Can we mathematically explain the “leverage effect” for stocks?
As per Text book explanation of "Leverage effect" :
The leverage effect describes the effect of debt on the return on equity: Additional debt can increase the return on equity for the owner. This applies as long as the total return on the project is higher than the cost of additional debt.I want to mathematically understand this concept.
- SGaurav Srivastava @srigaurav1986
The key to this is to think about the enterprise value of a business separately from how it is financed.
For simplicity sake, consider a business that comprises a sole gold bar (no workers, no extraction costs, etc). The value of the business is clearly just the value of the gold bar. If it were a listed company, with no debt, then the equity capitalization would be the value of the gold bar, and the volatility of the share price would be equal to the volatility of the gold price.
Now consider the same company financed with 50% debt (at zero interest) and 50% equity. The enterprise value of the geared company remains the same as before, but the equity capitalization is half as much (since the debt holders are owed the other half). However, whereas the claims of debt holders is fixed in nominal dollars, the equity holders get the benefit/cost of a higher/lower gold price.
E.g. If the gold bar is initially worth $100 (financed with $50 equity and $50 debt), but then rises to $110, then the value of equity becomes $60, while the value of debt remains at $50. Equity holders enjoy a 20% increase (=10/50) in share value, against 10% (=10100) in the unlevered case. In moving from 0% gearing to 50% gearing, the volatility of equity value has doubled.