The Hamada Equation

A big deal for companies is to decide whether to finance their company with debt (loans) or equity (stock). Too much debt can cause risk to the shareholders, but it offers tax advantages. Its complicated stuff, but there are equations to help.

Robert Hamada, in 1969 wrote a paper called "Portfolio Analysis, Market Equilibrium, and Corporation Finance" in which he came up with the Hamada Equation! This is exciting stuff.
First, you should know what a "Beta" is. According to "Wall Street Words" a Beta is:

A mathematical measure of the sensitivity of rates of return on a portfolio or a given stock compared with rates of return on the market as a whole. A high beta (greater than 1.0) indicates moderate or high price volatility. A beta of 1.5 forecasts a 1.5% change in the return on an asset for every 1% change in the return on the market. High-beta stocks are best to own in a strong bull market but are worst to own in a bear market.

Now, the Hamada equation formulated a way to show that the beta increases with financial leverage (debt financing rather than equity financing).
It is:
Bl=Bu [1+(1-t)(d/e)
where:
Bl=current beta
Bu=unleveraged beta (what would the beta be without the debt)
D/E debt to equity ratio

You can insert the unlevered beta into other equations to find out what the betas would be for different debt levels. You can use this to help you decide if you should use debt or equity to finance your business.

http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Beta_uc_lc.svg/800px-Beta_uc_lc.svg.png