In: Finance
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.
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.