$ 100	$ 100	$ 100
Interest Cost	8.00%	8.00%	8.00%
Outflow	$ 8.00	$ 8.00	$ 8.00
Arbitrage Gain	$ -	$ 4.00	$ 8.00

.If investor borrow money @ 8% then invest in XYZ Corporation then minimum return will be 8.42%, Which is higher than borrowing cost 8%, so if economy's Recession condition then also arbitrage opportunity exist.

Calculation of Arbitrage gain of XYZ Corporation
Particular	Recession	Expected	Expansion
Return	8.42%	15.44%	22.46%
Share Price	$ 95	$ 95	$ 95
Inflow	$ 8.00	$ 14.67	$ 21.34
Borrow	$ 95	$ 95	$ 95
Interest Cost	8.00%	8.00%	8.00%
Outflow	$ 7.60	$ 7.60	$ 7.60
Arbitrage Gain	$ 0.40	$ 7.07	$ 13.74

Conclusion :Here advisable to borrow and invest in XYZ Corporation equity and take advantage of arbitrage gain as calculated above.

Arbitrage gain calculated per share basis.

Assumption : Here assume that return calculated per share will be available to investor via dividend or appreciation of share price.

jeff jeffy answered 1 year ago

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